From eebbe3d2a30ac50d46c6ad8151f105335add597a Mon Sep 17 00:00:00 2001 From: josd Date: Mon, 6 Jan 2025 17:03:51 +0100 Subject: [PATCH] adding collatz case --- reasoning/collatz/README | 5 + reasoning/collatz/collatz-answer.n3 | 258 + reasoning/collatz/collatz-proof.n3 | 17635 ++++++++++++++++++++++++++ reasoning/collatz/collatz-query.n3 | 11 + reasoning/collatz/collatz.n3 | 17 + reasoning/collatz/test | 3 + 6 files changed, 17929 insertions(+) create mode 100644 reasoning/collatz/README create mode 100644 reasoning/collatz/collatz-answer.n3 create mode 100644 reasoning/collatz/collatz-proof.n3 create mode 100644 reasoning/collatz/collatz-query.n3 create mode 100644 reasoning/collatz/collatz.n3 create mode 100755 reasoning/collatz/test diff --git a/reasoning/collatz/README b/reasoning/collatz/README new file mode 100644 index 000000000..23a1769e4 --- /dev/null +++ b/reasoning/collatz/README @@ -0,0 +1,5 @@ +------------------ +Collatz conjecture +------------------ + +See 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391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +232 :collatz (1 (232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +233 :collatz (1 (233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +234 :collatz (1 (234 117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +235 :collatz (1 (235 706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +236 :collatz (1 (236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +237 :collatz (1 (237 712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +238 :collatz (1 (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +239 :collatz (1 (239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +240 :collatz (1 (240 120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +241 :collatz (1 (241 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +242 :collatz (1 (242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +243 :collatz (1 (243 730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +244 :collatz (1 (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +245 :collatz (1 (245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +246 :collatz (1 (246 123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +247 :collatz (1 (247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +248 :collatz (1 (248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +249 :collatz (1 (249 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +250 :collatz (1 (250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +251 :collatz (1 (251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +252 :collatz (1 (252 126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +253 :collatz (1 (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). +254 :collatz (1 (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +255 :collatz (1 (255 766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). +256 :collatz (1 (256 128 64 32 16 8 4 2 1)). diff --git a/reasoning/collatz/collatz-proof.n3 b/reasoning/collatz/collatz-proof.n3 new file mode 100644 index 000000000..5f733664b --- /dev/null +++ b/reasoning/collatz/collatz-proof.n3 @@ -0,0 +1,17635 @@ +@prefix skolem: . +@prefix r: . +@prefix : . +@prefix log: . +@prefix math: . +@prefix n3: . +@prefix var: . +@prefix list: . + +skolem:proof a r:Proof, r:Conjunction; + r:component skolem:lemma1; + r:component skolem:lemma2; + r:component skolem:lemma3; + r:component skolem:lemma4; + r:component skolem:lemma5; + r:component skolem:lemma6; + r:component skolem:lemma7; + r:component skolem:lemma8; + r:component skolem:lemma9; + r:component skolem:lemma10; + r:component skolem:lemma11; + r:component skolem:lemma12; + r:component skolem:lemma13; + r:component skolem:lemma14; + r:component skolem:lemma15; + r:component skolem:lemma16; + r:component skolem:lemma17; + r:component skolem:lemma18; + r:component skolem:lemma19; + r:component skolem:lemma20; + r:component skolem:lemma21; + r:component skolem:lemma22; + r:component skolem:lemma23; + r:component skolem:lemma24; + r:component skolem:lemma25; + r:component skolem:lemma26; + r:component skolem:lemma27; + r:component skolem:lemma28; + r:component skolem:lemma29; + r:component skolem:lemma30; + r:component skolem:lemma31; + r:component skolem:lemma32; + r:component skolem:lemma33; + r:component skolem:lemma34; + r:component skolem:lemma35; + r:component skolem:lemma36; + r:component skolem:lemma37; + r:component skolem:lemma38; + r:component skolem:lemma39; + r:component skolem:lemma40; + r:component skolem:lemma41; + r:component skolem:lemma42; + r:component skolem:lemma43; + r:component skolem:lemma44; + r:component skolem:lemma45; + r:component skolem:lemma46; + r:component skolem:lemma47; + r:component skolem:lemma48; + r:component skolem:lemma49; + r:component skolem:lemma50; + r:component skolem:lemma51; + r:component skolem:lemma52; + r:component skolem:lemma53; + r:component skolem:lemma54; + r:component skolem:lemma55; + r:component skolem:lemma56; + r:component skolem:lemma57; + r:component skolem:lemma58; + r:component skolem:lemma59; + r:component skolem:lemma60; + r:component skolem:lemma61; + r:component skolem:lemma62; + r:component skolem:lemma63; + r:component skolem:lemma64; + r:component skolem:lemma65; + r:component skolem:lemma66; + r:component skolem:lemma67; + r:component skolem:lemma68; + r:component skolem:lemma69; + r:component skolem:lemma70; + r:component skolem:lemma71; + r:component skolem:lemma72; + r:component skolem:lemma73; + r:component skolem:lemma74; + r:component skolem:lemma75; + r:component skolem:lemma76; + r:component skolem:lemma77; + r:component skolem:lemma78; + r:component skolem:lemma79; + r:component skolem:lemma80; + r:component skolem:lemma81; + r:component skolem:lemma82; + r:component skolem:lemma83; + r:component skolem:lemma84; + r:component skolem:lemma85; + r:component skolem:lemma86; + r:component skolem:lemma87; + r:component skolem:lemma88; + r:component skolem:lemma89; + r:component skolem:lemma90; + r:component skolem:lemma91; + r:component skolem:lemma92; + r:component skolem:lemma93; + r:component skolem:lemma94; + r:component skolem:lemma95; + r:component skolem:lemma96; + r:component skolem:lemma97; + r:component skolem:lemma98; + r:component skolem:lemma99; + r:component skolem:lemma100; + r:component skolem:lemma101; + r:component skolem:lemma102; + r:component skolem:lemma103; + r:component skolem:lemma104; + r:component skolem:lemma105; + r:component skolem:lemma106; + r:component skolem:lemma107; + r:component skolem:lemma108; + r:component skolem:lemma109; + r:component skolem:lemma110; + r:component skolem:lemma111; + r:component skolem:lemma112; + r:component skolem:lemma113; + r:component skolem:lemma114; + r:component skolem:lemma115; + r:component skolem:lemma116; + r:component skolem:lemma117; + r:component skolem:lemma118; + r:component skolem:lemma119; + r:component skolem:lemma120; + r:component skolem:lemma121; + r:component skolem:lemma122; + r:component skolem:lemma123; + r:component skolem:lemma124; + r:component skolem:lemma125; + r:component skolem:lemma126; + r:component skolem:lemma127; + r:component skolem:lemma128; + r:component skolem:lemma129; + r:component skolem:lemma130; + r:component skolem:lemma131; + r:component skolem:lemma132; + r:component skolem:lemma133; + r:component skolem:lemma134; + r:component skolem:lemma135; + r:component skolem:lemma136; + r:component skolem:lemma137; + r:component skolem:lemma138; + r:component skolem:lemma139; + r:component skolem:lemma140; + r:component skolem:lemma141; + r:component skolem:lemma142; + r:component skolem:lemma143; + r:component skolem:lemma144; + r:component skolem:lemma145; + r:component skolem:lemma146; + r:component skolem:lemma147; + r:component skolem:lemma148; + r:component skolem:lemma149; + r:component skolem:lemma150; + r:component skolem:lemma151; + r:component skolem:lemma152; + r:component skolem:lemma153; + r:component skolem:lemma154; + r:component skolem:lemma155; + r:component skolem:lemma156; + r:component skolem:lemma157; + r:component skolem:lemma158; + r:component skolem:lemma159; + r:component skolem:lemma160; + r:component skolem:lemma161; + r:component skolem:lemma162; + r:component skolem:lemma163; + r:component skolem:lemma164; + r:component skolem:lemma165; + r:component skolem:lemma166; + r:component skolem:lemma167; + r:component skolem:lemma168; + r:component skolem:lemma169; + r:component skolem:lemma170; + r:component skolem:lemma171; + r:component skolem:lemma172; + r:component skolem:lemma173; + r:component skolem:lemma174; + r:component skolem:lemma175; + r:component skolem:lemma176; + r:component skolem:lemma177; + r:component skolem:lemma178; + r:component skolem:lemma179; + r:component skolem:lemma180; + r:component skolem:lemma181; + r:component skolem:lemma182; + r:component skolem:lemma183; + r:component skolem:lemma184; + r:component skolem:lemma185; + r:component skolem:lemma186; + r:component skolem:lemma187; + r:component skolem:lemma188; + r:component skolem:lemma189; + r:component skolem:lemma190; + r:component skolem:lemma191; + r:component skolem:lemma192; + r:component skolem:lemma193; + r:component skolem:lemma194; + r:component skolem:lemma195; + r:component skolem:lemma196; + r:component skolem:lemma197; + r:component skolem:lemma198; + r:component skolem:lemma199; + r:component skolem:lemma200; + r:component skolem:lemma201; + r:component skolem:lemma202; + r:component skolem:lemma203; + r:component skolem:lemma204; + r:component skolem:lemma205; + r:component skolem:lemma206; + r:component skolem:lemma207; + r:component skolem:lemma208; + r:component skolem:lemma209; + r:component skolem:lemma210; + r:component skolem:lemma211; + r:component skolem:lemma212; + r:component skolem:lemma213; + r:component skolem:lemma214; + r:component skolem:lemma215; + r:component skolem:lemma216; + r:component skolem:lemma217; + r:component skolem:lemma218; + r:component skolem:lemma219; + r:component skolem:lemma220; + r:component skolem:lemma221; + r:component skolem:lemma222; + r:component skolem:lemma223; + r:component skolem:lemma224; + r:component skolem:lemma225; + r:component skolem:lemma226; + r:component skolem:lemma227; + r:component skolem:lemma228; + r:component skolem:lemma229; + r:component skolem:lemma230; + r:component skolem:lemma231; + r:component skolem:lemma232; + r:component skolem:lemma233; + r:component skolem:lemma234; + r:component skolem:lemma235; + r:component skolem:lemma236; + r:component skolem:lemma237; + r:component skolem:lemma238; + r:component skolem:lemma239; + r:component skolem:lemma240; + r:component skolem:lemma241; + r:component skolem:lemma242; + r:component skolem:lemma243; + r:component skolem:lemma244; + r:component skolem:lemma245; + r:component skolem:lemma246; + r:component skolem:lemma247; + r:component skolem:lemma248; + r:component skolem:lemma249; + r:component skolem:lemma250; + r:component skolem:lemma251; + r:component skolem:lemma252; + r:component skolem:lemma253; + r:component skolem:lemma254; + r:component skolem:lemma255; + r:component skolem:lemma256; + r:gives { + 1 :collatz (1 (1)). + 2 :collatz (1 (2 1)). + 3 :collatz (1 (3 10 5 16 8 4 2 1)). + 4 :collatz (1 (4 2 1)). + 5 :collatz (1 (5 16 8 4 2 1)). + 6 :collatz (1 (6 3 10 5 16 8 4 2 1)). + 7 :collatz (1 (7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 8 :collatz (1 (8 4 2 1)). + 9 :collatz (1 (9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 10 :collatz (1 (10 5 16 8 4 2 1)). + 11 :collatz (1 (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 12 :collatz (1 (12 6 3 10 5 16 8 4 2 1)). + 13 :collatz (1 (13 40 20 10 5 16 8 4 2 1)). + 14 :collatz (1 (14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 15 :collatz (1 (15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 16 :collatz (1 (16 8 4 2 1)). + 17 :collatz (1 (17 52 26 13 40 20 10 5 16 8 4 2 1)). + 18 :collatz (1 (18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 19 :collatz (1 (19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 20 :collatz (1 (20 10 5 16 8 4 2 1)). + 21 :collatz (1 (21 64 32 16 8 4 2 1)). + 22 :collatz (1 (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 23 :collatz (1 (23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 24 :collatz (1 (24 12 6 3 10 5 16 8 4 2 1)). + 25 :collatz (1 (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 26 :collatz (1 (26 13 40 20 10 5 16 8 4 2 1)). + 27 :collatz (1 (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 28 :collatz (1 (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 29 :collatz (1 (29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 30 :collatz (1 (30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 31 :collatz (1 (31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 32 :collatz (1 (32 16 8 4 2 1)). + 33 :collatz (1 (33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 34 :collatz (1 (34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 35 :collatz (1 (35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 36 :collatz (1 (36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 37 :collatz (1 (37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 38 :collatz (1 (38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 39 :collatz (1 (39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 40 :collatz (1 (40 20 10 5 16 8 4 2 1)). + 41 :collatz (1 (41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 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466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 253 :collatz (1 (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + 254 :collatz (1 (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 255 :collatz (1 (255 766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + 256 :collatz (1 (256 128 64 32 16 8 4 2 1)). + }. + +skolem:lemma1 a r:Inference; + r:gives { + 1 :collatz (1 (1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 0}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + skolem:lemma257 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1)]; + r:rule skolem:lemma258. + +skolem:lemma2 a r:Inference; + r:gives { + 2 :collatz (1 (2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 1}] + [ a r:Fact; r:gives {(1 1) math:sum 2}] + skolem:lemma259 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 1)]; + r:rule skolem:lemma258. + +skolem:lemma3 a r:Inference; + r:gives { + 3 :collatz (1 (3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 2}] + [ a r:Fact; r:gives {(2 1) math:sum 3}] + skolem:lemma260 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma4 a r:Inference; + r:gives { + 4 :collatz (1 (4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 3}] + [ a r:Fact; r:gives {(3 1) math:sum 4}] + skolem:lemma261 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma5 a r:Inference; + r:gives { + 5 :collatz (1 (5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 4}] + [ a r:Fact; r:gives {(4 1) math:sum 5}] + skolem:lemma262 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma6 a r:Inference; + r:gives { + 6 :collatz (1 (6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 5}] + [ a r:Fact; r:gives {(5 1) math:sum 6}] + skolem:lemma263 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma7 a r:Inference; + r:gives { + 7 :collatz (1 (7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 6}] + [ a r:Fact; r:gives {(6 1) math:sum 7}] + skolem:lemma264 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma8 a r:Inference; + r:gives { + 8 :collatz (1 (8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 7}] + [ a r:Fact; r:gives {(7 1) math:sum 8}] + skolem:lemma265 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma9 a r:Inference; + r:gives { + 9 :collatz (1 (9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 8}] + [ a r:Fact; r:gives {(8 1) math:sum 9}] + skolem:lemma266 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma10 a r:Inference; + r:gives { + 10 :collatz (1 (10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 9}] + [ a r:Fact; r:gives {(9 1) math:sum 10}] + skolem:lemma267 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma11 a r:Inference; + r:gives { + 11 :collatz (1 (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 10}] + [ a r:Fact; r:gives {(10 1) math:sum 11}] + skolem:lemma268 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma12 a r:Inference; + r:gives { + 12 :collatz (1 (12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 11}] + [ a r:Fact; r:gives {(11 1) math:sum 12}] + skolem:lemma269 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma13 a r:Inference; + r:gives { + 13 :collatz (1 (13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 12}] + [ a r:Fact; r:gives {(12 1) math:sum 13}] + skolem:lemma270 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma14 a r:Inference; + r:gives { + 14 :collatz (1 (14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 13}] + [ a r:Fact; r:gives {(13 1) math:sum 14}] + skolem:lemma271 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma15 a r:Inference; + r:gives { + 15 :collatz (1 (15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 14}] + [ a r:Fact; r:gives {(14 1) math:sum 15}] + skolem:lemma272 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma16 a r:Inference; + r:gives { + 16 :collatz (1 (16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 15}] + [ a r:Fact; r:gives {(15 1) math:sum 16}] + skolem:lemma273 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma17 a r:Inference; + r:gives { + 17 :collatz (1 (17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 16}] + [ a r:Fact; r:gives {(16 1) math:sum 17}] + skolem:lemma274 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma18 a r:Inference; + r:gives { + 18 :collatz (1 (18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 17}] + [ a r:Fact; r:gives {(17 1) math:sum 18}] + skolem:lemma275 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma19 a r:Inference; + r:gives { + 19 :collatz (1 (19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 18}] + [ a r:Fact; r:gives {(18 1) math:sum 19}] + skolem:lemma276 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma20 a r:Inference; + r:gives { + 20 :collatz (1 (20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 19}] + [ a r:Fact; r:gives {(19 1) math:sum 20}] + skolem:lemma277 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma21 a r:Inference; + r:gives { + 21 :collatz (1 (21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 20}] + [ a r:Fact; r:gives {(20 1) math:sum 21}] + skolem:lemma278 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma22 a r:Inference; + r:gives { + 22 :collatz (1 (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 21}] + [ a r:Fact; r:gives {(21 1) math:sum 22}] + skolem:lemma279 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma23 a r:Inference; + r:gives { + 23 :collatz (1 (23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 22}] + [ a r:Fact; r:gives {(22 1) math:sum 23}] + skolem:lemma280 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma24 a r:Inference; + r:gives { + 24 :collatz (1 (24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 23}] + [ a r:Fact; r:gives {(23 1) math:sum 24}] + skolem:lemma281 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma25 a r:Inference; + r:gives { + 25 :collatz (1 (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 24}] + [ a r:Fact; r:gives {(24 1) math:sum 25}] + skolem:lemma282 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma26 a r:Inference; + r:gives { + 26 :collatz (1 (26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 25}] + [ a r:Fact; r:gives {(25 1) math:sum 26}] + skolem:lemma283 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma27 a r:Inference; + r:gives { + 27 :collatz (1 (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 26}] + [ a r:Fact; r:gives {(26 1) math:sum 27}] + skolem:lemma284 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma28 a r:Inference; + r:gives { + 28 :collatz (1 (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 27}] + [ a r:Fact; r:gives {(27 1) math:sum 28}] + skolem:lemma285 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma29 a r:Inference; + r:gives { + 29 :collatz (1 (29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 28}] + [ a r:Fact; r:gives {(28 1) math:sum 29}] + skolem:lemma286 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma30 a r:Inference; + r:gives { + 30 :collatz (1 (30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 29}] + [ a r:Fact; r:gives {(29 1) math:sum 30}] + skolem:lemma287 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma31 a r:Inference; + r:gives { + 31 :collatz (1 (31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 30}] + [ a r:Fact; r:gives {(30 1) math:sum 31}] + skolem:lemma288 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma32 a r:Inference; + r:gives { + 32 :collatz (1 (32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 31}] + [ a r:Fact; r:gives {(31 1) math:sum 32}] + skolem:lemma289 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma33 a r:Inference; + r:gives { + 33 :collatz (1 (33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 32}] + [ a r:Fact; r:gives {(32 1) math:sum 33}] + skolem:lemma290 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma34 a r:Inference; + r:gives { + 34 :collatz (1 (34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 33}] + [ a r:Fact; r:gives {(33 1) math:sum 34}] + skolem:lemma291 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma35 a r:Inference; + r:gives { + 35 :collatz (1 (35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 34}] + [ a r:Fact; r:gives {(34 1) math:sum 35}] + skolem:lemma292 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma36 a r:Inference; + r:gives { + 36 :collatz (1 (36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 35}] + [ a r:Fact; r:gives {(35 1) math:sum 36}] + skolem:lemma293 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma37 a r:Inference; + r:gives { + 37 :collatz (1 (37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 36}] + [ a r:Fact; r:gives {(36 1) math:sum 37}] + skolem:lemma294 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma38 a r:Inference; + r:gives { + 38 :collatz (1 (38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 37}] + [ a r:Fact; r:gives {(37 1) math:sum 38}] + skolem:lemma295 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma39 a r:Inference; + r:gives { + 39 :collatz (1 (39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 38}] + [ a r:Fact; r:gives {(38 1) math:sum 39}] + skolem:lemma296 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma40 a r:Inference; + r:gives { + 40 :collatz (1 (40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 39}] + [ a r:Fact; r:gives {(39 1) math:sum 40}] + skolem:lemma297 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma41 a r:Inference; + r:gives { + 41 :collatz (1 (41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 40}] + [ a r:Fact; r:gives {(40 1) math:sum 41}] + skolem:lemma298 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma42 a r:Inference; + r:gives { + 42 :collatz (1 (42 21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 41}] + [ a r:Fact; r:gives {(41 1) math:sum 42}] + skolem:lemma299 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (42 21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma43 a r:Inference; + r:gives { + 43 :collatz (1 (43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 42}] + [ a r:Fact; r:gives {(42 1) math:sum 43}] + skolem:lemma300 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma44 a r:Inference; + r:gives { + 44 :collatz (1 (44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 43}] + [ a r:Fact; r:gives {(43 1) math:sum 44}] + skolem:lemma301 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma45 a r:Inference; + r:gives { + 45 :collatz (1 (45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 44}] + [ a r:Fact; r:gives {(44 1) math:sum 45}] + skolem:lemma302 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma46 a r:Inference; + r:gives { + 46 :collatz (1 (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 45}] + [ a r:Fact; r:gives {(45 1) math:sum 46}] + skolem:lemma303 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma47 a r:Inference; + r:gives { + 47 :collatz (1 (47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 46}] + [ a r:Fact; r:gives {(46 1) math:sum 47}] + skolem:lemma304 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma48 a r:Inference; + r:gives { + 48 :collatz (1 (48 24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 47}] + [ a r:Fact; r:gives {(47 1) math:sum 48}] + skolem:lemma305 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (48 24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma49 a r:Inference; + r:gives { + 49 :collatz (1 (49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 48}] + [ a r:Fact; r:gives {(48 1) math:sum 49}] + skolem:lemma306 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma50 a r:Inference; + r:gives { + 50 :collatz (1 (50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 49}] + [ a r:Fact; r:gives {(49 1) math:sum 50}] + skolem:lemma307 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma51 a r:Inference; + r:gives { + 51 :collatz (1 (51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 50}] + [ a r:Fact; r:gives {(50 1) math:sum 51}] + skolem:lemma308 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma52 a r:Inference; + r:gives { + 52 :collatz (1 (52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 51}] + [ a r:Fact; r:gives {(51 1) math:sum 52}] + skolem:lemma309 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma53 a r:Inference; + r:gives { + 53 :collatz (1 (53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 52}] + [ a r:Fact; r:gives {(52 1) math:sum 53}] + skolem:lemma310 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma54 a r:Inference; + r:gives { + 54 :collatz (1 (54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 53}] + [ a r:Fact; r:gives {(53 1) math:sum 54}] + skolem:lemma311 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma55 a r:Inference; + r:gives { + 55 :collatz (1 (55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 54}] + [ a r:Fact; r:gives {(54 1) math:sum 55}] + skolem:lemma312 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma56 a r:Inference; + r:gives { + 56 :collatz (1 (56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 55}] + [ a r:Fact; r:gives {(55 1) math:sum 56}] + skolem:lemma313 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma57 a r:Inference; + r:gives { + 57 :collatz (1 (57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 56}] + [ a r:Fact; r:gives {(56 1) math:sum 57}] + skolem:lemma314 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma58 a r:Inference; + r:gives { + 58 :collatz (1 (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 57}] + [ a r:Fact; r:gives {(57 1) math:sum 58}] + skolem:lemma315 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma59 a r:Inference; + r:gives { + 59 :collatz (1 (59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 58}] + [ a r:Fact; r:gives {(58 1) math:sum 59}] + skolem:lemma316 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma60 a r:Inference; + r:gives { + 60 :collatz (1 (60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 59}] + [ a r:Fact; r:gives {(59 1) math:sum 60}] + skolem:lemma317 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma61 a r:Inference; + r:gives { + 61 :collatz (1 (61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 60}] + [ a r:Fact; r:gives {(60 1) math:sum 61}] + skolem:lemma318 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma62 a r:Inference; + r:gives { + 62 :collatz (1 (62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 61}] + [ a r:Fact; r:gives {(61 1) math:sum 62}] + skolem:lemma319 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma63 a r:Inference; + r:gives { + 63 :collatz (1 (63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 62}] + [ a r:Fact; r:gives {(62 1) math:sum 63}] + skolem:lemma320 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma64 a r:Inference; + r:gives { + 64 :collatz (1 (64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 63}] + [ a r:Fact; r:gives {(63 1) math:sum 64}] + skolem:lemma321 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma65 a r:Inference; + r:gives { + 65 :collatz (1 (65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 64}] + [ a r:Fact; r:gives {(64 1) math:sum 65}] + skolem:lemma322 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma66 a r:Inference; + r:gives { + 66 :collatz (1 (66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 65}] + [ a r:Fact; r:gives {(65 1) math:sum 66}] + skolem:lemma323 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma67 a r:Inference; + r:gives { + 67 :collatz (1 (67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 66}] + [ a r:Fact; r:gives {(66 1) math:sum 67}] + skolem:lemma324 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma68 a r:Inference; + r:gives { + 68 :collatz (1 (68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 67}] + [ a r:Fact; r:gives {(67 1) math:sum 68}] + skolem:lemma325 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma69 a r:Inference; + r:gives { + 69 :collatz (1 (69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 68}] + [ a r:Fact; r:gives {(68 1) math:sum 69}] + skolem:lemma326 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma70 a r:Inference; + r:gives { + 70 :collatz (1 (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 69}] + [ a r:Fact; r:gives {(69 1) math:sum 70}] + skolem:lemma327 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma71 a r:Inference; + r:gives { + 71 :collatz (1 (71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 70}] + [ a r:Fact; r:gives {(70 1) math:sum 71}] + skolem:lemma328 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma72 a r:Inference; + r:gives { + 72 :collatz (1 (72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 71}] + [ a r:Fact; r:gives {(71 1) math:sum 72}] + skolem:lemma329 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma73 a r:Inference; + r:gives { + 73 :collatz (1 (73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 72}] + [ a r:Fact; r:gives {(72 1) math:sum 73}] + skolem:lemma330 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma74 a r:Inference; + r:gives { + 74 :collatz (1 (74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 73}] + [ a r:Fact; r:gives {(73 1) math:sum 74}] + skolem:lemma331 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma75 a r:Inference; + r:gives { + 75 :collatz (1 (75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 74}] + [ a r:Fact; r:gives {(74 1) math:sum 75}] + skolem:lemma332 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma76 a r:Inference; + r:gives { + 76 :collatz (1 (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 75}] + [ a r:Fact; r:gives {(75 1) math:sum 76}] + skolem:lemma333 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma77 a r:Inference; + r:gives { + 77 :collatz (1 (77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 76}] + [ a r:Fact; r:gives {(76 1) math:sum 77}] + skolem:lemma334 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma78 a r:Inference; + r:gives { + 78 :collatz (1 (78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 77}] + [ a r:Fact; r:gives {(77 1) math:sum 78}] + skolem:lemma335 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma79 a r:Inference; + r:gives { + 79 :collatz (1 (79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 78}] + [ a r:Fact; r:gives {(78 1) math:sum 79}] + skolem:lemma336 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma80 a r:Inference; + r:gives { + 80 :collatz (1 (80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 79}] + [ a r:Fact; r:gives {(79 1) math:sum 80}] + skolem:lemma337 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma81 a r:Inference; + r:gives { + 81 :collatz (1 (81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 80}] + [ a r:Fact; r:gives {(80 1) math:sum 81}] + skolem:lemma338 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma82 a r:Inference; + r:gives { + 82 :collatz (1 (82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 81}] + [ a r:Fact; r:gives {(81 1) math:sum 82}] + skolem:lemma339 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma83 a r:Inference; + r:gives { + 83 :collatz (1 (83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 82}] + [ a r:Fact; r:gives {(82 1) math:sum 83}] + skolem:lemma340 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma84 a r:Inference; + r:gives { + 84 :collatz (1 (84 42 21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 83}] + [ a r:Fact; r:gives {(83 1) math:sum 84}] + skolem:lemma341 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (84 42 21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma85 a r:Inference; + r:gives { + 85 :collatz (1 (85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 84}] + [ a r:Fact; r:gives {(84 1) math:sum 85}] + skolem:lemma342 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma86 a r:Inference; + r:gives { + 86 :collatz (1 (86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 85}] + [ a r:Fact; r:gives {(85 1) math:sum 86}] + skolem:lemma343 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma87 a r:Inference; + r:gives { + 87 :collatz (1 (87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 86}] + [ a r:Fact; r:gives {(86 1) math:sum 87}] + skolem:lemma344 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma88 a r:Inference; + r:gives { + 88 :collatz (1 (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 87}] + [ a r:Fact; r:gives {(87 1) math:sum 88}] + skolem:lemma345 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma89 a r:Inference; + r:gives { + 89 :collatz (1 (89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 88}] + [ a r:Fact; r:gives {(88 1) math:sum 89}] + skolem:lemma346 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma90 a r:Inference; + r:gives { + 90 :collatz (1 (90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 89}] + [ a r:Fact; r:gives {(89 1) math:sum 90}] + skolem:lemma347 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma91 a r:Inference; + r:gives { + 91 :collatz (1 (91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 90}] + [ a r:Fact; r:gives {(90 1) math:sum 91}] + skolem:lemma348 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma92 a r:Inference; + r:gives { + 92 :collatz (1 (92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 91}] + [ a r:Fact; r:gives {(91 1) math:sum 92}] + skolem:lemma349 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma93 a r:Inference; + r:gives { + 93 :collatz (1 (93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 92}] + [ a r:Fact; r:gives {(92 1) math:sum 93}] + skolem:lemma350 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma94 a r:Inference; + r:gives { + 94 :collatz (1 (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 93}] + [ a r:Fact; r:gives {(93 1) math:sum 94}] + skolem:lemma351 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma95 a r:Inference; + r:gives { + 95 :collatz (1 (95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 94}] + [ a r:Fact; r:gives {(94 1) math:sum 95}] + skolem:lemma352 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma96 a r:Inference; + r:gives { + 96 :collatz (1 (96 48 24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 95}] + [ a r:Fact; r:gives {(95 1) math:sum 96}] + skolem:lemma353 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (96 48 24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma97 a r:Inference; + r:gives { + 97 :collatz (1 (97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 96}] + [ a r:Fact; r:gives {(96 1) math:sum 97}] + skolem:lemma354 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma98 a r:Inference; + r:gives { + 98 :collatz (1 (98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 97}] + [ a r:Fact; r:gives {(97 1) math:sum 98}] + skolem:lemma355 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma99 a r:Inference; + r:gives { + 99 :collatz (1 (99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 98}] + [ a r:Fact; r:gives {(98 1) math:sum 99}] + skolem:lemma356 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma100 a r:Inference; + r:gives { + 100 :collatz (1 (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 99}] + [ a r:Fact; r:gives {(99 1) math:sum 100}] + skolem:lemma357 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma101 a r:Inference; + r:gives { + 101 :collatz (1 (101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 100}] + [ a r:Fact; r:gives {(100 1) math:sum 101}] + skolem:lemma358 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma102 a r:Inference; + r:gives { + 102 :collatz (1 (102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 101}] + [ a r:Fact; r:gives {(101 1) math:sum 102}] + skolem:lemma359 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma103 a r:Inference; + r:gives { + 103 :collatz (1 (103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 102}] + [ a r:Fact; r:gives {(102 1) math:sum 103}] + skolem:lemma360 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma104 a r:Inference; + r:gives { + 104 :collatz (1 (104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 103}] + [ a r:Fact; r:gives {(103 1) math:sum 104}] + skolem:lemma361 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma105 a r:Inference; + r:gives { + 105 :collatz (1 (105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 104}] + [ a r:Fact; r:gives {(104 1) math:sum 105}] + skolem:lemma362 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma106 a r:Inference; + r:gives { + 106 :collatz (1 (106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 105}] + [ a r:Fact; r:gives {(105 1) math:sum 106}] + skolem:lemma363 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma107 a r:Inference; + r:gives { + 107 :collatz (1 (107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 106}] + [ a r:Fact; r:gives {(106 1) math:sum 107}] + skolem:lemma364 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma108 a r:Inference; + r:gives { + 108 :collatz (1 (108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 107}] + [ a r:Fact; r:gives {(107 1) math:sum 108}] + skolem:lemma365 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma109 a r:Inference; + r:gives { + 109 :collatz (1 (109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 108}] + [ a r:Fact; r:gives {(108 1) math:sum 109}] + skolem:lemma366 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma110 a r:Inference; + r:gives { + 110 :collatz (1 (110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 109}] + [ a r:Fact; r:gives {(109 1) math:sum 110}] + skolem:lemma367 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma111 a r:Inference; + r:gives { + 111 :collatz (1 (111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 110}] + [ a r:Fact; r:gives {(110 1) math:sum 111}] + skolem:lemma368 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma112 a r:Inference; + r:gives { + 112 :collatz (1 (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 111}] + [ a r:Fact; r:gives {(111 1) math:sum 112}] + skolem:lemma369 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma113 a r:Inference; + r:gives { + 113 :collatz (1 (113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 112}] + [ a r:Fact; r:gives {(112 1) math:sum 113}] + skolem:lemma370 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma114 a r:Inference; + r:gives { + 114 :collatz (1 (114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 113}] + [ a r:Fact; r:gives {(113 1) math:sum 114}] + skolem:lemma371 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma115 a r:Inference; + r:gives { + 115 :collatz (1 (115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 114}] + [ a r:Fact; r:gives {(114 1) math:sum 115}] + skolem:lemma372 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma116 a r:Inference; + r:gives { + 116 :collatz (1 (116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 115}] + [ a r:Fact; r:gives {(115 1) math:sum 116}] + skolem:lemma373 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma117 a r:Inference; + r:gives { + 117 :collatz (1 (117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 116}] + [ a r:Fact; r:gives {(116 1) math:sum 117}] + skolem:lemma374 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma118 a r:Inference; + r:gives { + 118 :collatz (1 (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 117}] + [ a r:Fact; r:gives {(117 1) math:sum 118}] + skolem:lemma375 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma119 a r:Inference; + r:gives { + 119 :collatz (1 (119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 118}] + [ a r:Fact; r:gives {(118 1) math:sum 119}] + skolem:lemma376 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma120 a r:Inference; + r:gives { + 120 :collatz (1 (120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 119}] + [ a r:Fact; r:gives {(119 1) math:sum 120}] + skolem:lemma377 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma121 a r:Inference; + r:gives { + 121 :collatz (1 (121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 120}] + [ a r:Fact; r:gives {(120 1) math:sum 121}] + skolem:lemma378 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma122 a r:Inference; + r:gives { + 122 :collatz (1 (122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 121}] + [ a r:Fact; r:gives {(121 1) math:sum 122}] + skolem:lemma379 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma123 a r:Inference; + r:gives { + 123 :collatz (1 (123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 122}] + [ a r:Fact; r:gives {(122 1) math:sum 123}] + skolem:lemma380 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma124 a r:Inference; + r:gives { + 124 :collatz (1 (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 123}] + [ a r:Fact; r:gives {(123 1) math:sum 124}] + skolem:lemma381 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma125 a r:Inference; + r:gives { + 125 :collatz (1 (125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 124}] + [ a r:Fact; r:gives {(124 1) math:sum 125}] + skolem:lemma382 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma126 a r:Inference; + r:gives { + 126 :collatz (1 (126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 125}] + [ a r:Fact; r:gives {(125 1) math:sum 126}] + skolem:lemma383 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma127 a r:Inference; + r:gives { + 127 :collatz (1 (127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 126}] + [ a r:Fact; r:gives {(126 1) math:sum 127}] + skolem:lemma384 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma128 a r:Inference; + r:gives { + 128 :collatz (1 (128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 127}] + [ a r:Fact; r:gives {(127 1) math:sum 128}] + skolem:lemma385 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma129 a r:Inference; + r:gives { + 129 :collatz (1 (129 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 128}] + [ a r:Fact; r:gives {(128 1) math:sum 129}] + skolem:lemma386 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (129 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma130 a r:Inference; + r:gives { + 130 :collatz (1 (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 129}] + [ a r:Fact; r:gives {(129 1) math:sum 130}] + skolem:lemma387 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma131 a r:Inference; + r:gives { + 131 :collatz (1 (131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 130}] + [ a r:Fact; r:gives {(130 1) math:sum 131}] + skolem:lemma388 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma132 a r:Inference; + r:gives { + 132 :collatz (1 (132 66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 131}] + [ a r:Fact; r:gives {(131 1) math:sum 132}] + skolem:lemma389 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (132 66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma133 a r:Inference; + r:gives { + 133 :collatz (1 (133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 132}] + [ a r:Fact; r:gives {(132 1) math:sum 133}] + skolem:lemma390 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma134 a r:Inference; + r:gives { + 134 :collatz (1 (134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 133}] + [ a r:Fact; r:gives {(133 1) math:sum 134}] + skolem:lemma391 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma135 a r:Inference; + r:gives { + 135 :collatz (1 (135 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 134}] + [ a r:Fact; r:gives {(134 1) math:sum 135}] + skolem:lemma392 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (135 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma136 a r:Inference; + r:gives { + 136 :collatz (1 (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 135}] + [ a r:Fact; r:gives {(135 1) math:sum 136}] + skolem:lemma393 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma137 a r:Inference; + r:gives { + 137 :collatz (1 (137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 136}] + [ a r:Fact; r:gives {(136 1) math:sum 137}] + skolem:lemma394 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma138 a r:Inference; + r:gives { + 138 :collatz (1 (138 69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 137}] + [ a r:Fact; r:gives {(137 1) math:sum 138}] + skolem:lemma395 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (138 69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma139 a r:Inference; + r:gives { + 139 :collatz (1 (139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 138}] + [ a r:Fact; r:gives {(138 1) math:sum 139}] + skolem:lemma396 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma140 a r:Inference; + r:gives { + 140 :collatz (1 (140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 139}] + [ a r:Fact; r:gives {(139 1) math:sum 140}] + skolem:lemma397 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma141 a r:Inference; + r:gives { + 141 :collatz (1 (141 424 212 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 140}] + [ a r:Fact; r:gives {(140 1) math:sum 141}] + skolem:lemma398 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (141 424 212 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma142 a r:Inference; + r:gives { + 142 :collatz (1 (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 141}] + [ a r:Fact; r:gives {(141 1) math:sum 142}] + skolem:lemma399 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma143 a r:Inference; + r:gives { + 143 :collatz (1 (143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 142}] + [ a r:Fact; r:gives {(142 1) math:sum 143}] + skolem:lemma400 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma144 a r:Inference; + r:gives { + 144 :collatz (1 (144 72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 143}] + [ a r:Fact; r:gives {(143 1) math:sum 144}] + skolem:lemma401 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (144 72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma145 a r:Inference; + r:gives { + 145 :collatz (1 (145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 144}] + [ a r:Fact; r:gives {(144 1) math:sum 145}] + skolem:lemma402 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma146 a r:Inference; + r:gives { + 146 :collatz (1 (146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 145}] + [ a r:Fact; r:gives {(145 1) math:sum 146}] + skolem:lemma403 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma147 a r:Inference; + r:gives { + 147 :collatz (1 (147 442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 146}] + [ a r:Fact; r:gives {(146 1) math:sum 147}] + skolem:lemma404 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (147 442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma148 a r:Inference; + r:gives { + 148 :collatz (1 (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 147}] + [ a r:Fact; r:gives {(147 1) math:sum 148}] + skolem:lemma405 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma149 a r:Inference; + r:gives { + 149 :collatz (1 (149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 148}] + [ a r:Fact; r:gives {(148 1) math:sum 149}] + skolem:lemma406 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma150 a r:Inference; + r:gives { + 150 :collatz (1 (150 75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 149}] + [ a r:Fact; r:gives {(149 1) math:sum 150}] + skolem:lemma407 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (150 75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma151 a r:Inference; + r:gives { + 151 :collatz (1 (151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 150}] + [ a r:Fact; r:gives {(150 1) math:sum 151}] + skolem:lemma408 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma152 a r:Inference; + r:gives { + 152 :collatz (1 (152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 151}] + [ a r:Fact; r:gives {(151 1) math:sum 152}] + skolem:lemma409 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma153 a r:Inference; + r:gives { + 153 :collatz (1 (153 460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 152}] + [ a r:Fact; r:gives {(152 1) math:sum 153}] + skolem:lemma410 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (153 460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma154 a r:Inference; + r:gives { + 154 :collatz (1 (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 153}] + [ a r:Fact; r:gives {(153 1) math:sum 154}] + skolem:lemma411 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma155 a r:Inference; + r:gives { + 155 :collatz (1 (155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 154}] + [ a r:Fact; r:gives {(154 1) math:sum 155}] + skolem:lemma412 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma156 a r:Inference; + r:gives { + 156 :collatz (1 (156 78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 155}] + [ a r:Fact; r:gives {(155 1) math:sum 156}] + skolem:lemma413 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (156 78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma157 a r:Inference; + r:gives { + 157 :collatz (1 (157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 156}] + [ a r:Fact; r:gives {(156 1) math:sum 157}] + skolem:lemma414 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma158 a r:Inference; + r:gives { + 158 :collatz (1 (158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 157}] + [ a r:Fact; r:gives {(157 1) math:sum 158}] + skolem:lemma415 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma159 a r:Inference; + r:gives { + 159 :collatz (1 (159 478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 158}] + [ a r:Fact; r:gives {(158 1) math:sum 159}] + skolem:lemma416 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (159 478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma160 a r:Inference; + r:gives { + 160 :collatz (1 (160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 159}] + [ a r:Fact; r:gives {(159 1) math:sum 160}] + skolem:lemma417 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma161 a r:Inference; + r:gives { + 161 :collatz (1 (161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 160}] + [ a r:Fact; r:gives {(160 1) math:sum 161}] + skolem:lemma418 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma162 a r:Inference; + r:gives { + 162 :collatz (1 (162 81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 161}] + [ a r:Fact; r:gives {(161 1) math:sum 162}] + skolem:lemma419 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (162 81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma163 a r:Inference; + r:gives { + 163 :collatz (1 (163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 162}] + [ a r:Fact; r:gives {(162 1) math:sum 163}] + skolem:lemma420 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma164 a r:Inference; + r:gives { + 164 :collatz (1 (164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 163}] + [ a r:Fact; r:gives {(163 1) math:sum 164}] + skolem:lemma421 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma165 a r:Inference; + r:gives { + 165 :collatz (1 (165 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 164}] + [ a r:Fact; r:gives {(164 1) math:sum 165}] + skolem:lemma422 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (165 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma166 a r:Inference; + r:gives { + 166 :collatz (1 (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 165}] + [ a r:Fact; r:gives {(165 1) math:sum 166}] + skolem:lemma423 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma167 a r:Inference; + r:gives { + 167 :collatz (1 (167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 166}] + [ a r:Fact; r:gives {(166 1) math:sum 167}] + skolem:lemma424 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma168 a r:Inference; + r:gives { + 168 :collatz (1 (168 84 42 21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 167}] + [ a r:Fact; r:gives {(167 1) math:sum 168}] + skolem:lemma425 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (168 84 42 21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma169 a r:Inference; + r:gives { + 169 :collatz (1 (169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 168}] + [ a r:Fact; r:gives {(168 1) math:sum 169}] + skolem:lemma426 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma170 a r:Inference; + r:gives { + 170 :collatz (1 (170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 169}] + [ a r:Fact; r:gives {(169 1) math:sum 170}] + skolem:lemma427 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma171 a r:Inference; + r:gives { + 171 :collatz (1 (171 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 170}] + [ a r:Fact; r:gives {(170 1) math:sum 171}] + skolem:lemma428 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (171 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma172 a r:Inference; + r:gives { + 172 :collatz (1 (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 171}] + [ a r:Fact; r:gives {(171 1) math:sum 172}] + skolem:lemma429 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma173 a r:Inference; + r:gives { + 173 :collatz (1 (173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 172}] + [ a r:Fact; r:gives {(172 1) math:sum 173}] + skolem:lemma430 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma174 a r:Inference; + r:gives { + 174 :collatz (1 (174 87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 173}] + [ a r:Fact; r:gives {(173 1) math:sum 174}] + skolem:lemma431 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (174 87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma175 a r:Inference; + r:gives { + 175 :collatz (1 (175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 174}] + [ a r:Fact; r:gives {(174 1) math:sum 175}] + skolem:lemma432 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma176 a r:Inference; + r:gives { + 176 :collatz (1 (176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 175}] + [ a r:Fact; r:gives {(175 1) math:sum 176}] + skolem:lemma433 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma177 a r:Inference; + r:gives { + 177 :collatz (1 (177 532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 176}] + [ a r:Fact; r:gives {(176 1) math:sum 177}] + skolem:lemma434 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (177 532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma178 a r:Inference; + r:gives { + 178 :collatz (1 (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 177}] + [ a r:Fact; r:gives {(177 1) math:sum 178}] + skolem:lemma435 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma179 a r:Inference; + r:gives { + 179 :collatz (1 (179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 178}] + [ a r:Fact; r:gives {(178 1) math:sum 179}] + skolem:lemma436 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma180 a r:Inference; + r:gives { + 180 :collatz (1 (180 90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 179}] + [ a r:Fact; r:gives {(179 1) math:sum 180}] + skolem:lemma437 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (180 90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma181 a r:Inference; + r:gives { + 181 :collatz (1 (181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 180}] + [ a r:Fact; r:gives {(180 1) math:sum 181}] + skolem:lemma438 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma182 a r:Inference; + r:gives { + 182 :collatz (1 (182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 181}] + [ a r:Fact; r:gives {(181 1) math:sum 182}] + skolem:lemma439 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 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n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (183 550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma184 a r:Inference; + r:gives { + 184 :collatz (1 (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 183}] + [ a r:Fact; r:gives {(183 1) math:sum 184}] + skolem:lemma441 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma185 a r:Inference; + r:gives { + 185 :collatz (1 (185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 184}] + [ a r:Fact; r:gives {(184 1) math:sum 185}] + skolem:lemma442 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma186 a r:Inference; + r:gives { + 186 :collatz (1 (186 93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 185}] + [ a r:Fact; r:gives {(185 1) math:sum 186}] + skolem:lemma443 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (186 93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma187 a r:Inference; + r:gives { + 187 :collatz (1 (187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 186}] + [ a r:Fact; r:gives {(186 1) math:sum 187}] + skolem:lemma444 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma188 a r:Inference; + r:gives { + 188 :collatz (1 (188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 187}] + [ a r:Fact; r:gives {(187 1) math:sum 188}] + skolem:lemma445 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma189 a r:Inference; + r:gives { + 189 :collatz (1 (189 568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 188}] + [ a r:Fact; r:gives {(188 1) math:sum 189}] + skolem:lemma446 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (189 568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma190 a r:Inference; + r:gives { + 190 :collatz (1 (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 189}] + [ a r:Fact; r:gives {(189 1) math:sum 190}] + skolem:lemma447 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma191 a r:Inference; + r:gives { + 191 :collatz (1 (191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 190}] + [ a r:Fact; r:gives {(190 1) math:sum 191}] + skolem:lemma448 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma192 a r:Inference; + r:gives { + 192 :collatz (1 (192 96 48 24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 191}] + [ a r:Fact; r:gives {(191 1) math:sum 192}] + skolem:lemma449 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (192 96 48 24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma193 a r:Inference; + r:gives { + 193 :collatz (1 (193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 192}] + [ a r:Fact; r:gives {(192 1) math:sum 193}] + skolem:lemma450 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma194 a r:Inference; + r:gives { + 194 :collatz (1 (194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 193}] + [ a r:Fact; r:gives {(193 1) math:sum 194}] + skolem:lemma451 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma195 a r:Inference; + r:gives { + 195 :collatz (1 (195 586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 194}] + [ a r:Fact; r:gives {(194 1) math:sum 195}] + skolem:lemma452 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (195 586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma196 a r:Inference; + r:gives { + 196 :collatz (1 (196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 195}] + [ a r:Fact; r:gives {(195 1) math:sum 196}] + skolem:lemma453 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma197 a r:Inference; + r:gives { + 197 :collatz (1 (197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 196}] + [ a r:Fact; r:gives {(196 1) math:sum 197}] + skolem:lemma454 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma198 a r:Inference; + r:gives { + 198 :collatz (1 (198 99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 197}] + [ a r:Fact; r:gives {(197 1) math:sum 198}] + skolem:lemma455 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (198 99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma199 a r:Inference; + r:gives { + 199 :collatz (1 (199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 198}] + [ a r:Fact; r:gives {(198 1) math:sum 199}] + skolem:lemma456 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma200 a r:Inference; + r:gives { + 200 :collatz (1 (200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 199}] + [ a r:Fact; r:gives {(199 1) math:sum 200}] + skolem:lemma457 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma201 a r:Inference; + r:gives { + 201 :collatz (1 (201 604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 200}] + [ a r:Fact; r:gives {(200 1) math:sum 201}] + skolem:lemma458 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (201 604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma202 a r:Inference; + r:gives { + 202 :collatz (1 (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 201}] + [ a r:Fact; r:gives {(201 1) math:sum 202}] + skolem:lemma459 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma203 a r:Inference; + r:gives { + 203 :collatz (1 (203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 202}] + [ a r:Fact; r:gives {(202 1) math:sum 203}] + skolem:lemma460 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma204 a r:Inference; + r:gives { + 204 :collatz (1 (204 102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 203}] + [ a r:Fact; r:gives {(203 1) math:sum 204}] + skolem:lemma461 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (204 102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma205 a r:Inference; + r:gives { + 205 :collatz (1 (205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 204}] + [ a r:Fact; r:gives {(204 1) math:sum 205}] + skolem:lemma462 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma206 a r:Inference; + r:gives { + 206 :collatz (1 (206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 205}] + [ a r:Fact; r:gives {(205 1) math:sum 206}] + skolem:lemma463 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma207 a r:Inference; + r:gives { + 207 :collatz (1 (207 622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 206}] + [ a r:Fact; r:gives {(206 1) math:sum 207}] + skolem:lemma464 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (207 622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma208 a r:Inference; + r:gives { + 208 :collatz (1 (208 104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 207}] + [ a r:Fact; r:gives {(207 1) math:sum 208}] + skolem:lemma465 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma209 a r:Inference; + r:gives { + 209 :collatz (1 (209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 208}] + [ a r:Fact; r:gives {(208 1) math:sum 209}] + skolem:lemma466 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma210 a r:Inference; + r:gives { + 210 :collatz (1 (210 105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 209}] + [ a r:Fact; r:gives {(209 1) math:sum 210}] + skolem:lemma467 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (210 105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma211 a r:Inference; + r:gives { + 211 :collatz (1 (211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 210}] + [ a r:Fact; r:gives {(210 1) math:sum 211}] + skolem:lemma468 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma212 a r:Inference; + r:gives { + 212 :collatz (1 (212 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 211}] + [ a r:Fact; r:gives {(211 1) math:sum 212}] + skolem:lemma469 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (212 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma213 a r:Inference; + r:gives { + 213 :collatz (1 (213 640 320 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 212}] + [ a r:Fact; r:gives {(212 1) math:sum 213}] + skolem:lemma470 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (213 640 320 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma214 a r:Inference; + r:gives { + 214 :collatz (1 (214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 213}] + [ a r:Fact; r:gives {(213 1) math:sum 214}] + skolem:lemma471 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma215 a r:Inference; + r:gives { + 215 :collatz (1 (215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 214}] + [ a r:Fact; r:gives {(214 1) math:sum 215}] + skolem:lemma472 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma216 a r:Inference; + r:gives { + 216 :collatz (1 (216 108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 215}] + [ a r:Fact; r:gives {(215 1) math:sum 216}] + skolem:lemma473 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (216 108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma217 a r:Inference; + r:gives { + 217 :collatz (1 (217 652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 216}] + [ a r:Fact; r:gives {(216 1) math:sum 217}] + skolem:lemma474 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (217 652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma218 a r:Inference; + r:gives { + 218 :collatz (1 (218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 217}] + [ a r:Fact; r:gives {(217 1) math:sum 218}] + skolem:lemma475 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma219 a r:Inference; + r:gives { + 219 :collatz (1 (219 658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 218}] + [ a r:Fact; r:gives {(218 1) math:sum 219}] + skolem:lemma476 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (219 658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma220 a r:Inference; + r:gives { + 220 :collatz (1 (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 219}] + [ a r:Fact; r:gives {(219 1) math:sum 220}] + skolem:lemma477 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma221 a r:Inference; + r:gives { + 221 :collatz (1 (221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 220}] + [ a r:Fact; r:gives {(220 1) math:sum 221}] + skolem:lemma478 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma222 a r:Inference; + r:gives { + 222 :collatz (1 (222 111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 221}] + [ a r:Fact; r:gives {(221 1) math:sum 222}] + skolem:lemma479 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (222 111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma223 a r:Inference; + r:gives { + 223 :collatz (1 (223 670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 222}] + [ a r:Fact; r:gives {(222 1) math:sum 223}] + skolem:lemma480 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (223 670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma224 a r:Inference; + r:gives { + 224 :collatz (1 (224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 223}] + [ a r:Fact; r:gives {(223 1) math:sum 224}] + skolem:lemma481 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma225 a r:Inference; + r:gives { + 225 :collatz (1 (225 676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 224}] + [ a r:Fact; r:gives {(224 1) math:sum 225}] + skolem:lemma482 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (225 676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma226 a r:Inference; + r:gives { + 226 :collatz (1 (226 113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 225}] + [ a r:Fact; r:gives {(225 1) math:sum 226}] + skolem:lemma483 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma227 a r:Inference; + r:gives { + 227 :collatz (1 (227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 226}] + [ a r:Fact; r:gives {(226 1) math:sum 227}] + skolem:lemma484 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma228 a r:Inference; + r:gives { + 228 :collatz (1 (228 114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 227}] + [ a r:Fact; r:gives {(227 1) math:sum 228}] + skolem:lemma485 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (228 114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma229 a r:Inference; + r:gives { + 229 :collatz (1 (229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 228}] + [ a r:Fact; r:gives {(228 1) math:sum 229}] + skolem:lemma486 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma230 a r:Inference; + r:gives { + 230 :collatz (1 (230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 229}] + [ a r:Fact; r:gives {(229 1) math:sum 230}] + skolem:lemma487 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma231 a r:Inference; + r:gives { + 231 :collatz (1 (231 694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 230}] + [ a r:Fact; r:gives {(230 1) math:sum 231}] + skolem:lemma488 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (231 694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma232 a r:Inference; + r:gives { + 232 :collatz (1 (232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 231}] + [ a r:Fact; r:gives {(231 1) math:sum 232}] + skolem:lemma489 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma233 a r:Inference; + r:gives { + 233 :collatz (1 (233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 232}] + [ a r:Fact; r:gives {(232 1) math:sum 233}] + skolem:lemma490 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma234 a r:Inference; + r:gives { + 234 :collatz (1 (234 117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 233}] + [ a r:Fact; r:gives {(233 1) math:sum 234}] + skolem:lemma491 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (234 117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma235 a r:Inference; + r:gives { + 235 :collatz (1 (235 706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 234}] + [ a r:Fact; r:gives {(234 1) math:sum 235}] + skolem:lemma492 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (235 706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma236 a r:Inference; + r:gives { + 236 :collatz (1 (236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 235}] + [ a r:Fact; r:gives {(235 1) math:sum 236}] + skolem:lemma493 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma237 a r:Inference; + r:gives { + 237 :collatz (1 (237 712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 236}] + [ a r:Fact; r:gives {(236 1) math:sum 237}] + skolem:lemma494 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (237 712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma238 a r:Inference; + r:gives { + 238 :collatz (1 (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 237}] + [ a r:Fact; r:gives {(237 1) math:sum 238}] + skolem:lemma495 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma239 a r:Inference; + r:gives { + 239 :collatz (1 (239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 238}] + [ a r:Fact; r:gives {(238 1) math:sum 239}] + skolem:lemma496 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma240 a r:Inference; + r:gives { + 240 :collatz (1 (240 120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 239}] + [ a r:Fact; r:gives {(239 1) math:sum 240}] + skolem:lemma497 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (240 120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma241 a r:Inference; + r:gives { + 241 :collatz (1 (241 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 240}] + [ a r:Fact; r:gives {(240 1) math:sum 241}] + skolem:lemma498 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (241 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma242 a r:Inference; + r:gives { + 242 :collatz (1 (242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 241}] + [ a r:Fact; r:gives {(241 1) math:sum 242}] + skolem:lemma499 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma243 a r:Inference; + r:gives { + 243 :collatz (1 (243 730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 242}] + [ a r:Fact; r:gives {(242 1) math:sum 243}] + skolem:lemma500 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (243 730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma244 a r:Inference; + r:gives { + 244 :collatz (1 (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 243}] + [ a r:Fact; r:gives {(243 1) math:sum 244}] + skolem:lemma501 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma245 a r:Inference; + r:gives { + 245 :collatz (1 (245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 244}] + [ a r:Fact; r:gives {(244 1) math:sum 245}] + skolem:lemma502 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma246 a r:Inference; + r:gives { + 246 :collatz (1 (246 123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 245}] + [ a r:Fact; r:gives {(245 1) math:sum 246}] + skolem:lemma503 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (246 123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma247 a r:Inference; + r:gives { + 247 :collatz (1 (247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 246}] + [ a r:Fact; r:gives {(246 1) math:sum 247}] + skolem:lemma504 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma248 a r:Inference; + r:gives { + 248 :collatz (1 (248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 247}] + [ a r:Fact; r:gives {(247 1) math:sum 248}] + skolem:lemma505 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma249 a r:Inference; + r:gives { + 249 :collatz (1 (249 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 248}] + [ a r:Fact; r:gives {(248 1) math:sum 249}] + skolem:lemma506 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (249 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma250 a r:Inference; + r:gives { + 250 :collatz (1 (250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 249}] + [ a r:Fact; r:gives {(249 1) math:sum 250}] + skolem:lemma507 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma251 a r:Inference; + r:gives { + 251 :collatz (1 (251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 250}] + [ a r:Fact; r:gives {(250 1) math:sum 251}] + skolem:lemma508 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma252 a r:Inference; + r:gives { + 252 :collatz (1 (252 126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 251}] + [ a r:Fact; r:gives {(251 1) math:sum 252}] + skolem:lemma509 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (252 126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma253 a r:Inference; + r:gives { + 253 :collatz (1 (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 252}] + [ a r:Fact; r:gives {(252 1) math:sum 253}] + skolem:lemma510 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma254 a r:Inference; + r:gives { + 254 :collatz (1 (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 253}] + [ a r:Fact; r:gives {(253 1) math:sum 254}] + skolem:lemma511 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma255 a r:Inference; + r:gives { + 255 :collatz (1 (255 766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 254}] + [ a r:Fact; r:gives {(254 1) math:sum 255}] + skolem:lemma512 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (255 766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma256 a r:Inference; + r:gives { + 256 :collatz (1 (256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {256 log:repeat 255}] + [ a r:Fact; r:gives {(255 1) math:sum 256}] + skolem:lemma513 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma258. + +skolem:lemma257 a r:Inference; + r:gives { + 1 :collatz (1 (1)). + }; + r:evidence ( + [ a r:Fact; r:gives {true log:callWithCut true}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:rule skolem:lemma514. + +skolem:lemma258 a r:Extraction; + r:gives { + @forAll var:x_0, var:x_1, var:x_2. { + 256 log:repeat var:x_0. + (var:x_0 1) math:sum var:x_1. + var:x_1 :collatz (1 var:x_2). + } => { + var:x_1 :collatz (1 var:x_2). + }. + }; + r:because [ a r:Parsing; r:source ]. + +skolem:lemma259 a r:Inference; + r:gives { + 2 :collatz (1 (2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2 2) math:remainder 0. + } { + (2 2) math:integerQuotient 1. + } { + (3 2) math:product _:sk_0. + (_:sk_0 1) math:sum 1. + }) log:ifThenElseIn (() 1)}] + skolem:lemma257 + [ a r:Fact; r:gives {(2 1) list:firstRest (2 (1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2 1)]; + r:rule skolem:lemma515. + +skolem:lemma260 a r:Inference; + r:gives { + 3 :collatz (1 (3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (3 2) math:remainder 0. + } { + (3 2) math:integerQuotient 10. + } { + (3 3) math:product 9 . + (9 1) math:sum 10. + }) log:ifThenElseIn (() 1)}] + skolem:lemma267 + [ a r:Fact; r:gives {(3 10 5 16 8 4 2 1) list:firstRest (3 (10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma261 a r:Inference; + r:gives { + 4 :collatz (1 (4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (4 2) math:remainder 0. + } { + (4 2) math:integerQuotient 2. + } { + (3 4) math:product _:sk_0. + (_:sk_0 1) math:sum 2. + }) log:ifThenElseIn (() 1)}] + skolem:lemma259 + [ a r:Fact; r:gives {(4 2 1) list:firstRest (4 (2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma262 a r:Inference; + r:gives { + 5 :collatz (1 (5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (5 2) math:remainder 0. + } { + (5 2) math:integerQuotient 16. + } { + (3 5) math:product 15 . + (15 1) math:sum 16. + }) log:ifThenElseIn (() 1)}] + skolem:lemma273 + [ a r:Fact; r:gives {(5 16 8 4 2 1) list:firstRest (5 (16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma263 a r:Inference; + r:gives { + 6 :collatz (1 (6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (6 2) math:remainder 0. + } { + (6 2) math:integerQuotient 3. + } { + (3 6) math:product _:sk_0. + (_:sk_0 1) math:sum 3. + }) log:ifThenElseIn (() 1)}] + skolem:lemma260 + [ a r:Fact; r:gives {(6 3 10 5 16 8 4 2 1) list:firstRest (6 (3 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma264 a r:Inference; + r:gives { + 7 :collatz (1 (7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (7 2) math:remainder 0. + } { + (7 2) math:integerQuotient 22. + } { + (3 7) math:product 21 . + (21 1) math:sum 22. + }) log:ifThenElseIn (() 1)}] + skolem:lemma279 + [ a r:Fact; r:gives {(7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (7 (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma265 a r:Inference; + r:gives { + 8 :collatz (1 (8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (8 2) math:remainder 0. + } { + (8 2) math:integerQuotient 4. + } { + (3 8) math:product _:sk_0. + (_:sk_0 1) math:sum 4. + }) log:ifThenElseIn (() 1)}] + skolem:lemma261 + [ a r:Fact; r:gives {(8 4 2 1) list:firstRest (8 (4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma266 a r:Inference; + r:gives { + 9 :collatz (1 (9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (9 2) math:remainder 0. + } { + (9 2) math:integerQuotient 28. + } { + (3 9) math:product 27 . + (27 1) math:sum 28. + }) log:ifThenElseIn (() 1)}] + skolem:lemma285 + [ a r:Fact; r:gives {(9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (9 (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma267 a r:Inference; + r:gives { + 10 :collatz (1 (10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (10 2) math:remainder 0. + } { + (10 2) math:integerQuotient 5. + } { + (3 10) math:product _:sk_0. + (_:sk_0 1) math:sum 5. + }) log:ifThenElseIn (() 1)}] + skolem:lemma262 + [ a r:Fact; r:gives {(10 5 16 8 4 2 1) list:firstRest (10 (5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma268 a r:Inference; + r:gives { + 11 :collatz (1 (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (11 2) math:remainder 0. + } { + (11 2) math:integerQuotient 34. + } { + (3 11) math:product 33 . + (33 1) math:sum 34. + }) log:ifThenElseIn (() 1)}] + skolem:lemma291 + [ a r:Fact; r:gives {(11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (11 (34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma269 a r:Inference; + r:gives { + 12 :collatz (1 (12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (12 2) math:remainder 0. + } { + (12 2) math:integerQuotient 6. + } { + (3 12) math:product _:sk_0. + (_:sk_0 1) math:sum 6. + }) log:ifThenElseIn (() 1)}] + skolem:lemma263 + [ a r:Fact; r:gives {(12 6 3 10 5 16 8 4 2 1) list:firstRest (12 (6 3 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6 3 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma270 a r:Inference; + r:gives { + 13 :collatz (1 (13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (13 2) math:remainder 0. + } { + (13 2) math:integerQuotient 40. + } { + (3 13) math:product 39 . + (39 1) math:sum 40. + }) log:ifThenElseIn (() 1)}] + skolem:lemma297 + [ a r:Fact; r:gives {(13 40 20 10 5 16 8 4 2 1) list:firstRest (13 (40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma271 a r:Inference; + r:gives { + 14 :collatz (1 (14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (14 2) math:remainder 0. + } { + (14 2) math:integerQuotient 7. + } { + (3 14) math:product _:sk_0. + (_:sk_0 1) math:sum 7. + }) log:ifThenElseIn (() 1)}] + skolem:lemma264 + [ a r:Fact; r:gives {(14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (14 (7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma272 a r:Inference; + r:gives { + 15 :collatz (1 (15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (15 2) math:remainder 0. + } { + (15 2) math:integerQuotient 46. + } { + (3 15) math:product 45 . + (45 1) math:sum 46. + }) log:ifThenElseIn (() 1)}] + skolem:lemma303 + [ a r:Fact; r:gives {(15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (15 (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma273 a r:Inference; + r:gives { + 16 :collatz (1 (16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (16 2) math:remainder 0. + } { + (16 2) math:integerQuotient 8. + } { + (3 16) math:product _:sk_0. + (_:sk_0 1) math:sum 8. + }) log:ifThenElseIn (() 1)}] + skolem:lemma265 + [ a r:Fact; r:gives {(16 8 4 2 1) list:firstRest (16 (8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma274 a r:Inference; + r:gives { + 17 :collatz (1 (17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (17 2) math:remainder 0. + } { + (17 2) math:integerQuotient 52. + } { + (3 17) math:product 51 . + (51 1) math:sum 52. + }) log:ifThenElseIn (() 1)}] + skolem:lemma309 + [ a r:Fact; r:gives {(17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (17 (52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma275 a r:Inference; + r:gives { + 18 :collatz (1 (18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (18 2) math:remainder 0. + } { + (18 2) math:integerQuotient 9. + } { + (3 18) math:product _:sk_0. + (_:sk_0 1) math:sum 9. + }) log:ifThenElseIn (() 1)}] + skolem:lemma266 + [ a r:Fact; r:gives {(18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (18 (9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma276 a r:Inference; + r:gives { + 19 :collatz (1 (19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (19 2) math:remainder 0. + } { + (19 2) math:integerQuotient 58. + } { + (3 19) math:product 57 . + (57 1) math:sum 58. + }) log:ifThenElseIn (() 1)}] + skolem:lemma315 + [ a r:Fact; r:gives {(19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (19 (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma277 a r:Inference; + r:gives { + 20 :collatz (1 (20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (20 2) math:remainder 0. + } { + (20 2) math:integerQuotient 10. + } { + (3 20) math:product _:sk_0. + (_:sk_0 1) math:sum 10. + }) log:ifThenElseIn (() 1)}] + skolem:lemma267 + [ a r:Fact; r:gives {(20 10 5 16 8 4 2 1) list:firstRest (20 (10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma278 a r:Inference; + r:gives { + 21 :collatz (1 (21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (21 2) math:remainder 0. + } { + (21 2) math:integerQuotient 64. + } { + (3 21) math:product 63 . + (63 1) math:sum 64. + }) log:ifThenElseIn (() 1)}] + skolem:lemma321 + [ a r:Fact; r:gives {(21 64 32 16 8 4 2 1) list:firstRest (21 (64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma279 a r:Inference; + r:gives { + 22 :collatz (1 (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (22 2) math:remainder 0. + } { + (22 2) math:integerQuotient 11. + } { + (3 22) math:product _:sk_0. + (_:sk_0 1) math:sum 11. + }) log:ifThenElseIn (() 1)}] + skolem:lemma268 + [ a r:Fact; r:gives {(22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (22 (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma280 a r:Inference; + r:gives { + 23 :collatz (1 (23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (23 2) math:remainder 0. + } { + (23 2) math:integerQuotient 70. + } { + (3 23) math:product 69 . + (69 1) math:sum 70. + }) log:ifThenElseIn (() 1)}] + skolem:lemma327 + [ a r:Fact; r:gives {(23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (23 (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma281 a r:Inference; + r:gives { + 24 :collatz (1 (24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (24 2) math:remainder 0. + } { + (24 2) math:integerQuotient 12. + } { + (3 24) math:product _:sk_0. + (_:sk_0 1) math:sum 12. + }) log:ifThenElseIn (() 1)}] + skolem:lemma269 + [ a r:Fact; r:gives {(24 12 6 3 10 5 16 8 4 2 1) list:firstRest (24 (12 6 3 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (12 6 3 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma282 a r:Inference; + r:gives { + 25 :collatz (1 (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (25 2) math:remainder 0. + } { + (25 2) math:integerQuotient 76. + } { + (3 25) math:product 75 . + (75 1) math:sum 76. + }) log:ifThenElseIn (() 1)}] + skolem:lemma333 + [ a r:Fact; r:gives {(25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (25 (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma283 a r:Inference; + r:gives { + 26 :collatz (1 (26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (26 2) math:remainder 0. + } { + (26 2) math:integerQuotient 13. + } { + (3 26) math:product _:sk_0. + (_:sk_0 1) math:sum 13. + }) log:ifThenElseIn (() 1)}] + skolem:lemma270 + [ a r:Fact; r:gives {(26 13 40 20 10 5 16 8 4 2 1) list:firstRest (26 (13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma284 a r:Inference; + r:gives { + 27 :collatz (1 (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (27 2) math:remainder 0. + } { + (27 2) math:integerQuotient 82. + } { + (3 27) math:product 81 . + (81 1) math:sum 82. + }) log:ifThenElseIn (() 1)}] + skolem:lemma339 + [ a r:Fact; r:gives {(27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (27 (82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma285 a r:Inference; + r:gives { + 28 :collatz (1 (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (28 2) math:remainder 0. + } { + (28 2) math:integerQuotient 14. + } { + (3 28) math:product _:sk_0. + (_:sk_0 1) math:sum 14. + }) log:ifThenElseIn (() 1)}] + skolem:lemma271 + [ a r:Fact; r:gives {(28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (28 (14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma286 a r:Inference; + r:gives { + 29 :collatz (1 (29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (29 2) math:remainder 0. + } { + (29 2) math:integerQuotient 88. + } { + (3 29) math:product 87 . + (87 1) math:sum 88. + }) log:ifThenElseIn (() 1)}] + skolem:lemma345 + [ a r:Fact; r:gives {(29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (29 (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma287 a r:Inference; + r:gives { + 30 :collatz (1 (30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (30 2) math:remainder 0. + } { + (30 2) math:integerQuotient 15. + } { + (3 30) math:product _:sk_0. + (_:sk_0 1) math:sum 15. + }) log:ifThenElseIn (() 1)}] + skolem:lemma272 + [ a r:Fact; r:gives {(30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (30 (15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma288 a r:Inference; + r:gives { + 31 :collatz (1 (31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (31 2) math:remainder 0. + } { + (31 2) math:integerQuotient 94. + } { + (3 31) math:product 93 . + (93 1) math:sum 94. + }) log:ifThenElseIn (() 1)}] + skolem:lemma351 + [ a r:Fact; r:gives {(31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (31 (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma289 a r:Inference; + r:gives { + 32 :collatz (1 (32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (32 2) math:remainder 0. + } { + (32 2) math:integerQuotient 16. + } { + (3 32) math:product _:sk_0. + (_:sk_0 1) math:sum 16. + }) log:ifThenElseIn (() 1)}] + skolem:lemma273 + [ a r:Fact; r:gives {(32 16 8 4 2 1) list:firstRest (32 (16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma290 a r:Inference; + r:gives { + 33 :collatz (1 (33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (33 2) math:remainder 0. + } { + (33 2) math:integerQuotient 100. + } { + (3 33) math:product 99 . + (99 1) math:sum 100. + }) log:ifThenElseIn (() 1)}] + skolem:lemma357 + [ a r:Fact; r:gives {(33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (33 (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma291 a r:Inference; + r:gives { + 34 :collatz (1 (34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (34 2) math:remainder 0. + } { + (34 2) math:integerQuotient 17. + } { + (3 34) math:product _:sk_0. + (_:sk_0 1) math:sum 17. + }) log:ifThenElseIn (() 1)}] + skolem:lemma274 + [ a r:Fact; r:gives {(34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (34 (17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma292 a r:Inference; + r:gives { + 35 :collatz (1 (35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (35 2) math:remainder 0. + } { + (35 2) math:integerQuotient 106. + } { + (3 35) math:product 105 . + (105 1) math:sum 106. + }) log:ifThenElseIn (() 1)}] + skolem:lemma363 + [ a r:Fact; r:gives {(35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (35 (106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma293 a r:Inference; + r:gives { + 36 :collatz (1 (36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (36 2) math:remainder 0. + } { + (36 2) math:integerQuotient 18. + } { + (3 36) math:product _:sk_0. + (_:sk_0 1) math:sum 18. + }) log:ifThenElseIn (() 1)}] + skolem:lemma275 + [ a r:Fact; r:gives {(36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (36 (18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma294 a r:Inference; + r:gives { + 37 :collatz (1 (37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (37 2) math:remainder 0. + } { + (37 2) math:integerQuotient 112. + } { + (3 37) math:product 111 . + (111 1) math:sum 112. + }) log:ifThenElseIn (() 1)}] + skolem:lemma369 + [ a r:Fact; r:gives {(37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (37 (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma295 a r:Inference; + r:gives { + 38 :collatz (1 (38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (38 2) math:remainder 0. + } { + (38 2) math:integerQuotient 19. + } { + (3 38) math:product _:sk_0. + (_:sk_0 1) math:sum 19. + }) log:ifThenElseIn (() 1)}] + skolem:lemma276 + [ a r:Fact; r:gives {(38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (38 (19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma296 a r:Inference; + r:gives { + 39 :collatz (1 (39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (39 2) math:remainder 0. + } { + (39 2) math:integerQuotient 118. + } { + (3 39) math:product 117 . + (117 1) math:sum 118. + }) log:ifThenElseIn (() 1)}] + skolem:lemma375 + [ a r:Fact; r:gives {(39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (39 (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma297 a r:Inference; + r:gives { + 40 :collatz (1 (40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (40 2) math:remainder 0. + } { + (40 2) math:integerQuotient 20. + } { + (3 40) math:product _:sk_0. + (_:sk_0 1) math:sum 20. + }) log:ifThenElseIn (() 1)}] + skolem:lemma277 + [ a r:Fact; r:gives {(40 20 10 5 16 8 4 2 1) list:firstRest (40 (20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma298 a r:Inference; + r:gives { + 41 :collatz (1 (41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (41 2) math:remainder 0. + } { + (41 2) math:integerQuotient 124. + } { + (3 41) math:product 123 . + (123 1) math:sum 124. + }) log:ifThenElseIn (() 1)}] + skolem:lemma381 + [ a r:Fact; r:gives {(41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (41 (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma299 a r:Inference; + r:gives { + 42 :collatz (1 (42 21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (42 2) math:remainder 0. + } { + (42 2) math:integerQuotient 21. + } { + (3 42) math:product _:sk_0. + (_:sk_0 1) math:sum 21. + }) log:ifThenElseIn (() 1)}] + skolem:lemma278 + [ a r:Fact; r:gives {(42 21 64 32 16 8 4 2 1) list:firstRest (42 (21 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (21 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (42 21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma300 a r:Inference; + r:gives { + 43 :collatz (1 (43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (43 2) math:remainder 0. + } { + (43 2) math:integerQuotient 130. + } { + (3 43) math:product 129 . + (129 1) math:sum 130. + }) log:ifThenElseIn (() 1)}] + skolem:lemma387 + [ a r:Fact; r:gives {(43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (43 (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma301 a r:Inference; + r:gives { + 44 :collatz (1 (44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (44 2) math:remainder 0. + } { + (44 2) math:integerQuotient 22. + } { + (3 44) math:product _:sk_0. + (_:sk_0 1) math:sum 22. + }) log:ifThenElseIn (() 1)}] + skolem:lemma279 + [ a r:Fact; r:gives {(44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (44 (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma302 a r:Inference; + r:gives { + 45 :collatz (1 (45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (45 2) math:remainder 0. + } { + (45 2) math:integerQuotient 136. + } { + (3 45) math:product 135 . + (135 1) math:sum 136. + }) log:ifThenElseIn (() 1)}] + skolem:lemma393 + [ a r:Fact; r:gives {(45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (45 (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma303 a r:Inference; + r:gives { + 46 :collatz (1 (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (46 2) math:remainder 0. + } { + (46 2) math:integerQuotient 23. + } { + (3 46) math:product _:sk_0. + (_:sk_0 1) math:sum 23. + }) log:ifThenElseIn (() 1)}] + skolem:lemma280 + [ a r:Fact; r:gives {(46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (46 (23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma304 a r:Inference; + r:gives { + 47 :collatz (1 (47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (47 2) math:remainder 0. + } { + (47 2) math:integerQuotient 142. + } { + (3 47) math:product 141 . + (141 1) math:sum 142. + }) log:ifThenElseIn (() 1)}] + skolem:lemma399 + [ a r:Fact; r:gives {(47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (47 (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma305 a r:Inference; + r:gives { + 48 :collatz (1 (48 24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (48 2) math:remainder 0. + } { + (48 2) math:integerQuotient 24. + } { + (3 48) math:product _:sk_0. + (_:sk_0 1) math:sum 24. + }) log:ifThenElseIn (() 1)}] + skolem:lemma281 + [ a r:Fact; r:gives {(48 24 12 6 3 10 5 16 8 4 2 1) list:firstRest (48 (24 12 6 3 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (24 12 6 3 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (48 24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma306 a r:Inference; + r:gives { + 49 :collatz (1 (49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (49 2) math:remainder 0. + } { + (49 2) math:integerQuotient 148. + } { + (3 49) math:product 147 . + (147 1) math:sum 148. + }) log:ifThenElseIn (() 1)}] + skolem:lemma405 + [ a r:Fact; r:gives {(49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (49 (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma307 a r:Inference; + r:gives { + 50 :collatz (1 (50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (50 2) math:remainder 0. + } { + (50 2) math:integerQuotient 25. + } { + (3 50) math:product _:sk_0. + (_:sk_0 1) math:sum 25. + }) log:ifThenElseIn (() 1)}] + skolem:lemma282 + [ a r:Fact; r:gives {(50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (50 (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma308 a r:Inference; + r:gives { + 51 :collatz (1 (51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (51 2) math:remainder 0. + } { + (51 2) math:integerQuotient 154. + } { + (3 51) math:product 153 . + (153 1) math:sum 154. + }) log:ifThenElseIn (() 1)}] + skolem:lemma411 + [ a r:Fact; r:gives {(51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (51 (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma309 a r:Inference; + r:gives { + 52 :collatz (1 (52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (52 2) math:remainder 0. + } { + (52 2) math:integerQuotient 26. + } { + (3 52) math:product _:sk_0. + (_:sk_0 1) math:sum 26. + }) log:ifThenElseIn (() 1)}] + skolem:lemma283 + [ a r:Fact; r:gives {(52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (52 (26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma310 a r:Inference; + r:gives { + 53 :collatz (1 (53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (53 2) math:remainder 0. + } { + (53 2) math:integerQuotient 160. + } { + (3 53) math:product 159 . + (159 1) math:sum 160. + }) log:ifThenElseIn (() 1)}] + skolem:lemma417 + [ a r:Fact; r:gives {(53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (53 (160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma311 a r:Inference; + r:gives { + 54 :collatz (1 (54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (54 2) math:remainder 0. + } { + (54 2) math:integerQuotient 27. + } { + (3 54) math:product _:sk_0. + (_:sk_0 1) math:sum 27. + }) log:ifThenElseIn (() 1)}] + skolem:lemma284 + [ a r:Fact; r:gives {(54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (54 (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma312 a r:Inference; + r:gives { + 55 :collatz (1 (55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (55 2) math:remainder 0. + } { + (55 2) math:integerQuotient 166. + } { + (3 55) math:product 165 . + (165 1) math:sum 166. + }) log:ifThenElseIn (() 1)}] + skolem:lemma423 + [ a r:Fact; r:gives {(55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (55 (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma313 a r:Inference; + r:gives { + 56 :collatz (1 (56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (56 2) math:remainder 0. + } { + (56 2) math:integerQuotient 28. + } { + (3 56) math:product _:sk_0. + (_:sk_0 1) math:sum 28. + }) log:ifThenElseIn (() 1)}] + skolem:lemma285 + [ a r:Fact; r:gives {(56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (56 (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma314 a r:Inference; + r:gives { + 57 :collatz (1 (57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (57 2) math:remainder 0. + } { + (57 2) math:integerQuotient 172. + } { + (3 57) math:product 171 . + (171 1) math:sum 172. + }) log:ifThenElseIn (() 1)}] + skolem:lemma429 + [ a r:Fact; r:gives {(57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (57 (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma315 a r:Inference; + r:gives { + 58 :collatz (1 (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (58 2) math:remainder 0. + } { + (58 2) math:integerQuotient 29. + } { + (3 58) math:product _:sk_0. + (_:sk_0 1) math:sum 29. + }) log:ifThenElseIn (() 1)}] + skolem:lemma286 + [ a r:Fact; r:gives {(58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (58 (29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma316 a r:Inference; + r:gives { + 59 :collatz (1 (59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (59 2) math:remainder 0. + } { + (59 2) math:integerQuotient 178. + } { + (3 59) math:product 177 . + (177 1) math:sum 178. + }) log:ifThenElseIn (() 1)}] + skolem:lemma435 + [ a r:Fact; r:gives {(59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (59 (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma317 a r:Inference; + r:gives { + 60 :collatz (1 (60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (60 2) math:remainder 0. + } { + (60 2) math:integerQuotient 30. + } { + (3 60) math:product _:sk_0. + (_:sk_0 1) math:sum 30. + }) log:ifThenElseIn (() 1)}] + skolem:lemma287 + [ a r:Fact; r:gives {(60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (60 (30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma318 a r:Inference; + r:gives { + 61 :collatz (1 (61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (61 2) math:remainder 0. + } { + (61 2) math:integerQuotient 184. + } { + (3 61) math:product 183 . + (183 1) math:sum 184. + }) log:ifThenElseIn (() 1)}] + skolem:lemma441 + [ a r:Fact; r:gives {(61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (61 (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma319 a r:Inference; + r:gives { + 62 :collatz (1 (62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (62 2) math:remainder 0. + } { + (62 2) math:integerQuotient 31. + } { + (3 62) math:product _:sk_0. + (_:sk_0 1) math:sum 31. + }) log:ifThenElseIn (() 1)}] + skolem:lemma288 + [ a r:Fact; r:gives {(62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (62 (31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma320 a r:Inference; + r:gives { + 63 :collatz (1 (63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (63 2) math:remainder 0. + } { + (63 2) math:integerQuotient 190. + } { + (3 63) math:product 189 . + (189 1) math:sum 190. + }) log:ifThenElseIn (() 1)}] + skolem:lemma447 + [ a r:Fact; r:gives {(63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (63 (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma321 a r:Inference; + r:gives { + 64 :collatz (1 (64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (64 2) math:remainder 0. + } { + (64 2) math:integerQuotient 32. + } { + (3 64) math:product _:sk_0. + (_:sk_0 1) math:sum 32. + }) log:ifThenElseIn (() 1)}] + skolem:lemma289 + [ a r:Fact; r:gives {(64 32 16 8 4 2 1) list:firstRest (64 (32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma322 a r:Inference; + r:gives { + 65 :collatz (1 (65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (65 2) math:remainder 0. + } { + (65 2) math:integerQuotient 196. + } { + (3 65) math:product 195 . + (195 1) math:sum 196. + }) log:ifThenElseIn (() 1)}] + skolem:lemma453 + [ a r:Fact; r:gives {(65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (65 (196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma323 a r:Inference; + r:gives { + 66 :collatz (1 (66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (66 2) math:remainder 0. + } { + (66 2) math:integerQuotient 33. + } { + (3 66) math:product _:sk_0. + (_:sk_0 1) math:sum 33. + }) log:ifThenElseIn (() 1)}] + skolem:lemma290 + [ a r:Fact; r:gives {(66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (66 (33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma324 a r:Inference; + r:gives { + 67 :collatz (1 (67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (67 2) math:remainder 0. + } { + (67 2) math:integerQuotient 202. + } { + (3 67) math:product 201 . + (201 1) math:sum 202. + }) log:ifThenElseIn (() 1)}] + skolem:lemma459 + [ a r:Fact; r:gives {(67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (67 (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma325 a r:Inference; + r:gives { + 68 :collatz (1 (68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (68 2) math:remainder 0. + } { + (68 2) math:integerQuotient 34. + } { + (3 68) math:product _:sk_0. + (_:sk_0 1) math:sum 34. + }) log:ifThenElseIn (() 1)}] + skolem:lemma291 + [ a r:Fact; r:gives {(68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (68 (34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma326 a r:Inference; + r:gives { + 69 :collatz (1 (69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (69 2) math:remainder 0. + } { + (69 2) math:integerQuotient 208. + } { + (3 69) math:product 207 . + (207 1) math:sum 208. + }) log:ifThenElseIn (() 1)}] + skolem:lemma465 + [ a r:Fact; r:gives {(69 208 104 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (69 (208 104 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma327 a r:Inference; + r:gives { + 70 :collatz (1 (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (70 2) math:remainder 0. + } { + (70 2) math:integerQuotient 35. + } { + (3 70) math:product _:sk_0. + (_:sk_0 1) math:sum 35. + }) log:ifThenElseIn (() 1)}] + skolem:lemma292 + [ a r:Fact; r:gives {(70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (70 (35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma328 a r:Inference; + r:gives { + 71 :collatz (1 (71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (71 2) math:remainder 0. + } { + (71 2) math:integerQuotient 214. + } { + (3 71) math:product 213 . + (213 1) math:sum 214. + }) log:ifThenElseIn (() 1)}] + skolem:lemma471 + [ a r:Fact; r:gives {(71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (71 (214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma329 a r:Inference; + r:gives { + 72 :collatz (1 (72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (72 2) math:remainder 0. + } { + (72 2) math:integerQuotient 36. + } { + (3 72) math:product _:sk_0. + (_:sk_0 1) math:sum 36. + }) log:ifThenElseIn (() 1)}] + skolem:lemma293 + [ a r:Fact; r:gives {(72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (72 (36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma330 a r:Inference; + r:gives { + 73 :collatz (1 (73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (73 2) math:remainder 0. + } { + (73 2) math:integerQuotient 220. + } { + (3 73) math:product 219 . + (219 1) math:sum 220. + }) log:ifThenElseIn (() 1)}] + skolem:lemma477 + [ a r:Fact; r:gives {(73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (73 (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma331 a r:Inference; + r:gives { + 74 :collatz (1 (74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (74 2) math:remainder 0. + } { + (74 2) math:integerQuotient 37. + } { + (3 74) math:product _:sk_0. + (_:sk_0 1) math:sum 37. + }) log:ifThenElseIn (() 1)}] + skolem:lemma294 + [ a r:Fact; r:gives {(74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (74 (37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma332 a r:Inference; + r:gives { + 75 :collatz (1 (75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (75 2) math:remainder 0. + } { + (75 2) math:integerQuotient 226. + } { + (3 75) math:product 225 . + (225 1) math:sum 226. + }) log:ifThenElseIn (() 1)}] + skolem:lemma483 + [ a r:Fact; r:gives {(75 226 113 340 170 85 256 128 64 32 16 8 4 2 1) list:firstRest (75 (226 113 340 170 85 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma333 a r:Inference; + r:gives { + 76 :collatz (1 (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (76 2) math:remainder 0. + } { + (76 2) math:integerQuotient 38. + } { + (3 76) math:product _:sk_0. + (_:sk_0 1) math:sum 38. + }) log:ifThenElseIn (() 1)}] + skolem:lemma295 + [ a r:Fact; r:gives {(76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (76 (38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma334 a r:Inference; + r:gives { + 77 :collatz (1 (77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (77 2) math:remainder 0. + } { + (77 2) math:integerQuotient 232. + } { + (3 77) math:product 231 . + (231 1) math:sum 232. + }) log:ifThenElseIn (() 1)}] + skolem:lemma489 + [ a r:Fact; r:gives {(77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (77 (232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma335 a r:Inference; + r:gives { + 78 :collatz (1 (78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (78 2) math:remainder 0. + } { + (78 2) math:integerQuotient 39. + } { + (3 78) math:product _:sk_0. + (_:sk_0 1) math:sum 39. + }) log:ifThenElseIn (() 1)}] + skolem:lemma296 + [ a r:Fact; r:gives {(78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (78 (39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma336 a r:Inference; + r:gives { + 79 :collatz (1 (79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (79 2) math:remainder 0. + } { + (79 2) math:integerQuotient 238. + } { + (3 79) math:product 237 . + (237 1) math:sum 238. + }) log:ifThenElseIn (() 1)}] + skolem:lemma495 + [ a r:Fact; r:gives {(79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (79 (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma337 a r:Inference; + r:gives { + 80 :collatz (1 (80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (80 2) math:remainder 0. + } { + (80 2) math:integerQuotient 40. + } { + (3 80) math:product _:sk_0. + (_:sk_0 1) math:sum 40. + }) log:ifThenElseIn (() 1)}] + skolem:lemma297 + [ a r:Fact; r:gives {(80 40 20 10 5 16 8 4 2 1) list:firstRest (80 (40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma338 a r:Inference; + r:gives { + 81 :collatz (1 (81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (81 2) math:remainder 0. + } { + (81 2) math:integerQuotient 244. + } { + (3 81) math:product 243 . + (243 1) math:sum 244. + }) log:ifThenElseIn (() 1)}] + skolem:lemma501 + [ a r:Fact; r:gives {(81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (81 (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma339 a r:Inference; + r:gives { + 82 :collatz (1 (82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (82 2) math:remainder 0. + } { + (82 2) math:integerQuotient 41. + } { + (3 82) math:product _:sk_0. + (_:sk_0 1) math:sum 41. + }) log:ifThenElseIn (() 1)}] + skolem:lemma298 + [ a r:Fact; r:gives {(82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (82 (41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma340 a r:Inference; + r:gives { + 83 :collatz (1 (83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (83 2) math:remainder 0. + } { + (83 2) math:integerQuotient 250. + } { + (3 83) math:product 249 . + (249 1) math:sum 250. + }) log:ifThenElseIn (() 1)}] + skolem:lemma507 + [ a r:Fact; r:gives {(83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (83 (250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma341 a r:Inference; + r:gives { + 84 :collatz (1 (84 42 21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (84 2) math:remainder 0. + } { + (84 2) math:integerQuotient 42. + } { + (3 84) math:product _:sk_0. + (_:sk_0 1) math:sum 42. + }) log:ifThenElseIn (() 1)}] + skolem:lemma299 + [ a r:Fact; r:gives {(84 42 21 64 32 16 8 4 2 1) list:firstRest (84 (42 21 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (42 21 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (84 42 21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma342 a r:Inference; + r:gives { + 85 :collatz (1 (85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (85 2) math:remainder 0. + } { + (85 2) math:integerQuotient 256. + } { + (3 85) math:product 255 . + (255 1) math:sum 256. + }) log:ifThenElseIn (() 1)}] + skolem:lemma513 + [ a r:Fact; r:gives {(85 256 128 64 32 16 8 4 2 1) list:firstRest (85 (256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma343 a r:Inference; + r:gives { + 86 :collatz (1 (86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (86 2) math:remainder 0. + } { + (86 2) math:integerQuotient 43. + } { + (3 86) math:product _:sk_0. + (_:sk_0 1) math:sum 43. + }) log:ifThenElseIn (() 1)}] + skolem:lemma300 + [ a r:Fact; r:gives {(86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (86 (43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma344 a r:Inference; + r:gives { + 87 :collatz (1 (87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (87 2) math:remainder 0. + } { + (87 2) math:integerQuotient 262. + } { + (3 87) math:product 261 . + (261 1) math:sum 262. + }) log:ifThenElseIn (() 1)}] + skolem:lemma516 + [ a r:Fact; r:gives {(87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (87 (262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma345 a r:Inference; + r:gives { + 88 :collatz (1 (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (88 2) math:remainder 0. + } { + (88 2) math:integerQuotient 44. + } { + (3 88) math:product _:sk_0. + (_:sk_0 1) math:sum 44. + }) log:ifThenElseIn (() 1)}] + skolem:lemma301 + [ a r:Fact; r:gives {(88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (88 (44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma346 a r:Inference; + r:gives { + 89 :collatz (1 (89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (89 2) math:remainder 0. + } { + (89 2) math:integerQuotient 268. + } { + (3 89) math:product 267 . + (267 1) math:sum 268. + }) log:ifThenElseIn (() 1)}] + skolem:lemma517 + [ a r:Fact; r:gives {(89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (89 (268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma347 a r:Inference; + r:gives { + 90 :collatz (1 (90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (90 2) math:remainder 0. + } { + (90 2) math:integerQuotient 45. + } { + (3 90) math:product _:sk_0. + (_:sk_0 1) math:sum 45. + }) log:ifThenElseIn (() 1)}] + skolem:lemma302 + [ a r:Fact; r:gives {(90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (90 (45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma348 a r:Inference; + r:gives { + 91 :collatz (1 (91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (91 2) math:remainder 0. + } { + (91 2) math:integerQuotient 274. + } { + (3 91) math:product 273 . + (273 1) math:sum 274. + }) log:ifThenElseIn (() 1)}] + skolem:lemma518 + [ a r:Fact; r:gives {(91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (91 (274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma349 a r:Inference; + r:gives { + 92 :collatz (1 (92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (92 2) math:remainder 0. + } { + (92 2) math:integerQuotient 46. + } { + (3 92) math:product _:sk_0. + (_:sk_0 1) math:sum 46. + }) log:ifThenElseIn (() 1)}] + skolem:lemma303 + [ a r:Fact; r:gives {(92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (92 (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma350 a r:Inference; + r:gives { + 93 :collatz (1 (93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (93 2) math:remainder 0. + } { + (93 2) math:integerQuotient 280. + } { + (3 93) math:product 279 . + (279 1) math:sum 280. + }) log:ifThenElseIn (() 1)}] + skolem:lemma519 + [ a r:Fact; r:gives {(93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (93 (280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma351 a r:Inference; + r:gives { + 94 :collatz (1 (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (94 2) math:remainder 0. + } { + (94 2) math:integerQuotient 47. + } { + (3 94) math:product _:sk_0. + (_:sk_0 1) math:sum 47. + }) log:ifThenElseIn (() 1)}] + skolem:lemma304 + [ a r:Fact; r:gives {(94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (94 (47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma352 a r:Inference; + r:gives { + 95 :collatz (1 (95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (95 2) math:remainder 0. + } { + (95 2) math:integerQuotient 286. + } { + (3 95) math:product 285 . + (285 1) math:sum 286. + }) log:ifThenElseIn (() 1)}] + skolem:lemma520 + [ a r:Fact; r:gives {(95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (95 (286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma353 a r:Inference; + r:gives { + 96 :collatz (1 (96 48 24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (96 2) math:remainder 0. + } { + (96 2) math:integerQuotient 48. + } { + (3 96) math:product _:sk_0. + (_:sk_0 1) math:sum 48. + }) log:ifThenElseIn (() 1)}] + skolem:lemma305 + [ a r:Fact; r:gives {(96 48 24 12 6 3 10 5 16 8 4 2 1) list:firstRest (96 (48 24 12 6 3 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (48 24 12 6 3 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (96 48 24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma354 a r:Inference; + r:gives { + 97 :collatz (1 (97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (97 2) math:remainder 0. + } { + (97 2) math:integerQuotient 292. + } { + (3 97) math:product 291 . + (291 1) math:sum 292. + }) log:ifThenElseIn (() 1)}] + skolem:lemma521 + [ a r:Fact; r:gives {(97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (97 (292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma355 a r:Inference; + r:gives { + 98 :collatz (1 (98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (98 2) math:remainder 0. + } { + (98 2) math:integerQuotient 49. + } { + (3 98) math:product _:sk_0. + (_:sk_0 1) math:sum 49. + }) log:ifThenElseIn (() 1)}] + skolem:lemma306 + [ a r:Fact; r:gives {(98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (98 (49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma356 a r:Inference; + r:gives { + 99 :collatz (1 (99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (99 2) math:remainder 0. + } { + (99 2) math:integerQuotient 298. + } { + (3 99) math:product 297 . + (297 1) math:sum 298. + }) log:ifThenElseIn (() 1)}] + skolem:lemma522 + [ a r:Fact; r:gives {(99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (99 (298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma357 a r:Inference; + r:gives { + 100 :collatz (1 (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (100 2) math:remainder 0. + } { + (100 2) math:integerQuotient 50. + } { + (3 100) math:product _:sk_0. + (_:sk_0 1) math:sum 50. + }) log:ifThenElseIn (() 1)}] + skolem:lemma307 + [ a r:Fact; r:gives {(100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (100 (50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma358 a r:Inference; + r:gives { + 101 :collatz (1 (101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (101 2) math:remainder 0. + } { + (101 2) math:integerQuotient 304. + } { + (3 101) math:product 303 . + (303 1) math:sum 304. + }) log:ifThenElseIn (() 1)}] + skolem:lemma523 + [ a r:Fact; r:gives {(101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (101 (304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma359 a r:Inference; + r:gives { + 102 :collatz (1 (102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (102 2) math:remainder 0. + } { + (102 2) math:integerQuotient 51. + } { + (3 102) math:product _:sk_0. + (_:sk_0 1) math:sum 51. + }) log:ifThenElseIn (() 1)}] + skolem:lemma308 + [ a r:Fact; r:gives {(102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (102 (51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma360 a r:Inference; + r:gives { + 103 :collatz (1 (103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (103 2) math:remainder 0. + } { + (103 2) math:integerQuotient 310. + } { + (3 103) math:product 309 . + (309 1) math:sum 310. + }) log:ifThenElseIn (() 1)}] + skolem:lemma524 + [ a r:Fact; r:gives {(103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (103 (310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma361 a r:Inference; + r:gives { + 104 :collatz (1 (104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (104 2) math:remainder 0. + } { + (104 2) math:integerQuotient 52. + } { + (3 104) math:product _:sk_0. + (_:sk_0 1) math:sum 52. + }) log:ifThenElseIn (() 1)}] + skolem:lemma309 + [ a r:Fact; r:gives {(104 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (104 (52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma362 a r:Inference; + r:gives { + 105 :collatz (1 (105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (105 2) math:remainder 0. + } { + (105 2) math:integerQuotient 316. + } { + (3 105) math:product 315 . + (315 1) math:sum 316. + }) log:ifThenElseIn (() 1)}] + skolem:lemma525 + [ a r:Fact; r:gives {(105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (105 (316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma363 a r:Inference; + r:gives { + 106 :collatz (1 (106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (106 2) math:remainder 0. + } { + (106 2) math:integerQuotient 53. + } { + (3 106) math:product _:sk_0. + (_:sk_0 1) math:sum 53. + }) log:ifThenElseIn (() 1)}] + skolem:lemma310 + [ a r:Fact; r:gives {(106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (106 (53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma364 a r:Inference; + r:gives { + 107 :collatz (1 (107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (107 2) math:remainder 0. + } { + (107 2) math:integerQuotient 322. + } { + (3 107) math:product 321 . + (321 1) math:sum 322. + }) log:ifThenElseIn (() 1)}] + skolem:lemma526 + [ a r:Fact; r:gives {(107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (107 (322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma365 a r:Inference; + r:gives { + 108 :collatz (1 (108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (108 2) math:remainder 0. + } { + (108 2) math:integerQuotient 54. + } { + (3 108) math:product _:sk_0. + (_:sk_0 1) math:sum 54. + }) log:ifThenElseIn (() 1)}] + skolem:lemma311 + [ a r:Fact; r:gives {(108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (108 (54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma366 a r:Inference; + r:gives { + 109 :collatz (1 (109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (109 2) math:remainder 0. + } { + (109 2) math:integerQuotient 328. + } { + (3 109) math:product 327 . + (327 1) math:sum 328. + }) log:ifThenElseIn (() 1)}] + skolem:lemma527 + [ a r:Fact; r:gives {(109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (109 (328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma367 a r:Inference; + r:gives { + 110 :collatz (1 (110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (110 2) math:remainder 0. + } { + (110 2) math:integerQuotient 55. + } { + (3 110) math:product _:sk_0. + (_:sk_0 1) math:sum 55. + }) log:ifThenElseIn (() 1)}] + skolem:lemma312 + [ a r:Fact; r:gives {(110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (110 (55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma368 a r:Inference; + r:gives { + 111 :collatz (1 (111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (111 2) math:remainder 0. + } { + (111 2) math:integerQuotient 334. + } { + (3 111) math:product 333 . + (333 1) math:sum 334. + }) log:ifThenElseIn (() 1)}] + skolem:lemma528 + [ a r:Fact; r:gives {(111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (111 (334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma369 a r:Inference; + r:gives { + 112 :collatz (1 (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (112 2) math:remainder 0. + } { + (112 2) math:integerQuotient 56. + } { + (3 112) math:product _:sk_0. + (_:sk_0 1) math:sum 56. + }) log:ifThenElseIn (() 1)}] + skolem:lemma313 + [ a r:Fact; r:gives {(112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (112 (56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma370 a r:Inference; + r:gives { + 113 :collatz (1 (113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (113 2) math:remainder 0. + } { + (113 2) math:integerQuotient 340. + } { + (3 113) math:product 339 . + (339 1) math:sum 340. + }) log:ifThenElseIn (() 1)}] + skolem:lemma529 + [ a r:Fact; r:gives {(113 340 170 85 256 128 64 32 16 8 4 2 1) list:firstRest (113 (340 170 85 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (340 170 85 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma371 a r:Inference; + r:gives { + 114 :collatz (1 (114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (114 2) math:remainder 0. + } { + (114 2) math:integerQuotient 57. + } { + (3 114) math:product _:sk_0. + (_:sk_0 1) math:sum 57. + }) log:ifThenElseIn (() 1)}] + skolem:lemma314 + [ a r:Fact; r:gives {(114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (114 (57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma372 a r:Inference; + r:gives { + 115 :collatz (1 (115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (115 2) math:remainder 0. + } { + (115 2) math:integerQuotient 346. + } { + (3 115) math:product 345 . + (345 1) math:sum 346. + }) log:ifThenElseIn (() 1)}] + skolem:lemma530 + [ a r:Fact; r:gives {(115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (115 (346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma373 a r:Inference; + r:gives { + 116 :collatz (1 (116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (116 2) math:remainder 0. + } { + (116 2) math:integerQuotient 58. + } { + (3 116) math:product _:sk_0. + (_:sk_0 1) math:sum 58. + }) log:ifThenElseIn (() 1)}] + skolem:lemma315 + [ a r:Fact; r:gives {(116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (116 (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma374 a r:Inference; + r:gives { + 117 :collatz (1 (117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (117 2) math:remainder 0. + } { + (117 2) math:integerQuotient 352. + } { + (3 117) math:product 351 . + (351 1) math:sum 352. + }) log:ifThenElseIn (() 1)}] + skolem:lemma531 + [ a r:Fact; r:gives {(117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (117 (352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma375 a r:Inference; + r:gives { + 118 :collatz (1 (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (118 2) math:remainder 0. + } { + (118 2) math:integerQuotient 59. + } { + (3 118) math:product _:sk_0. + (_:sk_0 1) math:sum 59. + }) log:ifThenElseIn (() 1)}] + skolem:lemma316 + [ a r:Fact; r:gives {(118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (118 (59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma376 a r:Inference; + r:gives { + 119 :collatz (1 (119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (119 2) math:remainder 0. + } { + (119 2) math:integerQuotient 358. + } { + (3 119) math:product 357 . + (357 1) math:sum 358. + }) log:ifThenElseIn (() 1)}] + skolem:lemma532 + [ a r:Fact; r:gives {(119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (119 (358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma377 a r:Inference; + r:gives { + 120 :collatz (1 (120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (120 2) math:remainder 0. + } { + (120 2) math:integerQuotient 60. + } { + (3 120) math:product _:sk_0. + (_:sk_0 1) math:sum 60. + }) log:ifThenElseIn (() 1)}] + skolem:lemma317 + [ a r:Fact; r:gives {(120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (120 (60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma378 a r:Inference; + r:gives { + 121 :collatz (1 (121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (121 2) math:remainder 0. + } { + (121 2) math:integerQuotient 364. + } { + (3 121) math:product 363 . + (363 1) math:sum 364. + }) log:ifThenElseIn (() 1)}] + skolem:lemma533 + [ a r:Fact; r:gives {(121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (121 (364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma379 a r:Inference; + r:gives { + 122 :collatz (1 (122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (122 2) math:remainder 0. + } { + (122 2) math:integerQuotient 61. + } { + (3 122) math:product _:sk_0. + (_:sk_0 1) math:sum 61. + }) log:ifThenElseIn (() 1)}] + skolem:lemma318 + [ a r:Fact; r:gives {(122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (122 (61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma380 a r:Inference; + r:gives { + 123 :collatz (1 (123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (123 2) math:remainder 0. + } { + (123 2) math:integerQuotient 370. + } { + (3 123) math:product 369 . + (369 1) math:sum 370. + }) log:ifThenElseIn (() 1)}] + skolem:lemma534 + [ a r:Fact; r:gives {(123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (123 (370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma381 a r:Inference; + r:gives { + 124 :collatz (1 (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (124 2) math:remainder 0. + } { + (124 2) math:integerQuotient 62. + } { + (3 124) math:product _:sk_0. + (_:sk_0 1) math:sum 62. + }) log:ifThenElseIn (() 1)}] + skolem:lemma319 + [ a r:Fact; r:gives {(124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (124 (62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma382 a r:Inference; + r:gives { + 125 :collatz (1 (125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (125 2) math:remainder 0. + } { + (125 2) math:integerQuotient 376. + } { + (3 125) math:product 375 . + (375 1) math:sum 376. + }) log:ifThenElseIn (() 1)}] + skolem:lemma535 + [ a r:Fact; r:gives {(125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (125 (376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma383 a r:Inference; + r:gives { + 126 :collatz (1 (126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (126 2) math:remainder 0. + } { + (126 2) math:integerQuotient 63. + } { + (3 126) math:product _:sk_0. + (_:sk_0 1) math:sum 63. + }) log:ifThenElseIn (() 1)}] + skolem:lemma320 + [ a r:Fact; r:gives {(126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (126 (63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma384 a r:Inference; + r:gives { + 127 :collatz (1 (127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (127 2) math:remainder 0. + } { + (127 2) math:integerQuotient 382. + } { + (3 127) math:product 381 . + (381 1) math:sum 382. + }) log:ifThenElseIn (() 1)}] + skolem:lemma536 + [ a r:Fact; r:gives {(127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (127 (382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma385 a r:Inference; + r:gives { + 128 :collatz (1 (128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (128 2) math:remainder 0. + } { + (128 2) math:integerQuotient 64. + } { + (3 128) math:product _:sk_0. + (_:sk_0 1) math:sum 64. + }) log:ifThenElseIn (() 1)}] + skolem:lemma321 + [ a r:Fact; r:gives {(128 64 32 16 8 4 2 1) list:firstRest (128 (64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma386 a r:Inference; + r:gives { + 129 :collatz (1 (129 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (129 2) math:remainder 0. + } { + (129 2) math:integerQuotient 388. + } { + (3 129) math:product 387 . + (387 1) math:sum 388. + }) log:ifThenElseIn (() 1)}] + skolem:lemma537 + [ a r:Fact; r:gives {(129 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (129 (388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (129 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma387 a r:Inference; + r:gives { + 130 :collatz (1 (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (130 2) math:remainder 0. + } { + (130 2) math:integerQuotient 65. + } { + (3 130) math:product _:sk_0. + (_:sk_0 1) math:sum 65. + }) log:ifThenElseIn (() 1)}] + skolem:lemma322 + [ a r:Fact; r:gives {(130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (130 (65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma388 a r:Inference; + r:gives { + 131 :collatz (1 (131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (131 2) math:remainder 0. + } { + (131 2) math:integerQuotient 394. + } { + (3 131) math:product 393 . + (393 1) math:sum 394. + }) log:ifThenElseIn (() 1)}] + skolem:lemma538 + [ a r:Fact; r:gives {(131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (131 (394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma389 a r:Inference; + r:gives { + 132 :collatz (1 (132 66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (132 2) math:remainder 0. + } { + (132 2) math:integerQuotient 66. + } { + (3 132) math:product _:sk_0. + (_:sk_0 1) math:sum 66. + }) log:ifThenElseIn (() 1)}] + skolem:lemma323 + [ a r:Fact; r:gives {(132 66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (132 (66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (132 66 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma390 a r:Inference; + r:gives { + 133 :collatz (1 (133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (133 2) math:remainder 0. + } { + (133 2) math:integerQuotient 400. + } { + (3 133) math:product 399 . + (399 1) math:sum 400. + }) log:ifThenElseIn (() 1)}] + skolem:lemma539 + [ a r:Fact; r:gives {(133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (133 (400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma391 a r:Inference; + r:gives { + 134 :collatz (1 (134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (134 2) math:remainder 0. + } { + (134 2) math:integerQuotient 67. + } { + (3 134) math:product _:sk_0. + (_:sk_0 1) math:sum 67. + }) log:ifThenElseIn (() 1)}] + skolem:lemma324 + [ a r:Fact; r:gives {(134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (134 (67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma392 a r:Inference; + r:gives { + 135 :collatz (1 (135 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (135 2) math:remainder 0. + } { + (135 2) math:integerQuotient 406. + } { + (3 135) math:product 405 . + (405 1) math:sum 406. + }) log:ifThenElseIn (() 1)}] + skolem:lemma540 + [ a r:Fact; r:gives {(135 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (135 (406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (135 406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma393 a r:Inference; + r:gives { + 136 :collatz (1 (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (136 2) math:remainder 0. + } { + (136 2) math:integerQuotient 68. + } { + (3 136) math:product _:sk_0. + (_:sk_0 1) math:sum 68. + }) log:ifThenElseIn (() 1)}] + skolem:lemma325 + [ a r:Fact; r:gives {(136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (136 (68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma394 a r:Inference; + r:gives { + 137 :collatz (1 (137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (137 2) math:remainder 0. + } { + (137 2) math:integerQuotient 412. + } { + (3 137) math:product 411 . + (411 1) math:sum 412. + }) log:ifThenElseIn (() 1)}] + skolem:lemma541 + [ a r:Fact; r:gives {(137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (137 (412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma395 a r:Inference; + r:gives { + 138 :collatz (1 (138 69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (138 2) math:remainder 0. + } { + (138 2) math:integerQuotient 69. + } { + (3 138) math:product _:sk_0. + (_:sk_0 1) math:sum 69. + }) log:ifThenElseIn (() 1)}] + skolem:lemma326 + [ a r:Fact; r:gives {(138 69 208 104 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (138 (69 208 104 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (138 69 208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma396 a r:Inference; + r:gives { + 139 :collatz (1 (139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (139 2) math:remainder 0. + } { + (139 2) math:integerQuotient 418. + } { + (3 139) math:product 417 . + (417 1) math:sum 418. + }) log:ifThenElseIn (() 1)}] + skolem:lemma542 + [ a r:Fact; r:gives {(139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (139 (418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma397 a r:Inference; + r:gives { + 140 :collatz (1 (140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (140 2) math:remainder 0. + } { + (140 2) math:integerQuotient 70. + } { + (3 140) math:product _:sk_0. + (_:sk_0 1) math:sum 70. + }) log:ifThenElseIn (() 1)}] + skolem:lemma327 + [ a r:Fact; r:gives {(140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (140 (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma398 a r:Inference; + r:gives { + 141 :collatz (1 (141 424 212 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (141 2) math:remainder 0. + } { + (141 2) math:integerQuotient 424. + } { + (3 141) math:product 423 . + (423 1) math:sum 424. + }) log:ifThenElseIn (() 1)}] + skolem:lemma543 + [ a r:Fact; r:gives {(141 424 212 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (141 (424 212 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (424 212 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (141 424 212 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma399 a r:Inference; + r:gives { + 142 :collatz (1 (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (142 2) math:remainder 0. + } { + (142 2) math:integerQuotient 71. + } { + (3 142) math:product _:sk_0. + (_:sk_0 1) math:sum 71. + }) log:ifThenElseIn (() 1)}] + skolem:lemma328 + [ a r:Fact; r:gives {(142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (142 (71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma400 a r:Inference; + r:gives { + 143 :collatz (1 (143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (143 2) math:remainder 0. + } { + (143 2) math:integerQuotient 430. + } { + (3 143) math:product 429 . + (429 1) math:sum 430. + }) log:ifThenElseIn (() 1)}] + skolem:lemma544 + [ a r:Fact; r:gives {(143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (143 (430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma401 a r:Inference; + r:gives { + 144 :collatz (1 (144 72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (144 2) math:remainder 0. + } { + (144 2) math:integerQuotient 72. + } { + (3 144) math:product _:sk_0. + (_:sk_0 1) math:sum 72. + }) log:ifThenElseIn (() 1)}] + skolem:lemma329 + [ a r:Fact; r:gives {(144 72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (144 (72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (144 72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma402 a r:Inference; + r:gives { + 145 :collatz (1 (145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (145 2) math:remainder 0. + } { + (145 2) math:integerQuotient 436. + } { + (3 145) math:product 435 . + (435 1) math:sum 436. + }) log:ifThenElseIn (() 1)}] + skolem:lemma545 + [ a r:Fact; r:gives {(145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (145 (436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma403 a r:Inference; + r:gives { + 146 :collatz (1 (146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (146 2) math:remainder 0. + } { + (146 2) math:integerQuotient 73. + } { + (3 146) math:product _:sk_0. + (_:sk_0 1) math:sum 73. + }) log:ifThenElseIn (() 1)}] + skolem:lemma330 + [ a r:Fact; r:gives {(146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (146 (73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma404 a r:Inference; + r:gives { + 147 :collatz (1 (147 442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (147 2) math:remainder 0. + } { + (147 2) math:integerQuotient 442. + } { + (3 147) math:product 441 . + (441 1) math:sum 442. + }) log:ifThenElseIn (() 1)}] + skolem:lemma546 + [ a r:Fact; r:gives {(147 442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (147 (442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (147 442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma405 a r:Inference; + r:gives { + 148 :collatz (1 (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (148 2) math:remainder 0. + } { + (148 2) math:integerQuotient 74. + } { + (3 148) math:product _:sk_0. + (_:sk_0 1) math:sum 74. + }) log:ifThenElseIn (() 1)}] + skolem:lemma331 + [ a r:Fact; r:gives {(148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (148 (74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma406 a r:Inference; + r:gives { + 149 :collatz (1 (149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (149 2) math:remainder 0. + } { + (149 2) math:integerQuotient 448. + } { + (3 149) math:product 447 . + (447 1) math:sum 448. + }) log:ifThenElseIn (() 1)}] + skolem:lemma547 + [ a r:Fact; r:gives {(149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (149 (448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma407 a r:Inference; + r:gives { + 150 :collatz (1 (150 75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (150 2) math:remainder 0. + } { + (150 2) math:integerQuotient 75. + } { + (3 150) math:product _:sk_0. + (_:sk_0 1) math:sum 75. + }) log:ifThenElseIn (() 1)}] + skolem:lemma332 + [ a r:Fact; r:gives {(150 75 226 113 340 170 85 256 128 64 32 16 8 4 2 1) list:firstRest (150 (75 226 113 340 170 85 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (150 75 226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma408 a r:Inference; + r:gives { + 151 :collatz (1 (151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (151 2) math:remainder 0. + } { + (151 2) math:integerQuotient 454. + } { + (3 151) math:product 453 . + (453 1) math:sum 454. + }) log:ifThenElseIn (() 1)}] + skolem:lemma548 + [ a r:Fact; r:gives {(151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (151 (454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma409 a r:Inference; + r:gives { + 152 :collatz (1 (152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (152 2) math:remainder 0. + } { + (152 2) math:integerQuotient 76. + } { + (3 152) math:product _:sk_0. + (_:sk_0 1) math:sum 76. + }) log:ifThenElseIn (() 1)}] + skolem:lemma333 + [ a r:Fact; r:gives {(152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (152 (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma410 a r:Inference; + r:gives { + 153 :collatz (1 (153 460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (153 2) math:remainder 0. + } { + (153 2) math:integerQuotient 460. + } { + (3 153) math:product 459 . + (459 1) math:sum 460. + }) log:ifThenElseIn (() 1)}] + skolem:lemma549 + [ a r:Fact; r:gives {(153 460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (153 (460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (153 460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma411 a r:Inference; + r:gives { + 154 :collatz (1 (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (154 2) math:remainder 0. + } { + (154 2) math:integerQuotient 77. + } { + (3 154) math:product _:sk_0. + (_:sk_0 1) math:sum 77. + }) log:ifThenElseIn (() 1)}] + skolem:lemma334 + [ a r:Fact; r:gives {(154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (154 (77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma412 a r:Inference; + r:gives { + 155 :collatz (1 (155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (155 2) math:remainder 0. + } { + (155 2) math:integerQuotient 466. + } { + (3 155) math:product 465 . + (465 1) math:sum 466. + }) log:ifThenElseIn (() 1)}] + skolem:lemma550 + [ a r:Fact; r:gives {(155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (155 (466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma413 a r:Inference; + r:gives { + 156 :collatz (1 (156 78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (156 2) math:remainder 0. + } { + (156 2) math:integerQuotient 78. + } { + (3 156) math:product _:sk_0. + (_:sk_0 1) math:sum 78. + }) log:ifThenElseIn (() 1)}] + skolem:lemma335 + [ a r:Fact; r:gives {(156 78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (156 (78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (156 78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma414 a r:Inference; + r:gives { + 157 :collatz (1 (157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (157 2) math:remainder 0. + } { + (157 2) math:integerQuotient 472. + } { + (3 157) math:product 471 . + (471 1) math:sum 472. + }) log:ifThenElseIn (() 1)}] + skolem:lemma551 + [ a r:Fact; r:gives {(157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (157 (472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma415 a r:Inference; + r:gives { + 158 :collatz (1 (158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (158 2) math:remainder 0. + } { + (158 2) math:integerQuotient 79. + } { + (3 158) math:product _:sk_0. + (_:sk_0 1) math:sum 79. + }) log:ifThenElseIn (() 1)}] + skolem:lemma336 + [ a r:Fact; r:gives {(158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (158 (79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma416 a r:Inference; + r:gives { + 159 :collatz (1 (159 478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (159 2) math:remainder 0. + } { + (159 2) math:integerQuotient 478. + } { + (3 159) math:product 477 . + (477 1) math:sum 478. + }) log:ifThenElseIn (() 1)}] + skolem:lemma552 + [ a r:Fact; r:gives {(159 478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (159 (478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (159 478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma417 a r:Inference; + r:gives { + 160 :collatz (1 (160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (160 2) math:remainder 0. + } { + (160 2) math:integerQuotient 80. + } { + (3 160) math:product _:sk_0. + (_:sk_0 1) math:sum 80. + }) log:ifThenElseIn (() 1)}] + skolem:lemma337 + [ a r:Fact; r:gives {(160 80 40 20 10 5 16 8 4 2 1) list:firstRest (160 (80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma418 a r:Inference; + r:gives { + 161 :collatz (1 (161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (161 2) math:remainder 0. + } { + (161 2) math:integerQuotient 484. + } { + (3 161) math:product 483 . + (483 1) math:sum 484. + }) log:ifThenElseIn (() 1)}] + skolem:lemma553 + [ a r:Fact; r:gives {(161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (161 (484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma419 a r:Inference; + r:gives { + 162 :collatz (1 (162 81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (162 2) math:remainder 0. + } { + (162 2) math:integerQuotient 81. + } { + (3 162) math:product _:sk_0. + (_:sk_0 1) math:sum 81. + }) log:ifThenElseIn (() 1)}] + skolem:lemma338 + [ a r:Fact; r:gives {(162 81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (162 (81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (162 81 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma420 a r:Inference; + r:gives { + 163 :collatz (1 (163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (163 2) math:remainder 0. + } { + (163 2) math:integerQuotient 490. + } { + (3 163) math:product 489 . + (489 1) math:sum 490. + }) log:ifThenElseIn (() 1)}] + skolem:lemma554 + [ a r:Fact; r:gives {(163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (163 (490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma421 a r:Inference; + r:gives { + 164 :collatz (1 (164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 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412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma422 a r:Inference; + r:gives { + 165 :collatz (1 (165 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (165 2) math:remainder 0. + } { + (165 2) math:integerQuotient 496. + } { + (3 165) math:product 495 . + (495 1) math:sum 496. + }) log:ifThenElseIn (() 1)}] + skolem:lemma555 + [ a r:Fact; r:gives {(165 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (165 (496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (165 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma423 a r:Inference; + r:gives { + 166 :collatz (1 (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (166 2) math:remainder 0. + } { + (166 2) math:integerQuotient 83. + } { + (3 166) math:product _:sk_0. + (_:sk_0 1) math:sum 83. + }) log:ifThenElseIn (() 1)}] + skolem:lemma340 + [ a r:Fact; r:gives {(166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (166 (83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma424 a r:Inference; + r:gives { + 167 :collatz (1 (167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (167 2) math:remainder 0. + } { + (167 2) math:integerQuotient 502. + } { + (3 167) math:product 501 . + (501 1) math:sum 502. + }) log:ifThenElseIn (() 1)}] + skolem:lemma556 + [ a r:Fact; r:gives {(167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (167 (502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma425 a r:Inference; + r:gives { + 168 :collatz (1 (168 84 42 21 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (168 2) math:remainder 0. + } { + (168 2) math:integerQuotient 84. + } { + (3 168) math:product _:sk_0. + (_:sk_0 1) math:sum 84. + }) log:ifThenElseIn (() 1)}] + skolem:lemma341 + [ a r:Fact; r:gives {(168 84 42 21 64 32 16 8 4 2 1) list:firstRest (168 (84 42 21 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (84 42 21 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (168 84 42 21 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma426 a r:Inference; + r:gives { + 169 :collatz (1 (169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (169 2) math:remainder 0. + } { + (169 2) math:integerQuotient 508. + } { + (3 169) math:product 507 . + (507 1) math:sum 508. + }) log:ifThenElseIn (() 1)}] + skolem:lemma557 + [ a r:Fact; r:gives {(169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (169 (508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma427 a r:Inference; + r:gives { + 170 :collatz (1 (170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (170 2) math:remainder 0. + } { + (170 2) math:integerQuotient 85. + } { + (3 170) math:product _:sk_0. + (_:sk_0 1) math:sum 85. + }) log:ifThenElseIn (() 1)}] + skolem:lemma342 + [ a r:Fact; r:gives {(170 85 256 128 64 32 16 8 4 2 1) list:firstRest (170 (85 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (85 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma428 a r:Inference; + r:gives { + 171 :collatz (1 (171 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (171 2) math:remainder 0. + } { + (171 2) math:integerQuotient 514. + } { + (3 171) math:product 513 . + (513 1) math:sum 514. + }) log:ifThenElseIn (() 1)}] + skolem:lemma558 + [ a r:Fact; r:gives {(171 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (171 (514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (171 514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma429 a r:Inference; + r:gives { + 172 :collatz (1 (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (172 2) math:remainder 0. + } { + (172 2) math:integerQuotient 86. + } { + (3 172) math:product _:sk_0. + (_:sk_0 1) math:sum 86. + }) log:ifThenElseIn (() 1)}] + skolem:lemma343 + [ a r:Fact; r:gives {(172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (172 (86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma430 a r:Inference; + r:gives { + 173 :collatz (1 (173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (173 2) math:remainder 0. + } { + (173 2) math:integerQuotient 520. + } { + (3 173) math:product 519 . + (519 1) math:sum 520. + }) log:ifThenElseIn (() 1)}] + skolem:lemma559 + [ a r:Fact; r:gives {(173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (173 (520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma431 a r:Inference; + r:gives { + 174 :collatz (1 (174 87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (174 2) math:remainder 0. + } { + (174 2) math:integerQuotient 87. + } { + (3 174) math:product _:sk_0. + (_:sk_0 1) math:sum 87. + }) log:ifThenElseIn (() 1)}] + skolem:lemma344 + [ a r:Fact; r:gives {(174 87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (174 (87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (174 87 262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma432 a r:Inference; + r:gives { + 175 :collatz (1 (175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (175 2) math:remainder 0. + } { + (175 2) math:integerQuotient 526. + } { + (3 175) math:product 525 . + (525 1) math:sum 526. + }) log:ifThenElseIn (() 1)}] + skolem:lemma560 + [ a r:Fact; r:gives {(175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (175 (526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma433 a r:Inference; + r:gives { + 176 :collatz (1 (176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (176 2) math:remainder 0. + } { + (176 2) math:integerQuotient 88. + } { + (3 176) math:product _:sk_0. + (_:sk_0 1) math:sum 88. + }) log:ifThenElseIn (() 1)}] + skolem:lemma345 + [ a r:Fact; r:gives {(176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (176 (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma434 a r:Inference; + r:gives { + 177 :collatz (1 (177 532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (177 2) math:remainder 0. + } { + (177 2) math:integerQuotient 532. + } { + (3 177) math:product 531 . + (531 1) math:sum 532. + }) log:ifThenElseIn (() 1)}] + skolem:lemma561 + [ a r:Fact; r:gives {(177 532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (177 (532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (177 532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma435 a r:Inference; + r:gives { + 178 :collatz (1 (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (178 2) math:remainder 0. + } { + (178 2) math:integerQuotient 89. + } { + (3 178) math:product _:sk_0. + (_:sk_0 1) math:sum 89. + }) log:ifThenElseIn (() 1)}] + skolem:lemma346 + [ a r:Fact; r:gives {(178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (178 (89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma436 a r:Inference; + r:gives { + 179 :collatz (1 (179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (179 2) math:remainder 0. + } { + (179 2) math:integerQuotient 538. + } { + (3 179) math:product 537 . + (537 1) math:sum 538. + }) log:ifThenElseIn (() 1)}] + skolem:lemma562 + [ a r:Fact; r:gives {(179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (179 (538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma437 a r:Inference; + r:gives { + 180 :collatz (1 (180 90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (180 2) math:remainder 0. + } { + (180 2) math:integerQuotient 90. + } { + (3 180) math:product _:sk_0. + (_:sk_0 1) math:sum 90. + }) log:ifThenElseIn (() 1)}] + skolem:lemma347 + [ a r:Fact; r:gives {(180 90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (180 (90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (180 90 45 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma438 a r:Inference; + r:gives { + 181 :collatz (1 (181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (181 2) math:remainder 0. + } { + (181 2) math:integerQuotient 544. + } { + (3 181) math:product 543 . + (543 1) math:sum 544. + }) log:ifThenElseIn (() 1)}] + skolem:lemma563 + [ a r:Fact; r:gives {(181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (181 (544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma439 a r:Inference; + r:gives { + 182 :collatz (1 (182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (182 2) math:remainder 0. + } { + (182 2) math:integerQuotient 91. + } { + (3 182) math:product _:sk_0. + (_:sk_0 1) math:sum 91. + }) log:ifThenElseIn (() 1)}] + skolem:lemma348 + [ a r:Fact; r:gives {(182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (182 (91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma440 a r:Inference; + r:gives { + 183 :collatz (1 (183 550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (183 2) math:remainder 0. + } { + (183 2) math:integerQuotient 550. + } { + (3 183) math:product 549 . + (549 1) math:sum 550. + }) log:ifThenElseIn (() 1)}] + skolem:lemma564 + [ a r:Fact; r:gives {(183 550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (183 (550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (183 550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma441 a r:Inference; + r:gives { + 184 :collatz (1 (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (184 2) math:remainder 0. + } { + (184 2) math:integerQuotient 92. + } { + (3 184) math:product _:sk_0. + (_:sk_0 1) math:sum 92. + }) log:ifThenElseIn (() 1)}] + skolem:lemma349 + [ a r:Fact; r:gives {(184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (184 (92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma442 a r:Inference; + r:gives { + 185 :collatz (1 (185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (185 2) math:remainder 0. + } { + (185 2) math:integerQuotient 556. + } { + (3 185) math:product 555 . + (555 1) math:sum 556. + }) log:ifThenElseIn (() 1)}] + skolem:lemma565 + [ a r:Fact; r:gives {(185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (185 (556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma443 a r:Inference; + r:gives { + 186 :collatz (1 (186 93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (186 2) math:remainder 0. + } { + (186 2) math:integerQuotient 93. + } { + (3 186) math:product _:sk_0. + (_:sk_0 1) math:sum 93. + }) log:ifThenElseIn (() 1)}] + skolem:lemma350 + [ a r:Fact; r:gives {(186 93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (186 (93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (186 93 280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma444 a r:Inference; + r:gives { + 187 :collatz (1 (187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (187 2) math:remainder 0. + } { + (187 2) math:integerQuotient 562. + } { + (3 187) math:product 561 . + (561 1) math:sum 562. + }) log:ifThenElseIn (() 1)}] + skolem:lemma566 + [ a r:Fact; r:gives {(187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (187 (562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma445 a r:Inference; + r:gives { + 188 :collatz (1 (188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (188 2) math:remainder 0. + } { + (188 2) math:integerQuotient 94. + } { + (3 188) math:product _:sk_0. + (_:sk_0 1) math:sum 94. + }) log:ifThenElseIn (() 1)}] + skolem:lemma351 + [ a r:Fact; r:gives {(188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (188 (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma446 a r:Inference; + r:gives { + 189 :collatz (1 (189 568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (189 2) math:remainder 0. + } { + (189 2) math:integerQuotient 568. + } { + (3 189) math:product 567 . + (567 1) math:sum 568. + }) log:ifThenElseIn (() 1)}] + skolem:lemma567 + [ a r:Fact; r:gives {(189 568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (189 (568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (189 568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma447 a r:Inference; + r:gives { + 190 :collatz (1 (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (190 2) math:remainder 0. + } { + (190 2) math:integerQuotient 95. + } { + (3 190) math:product _:sk_0. + (_:sk_0 1) math:sum 95. + }) log:ifThenElseIn (() 1)}] + skolem:lemma352 + [ a r:Fact; r:gives {(190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (190 (95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma448 a r:Inference; + r:gives { + 191 :collatz (1 (191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (191 2) math:remainder 0. + } { + (191 2) math:integerQuotient 574. + } { + (3 191) math:product 573 . + (573 1) math:sum 574. + }) log:ifThenElseIn (() 1)}] + skolem:lemma568 + [ a r:Fact; r:gives {(191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (191 (574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma449 a r:Inference; + r:gives { + 192 :collatz (1 (192 96 48 24 12 6 3 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (192 2) math:remainder 0. + } { + (192 2) math:integerQuotient 96. + } { + (3 192) math:product _:sk_0. + (_:sk_0 1) math:sum 96. + }) log:ifThenElseIn (() 1)}] + skolem:lemma353 + [ a r:Fact; r:gives {(192 96 48 24 12 6 3 10 5 16 8 4 2 1) list:firstRest (192 (96 48 24 12 6 3 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (96 48 24 12 6 3 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (192 96 48 24 12 6 3 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma450 a r:Inference; + r:gives { + 193 :collatz (1 (193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (193 2) math:remainder 0. + } { + (193 2) math:integerQuotient 580. + } { + (3 193) math:product 579 . + (579 1) math:sum 580. + }) log:ifThenElseIn (() 1)}] + skolem:lemma569 + [ a r:Fact; r:gives {(193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (193 (580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma451 a r:Inference; + r:gives { + 194 :collatz (1 (194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (194 2) math:remainder 0. + } { + (194 2) math:integerQuotient 97. + } { + (3 194) math:product _:sk_0. + (_:sk_0 1) math:sum 97. + }) log:ifThenElseIn (() 1)}] + skolem:lemma354 + [ a r:Fact; r:gives {(194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (194 (97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma452 a r:Inference; + r:gives { + 195 :collatz (1 (195 586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (195 2) math:remainder 0. + } { + (195 2) math:integerQuotient 586. + } { + (3 195) math:product 585 . + (585 1) math:sum 586. + }) log:ifThenElseIn (() 1)}] + skolem:lemma570 + [ a r:Fact; r:gives {(195 586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (195 (586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (195 586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma453 a r:Inference; + r:gives { + 196 :collatz (1 (196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (196 2) math:remainder 0. + } { + (196 2) math:integerQuotient 98. + } { + (3 196) math:product _:sk_0. + (_:sk_0 1) math:sum 98. + }) log:ifThenElseIn (() 1)}] + skolem:lemma355 + [ a r:Fact; r:gives {(196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (196 (98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma454 a r:Inference; + r:gives { + 197 :collatz (1 (197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (197 2) math:remainder 0. + } { + (197 2) math:integerQuotient 592. + } { + (3 197) math:product 591 . + (591 1) math:sum 592. + }) log:ifThenElseIn (() 1)}] + skolem:lemma571 + [ a r:Fact; r:gives {(197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (197 (592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma455 a r:Inference; + r:gives { + 198 :collatz (1 (198 99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (198 2) math:remainder 0. + } { + (198 2) math:integerQuotient 99. + } { + (3 198) math:product _:sk_0. + (_:sk_0 1) math:sum 99. + }) log:ifThenElseIn (() 1)}] + skolem:lemma356 + [ a r:Fact; r:gives {(198 99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (198 (99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (198 99 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma456 a r:Inference; + r:gives { + 199 :collatz (1 (199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (199 2) math:remainder 0. + } { + (199 2) math:integerQuotient 598. + } { + (3 199) math:product 597 . + (597 1) math:sum 598. + }) log:ifThenElseIn (() 1)}] + skolem:lemma572 + [ a r:Fact; r:gives {(199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (199 (598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma457 a r:Inference; + r:gives { + 200 :collatz (1 (200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (200 2) math:remainder 0. + } { + (200 2) math:integerQuotient 100. + } { + (3 200) math:product _:sk_0. + (_:sk_0 1) math:sum 100. + }) log:ifThenElseIn (() 1)}] + skolem:lemma357 + [ a r:Fact; r:gives {(200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (200 (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma458 a r:Inference; + r:gives { + 201 :collatz (1 (201 604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (201 2) math:remainder 0. + } { + (201 2) math:integerQuotient 604. + } { + (3 201) math:product 603 . + (603 1) math:sum 604. + }) log:ifThenElseIn (() 1)}] + skolem:lemma573 + [ a r:Fact; r:gives {(201 604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (201 (604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (201 604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma459 a r:Inference; + r:gives { + 202 :collatz (1 (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (202 2) math:remainder 0. + } { + (202 2) math:integerQuotient 101. + } { + (3 202) math:product _:sk_0. + (_:sk_0 1) math:sum 101. + }) log:ifThenElseIn (() 1)}] + skolem:lemma358 + [ a r:Fact; r:gives {(202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (202 (101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma460 a r:Inference; + r:gives { + 203 :collatz (1 (203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (203 2) math:remainder 0. + } { + (203 2) math:integerQuotient 610. + } { + (3 203) math:product 609 . + (609 1) math:sum 610. + }) log:ifThenElseIn (() 1)}] + skolem:lemma574 + [ a r:Fact; r:gives {(203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (203 (610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma461 a r:Inference; + r:gives { + 204 :collatz (1 (204 102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (204 2) math:remainder 0. + } { + (204 2) math:integerQuotient 102. + } { + (3 204) math:product _:sk_0. + (_:sk_0 1) math:sum 102. + }) log:ifThenElseIn (() 1)}] + skolem:lemma359 + [ a r:Fact; r:gives {(204 102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (204 (102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (204 102 51 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma462 a r:Inference; + r:gives { + 205 :collatz (1 (205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (205 2) math:remainder 0. + } { + (205 2) math:integerQuotient 616. + } { + (3 205) math:product 615 . + (615 1) math:sum 616. + }) log:ifThenElseIn (() 1)}] + skolem:lemma575 + [ a r:Fact; r:gives {(205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (205 (616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma463 a r:Inference; + r:gives { + 206 :collatz (1 (206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (206 2) math:remainder 0. + } { + (206 2) math:integerQuotient 103. + } { + (3 206) math:product _:sk_0. + (_:sk_0 1) math:sum 103. + }) log:ifThenElseIn (() 1)}] + skolem:lemma360 + [ a r:Fact; r:gives {(206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (206 (103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma464 a r:Inference; + r:gives { + 207 :collatz (1 (207 622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (207 2) math:remainder 0. + } { + (207 2) math:integerQuotient 622. + } { + (3 207) math:product 621 . + (621 1) math:sum 622. + }) log:ifThenElseIn (() 1)}] + skolem:lemma576 + [ a r:Fact; r:gives {(207 622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (207 (622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (207 622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma465 a r:Inference; + r:gives { + 208 :collatz (1 (208 104 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (208 2) math:remainder 0. + } { + (208 2) math:integerQuotient 104. + } { + (3 208) math:product _:sk_0. + (_:sk_0 1) math:sum 104. + }) log:ifThenElseIn (() 1)}] + skolem:lemma361 + [ a r:Fact; r:gives {(208 104 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (208 (104 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (208 104 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma466 a r:Inference; + r:gives { + 209 :collatz (1 (209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (209 2) math:remainder 0. + } { + (209 2) math:integerQuotient 628. + } { + (3 209) math:product 627 . + (627 1) math:sum 628. + }) log:ifThenElseIn (() 1)}] + skolem:lemma577 + [ a r:Fact; r:gives {(209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (209 (628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma467 a r:Inference; + r:gives { + 210 :collatz (1 (210 105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (210 2) math:remainder 0. + } { + (210 2) math:integerQuotient 105. + } { + (3 210) math:product _:sk_0. + (_:sk_0 1) math:sum 105. + }) log:ifThenElseIn (() 1)}] + skolem:lemma362 + [ a r:Fact; r:gives {(210 105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (210 (105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (210 105 316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma468 a r:Inference; + r:gives { + 211 :collatz (1 (211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (211 2) math:remainder 0. + } { + (211 2) math:integerQuotient 634. + } { + (3 211) math:product 633 . + (633 1) math:sum 634. + }) log:ifThenElseIn (() 1)}] + skolem:lemma578 + [ a r:Fact; r:gives {(211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (211 (634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma469 a r:Inference; + r:gives { + 212 :collatz (1 (212 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (212 2) math:remainder 0. + } { + (212 2) math:integerQuotient 106. + } { + (3 212) math:product _:sk_0. + (_:sk_0 1) math:sum 106. + }) log:ifThenElseIn (() 1)}] + skolem:lemma363 + [ a r:Fact; r:gives {(212 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (212 (106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (212 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma470 a r:Inference; + r:gives { + 213 :collatz (1 (213 640 320 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (213 2) math:remainder 0. + } { + (213 2) math:integerQuotient 640. + } { + (3 213) math:product 639 . + (639 1) math:sum 640. + }) log:ifThenElseIn (() 1)}] + skolem:lemma579 + [ a r:Fact; r:gives {(213 640 320 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (213 (640 320 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (640 320 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (213 640 320 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma471 a r:Inference; + r:gives { + 214 :collatz (1 (214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (214 2) math:remainder 0. + } { + (214 2) math:integerQuotient 107. + } { + (3 214) math:product _:sk_0. + (_:sk_0 1) math:sum 107. + }) log:ifThenElseIn (() 1)}] + skolem:lemma364 + [ a r:Fact; r:gives {(214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (214 (107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma472 a r:Inference; + r:gives { + 215 :collatz (1 (215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (215 2) math:remainder 0. + } { + (215 2) math:integerQuotient 646. + } { + (3 215) math:product 645 . + (645 1) math:sum 646. + }) log:ifThenElseIn (() 1)}] + skolem:lemma580 + [ a r:Fact; r:gives {(215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (215 (646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma473 a r:Inference; + r:gives { + 216 :collatz (1 (216 108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (216 2) math:remainder 0. + } { + (216 2) math:integerQuotient 108. + } { + (3 216) math:product _:sk_0. + (_:sk_0 1) math:sum 108. + }) log:ifThenElseIn (() 1)}] + skolem:lemma365 + [ a r:Fact; r:gives {(216 108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (216 (108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (216 108 54 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma474 a r:Inference; + r:gives { + 217 :collatz (1 (217 652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (217 2) math:remainder 0. + } { + (217 2) math:integerQuotient 652. + } { + (3 217) math:product 651 . + (651 1) math:sum 652. + }) log:ifThenElseIn (() 1)}] + skolem:lemma581 + [ a r:Fact; r:gives {(217 652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (217 (652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (217 652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma475 a r:Inference; + r:gives { + 218 :collatz (1 (218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (218 2) math:remainder 0. + } { + (218 2) math:integerQuotient 109. + } { + (3 218) math:product _:sk_0. + (_:sk_0 1) math:sum 109. + }) log:ifThenElseIn (() 1)}] + skolem:lemma366 + [ a r:Fact; r:gives {(218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (218 (109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma476 a r:Inference; + r:gives { + 219 :collatz (1 (219 658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (219 2) math:remainder 0. + } { + (219 2) math:integerQuotient 658. + } { + (3 219) math:product 657 . + (657 1) math:sum 658. + }) log:ifThenElseIn (() 1)}] + skolem:lemma582 + [ a r:Fact; r:gives {(219 658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (219 (658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (219 658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma477 a r:Inference; + r:gives { + 220 :collatz (1 (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (220 2) math:remainder 0. + } { + (220 2) math:integerQuotient 110. + } { + (3 220) math:product _:sk_0. + (_:sk_0 1) math:sum 110. + }) log:ifThenElseIn (() 1)}] + skolem:lemma367 + [ a r:Fact; r:gives {(220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (220 (110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma478 a r:Inference; + r:gives { + 221 :collatz (1 (221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (221 2) math:remainder 0. + } { + (221 2) math:integerQuotient 664. + } { + (3 221) math:product 663 . + (663 1) math:sum 664. + }) log:ifThenElseIn (() 1)}] + skolem:lemma583 + [ a r:Fact; r:gives {(221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (221 (664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma479 a r:Inference; + r:gives { + 222 :collatz (1 (222 111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (222 2) math:remainder 0. + } { + (222 2) math:integerQuotient 111. + } { + (3 222) math:product _:sk_0. + (_:sk_0 1) math:sum 111. + }) log:ifThenElseIn (() 1)}] + skolem:lemma368 + [ a r:Fact; r:gives {(222 111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (222 (111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (222 111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma480 a r:Inference; + r:gives { + 223 :collatz (1 (223 670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (223 2) math:remainder 0. + } { + (223 2) math:integerQuotient 670. + } { + (3 223) math:product 669 . + (669 1) math:sum 670. + }) log:ifThenElseIn (() 1)}] + skolem:lemma584 + [ a r:Fact; r:gives {(223 670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (223 (670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (223 670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma481 a r:Inference; + r:gives { + 224 :collatz (1 (224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (224 2) math:remainder 0. + } { + (224 2) math:integerQuotient 112. + } { + (3 224) math:product _:sk_0. + (_:sk_0 1) math:sum 112. + }) log:ifThenElseIn (() 1)}] + skolem:lemma369 + [ a r:Fact; r:gives {(224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (224 (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma482 a r:Inference; + r:gives { + 225 :collatz (1 (225 676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (225 2) math:remainder 0. + } { + (225 2) math:integerQuotient 676. + } { + (3 225) math:product 675 . + (675 1) math:sum 676. + }) log:ifThenElseIn (() 1)}] + skolem:lemma585 + [ a r:Fact; r:gives {(225 676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (225 (676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (225 676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma483 a r:Inference; + r:gives { + 226 :collatz (1 (226 113 340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (226 2) math:remainder 0. + } { + (226 2) math:integerQuotient 113. + } { + (3 226) math:product _:sk_0. + (_:sk_0 1) math:sum 113. + }) log:ifThenElseIn (() 1)}] + skolem:lemma370 + [ a r:Fact; r:gives {(226 113 340 170 85 256 128 64 32 16 8 4 2 1) list:firstRest (226 (113 340 170 85 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (226 113 340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma484 a r:Inference; + r:gives { + 227 :collatz (1 (227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (227 2) math:remainder 0. + } { + (227 2) math:integerQuotient 682. + } { + (3 227) math:product 681 . + (681 1) math:sum 682. + }) log:ifThenElseIn (() 1)}] + skolem:lemma586 + [ a r:Fact; r:gives {(227 682 341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (227 (682 341 1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma485 a r:Inference; + r:gives { + 228 :collatz (1 (228 114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (228 2) math:remainder 0. + } { + (228 2) math:integerQuotient 114. + } { + (3 228) math:product _:sk_0. + (_:sk_0 1) math:sum 114. + }) log:ifThenElseIn (() 1)}] + skolem:lemma371 + [ a r:Fact; r:gives {(228 114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (228 (114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (228 114 57 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma486 a r:Inference; + r:gives { + 229 :collatz (1 (229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (229 2) math:remainder 0. + } { + (229 2) math:integerQuotient 688. + } { + (3 229) math:product 687 . + (687 1) math:sum 688. + }) log:ifThenElseIn (() 1)}] + skolem:lemma587 + [ a r:Fact; r:gives {(229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (229 (688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma487 a r:Inference; + r:gives { + 230 :collatz (1 (230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (230 2) math:remainder 0. + } { + (230 2) math:integerQuotient 115. + } { + (3 230) math:product _:sk_0. + (_:sk_0 1) math:sum 115. + }) log:ifThenElseIn (() 1)}] + skolem:lemma372 + [ a r:Fact; r:gives {(230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (230 (115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma488 a r:Inference; + r:gives { + 231 :collatz (1 (231 694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (231 2) math:remainder 0. + } { + (231 2) math:integerQuotient 694. + } { + (3 231) math:product 693 . + (693 1) math:sum 694. + }) log:ifThenElseIn (() 1)}] + skolem:lemma588 + [ a r:Fact; r:gives {(231 694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (231 (694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (231 694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma489 a r:Inference; + r:gives { + 232 :collatz (1 (232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (232 2) math:remainder 0. + } { + (232 2) math:integerQuotient 116. + } { + (3 232) math:product _:sk_0. + (_:sk_0 1) math:sum 116. + }) log:ifThenElseIn (() 1)}] + skolem:lemma373 + [ a r:Fact; r:gives {(232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (232 (116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma490 a r:Inference; + r:gives { + 233 :collatz (1 (233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (233 2) math:remainder 0. + } { + (233 2) math:integerQuotient 700. + } { + (3 233) math:product 699 . + (699 1) math:sum 700. + }) log:ifThenElseIn (() 1)}] + skolem:lemma589 + [ a r:Fact; r:gives {(233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (233 (700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma491 a r:Inference; + r:gives { + 234 :collatz (1 (234 117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (234 2) math:remainder 0. + } { + (234 2) math:integerQuotient 117. + } { + (3 234) math:product _:sk_0. + (_:sk_0 1) math:sum 117. + }) log:ifThenElseIn (() 1)}] + skolem:lemma374 + [ a r:Fact; r:gives {(234 117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (234 (117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (234 117 352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma492 a r:Inference; + r:gives { + 235 :collatz (1 (235 706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (235 2) math:remainder 0. + } { + (235 2) math:integerQuotient 706. + } { + (3 235) math:product 705 . + (705 1) math:sum 706. + }) log:ifThenElseIn (() 1)}] + skolem:lemma590 + [ a r:Fact; r:gives {(235 706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (235 (706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (235 706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma493 a r:Inference; + r:gives { + 236 :collatz (1 (236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (236 2) math:remainder 0. + } { + (236 2) math:integerQuotient 118. + } { + (3 236) math:product _:sk_0. + (_:sk_0 1) math:sum 118. + }) log:ifThenElseIn (() 1)}] + skolem:lemma375 + [ a r:Fact; r:gives {(236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (236 (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma494 a r:Inference; + r:gives { + 237 :collatz (1 (237 712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (237 2) math:remainder 0. + } { + (237 2) math:integerQuotient 712. + } { + (3 237) math:product 711 . + (711 1) math:sum 712. + }) log:ifThenElseIn (() 1)}] + skolem:lemma591 + [ a r:Fact; r:gives {(237 712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (237 (712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (237 712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma495 a r:Inference; + r:gives { + 238 :collatz (1 (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (238 2) math:remainder 0. + } { + (238 2) math:integerQuotient 119. + } { + (3 238) math:product _:sk_0. + (_:sk_0 1) math:sum 119. + }) log:ifThenElseIn (() 1)}] + skolem:lemma376 + [ a r:Fact; r:gives {(238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (238 (119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma496 a r:Inference; + r:gives { + 239 :collatz (1 (239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (239 2) math:remainder 0. + } { + (239 2) math:integerQuotient 718. + } { + (3 239) math:product 717 . + (717 1) math:sum 718. + }) log:ifThenElseIn (() 1)}] + skolem:lemma592 + [ a r:Fact; r:gives {(239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (239 (718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma497 a r:Inference; + r:gives { + 240 :collatz (1 (240 120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (240 2) math:remainder 0. + } { + (240 2) math:integerQuotient 120. + } { + (3 240) math:product _:sk_0. + (_:sk_0 1) math:sum 120. + }) log:ifThenElseIn (() 1)}] + skolem:lemma377 + [ a r:Fact; r:gives {(240 120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (240 (120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (240 120 60 30 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma498 a r:Inference; + r:gives { + 241 :collatz (1 (241 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (241 2) math:remainder 0. + } { + (241 2) math:integerQuotient 724. + } { + (3 241) math:product 723 . + (723 1) math:sum 724. + }) log:ifThenElseIn (() 1)}] + skolem:lemma593 + [ a r:Fact; r:gives {(241 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (241 (724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (241 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma499 a r:Inference; + r:gives { + 242 :collatz (1 (242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (242 2) math:remainder 0. + } { + (242 2) math:integerQuotient 121. + } { + (3 242) math:product _:sk_0. + (_:sk_0 1) math:sum 121. + }) log:ifThenElseIn (() 1)}] + skolem:lemma378 + [ a r:Fact; r:gives {(242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (242 (121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma500 a r:Inference; + r:gives { + 243 :collatz (1 (243 730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (243 2) math:remainder 0. + } { + (243 2) math:integerQuotient 730. + } { + (3 243) math:product 729 . + (729 1) math:sum 730. + }) log:ifThenElseIn (() 1)}] + skolem:lemma594 + [ a r:Fact; r:gives {(243 730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (243 (730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (243 730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma501 a r:Inference; + r:gives { + 244 :collatz (1 (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (244 2) math:remainder 0. + } { + (244 2) math:integerQuotient 122. + } { + (3 244) math:product _:sk_0. + (_:sk_0 1) math:sum 122. + }) log:ifThenElseIn (() 1)}] + skolem:lemma379 + [ a r:Fact; r:gives {(244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (244 (122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma502 a r:Inference; + r:gives { + 245 :collatz (1 (245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (245 2) math:remainder 0. + } { + (245 2) math:integerQuotient 736. + } { + (3 245) math:product 735 . + (735 1) math:sum 736. + }) log:ifThenElseIn (() 1)}] + skolem:lemma595 + [ a r:Fact; r:gives {(245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (245 (736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma503 a r:Inference; + r:gives { + 246 :collatz (1 (246 123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (246 2) math:remainder 0. + } { + (246 2) math:integerQuotient 123. + } { + (3 246) math:product _:sk_0. + (_:sk_0 1) math:sum 123. + }) log:ifThenElseIn (() 1)}] + skolem:lemma380 + [ a r:Fact; r:gives {(246 123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (246 (123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (246 123 370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma504 a r:Inference; + r:gives { + 247 :collatz (1 (247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (247 2) math:remainder 0. + } { + (247 2) math:integerQuotient 742. + } { + (3 247) math:product 741 . + (741 1) math:sum 742. + }) log:ifThenElseIn (() 1)}] + skolem:lemma596 + [ a r:Fact; r:gives {(247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (247 (742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma505 a r:Inference; + r:gives { + 248 :collatz (1 (248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (248 2) math:remainder 0. + } { + (248 2) math:integerQuotient 124. + } { + (3 248) math:product _:sk_0. + (_:sk_0 1) math:sum 124. + }) log:ifThenElseIn (() 1)}] + skolem:lemma381 + [ a r:Fact; r:gives {(248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (248 (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma506 a r:Inference; + r:gives { + 249 :collatz (1 (249 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (249 2) math:remainder 0. + } { + (249 2) math:integerQuotient 748. + } { + (3 249) math:product 747 . + (747 1) math:sum 748. + }) log:ifThenElseIn (() 1)}] + skolem:lemma597 + [ a r:Fact; r:gives {(249 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (249 (748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (249 748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma507 a r:Inference; + r:gives { + 250 :collatz (1 (250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (250 2) math:remainder 0. + } { + (250 2) math:integerQuotient 125. + } { + (3 250) math:product _:sk_0. + (_:sk_0 1) math:sum 125. + }) log:ifThenElseIn (() 1)}] + skolem:lemma382 + [ a r:Fact; r:gives {(250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (250 (125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma508 a r:Inference; + r:gives { + 251 :collatz (1 (251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (251 2) math:remainder 0. + } { + (251 2) math:integerQuotient 754. + } { + (3 251) math:product 753 . + (753 1) math:sum 754. + }) log:ifThenElseIn (() 1)}] + skolem:lemma598 + [ a r:Fact; r:gives {(251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (251 (754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma509 a r:Inference; + r:gives { + 252 :collatz (1 (252 126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (252 2) math:remainder 0. + } { + (252 2) math:integerQuotient 126. + } { + (3 252) math:product _:sk_0. + (_:sk_0 1) math:sum 126. + }) log:ifThenElseIn (() 1)}] + skolem:lemma383 + [ a r:Fact; r:gives {(252 126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (252 (126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (252 126 63 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma510 a r:Inference; + r:gives { + 253 :collatz (1 (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (253 2) math:remainder 0. + } { + (253 2) math:integerQuotient 760. + } { + (3 253) math:product 759 . + (759 1) math:sum 760. + }) log:ifThenElseIn (() 1)}] + skolem:lemma599 + [ a r:Fact; r:gives {(253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (253 (760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma511 a r:Inference; + r:gives { + 254 :collatz (1 (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (254 2) math:remainder 0. + } { + (254 2) math:integerQuotient 127. + } { + (3 254) math:product _:sk_0. + (_:sk_0 1) math:sum 127. + }) log:ifThenElseIn (() 1)}] + skolem:lemma384 + [ a r:Fact; r:gives {(254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (254 (127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma512 a r:Inference; + r:gives { + 255 :collatz (1 (255 766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (255 2) math:remainder 0. + } { + (255 2) math:integerQuotient 766. + } { + (3 255) math:product 765 . + (765 1) math:sum 766. + }) log:ifThenElseIn (() 1)}] + skolem:lemma600 + [ a r:Fact; r:gives {(255 766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (255 (766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (255 766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma513 a r:Inference; + r:gives { + 256 :collatz (1 (256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (256 2) math:remainder 0. + } { + (256 2) math:integerQuotient 128. + } { + (3 256) math:product _:sk_0. + (_:sk_0 1) math:sum 128. + }) log:ifThenElseIn (() 1)}] + skolem:lemma385 + [ a r:Fact; r:gives {(256 128 64 32 16 8 4 2 1) list:firstRest (256 (128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma514 a r:Extraction; + r:gives { + @forSome var:x_0. { + var:x_0 :collatz (var:x_0 (var:x_0)). + } <= { + true log:callWithCut true. + }. + }; + r:because [ a r:Parsing; r:source ]. + +skolem:lemma515 a r:Extraction; + r:gives { + @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4, var:x_5, var:x_6. { + var:x_0 :collatz (var:x_4 var:x_6). + } <= { + ({ + (var:x_0 2) math:remainder 0. + } { + (var:x_0 2) math:integerQuotient var:x_1. + } { + (3 var:x_0) math:product var:x_2. + (var:x_2 1) math:sum var:x_1. + }) log:ifThenElseIn var:x_3. + var:x_1 :collatz (var:x_4 var:x_5). + var:x_6 list:firstRest (var:x_0 var:x_5). + }. + }; + r:because [ a r:Parsing; r:source ]. + +skolem:lemma516 a r:Inference; + r:gives { + 262 :collatz (1 (262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (262 2) math:remainder 0. + } { + (262 2) math:integerQuotient 131. + } { + (3 262) math:product _:sk_0. + (_:sk_0 1) math:sum 131. + }) log:ifThenElseIn (() 1)}] + skolem:lemma388 + [ a r:Fact; r:gives {(262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (262 (131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (262 131 394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma517 a r:Inference; + r:gives { + 268 :collatz (1 (268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (268 2) math:remainder 0. + } { + (268 2) math:integerQuotient 134. + } { + (3 268) math:product _:sk_0. + (_:sk_0 1) math:sum 134. + }) log:ifThenElseIn (() 1)}] + skolem:lemma391 + [ a r:Fact; r:gives {(268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (268 (134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma518 a r:Inference; + r:gives { + 274 :collatz (1 (274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (274 2) math:remainder 0. + } { + (274 2) math:integerQuotient 137. + } { + (3 274) math:product _:sk_0. + (_:sk_0 1) math:sum 137. + }) log:ifThenElseIn (() 1)}] + skolem:lemma394 + [ a r:Fact; r:gives {(274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (274 (137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 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"http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (280 140 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma520 a r:Inference; + r:gives { + 286 :collatz (1 (286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (286 2) math:remainder 0. + } { + (286 2) math:integerQuotient 143. + } { + (3 286) math:product _:sk_0. + (_:sk_0 1) math:sum 143. + }) log:ifThenElseIn (() 1)}] + skolem:lemma400 + [ a r:Fact; r:gives {(286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (286 (143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma521 a r:Inference; + r:gives { + 292 :collatz (1 (292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (292 2) math:remainder 0. + } { + (292 2) math:integerQuotient 146. + } { + (3 292) math:product _:sk_0. + (_:sk_0 1) math:sum 146. + }) log:ifThenElseIn (() 1)}] + skolem:lemma403 + [ a r:Fact; r:gives {(292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (292 (146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma522 a r:Inference; + r:gives { + 298 :collatz (1 (298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (298 2) math:remainder 0. + } { + (298 2) math:integerQuotient 149. + } { + (3 298) math:product _:sk_0. + (_:sk_0 1) math:sum 149. + }) log:ifThenElseIn (() 1)}] + skolem:lemma406 + [ a r:Fact; r:gives {(298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (298 (149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma523 a r:Inference; + r:gives { + 304 :collatz (1 (304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (304 2) math:remainder 0. + } { + (304 2) math:integerQuotient 152. + } { + (3 304) math:product _:sk_0. + (_:sk_0 1) math:sum 152. + }) log:ifThenElseIn (() 1)}] + skolem:lemma409 + [ a r:Fact; r:gives {(304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (304 (152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma524 a r:Inference; + r:gives { + 310 :collatz (1 (310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (310 2) math:remainder 0. + } { + (310 2) math:integerQuotient 155. + } { + (3 310) math:product _:sk_0. + (_:sk_0 1) math:sum 155. + }) log:ifThenElseIn (() 1)}] + skolem:lemma412 + [ a r:Fact; r:gives {(310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (310 (155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma525 a r:Inference; + r:gives { + 316 :collatz (1 (316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (316 2) math:remainder 0. + } { + (316 2) math:integerQuotient 158. + } { + (3 316) math:product _:sk_0. + (_:sk_0 1) math:sum 158. + }) log:ifThenElseIn (() 1)}] + skolem:lemma415 + [ a r:Fact; r:gives {(316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (316 (158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (316 158 79 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma526 a r:Inference; + r:gives { + 322 :collatz (1 (322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (322 2) math:remainder 0. + } { + (322 2) math:integerQuotient 161. + } { + (3 322) math:product _:sk_0. + (_:sk_0 1) math:sum 161. + }) log:ifThenElseIn (() 1)}] + skolem:lemma418 + [ a r:Fact; r:gives {(322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (322 (161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma527 a r:Inference; + r:gives { + 328 :collatz (1 (328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (328 2) math:remainder 0. + } { + (328 2) math:integerQuotient 164. + } { + (3 328) math:product _:sk_0. + (_:sk_0 1) math:sum 164. + }) log:ifThenElseIn (() 1)}] + skolem:lemma421 + [ a r:Fact; r:gives {(328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (328 (164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma528 a r:Inference; + r:gives { + 334 :collatz (1 (334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (334 2) math:remainder 0. + } { + (334 2) math:integerQuotient 167. + } { + (3 334) math:product _:sk_0. + (_:sk_0 1) math:sum 167. + }) log:ifThenElseIn (() 1)}] + skolem:lemma424 + [ a r:Fact; r:gives {(334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (334 (167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma529 a r:Inference; + r:gives { + 340 :collatz (1 (340 170 85 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (340 2) math:remainder 0. + } { + (340 2) math:integerQuotient 170. + } { + (3 340) math:product _:sk_0. + (_:sk_0 1) math:sum 170. + }) log:ifThenElseIn (() 1)}] + skolem:lemma427 + [ a r:Fact; r:gives {(340 170 85 256 128 64 32 16 8 4 2 1) list:firstRest (340 (170 85 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (170 85 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (340 170 85 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma530 a r:Inference; + r:gives { + 346 :collatz (1 (346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (346 2) math:remainder 0. + } { + (346 2) math:integerQuotient 173. + } { + (3 346) math:product _:sk_0. + (_:sk_0 1) math:sum 173. + }) log:ifThenElseIn (() 1)}] + skolem:lemma430 + [ a r:Fact; r:gives {(346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (346 (173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma531 a r:Inference; + r:gives { + 352 :collatz (1 (352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (352 2) math:remainder 0. + } { + (352 2) math:integerQuotient 176. + } { + (3 352) math:product _:sk_0. + (_:sk_0 1) math:sum 176. + }) log:ifThenElseIn (() 1)}] + skolem:lemma433 + [ a r:Fact; r:gives {(352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (352 (176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (352 176 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma532 a r:Inference; + r:gives { + 358 :collatz (1 (358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (358 2) math:remainder 0. + } { + (358 2) math:integerQuotient 179. + } { + (3 358) math:product _:sk_0. + (_:sk_0 1) math:sum 179. + }) log:ifThenElseIn (() 1)}] + skolem:lemma436 + [ a r:Fact; r:gives {(358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (358 (179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma533 a r:Inference; + r:gives { + 364 :collatz (1 (364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (364 2) math:remainder 0. + } { + (364 2) math:integerQuotient 182. + } { + (3 364) math:product _:sk_0. + (_:sk_0 1) math:sum 182. + }) log:ifThenElseIn (() 1)}] + skolem:lemma439 + [ a r:Fact; r:gives {(364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (364 (182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma534 a r:Inference; + r:gives { + 370 :collatz (1 (370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (370 2) math:remainder 0. + } { + (370 2) math:integerQuotient 185. + } { + (3 370) math:product _:sk_0. + (_:sk_0 1) math:sum 185. + }) log:ifThenElseIn (() 1)}] + skolem:lemma442 + [ a r:Fact; r:gives {(370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (370 (185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (370 185 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma535 a r:Inference; + r:gives { + 376 :collatz (1 (376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (376 2) math:remainder 0. + } { + (376 2) math:integerQuotient 188. + } { + (3 376) math:product _:sk_0. + (_:sk_0 1) math:sum 188. + }) log:ifThenElseIn (() 1)}] + skolem:lemma445 + [ a r:Fact; r:gives {(376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (376 (188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma536 a r:Inference; + r:gives { + 382 :collatz (1 (382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (382 2) math:remainder 0. + } { + (382 2) math:integerQuotient 191. + } { + (3 382) math:product _:sk_0. + (_:sk_0 1) math:sum 191. + }) log:ifThenElseIn (() 1)}] + skolem:lemma448 + [ a r:Fact; r:gives {(382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (382 (191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma537 a r:Inference; + r:gives { + 388 :collatz (1 (388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (388 2) math:remainder 0. + } { + (388 2) math:integerQuotient 194. + } { + (3 388) math:product _:sk_0. + (_:sk_0 1) math:sum 194. + }) log:ifThenElseIn (() 1)}] + skolem:lemma451 + [ a r:Fact; r:gives {(388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (388 (194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma538 a r:Inference; + r:gives { + 394 :collatz (1 (394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (394 2) math:remainder 0. + } { + (394 2) math:integerQuotient 197. + } { + (3 394) math:product _:sk_0. + (_:sk_0 1) math:sum 197. + }) log:ifThenElseIn (() 1)}] + skolem:lemma454 + [ a r:Fact; r:gives {(394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (394 (197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (394 197 592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma539 a r:Inference; + r:gives { + 400 :collatz (1 (400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (400 2) math:remainder 0. + } { + (400 2) math:integerQuotient 200. + } { + (3 400) math:product _:sk_0. + (_:sk_0 1) math:sum 200. + }) log:ifThenElseIn (() 1)}] + skolem:lemma457 + [ a r:Fact; r:gives {(400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (400 (200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma540 a r:Inference; + r:gives { + 406 :collatz (1 (406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (406 2) math:remainder 0. + } { + (406 2) math:integerQuotient 203. + } { + (3 406) math:product _:sk_0. + (_:sk_0 1) math:sum 203. + }) log:ifThenElseIn (() 1)}] + skolem:lemma460 + [ a r:Fact; r:gives {(406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (406 (203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (406 203 610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma541 a r:Inference; + r:gives { + 412 :collatz (1 (412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (412 2) math:remainder 0. + } { + (412 2) math:integerQuotient 206. + } { + (3 412) math:product _:sk_0. + (_:sk_0 1) math:sum 206. + }) log:ifThenElseIn (() 1)}] + skolem:lemma463 + [ a r:Fact; r:gives {(412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (412 (206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma542 a r:Inference; + r:gives { + 418 :collatz (1 (418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (418 2) math:remainder 0. + } { + (418 2) math:integerQuotient 209. + } { + (3 418) math:product _:sk_0. + (_:sk_0 1) math:sum 209. + }) log:ifThenElseIn (() 1)}] + skolem:lemma466 + [ a r:Fact; r:gives {(418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (418 (209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma543 a r:Inference; + r:gives { + 424 :collatz (1 (424 212 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (424 2) math:remainder 0. + } { + (424 2) math:integerQuotient 212. + } { + (3 424) math:product _:sk_0. + (_:sk_0 1) math:sum 212. + }) log:ifThenElseIn (() 1)}] + skolem:lemma469 + [ a r:Fact; r:gives {(424 212 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (424 (212 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (212 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (424 212 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma544 a r:Inference; + r:gives { + 430 :collatz (1 (430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (430 2) math:remainder 0. + } { + (430 2) math:integerQuotient 215. + } { + (3 430) math:product _:sk_0. + (_:sk_0 1) math:sum 215. + }) log:ifThenElseIn (() 1)}] + skolem:lemma472 + [ a r:Fact; r:gives {(430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (430 (215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma545 a r:Inference; + r:gives { + 436 :collatz (1 (436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (436 2) math:remainder 0. + } { + (436 2) math:integerQuotient 218. + } { + (3 436) math:product _:sk_0. + (_:sk_0 1) math:sum 218. + }) log:ifThenElseIn (() 1)}] + skolem:lemma475 + [ a r:Fact; r:gives {(436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (436 (218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma546 a r:Inference; + r:gives { + 442 :collatz (1 (442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (442 2) math:remainder 0. + } { + (442 2) math:integerQuotient 221. + } { + (3 442) math:product _:sk_0. + (_:sk_0 1) math:sum 221. + }) log:ifThenElseIn (() 1)}] + skolem:lemma478 + [ a r:Fact; r:gives {(442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (442 (221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (442 221 664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma547 a r:Inference; + r:gives { + 448 :collatz (1 (448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (448 2) math:remainder 0. + } { + (448 2) math:integerQuotient 224. + } { + (3 448) math:product _:sk_0. + (_:sk_0 1) math:sum 224. + }) log:ifThenElseIn (() 1)}] + skolem:lemma481 + [ a r:Fact; r:gives {(448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (448 (224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma548 a r:Inference; + r:gives { + 454 :collatz (1 (454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (454 2) math:remainder 0. + } { + (454 2) math:integerQuotient 227. + } { + (3 454) math:product _:sk_0. + (_:sk_0 1) math:sum 227. + }) log:ifThenElseIn (() 1)}] + skolem:lemma484 + [ a r:Fact; r:gives {(454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (454 (227 682 341 1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma549 a r:Inference; + r:gives { + 460 :collatz (1 (460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (460 2) math:remainder 0. + } { + (460 2) math:integerQuotient 230. + } { + (3 460) math:product _:sk_0. + (_:sk_0 1) math:sum 230. + }) log:ifThenElseIn (() 1)}] + skolem:lemma487 + [ a r:Fact; r:gives {(460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (460 (230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (460 230 115 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma550 a r:Inference; + r:gives { + 466 :collatz (1 (466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (466 2) math:remainder 0. + } { + (466 2) math:integerQuotient 233. + } { + (3 466) math:product _:sk_0. + (_:sk_0 1) math:sum 233. + }) log:ifThenElseIn (() 1)}] + skolem:lemma490 + [ a r:Fact; r:gives {(466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (466 (233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma551 a r:Inference; + r:gives { + 472 :collatz (1 (472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (472 2) math:remainder 0. + } { + (472 2) math:integerQuotient 236. + } { + (3 472) math:product _:sk_0. + (_:sk_0 1) math:sum 236. + }) log:ifThenElseIn (() 1)}] + skolem:lemma493 + [ a r:Fact; r:gives {(472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (472 (236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma552 a r:Inference; + r:gives { + 478 :collatz (1 (478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (478 2) math:remainder 0. + } { + (478 2) math:integerQuotient 239. + } { + (3 478) math:product _:sk_0. + (_:sk_0 1) math:sum 239. + }) log:ifThenElseIn (() 1)}] + skolem:lemma496 + [ a r:Fact; r:gives {(478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (478 (239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (478 239 718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma553 a r:Inference; + r:gives { + 484 :collatz (1 (484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (484 2) math:remainder 0. + } { + (484 2) math:integerQuotient 242. + } { + (3 484) math:product _:sk_0. + (_:sk_0 1) math:sum 242. + }) log:ifThenElseIn (() 1)}] + skolem:lemma499 + [ a r:Fact; r:gives {(484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (484 (242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma554 a r:Inference; + r:gives { + 490 :collatz (1 (490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (490 2) math:remainder 0. + } { + (490 2) math:integerQuotient 245. + } { + (3 490) math:product _:sk_0. + (_:sk_0 1) math:sum 245. + }) log:ifThenElseIn (() 1)}] + skolem:lemma502 + [ a r:Fact; r:gives {(490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (490 (245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma555 a r:Inference; + r:gives { + 496 :collatz (1 (496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (496 2) math:remainder 0. + } { + (496 2) math:integerQuotient 248. + } { + (3 496) math:product _:sk_0. + (_:sk_0 1) math:sum 248. + }) log:ifThenElseIn (() 1)}] + skolem:lemma505 + [ a r:Fact; r:gives {(496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (496 (248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma556 a r:Inference; + r:gives { + 502 :collatz (1 (502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (502 2) math:remainder 0. + } { + (502 2) math:integerQuotient 251. + } { + (3 502) math:product _:sk_0. + (_:sk_0 1) math:sum 251. + }) log:ifThenElseIn (() 1)}] + skolem:lemma508 + [ a r:Fact; r:gives {(502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (502 (251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma557 a r:Inference; + r:gives { + 508 :collatz (1 (508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (508 2) math:remainder 0. + } { + (508 2) math:integerQuotient 254. + } { + (3 508) math:product _:sk_0. + (_:sk_0 1) math:sum 254. + }) log:ifThenElseIn (() 1)}] + skolem:lemma511 + [ a r:Fact; r:gives {(508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (508 (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma558 a r:Inference; + r:gives { + 514 :collatz (1 (514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (514 2) math:remainder 0. + } { + (514 2) math:integerQuotient 257. + } { + (3 514) math:product _:sk_0. + (_:sk_0 1) math:sum 257. + }) log:ifThenElseIn (() 1)}] + skolem:lemma601 + [ a r:Fact; r:gives {(514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (514 (257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (514 257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma559 a r:Inference; + r:gives { + 520 :collatz (1 (520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (520 2) math:remainder 0. + } { + (520 2) math:integerQuotient 260. + } { + (3 520) math:product _:sk_0. + (_:sk_0 1) math:sum 260. + }) log:ifThenElseIn (() 1)}] + skolem:lemma602 + [ a r:Fact; r:gives {(520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (520 (260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma560 a r:Inference; + r:gives { + 526 :collatz (1 (526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (526 2) math:remainder 0. + } { + (526 2) math:integerQuotient 263. + } { + (3 526) math:product _:sk_0. + (_:sk_0 1) math:sum 263. + }) log:ifThenElseIn (() 1)}] + skolem:lemma603 + [ a r:Fact; r:gives {(526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (526 (263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma561 a r:Inference; + r:gives { + 532 :collatz (1 (532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (532 2) math:remainder 0. + } { + (532 2) math:integerQuotient 266. + } { + (3 532) math:product _:sk_0. + (_:sk_0 1) math:sum 266. + }) log:ifThenElseIn (() 1)}] + skolem:lemma604 + [ a r:Fact; r:gives {(532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (532 (266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (532 266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma562 a r:Inference; + r:gives { + 538 :collatz (1 (538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (538 2) math:remainder 0. + } { + (538 2) math:integerQuotient 269. + } { + (3 538) math:product _:sk_0. + (_:sk_0 1) math:sum 269. + }) log:ifThenElseIn (() 1)}] + skolem:lemma605 + [ a r:Fact; r:gives {(538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (538 (269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma563 a r:Inference; + r:gives { + 544 :collatz (1 (544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (544 2) math:remainder 0. + } { + (544 2) math:integerQuotient 272. + } { + (3 544) math:product _:sk_0. + (_:sk_0 1) math:sum 272. + }) log:ifThenElseIn (() 1)}] + skolem:lemma606 + [ a r:Fact; r:gives {(544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (544 (272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma564 a r:Inference; + r:gives { + 550 :collatz (1 (550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (550 2) math:remainder 0. + } { + (550 2) math:integerQuotient 275. + } { + (3 550) math:product _:sk_0. + (_:sk_0 1) math:sum 275. + }) log:ifThenElseIn (() 1)}] + skolem:lemma607 + [ a r:Fact; r:gives {(550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (550 (275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (550 275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma565 a r:Inference; + r:gives { + 556 :collatz (1 (556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (556 2) math:remainder 0. + } { + (556 2) math:integerQuotient 278. + } { + (3 556) math:product _:sk_0. + (_:sk_0 1) math:sum 278. + }) log:ifThenElseIn (() 1)}] + skolem:lemma608 + [ a r:Fact; r:gives {(556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (556 (278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma566 a r:Inference; + r:gives { + 562 :collatz (1 (562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (562 2) math:remainder 0. + } { + (562 2) math:integerQuotient 281. + } { + (3 562) math:product _:sk_0. + (_:sk_0 1) math:sum 281. + }) log:ifThenElseIn (() 1)}] + skolem:lemma609 + [ a r:Fact; r:gives {(562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (562 (281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma567 a r:Inference; + r:gives { + 568 :collatz (1 (568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (568 2) math:remainder 0. + } { + (568 2) math:integerQuotient 284. + } { + (3 568) math:product _:sk_0. + (_:sk_0 1) math:sum 284. + }) log:ifThenElseIn (() 1)}] + skolem:lemma610 + [ a r:Fact; r:gives {(568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (568 (284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma568 a r:Inference; + r:gives { + 574 :collatz (1 (574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (574 2) math:remainder 0. + } { + (574 2) math:integerQuotient 287. + } { + (3 574) math:product _:sk_0. + (_:sk_0 1) math:sum 287. + }) log:ifThenElseIn (() 1)}] + skolem:lemma611 + [ a r:Fact; r:gives {(574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (574 (287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma569 a r:Inference; + r:gives { + 580 :collatz (1 (580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (580 2) math:remainder 0. + } { + (580 2) math:integerQuotient 290. + } { + (3 580) math:product _:sk_0. + (_:sk_0 1) math:sum 290. + }) log:ifThenElseIn (() 1)}] + skolem:lemma612 + [ a r:Fact; r:gives {(580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (580 (290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma570 a r:Inference; + r:gives { + 586 :collatz (1 (586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (586 2) math:remainder 0. + } { + (586 2) math:integerQuotient 293. + } { + (3 586) math:product _:sk_0. + (_:sk_0 1) math:sum 293. + }) log:ifThenElseIn (() 1)}] + skolem:lemma613 + [ a r:Fact; r:gives {(586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (586 (293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma571 a r:Inference; + r:gives { + 592 :collatz (1 (592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (592 2) math:remainder 0. + } { + (592 2) math:integerQuotient 296. + } { + (3 592) math:product _:sk_0. + (_:sk_0 1) math:sum 296. + }) log:ifThenElseIn (() 1)}] + skolem:lemma614 + [ a r:Fact; r:gives {(592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (592 (296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (592 296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma572 a r:Inference; + r:gives { + 598 :collatz (1 (598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (598 2) math:remainder 0. + } { + (598 2) math:integerQuotient 299. + } { + (3 598) math:product _:sk_0. + (_:sk_0 1) math:sum 299. + }) log:ifThenElseIn (() 1)}] + skolem:lemma615 + [ a r:Fact; r:gives {(598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (598 (299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma573 a r:Inference; + r:gives { + 604 :collatz (1 (604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (604 2) math:remainder 0. + } { + (604 2) math:integerQuotient 302. + } { + (3 604) math:product _:sk_0. + (_:sk_0 1) math:sum 302. + }) log:ifThenElseIn (() 1)}] + skolem:lemma616 + [ a r:Fact; r:gives {(604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (604 (302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (604 302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma574 a r:Inference; + r:gives { + 610 :collatz (1 (610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (610 2) math:remainder 0. + } { + (610 2) math:integerQuotient 305. + } { + (3 610) math:product _:sk_0. + (_:sk_0 1) math:sum 305. + }) log:ifThenElseIn (() 1)}] + skolem:lemma617 + [ a r:Fact; r:gives {(610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (610 (305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (610 305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma575 a r:Inference; + r:gives { + 616 :collatz (1 (616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (616 2) math:remainder 0. + } { + (616 2) math:integerQuotient 308. + } { + (3 616) math:product _:sk_0. + (_:sk_0 1) math:sum 308. + }) log:ifThenElseIn (() 1)}] + skolem:lemma618 + [ a r:Fact; r:gives {(616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (616 (308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma576 a r:Inference; + r:gives { + 622 :collatz (1 (622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (622 2) math:remainder 0. + } { + (622 2) math:integerQuotient 311. + } { + (3 622) math:product _:sk_0. + (_:sk_0 1) math:sum 311. + }) log:ifThenElseIn (() 1)}] + skolem:lemma619 + [ a r:Fact; r:gives {(622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (622 (311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (622 311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma577 a r:Inference; + r:gives { + 628 :collatz (1 (628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (628 2) math:remainder 0. + } { + (628 2) math:integerQuotient 314. + } { + (3 628) math:product _:sk_0. + (_:sk_0 1) math:sum 314. + }) log:ifThenElseIn (() 1)}] + skolem:lemma620 + [ a r:Fact; r:gives {(628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (628 (314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma578 a r:Inference; + r:gives { + 634 :collatz (1 (634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (634 2) math:remainder 0. + } { + (634 2) math:integerQuotient 317. + } { + (3 634) math:product _:sk_0. + (_:sk_0 1) math:sum 317. + }) log:ifThenElseIn (() 1)}] + skolem:lemma621 + [ a r:Fact; r:gives {(634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (634 (317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma579 a r:Inference; + r:gives { + 640 :collatz (1 (640 320 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (640 2) math:remainder 0. + } { + (640 2) math:integerQuotient 320. + } { + (3 640) math:product _:sk_0. + (_:sk_0 1) math:sum 320. + }) log:ifThenElseIn (() 1)}] + skolem:lemma622 + [ a r:Fact; r:gives {(640 320 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (640 (320 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (320 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (640 320 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma580 a r:Inference; + r:gives { + 646 :collatz (1 (646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (646 2) math:remainder 0. + } { + (646 2) math:integerQuotient 323. + } { + (3 646) math:product _:sk_0. + (_:sk_0 1) math:sum 323. + }) log:ifThenElseIn (() 1)}] + skolem:lemma623 + [ a r:Fact; r:gives {(646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (646 (323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma581 a r:Inference; + r:gives { + 652 :collatz (1 (652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (652 2) math:remainder 0. + } { + (652 2) math:integerQuotient 326. + } { + (3 652) math:product _:sk_0. + (_:sk_0 1) math:sum 326. + }) log:ifThenElseIn (() 1)}] + skolem:lemma624 + [ a r:Fact; r:gives {(652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (652 (326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (652 326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma582 a r:Inference; + r:gives { + 658 :collatz (1 (658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (658 2) math:remainder 0. + } { + (658 2) math:integerQuotient 329. + } { + (3 658) math:product _:sk_0. + (_:sk_0 1) math:sum 329. + }) log:ifThenElseIn (() 1)}] + skolem:lemma625 + [ a r:Fact; r:gives {(658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (658 (329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (658 329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma583 a r:Inference; + r:gives { + 664 :collatz (1 (664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (664 2) math:remainder 0. + } { + (664 2) math:integerQuotient 332. + } { + (3 664) math:product _:sk_0. + (_:sk_0 1) math:sum 332. + }) log:ifThenElseIn (() 1)}] + skolem:lemma626 + [ a r:Fact; r:gives {(664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (664 (332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (664 332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma584 a r:Inference; + r:gives { + 670 :collatz (1 (670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (670 2) math:remainder 0. + } { + (670 2) math:integerQuotient 335. + } { + (3 670) math:product _:sk_0. + (_:sk_0 1) math:sum 335. + }) log:ifThenElseIn (() 1)}] + skolem:lemma627 + [ a r:Fact; r:gives {(670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (670 (335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (670 335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma585 a r:Inference; + r:gives { + 676 :collatz (1 (676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (676 2) math:remainder 0. + } { + (676 2) math:integerQuotient 338. + } { + (3 676) math:product _:sk_0. + (_:sk_0 1) math:sum 338. + }) log:ifThenElseIn (() 1)}] + skolem:lemma628 + [ a r:Fact; r:gives {(676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (676 (338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (676 338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma586 a r:Inference; + r:gives { + 682 :collatz (1 (682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (682 2) math:remainder 0. + } { + (682 2) math:integerQuotient 341. + } { + (3 682) math:product _:sk_0. + (_:sk_0 1) math:sum 341. + }) log:ifThenElseIn (() 1)}] + skolem:lemma629 + [ a r:Fact; r:gives {(682 341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (682 (341 1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma587 a r:Inference; + r:gives { + 688 :collatz (1 (688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (688 2) math:remainder 0. + } { + (688 2) math:integerQuotient 344. + } { + (3 688) math:product _:sk_0. + (_:sk_0 1) math:sum 344. + }) log:ifThenElseIn (() 1)}] + skolem:lemma630 + [ a r:Fact; r:gives {(688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (688 (344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma588 a r:Inference; + r:gives { + 694 :collatz (1 (694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (694 2) math:remainder 0. + } { + (694 2) math:integerQuotient 347. + } { + (3 694) math:product _:sk_0. + (_:sk_0 1) math:sum 347. + }) log:ifThenElseIn (() 1)}] + skolem:lemma631 + [ a r:Fact; r:gives {(694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (694 (347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (694 347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma589 a r:Inference; + r:gives { + 700 :collatz (1 (700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (700 2) math:remainder 0. + } { + (700 2) math:integerQuotient 350. + } { + (3 700) math:product _:sk_0. + (_:sk_0 1) math:sum 350. + }) log:ifThenElseIn (() 1)}] + skolem:lemma632 + [ a r:Fact; r:gives {(700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (700 (350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma590 a r:Inference; + r:gives { + 706 :collatz (1 (706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (706 2) math:remainder 0. + } { + (706 2) math:integerQuotient 353. + } { + (3 706) math:product _:sk_0. + (_:sk_0 1) math:sum 353. + }) log:ifThenElseIn (() 1)}] + skolem:lemma633 + [ a r:Fact; r:gives {(706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (706 (353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (706 353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma591 a r:Inference; + r:gives { + 712 :collatz (1 (712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (712 2) math:remainder 0. + } { + (712 2) math:integerQuotient 356. + } { + (3 712) math:product _:sk_0. + (_:sk_0 1) math:sum 356. + }) log:ifThenElseIn (() 1)}] + skolem:lemma634 + [ a r:Fact; r:gives {(712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (712 (356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (712 356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma592 a r:Inference; + r:gives { + 718 :collatz (1 (718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (718 2) math:remainder 0. + } { + (718 2) math:integerQuotient 359. + } { + (3 718) math:product _:sk_0. + (_:sk_0 1) math:sum 359. + }) log:ifThenElseIn (() 1)}] + skolem:lemma635 + [ a r:Fact; r:gives {(718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (718 (359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (718 359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma593 a r:Inference; + r:gives { + 724 :collatz (1 (724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (724 2) math:remainder 0. + } { + (724 2) math:integerQuotient 362. + } { + (3 724) math:product _:sk_0. + (_:sk_0 1) math:sum 362. + }) log:ifThenElseIn (() 1)}] + skolem:lemma636 + [ a r:Fact; r:gives {(724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (724 (362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma594 a r:Inference; + r:gives { + 730 :collatz (1 (730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (730 2) math:remainder 0. + } { + (730 2) math:integerQuotient 365. + } { + (3 730) math:product _:sk_0. + (_:sk_0 1) math:sum 365. + }) log:ifThenElseIn (() 1)}] + skolem:lemma637 + [ a r:Fact; r:gives {(730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (730 (365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (730 365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma595 a r:Inference; + r:gives { + 736 :collatz (1 (736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (736 2) math:remainder 0. + } { + (736 2) math:integerQuotient 368. + } { + (3 736) math:product _:sk_0. + (_:sk_0 1) math:sum 368. + }) log:ifThenElseIn (() 1)}] + skolem:lemma638 + [ a r:Fact; r:gives {(736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (736 (368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma596 a r:Inference; + r:gives { + 742 :collatz (1 (742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (742 2) math:remainder 0. + } { + (742 2) math:integerQuotient 371. + } { + (3 742) math:product _:sk_0. + (_:sk_0 1) math:sum 371. + }) log:ifThenElseIn (() 1)}] + skolem:lemma639 + [ a r:Fact; r:gives {(742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (742 (371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma597 a r:Inference; + r:gives { + 748 :collatz (1 (748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (748 2) math:remainder 0. + } { + (748 2) math:integerQuotient 374. + } { + (3 748) math:product _:sk_0. + (_:sk_0 1) math:sum 374. + }) log:ifThenElseIn (() 1)}] + skolem:lemma640 + [ a r:Fact; r:gives {(748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (748 (374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (748 374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma598 a r:Inference; + r:gives { + 754 :collatz (1 (754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (754 2) math:remainder 0. + } { + (754 2) math:integerQuotient 377. + } { + (3 754) math:product _:sk_0. + (_:sk_0 1) math:sum 377. + }) log:ifThenElseIn (() 1)}] + skolem:lemma641 + [ a r:Fact; r:gives {(754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (754 (377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma599 a r:Inference; + r:gives { + 760 :collatz (1 (760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (760 2) math:remainder 0. + } { + (760 2) math:integerQuotient 380. + } { + (3 760) math:product _:sk_0. + (_:sk_0 1) math:sum 380. + }) log:ifThenElseIn (() 1)}] + skolem:lemma642 + [ a r:Fact; r:gives {(760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (760 (380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma600 a r:Inference; + r:gives { + 766 :collatz (1 (766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (766 2) math:remainder 0. + } { + (766 2) math:integerQuotient 383. + } { + (3 766) math:product _:sk_0. + (_:sk_0 1) math:sum 383. + }) log:ifThenElseIn (() 1)}] + skolem:lemma643 + [ a r:Fact; r:gives {(766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (766 (383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (766 383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma601 a r:Inference; + r:gives { + 257 :collatz (1 (257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (257 2) math:remainder 0. + } { + (257 2) math:integerQuotient 772. + } { + (3 257) math:product 771 . + (771 1) math:sum 772. + }) log:ifThenElseIn (() 1)}] + skolem:lemma644 + [ a r:Fact; r:gives {(257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (257 (772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (257 772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma602 a r:Inference; + r:gives { + 260 :collatz (1 (260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (260 2) math:remainder 0. + } { + (260 2) math:integerQuotient 130. + } { + (3 260) math:product _:sk_0. + (_:sk_0 1) math:sum 130. + }) log:ifThenElseIn (() 1)}] + skolem:lemma387 + [ a r:Fact; r:gives {(260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (260 (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma603 a r:Inference; + r:gives { + 263 :collatz (1 (263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (263 2) math:remainder 0. + } { + (263 2) math:integerQuotient 790. + } { + (3 263) math:product 789 . + (789 1) math:sum 790. + }) log:ifThenElseIn (() 1)}] + skolem:lemma645 + [ a r:Fact; r:gives {(263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (263 (790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma604 a r:Inference; + r:gives { + 266 :collatz (1 (266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (266 2) math:remainder 0. + } { + (266 2) math:integerQuotient 133. + } { + (3 266) math:product _:sk_0. + (_:sk_0 1) math:sum 133. + }) log:ifThenElseIn (() 1)}] + skolem:lemma390 + [ a r:Fact; r:gives {(266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (266 (133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (266 133 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma605 a r:Inference; + r:gives { + 269 :collatz (1 (269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (269 2) math:remainder 0. + } { + (269 2) math:integerQuotient 808. + } { + (3 269) math:product 807 . + (807 1) math:sum 808. + }) log:ifThenElseIn (() 1)}] + skolem:lemma646 + [ a r:Fact; r:gives {(269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (269 (808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma606 a r:Inference; + r:gives { + 272 :collatz (1 (272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (272 2) math:remainder 0. + } { + (272 2) math:integerQuotient 136. + } { + (3 272) math:product _:sk_0. + (_:sk_0 1) math:sum 136. + }) log:ifThenElseIn (() 1)}] + skolem:lemma393 + [ a r:Fact; r:gives {(272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (272 (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma607 a r:Inference; + r:gives { + 275 :collatz (1 (275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (275 2) math:remainder 0. + } { + (275 2) math:integerQuotient 826. + } { + (3 275) math:product 825 . + (825 1) math:sum 826. + }) log:ifThenElseIn (() 1)}] + skolem:lemma647 + [ a r:Fact; r:gives {(275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (275 (826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (275 826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma608 a r:Inference; + r:gives { + 278 :collatz (1 (278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (278 2) math:remainder 0. + } { + (278 2) math:integerQuotient 139. + } { + (3 278) math:product _:sk_0. + (_:sk_0 1) math:sum 139. + }) log:ifThenElseIn (() 1)}] + skolem:lemma396 + [ a r:Fact; r:gives {(278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (278 (139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (278 139 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma609 a r:Inference; + r:gives { + 281 :collatz (1 (281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (281 2) math:remainder 0. + } { + (281 2) math:integerQuotient 844. + } { + (3 281) math:product 843 . + (843 1) math:sum 844. + }) log:ifThenElseIn (() 1)}] + skolem:lemma648 + [ a r:Fact; r:gives {(281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (281 (844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma610 a r:Inference; + r:gives { + 284 :collatz (1 (284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (284 2) math:remainder 0. + } { + (284 2) math:integerQuotient 142. + } { + (3 284) math:product _:sk_0. + (_:sk_0 1) math:sum 142. + }) log:ifThenElseIn (() 1)}] + skolem:lemma399 + [ a r:Fact; r:gives {(284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (284 (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma611 a r:Inference; + r:gives { + 287 :collatz (1 (287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (287 2) math:remainder 0. + } { + (287 2) math:integerQuotient 862. + } { + (3 287) math:product 861 . + (861 1) math:sum 862. + }) log:ifThenElseIn (() 1)}] + skolem:lemma649 + [ a r:Fact; r:gives {(287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (287 (862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma612 a r:Inference; + r:gives { + 290 :collatz (1 (290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (290 2) math:remainder 0. + } { + (290 2) math:integerQuotient 145. + } { + (3 290) math:product _:sk_0. + (_:sk_0 1) math:sum 145. + }) log:ifThenElseIn (() 1)}] + skolem:lemma402 + [ a r:Fact; r:gives {(290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (290 (145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma613 a r:Inference; + r:gives { + 293 :collatz (1 (293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (293 2) math:remainder 0. + } { + (293 2) math:integerQuotient 880. + } { + (3 293) math:product 879 . + (879 1) math:sum 880. + }) log:ifThenElseIn (() 1)}] + skolem:lemma650 + [ a r:Fact; r:gives {(293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (293 (880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma614 a r:Inference; + r:gives { + 296 :collatz (1 (296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (296 2) math:remainder 0. + } { + (296 2) math:integerQuotient 148. + } { + (3 296) math:product _:sk_0. + (_:sk_0 1) math:sum 148. + }) log:ifThenElseIn (() 1)}] + skolem:lemma405 + [ a r:Fact; r:gives {(296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (296 (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (296 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma615 a r:Inference; + r:gives { + 299 :collatz (1 (299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (299 2) math:remainder 0. + } { + (299 2) math:integerQuotient 898. + } { + (3 299) math:product 897 . + (897 1) math:sum 898. + }) log:ifThenElseIn (() 1)}] + skolem:lemma651 + [ a r:Fact; r:gives {(299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (299 (898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma616 a r:Inference; + r:gives { + 302 :collatz (1 (302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (302 2) math:remainder 0. + } { + (302 2) math:integerQuotient 151. + } { + (3 302) math:product _:sk_0. + (_:sk_0 1) math:sum 151. + }) log:ifThenElseIn (() 1)}] + skolem:lemma408 + [ a r:Fact; r:gives {(302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (302 (151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (302 151 454 227 682 341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma617 a r:Inference; + r:gives { + 305 :collatz (1 (305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (305 2) math:remainder 0. + } { + (305 2) math:integerQuotient 916. + } { + (3 305) math:product 915 . + (915 1) math:sum 916. + }) log:ifThenElseIn (() 1)}] + skolem:lemma652 + [ a r:Fact; r:gives {(305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (305 (916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (305 916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma618 a r:Inference; + r:gives { + 308 :collatz (1 (308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (308 2) math:remainder 0. + } { + (308 2) math:integerQuotient 154. + } { + (3 308) math:product _:sk_0. + (_:sk_0 1) math:sum 154. + }) log:ifThenElseIn (() 1)}] + skolem:lemma411 + [ a r:Fact; r:gives {(308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (308 (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma619 a r:Inference; + r:gives { + 311 :collatz (1 (311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (311 2) math:remainder 0. + } { + (311 2) math:integerQuotient 934. + } { + (3 311) math:product 933 . + (933 1) math:sum 934. + }) log:ifThenElseIn (() 1)}] + skolem:lemma653 + [ a r:Fact; r:gives {(311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (311 (934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (311 934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma620 a r:Inference; + r:gives { + 314 :collatz (1 (314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (314 2) math:remainder 0. + } { + (314 2) math:integerQuotient 157. + } { + (3 314) math:product _:sk_0. + (_:sk_0 1) math:sum 157. + }) log:ifThenElseIn (() 1)}] + skolem:lemma414 + [ a r:Fact; r:gives {(314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (314 (157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma621 a r:Inference; + r:gives { + 317 :collatz (1 (317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (317 2) math:remainder 0. + } { + (317 2) math:integerQuotient 952. + } { + (3 317) math:product 951 . + (951 1) math:sum 952. + }) log:ifThenElseIn (() 1)}] + skolem:lemma654 + [ a r:Fact; r:gives {(317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (317 (952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma622 a r:Inference; + r:gives { + 320 :collatz (1 (320 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (320 2) math:remainder 0. + } { + (320 2) math:integerQuotient 160. + } { + (3 320) math:product _:sk_0. + (_:sk_0 1) math:sum 160. + }) log:ifThenElseIn (() 1)}] + skolem:lemma417 + [ a r:Fact; r:gives {(320 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (320 (160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (320 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma623 a r:Inference; + r:gives { + 323 :collatz (1 (323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (323 2) math:remainder 0. + } { + (323 2) math:integerQuotient 970. + } { + (3 323) math:product 969 . + (969 1) math:sum 970. + }) log:ifThenElseIn (() 1)}] + skolem:lemma655 + [ a r:Fact; r:gives {(323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (323 (970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma624 a r:Inference; + r:gives { + 326 :collatz (1 (326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (326 2) math:remainder 0. + } { + (326 2) math:integerQuotient 163. + } { + (3 326) math:product _:sk_0. + (_:sk_0 1) math:sum 163. + }) log:ifThenElseIn (() 1)}] + skolem:lemma420 + [ a r:Fact; r:gives {(326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (326 (163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (326 163 490 245 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma625 a r:Inference; + r:gives { + 329 :collatz (1 (329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (329 2) math:remainder 0. + } { + (329 2) math:integerQuotient 988. + } { + (3 329) math:product 987 . + (987 1) math:sum 988. + }) log:ifThenElseIn (() 1)}] + skolem:lemma656 + [ a r:Fact; r:gives {(329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (329 (988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (329 988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma626 a r:Inference; + r:gives { + 332 :collatz (1 (332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (332 2) math:remainder 0. + } { + (332 2) math:integerQuotient 166. + } { + (3 332) math:product _:sk_0. + (_:sk_0 1) math:sum 166. + }) log:ifThenElseIn (() 1)}] + skolem:lemma423 + [ a r:Fact; r:gives {(332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (332 (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (332 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma627 a r:Inference; + r:gives { + 335 :collatz (1 (335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (335 2) math:remainder 0. + } { + (335 2) math:integerQuotient 1006. + } { + (3 335) math:product 1005 . + (1005 1) math:sum 1006. + }) log:ifThenElseIn (() 1)}] + skolem:lemma657 + [ a r:Fact; r:gives {(335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (335 (1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1005]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (335 1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma628 a r:Inference; + r:gives { + 338 :collatz (1 (338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (338 2) math:remainder 0. + } { + (338 2) math:integerQuotient 169. + } { + (3 338) math:product _:sk_0. + (_:sk_0 1) math:sum 169. + }) log:ifThenElseIn (() 1)}] + skolem:lemma426 + [ a r:Fact; r:gives {(338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (338 (169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (338 169 508 254 127 382 191 574 287 862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma629 a r:Inference; + r:gives { + 341 :collatz (1 (341 1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (341 2) math:remainder 0. + } { + (341 2) math:integerQuotient 1024. + } { + (3 341) math:product 1023 . + (1023 1) math:sum 1024. + }) log:ifThenElseIn (() 1)}] + skolem:lemma658 + [ a r:Fact; r:gives {(341 1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (341 (1024 512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1023]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1024 512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (341 1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma630 a r:Inference; + r:gives { + 344 :collatz (1 (344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (344 2) math:remainder 0. + } { + (344 2) math:integerQuotient 172. + } { + (3 344) math:product _:sk_0. + (_:sk_0 1) math:sum 172. + }) log:ifThenElseIn (() 1)}] + skolem:lemma429 + [ a r:Fact; r:gives {(344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (344 (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma631 a r:Inference; + r:gives { + 347 :collatz (1 (347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (347 2) math:remainder 0. + } { + (347 2) math:integerQuotient 1042. + } { + (3 347) math:product 1041 . + (1041 1) math:sum 1042. + }) log:ifThenElseIn (() 1)}] + skolem:lemma659 + [ a r:Fact; r:gives {(347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (347 (1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1041]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (347 1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma632 a r:Inference; + r:gives { + 350 :collatz (1 (350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (350 2) math:remainder 0. + } { + (350 2) math:integerQuotient 175. + } { + (3 350) math:product _:sk_0. + (_:sk_0 1) math:sum 175. + }) log:ifThenElseIn (() 1)}] + skolem:lemma432 + [ a r:Fact; r:gives {(350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (350 (175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma633 a r:Inference; + r:gives { + 353 :collatz (1 (353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (353 2) math:remainder 0. + } { + (353 2) math:integerQuotient 1060. + } { + (3 353) math:product 1059 . + (1059 1) math:sum 1060. + }) log:ifThenElseIn (() 1)}] + skolem:lemma660 + [ a r:Fact; r:gives {(353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (353 (1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1060]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1059]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (353 1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma634 a r:Inference; + r:gives { + 356 :collatz (1 (356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (356 2) math:remainder 0. + } { + (356 2) math:integerQuotient 178. + } { + (3 356) math:product _:sk_0. + (_:sk_0 1) math:sum 178. + }) log:ifThenElseIn (() 1)}] + skolem:lemma435 + [ a r:Fact; r:gives {(356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (356 (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (356 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma635 a r:Inference; + r:gives { + 359 :collatz (1 (359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (359 2) math:remainder 0. + } { + (359 2) math:integerQuotient 1078. + } { + (3 359) math:product 1077 . + (1077 1) math:sum 1078. + }) log:ifThenElseIn (() 1)}] + skolem:lemma661 + [ a r:Fact; r:gives {(359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (359 (1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (359 1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma636 a r:Inference; + r:gives { + 362 :collatz (1 (362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (362 2) math:remainder 0. + } { + (362 2) math:integerQuotient 181. + } { + (3 362) math:product _:sk_0. + (_:sk_0 1) math:sum 181. + }) log:ifThenElseIn (() 1)}] + skolem:lemma438 + [ a r:Fact; r:gives {(362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (362 (181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma637 a r:Inference; + r:gives { + 365 :collatz (1 (365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (365 2) math:remainder 0. + } { + (365 2) math:integerQuotient 1096. + } { + (3 365) math:product 1095 . + (1095 1) math:sum 1096. + }) log:ifThenElseIn (() 1)}] + skolem:lemma662 + [ a r:Fact; r:gives {(365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (365 (1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1095]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (365 1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma638 a r:Inference; + r:gives { + 368 :collatz (1 (368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (368 2) math:remainder 0. + } { + (368 2) math:integerQuotient 184. + } { + (3 368) math:product _:sk_0. + (_:sk_0 1) math:sum 184. + }) log:ifThenElseIn (() 1)}] + skolem:lemma441 + [ a r:Fact; r:gives {(368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (368 (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma639 a r:Inference; + r:gives { + 371 :collatz (1 (371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (371 2) math:remainder 0. + } { + (371 2) math:integerQuotient 1114. + } { + (3 371) math:product 1113 . + (1113 1) math:sum 1114. + }) log:ifThenElseIn (() 1)}] + skolem:lemma663 + [ a r:Fact; r:gives {(371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (371 (1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma640 a r:Inference; + r:gives { + 374 :collatz (1 (374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (374 2) math:remainder 0. + } { + (374 2) math:integerQuotient 187. + } { + (3 374) math:product _:sk_0. + (_:sk_0 1) math:sum 187. + }) log:ifThenElseIn (() 1)}] + skolem:lemma444 + [ a r:Fact; r:gives {(374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (374 (187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (374 187 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma641 a r:Inference; + r:gives { + 377 :collatz (1 (377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (377 2) math:remainder 0. + } { + (377 2) math:integerQuotient 1132. + } { + (3 377) math:product 1131 . + (1131 1) math:sum 1132. + }) log:ifThenElseIn (() 1)}] + skolem:lemma664 + [ a r:Fact; r:gives {(377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (377 (1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma642 a r:Inference; + r:gives { + 380 :collatz (1 (380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (380 2) math:remainder 0. + } { + (380 2) math:integerQuotient 190. + } { + (3 380) math:product _:sk_0. + (_:sk_0 1) math:sum 190. + }) log:ifThenElseIn (() 1)}] + skolem:lemma447 + [ a r:Fact; r:gives {(380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (380 (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma643 a r:Inference; + r:gives { + 383 :collatz (1 (383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (383 2) math:remainder 0. + } { + (383 2) math:integerQuotient 1150. + } { + (3 383) math:product 1149 . + (1149 1) math:sum 1150. + }) log:ifThenElseIn (() 1)}] + skolem:lemma665 + [ a r:Fact; r:gives {(383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (383 (1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (383 1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma644 a r:Inference; + r:gives { + 772 :collatz (1 (772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (772 2) math:remainder 0. + } { + (772 2) math:integerQuotient 386. + } { + (3 772) math:product _:sk_0. + (_:sk_0 1) math:sum 386. + }) log:ifThenElseIn (() 1)}] + skolem:lemma666 + [ a r:Fact; r:gives {(772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (772 (386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (772 386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma645 a r:Inference; + r:gives { + 790 :collatz (1 (790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (790 2) math:remainder 0. + } { + (790 2) math:integerQuotient 395. + } { + (3 790) math:product _:sk_0. + (_:sk_0 1) math:sum 395. + }) log:ifThenElseIn (() 1)}] + skolem:lemma667 + [ a r:Fact; r:gives {(790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (790 (395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma646 a r:Inference; + r:gives { + 808 :collatz (1 (808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (808 2) math:remainder 0. + } { + (808 2) math:integerQuotient 404. + } { + (3 808) math:product _:sk_0. + (_:sk_0 1) math:sum 404. + }) log:ifThenElseIn (() 1)}] + skolem:lemma668 + [ a r:Fact; r:gives {(808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (808 (404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma647 a r:Inference; + r:gives { + 826 :collatz (1 (826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (826 2) math:remainder 0. + } { + (826 2) math:integerQuotient 413. + } { + (3 826) math:product _:sk_0. + (_:sk_0 1) math:sum 413. + }) log:ifThenElseIn (() 1)}] + skolem:lemma669 + [ a r:Fact; r:gives {(826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (826 (413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (826 413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma648 a r:Inference; + r:gives { + 844 :collatz (1 (844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (844 2) math:remainder 0. + } { + (844 2) math:integerQuotient 422. + } { + (3 844) math:product _:sk_0. + (_:sk_0 1) math:sum 422. + }) log:ifThenElseIn (() 1)}] + skolem:lemma670 + [ a r:Fact; r:gives {(844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (844 (422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma649 a r:Inference; + r:gives { + 862 :collatz (1 (862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (862 2) math:remainder 0. + } { + (862 2) math:integerQuotient 431. + } { + (3 862) math:product _:sk_0. + (_:sk_0 1) math:sum 431. + }) log:ifThenElseIn (() 1)}] + skolem:lemma671 + [ a r:Fact; r:gives {(862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (862 (431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (862 431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma650 a r:Inference; + r:gives { + 880 :collatz (1 (880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (880 2) math:remainder 0. + } { + (880 2) math:integerQuotient 440. + } { + (3 880) math:product _:sk_0. + (_:sk_0 1) math:sum 440. + }) log:ifThenElseIn (() 1)}] + skolem:lemma672 + [ a r:Fact; r:gives {(880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (880 (440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma651 a r:Inference; + r:gives { + 898 :collatz (1 (898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (898 2) math:remainder 0. + } { + (898 2) math:integerQuotient 449. + } { + (3 898) math:product _:sk_0. + (_:sk_0 1) math:sum 449. + }) log:ifThenElseIn (() 1)}] + skolem:lemma673 + [ a r:Fact; r:gives {(898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (898 (449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma652 a r:Inference; + r:gives { + 916 :collatz (1 (916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (916 2) math:remainder 0. + } { + (916 2) math:integerQuotient 458. + } { + (3 916) math:product _:sk_0. + (_:sk_0 1) math:sum 458. + }) log:ifThenElseIn (() 1)}] + skolem:lemma674 + [ a r:Fact; r:gives {(916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (916 (458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (916 458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma653 a r:Inference; + r:gives { + 934 :collatz (1 (934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (934 2) math:remainder 0. + } { + (934 2) math:integerQuotient 467. + } { + (3 934) math:product _:sk_0. + (_:sk_0 1) math:sum 467. + }) log:ifThenElseIn (() 1)}] + skolem:lemma675 + [ a r:Fact; r:gives {(934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (934 (467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (934 467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma654 a r:Inference; + r:gives { + 952 :collatz (1 (952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (952 2) math:remainder 0. + } { + (952 2) math:integerQuotient 476. + } { + (3 952) math:product _:sk_0. + (_:sk_0 1) math:sum 476. + }) log:ifThenElseIn (() 1)}] + skolem:lemma676 + [ a r:Fact; r:gives {(952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (952 (476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma655 a r:Inference; + r:gives { + 970 :collatz (1 (970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (970 2) math:remainder 0. + } { + (970 2) math:integerQuotient 485. + } { + (3 970) math:product _:sk_0. + (_:sk_0 1) math:sum 485. + }) log:ifThenElseIn (() 1)}] + skolem:lemma677 + [ a r:Fact; r:gives {(970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (970 (485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma656 a r:Inference; + r:gives { + 988 :collatz (1 (988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (988 2) math:remainder 0. + } { + (988 2) math:integerQuotient 494. + } { + (3 988) math:product _:sk_0. + (_:sk_0 1) math:sum 494. + }) log:ifThenElseIn (() 1)}] + skolem:lemma678 + [ a r:Fact; r:gives {(988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (988 (494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (988 494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma657 a r:Inference; + r:gives { + 1006 :collatz (1 (1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1006 2) math:remainder 0. + } { + (1006 2) math:integerQuotient 503. + } { + (3 1006) math:product _:sk_0. + (_:sk_0 1) math:sum 503. + }) log:ifThenElseIn (() 1)}] + skolem:lemma679 + [ a r:Fact; r:gives {(1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1006 (503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1006 503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma658 a r:Inference; + r:gives { + 1024 :collatz (1 (1024 512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1024 2) math:remainder 0. + } { + (1024 2) math:integerQuotient 512. + } { + (3 1024) math:product _:sk_0. + (_:sk_0 1) math:sum 512. + }) log:ifThenElseIn (() 1)}] + skolem:lemma680 + [ a r:Fact; r:gives {(1024 512 256 128 64 32 16 8 4 2 1) list:firstRest (1024 (512 256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (512 256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1024 512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma659 a r:Inference; + r:gives { + 1042 :collatz (1 (1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1042 2) math:remainder 0. + } { + (1042 2) math:integerQuotient 521. + } { + (3 1042) math:product _:sk_0. + (_:sk_0 1) math:sum 521. + }) log:ifThenElseIn (() 1)}] + skolem:lemma681 + [ a r:Fact; r:gives {(1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1042 (521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1042 521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma660 a r:Inference; + r:gives { + 1060 :collatz (1 (1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1060 2) math:remainder 0. + } { + (1060 2) math:integerQuotient 530. + } { + (3 1060) math:product _:sk_0. + (_:sk_0 1) math:sum 530. + }) log:ifThenElseIn (() 1)}] + skolem:lemma682 + [ a r:Fact; r:gives {(1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1060 (530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1060]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1060 530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma661 a r:Inference; + r:gives { + 1078 :collatz (1 (1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1078 2) math:remainder 0. + } { + (1078 2) math:integerQuotient 539. + } { + (3 1078) math:product _:sk_0. + (_:sk_0 1) math:sum 539. + }) log:ifThenElseIn (() 1)}] + skolem:lemma683 + [ a r:Fact; r:gives {(1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1078 (539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1078 539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma662 a r:Inference; + r:gives { + 1096 :collatz (1 (1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1096 2) math:remainder 0. + } { + (1096 2) math:integerQuotient 548. + } { + (3 1096) math:product _:sk_0. + (_:sk_0 1) math:sum 548. + }) log:ifThenElseIn (() 1)}] + skolem:lemma684 + [ a r:Fact; r:gives {(1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1096 (548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1096 548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 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r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma664 a r:Inference; + r:gives { + 1132 :collatz (1 (1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1132 2) math:remainder 0. + } { + (1132 2) math:integerQuotient 566. + } { + (3 1132) math:product _:sk_0. + (_:sk_0 1) math:sum 566. + }) log:ifThenElseIn (() 1)}] + skolem:lemma686 + [ a r:Fact; r:gives {(1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1132 (566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma665 a r:Inference; + r:gives { + 1150 :collatz (1 (1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1150 2) math:remainder 0. + } { + (1150 2) math:integerQuotient 575. + } { + (3 1150) math:product _:sk_0. + (_:sk_0 1) math:sum 575. + }) log:ifThenElseIn (() 1)}] + skolem:lemma687 + [ a r:Fact; r:gives {(1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1150 (575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1150 575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma666 a r:Inference; + r:gives { + 386 :collatz (1 (386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (386 2) math:remainder 0. + } { + (386 2) math:integerQuotient 193. + } { + (3 386) math:product _:sk_0. + (_:sk_0 1) math:sum 193. + }) log:ifThenElseIn (() 1)}] + skolem:lemma450 + [ a r:Fact; r:gives {(386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (386 (193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (386 193 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma667 a r:Inference; + r:gives { + 395 :collatz (1 (395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (395 2) math:remainder 0. + } { + (395 2) math:integerQuotient 1186. + } { + (3 395) math:product 1185 . + (1185 1) math:sum 1186. + }) log:ifThenElseIn (() 1)}] + skolem:lemma688 + [ a r:Fact; r:gives {(395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (395 (1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma668 a r:Inference; + r:gives { + 404 :collatz (1 (404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (404 2) math:remainder 0. + } { + (404 2) math:integerQuotient 202. + } { + (3 404) math:product _:sk_0. + (_:sk_0 1) math:sum 202. + }) log:ifThenElseIn (() 1)}] + skolem:lemma459 + [ a r:Fact; r:gives {(404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (404 (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma669 a r:Inference; + r:gives { + 413 :collatz (1 (413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (413 2) math:remainder 0. + } { + (413 2) math:integerQuotient 1240. + } { + (3 413) math:product 1239 . + (1239 1) math:sum 1240. + }) log:ifThenElseIn (() 1)}] + skolem:lemma689 + [ a r:Fact; r:gives {(413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (413 (1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (413 1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma670 a r:Inference; + r:gives { + 422 :collatz (1 (422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (422 2) math:remainder 0. + } { + (422 2) math:integerQuotient 211. + } { + (3 422) math:product _:sk_0. + (_:sk_0 1) math:sum 211. + }) log:ifThenElseIn (() 1)}] + skolem:lemma468 + [ a r:Fact; r:gives {(422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (422 (211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma671 a r:Inference; + r:gives { + 431 :collatz (1 (431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (431 2) math:remainder 0. + } { + (431 2) math:integerQuotient 1294. + } { + (3 431) math:product 1293 . + (1293 1) math:sum 1294. + }) log:ifThenElseIn (() 1)}] + skolem:lemma690 + [ a r:Fact; r:gives {(431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (431 (1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (431 1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma672 a r:Inference; + r:gives { + 440 :collatz (1 (440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (440 2) math:remainder 0. + } { + (440 2) math:integerQuotient 220. + } { + (3 440) math:product _:sk_0. + (_:sk_0 1) math:sum 220. + }) log:ifThenElseIn (() 1)}] + skolem:lemma477 + [ a r:Fact; r:gives {(440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (440 (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma673 a r:Inference; + r:gives { + 449 :collatz (1 (449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (449 2) math:remainder 0. + } { + (449 2) math:integerQuotient 1348. + } { + (3 449) math:product 1347 . + (1347 1) math:sum 1348. + }) log:ifThenElseIn (() 1)}] + skolem:lemma691 + [ a r:Fact; r:gives {(449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (449 (1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma674 a r:Inference; + r:gives { + 458 :collatz (1 (458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (458 2) math:remainder 0. + } { + (458 2) math:integerQuotient 229. + } { + (3 458) math:product _:sk_0. + (_:sk_0 1) math:sum 229. + }) log:ifThenElseIn (() 1)}] + skolem:lemma486 + [ a r:Fact; r:gives {(458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (458 (229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (458 229 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma675 a r:Inference; + r:gives { + 467 :collatz (1 (467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (467 2) math:remainder 0. + } { + (467 2) math:integerQuotient 1402. + } { + (3 467) math:product 1401 . + (1401 1) math:sum 1402. + }) log:ifThenElseIn (() 1)}] + skolem:lemma692 + [ a r:Fact; r:gives {(467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (467 (1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (467 1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma676 a r:Inference; + r:gives { + 476 :collatz (1 (476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (476 2) math:remainder 0. + } { + (476 2) math:integerQuotient 238. + } { + (3 476) math:product _:sk_0. + (_:sk_0 1) math:sum 238. + }) log:ifThenElseIn (() 1)}] + skolem:lemma495 + [ a r:Fact; r:gives {(476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (476 (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (476 238 119 358 179 538 269 808 404 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma677 a r:Inference; + r:gives { + 485 :collatz (1 (485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (485 2) math:remainder 0. + } { + (485 2) math:integerQuotient 1456. + } { + (3 485) math:product 1455 . + (1455 1) math:sum 1456. + }) log:ifThenElseIn (() 1)}] + skolem:lemma693 + [ a r:Fact; r:gives {(485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (485 (1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma678 a r:Inference; + r:gives { + 494 :collatz (1 (494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (494 2) math:remainder 0. + } { + (494 2) math:integerQuotient 247. + } { + (3 494) math:product _:sk_0. + (_:sk_0 1) math:sum 247. + }) log:ifThenElseIn (() 1)}] + skolem:lemma504 + [ a r:Fact; r:gives {(494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (494 (247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (494 247 742 371 1114 557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma679 a r:Inference; + r:gives { + 503 :collatz (1 (503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (503 2) math:remainder 0. + } { + (503 2) math:integerQuotient 1510. + } { + (3 503) math:product 1509 . + (1509 1) math:sum 1510. + }) log:ifThenElseIn (() 1)}] + skolem:lemma694 + [ a r:Fact; r:gives {(503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (503 (1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (503 1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma680 a r:Inference; + r:gives { + 512 :collatz (1 (512 256 128 64 32 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (512 2) math:remainder 0. + } { + (512 2) math:integerQuotient 256. + } { + (3 512) math:product _:sk_0. + (_:sk_0 1) math:sum 256. + }) log:ifThenElseIn (() 1)}] + skolem:lemma513 + [ a r:Fact; r:gives {(512 256 128 64 32 16 8 4 2 1) list:firstRest (512 (256 128 64 32 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (256 128 64 32 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (512 256 128 64 32 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma681 a r:Inference; + r:gives { + 521 :collatz (1 (521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (521 2) math:remainder 0. + } { + (521 2) math:integerQuotient 1564. + } { + (3 521) math:product 1563 . + (1563 1) math:sum 1564. + }) log:ifThenElseIn (() 1)}] + skolem:lemma695 + [ a r:Fact; r:gives {(521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (521 (1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (521 1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma682 a r:Inference; + r:gives { + 530 :collatz (1 (530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (530 2) math:remainder 0. + } { + (530 2) math:integerQuotient 265. + } { + (3 530) math:product _:sk_0. + (_:sk_0 1) math:sum 265. + }) log:ifThenElseIn (() 1)}] + skolem:lemma696 + [ a r:Fact; r:gives {(530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (530 (265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (530 265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma683 a r:Inference; + r:gives { + 539 :collatz (1 (539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (539 2) math:remainder 0. + } { + (539 2) math:integerQuotient 1618. + } { + (3 539) math:product 1617 . + (1617 1) math:sum 1618. + }) log:ifThenElseIn (() 1)}] + skolem:lemma697 + [ a r:Fact; r:gives {(539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (539 (1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (539 1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma684 a r:Inference; + r:gives { + 548 :collatz (1 (548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (548 2) math:remainder 0. + } { + (548 2) math:integerQuotient 274. + } { + (3 548) math:product _:sk_0. + (_:sk_0 1) math:sum 274. + }) log:ifThenElseIn (() 1)}] + skolem:lemma518 + [ a r:Fact; r:gives {(548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (548 (274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (548 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma685 a r:Inference; + r:gives { + 557 :collatz (1 (557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (557 2) math:remainder 0. + } { + (557 2) math:integerQuotient 1672. + } { + (3 557) math:product 1671 . + (1671 1) math:sum 1672. + }) log:ifThenElseIn (() 1)}] + skolem:lemma698 + [ a r:Fact; r:gives {(557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (557 (1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (557 1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma686 a r:Inference; + r:gives { + 566 :collatz (1 (566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (566 2) math:remainder 0. + } { + (566 2) math:integerQuotient 283. + } { + (3 566) math:product _:sk_0. + (_:sk_0 1) math:sum 283. + }) log:ifThenElseIn (() 1)}] + skolem:lemma699 + [ a r:Fact; r:gives {(566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (566 (283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma687 a r:Inference; + r:gives { + 575 :collatz (1 (575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (575 2) math:remainder 0. + } { + (575 2) math:integerQuotient 1726. + } { + (3 575) math:product 1725 . + (1725 1) math:sum 1726. + }) log:ifThenElseIn (() 1)}] + skolem:lemma700 + [ a r:Fact; r:gives {(575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (575 (1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (575 1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma688 a r:Inference; + r:gives { + 1186 :collatz (1 (1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1186 2) math:remainder 0. + } { + (1186 2) math:integerQuotient 593. + } { + (3 1186) math:product _:sk_0. + (_:sk_0 1) math:sum 593. + }) log:ifThenElseIn (() 1)}] + skolem:lemma701 + [ a r:Fact; r:gives {(1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1186 (593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma689 a r:Inference; + r:gives { + 1240 :collatz (1 (1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1240 2) math:remainder 0. + } { + (1240 2) math:integerQuotient 620. + } { + (3 1240) math:product _:sk_0. + (_:sk_0 1) math:sum 620. + }) log:ifThenElseIn (() 1)}] + skolem:lemma702 + [ a r:Fact; r:gives {(1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1240 (620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1240 620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma690 a r:Inference; + r:gives { + 1294 :collatz (1 (1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1294 2) math:remainder 0. + } { + (1294 2) math:integerQuotient 647. + } { + (3 1294) math:product _:sk_0. + (_:sk_0 1) math:sum 647. + }) log:ifThenElseIn (() 1)}] + skolem:lemma703 + [ a r:Fact; r:gives {(1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1294 (647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1294 647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma691 a r:Inference; + r:gives { + 1348 :collatz (1 (1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1348 2) math:remainder 0. + } { + (1348 2) math:integerQuotient 674. + } { + (3 1348) math:product _:sk_0. + (_:sk_0 1) math:sum 674. + }) log:ifThenElseIn (() 1)}] + skolem:lemma704 + [ a r:Fact; r:gives {(1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1348 (674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma692 a r:Inference; + r:gives { + 1402 :collatz (1 (1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1402 2) math:remainder 0. + } { + (1402 2) math:integerQuotient 701. + } { + (3 1402) math:product _:sk_0. + (_:sk_0 1) math:sum 701. + }) log:ifThenElseIn (() 1)}] + skolem:lemma705 + [ a r:Fact; r:gives {(1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1402 (701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1402 701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma693 a r:Inference; + r:gives { + 1456 :collatz (1 (1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1456 2) math:remainder 0. + } { + (1456 2) math:integerQuotient 728. + } { + (3 1456) math:product _:sk_0. + (_:sk_0 1) math:sum 728. + }) log:ifThenElseIn (() 1)}] + skolem:lemma706 + [ a r:Fact; r:gives {(1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1456 (728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma694 a r:Inference; + r:gives { + 1510 :collatz (1 (1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1510 2) math:remainder 0. + } { + (1510 2) math:integerQuotient 755. + } { + (3 1510) math:product _:sk_0. + (_:sk_0 1) math:sum 755. + }) log:ifThenElseIn (() 1)}] + skolem:lemma707 + [ a r:Fact; r:gives {(1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1510 (755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1510 755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma695 a r:Inference; + r:gives { + 1564 :collatz (1 (1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1564 2) math:remainder 0. + } { + (1564 2) math:integerQuotient 782. + } { + (3 1564) math:product _:sk_0. + (_:sk_0 1) math:sum 782. + }) log:ifThenElseIn (() 1)}] + skolem:lemma708 + [ a r:Fact; r:gives {(1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1564 (782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1564 782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma696 a r:Inference; + r:gives { + 265 :collatz (1 (265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (265 2) math:remainder 0. + } { + (265 2) math:integerQuotient 796. + } { + (3 265) math:product 795 . + (795 1) math:sum 796. + }) log:ifThenElseIn (() 1)}] + skolem:lemma709 + [ a r:Fact; r:gives {(265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (265 (796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (265 796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma697 a r:Inference; + r:gives { + 1618 :collatz (1 (1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1618 2) math:remainder 0. + } { + (1618 2) math:integerQuotient 809. + } { + (3 1618) math:product _:sk_0. + (_:sk_0 1) math:sum 809. + }) log:ifThenElseIn (() 1)}] + skolem:lemma710 + [ a r:Fact; r:gives {(1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1618 (809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1618 809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma698 a r:Inference; + r:gives { + 1672 :collatz (1 (1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1672 2) math:remainder 0. + } { + (1672 2) math:integerQuotient 836. + } { + (3 1672) math:product _:sk_0. + (_:sk_0 1) math:sum 836. + }) log:ifThenElseIn (() 1)}] + skolem:lemma711 + [ a r:Fact; r:gives {(1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1672 (836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma699 a r:Inference; + r:gives { + 283 :collatz (1 (283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (283 2) math:remainder 0. + } { + (283 2) math:integerQuotient 850. + } { + (3 283) math:product 849 . + (849 1) math:sum 850. + }) log:ifThenElseIn (() 1)}] + skolem:lemma712 + [ a r:Fact; r:gives {(283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (283 (850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma700 a r:Inference; + r:gives { + 1726 :collatz (1 (1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1726 2) math:remainder 0. + } { + (1726 2) math:integerQuotient 863. + } { + (3 1726) math:product _:sk_0. + (_:sk_0 1) math:sum 863. + }) log:ifThenElseIn (() 1)}] + skolem:lemma713 + [ a r:Fact; r:gives {(1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1726 (863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1726 863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma701 a r:Inference; + r:gives { + 593 :collatz (1 (593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (593 2) math:remainder 0. + } { + (593 2) math:integerQuotient 1780. + } { + (3 593) math:product 1779 . + (1779 1) math:sum 1780. + }) log:ifThenElseIn (() 1)}] + skolem:lemma714 + [ a r:Fact; r:gives {(593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (593 (1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma702 a r:Inference; + r:gives { + 620 :collatz (1 (620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (620 2) math:remainder 0. + } { + (620 2) math:integerQuotient 310. + } { + (3 620) math:product _:sk_0. + (_:sk_0 1) math:sum 310. + }) log:ifThenElseIn (() 1)}] + skolem:lemma524 + [ a r:Fact; r:gives {(620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (620 (310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (620 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma703 a r:Inference; + r:gives { + 647 :collatz (1 (647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (647 2) math:remainder 0. + } { + (647 2) math:integerQuotient 1942. + } { + (3 647) math:product 1941 . + (1941 1) math:sum 1942. + }) log:ifThenElseIn (() 1)}] + skolem:lemma715 + [ a r:Fact; r:gives {(647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (647 (1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (647 1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma704 a r:Inference; + r:gives { + 674 :collatz (1 (674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (674 2) math:remainder 0. + } { + (674 2) math:integerQuotient 337. + } { + (3 674) math:product _:sk_0. + (_:sk_0 1) math:sum 337. + }) log:ifThenElseIn (() 1)}] + skolem:lemma716 + [ a r:Fact; r:gives {(674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (674 (337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma705 a r:Inference; + r:gives { + 701 :collatz (1 (701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (701 2) math:remainder 0. + } { + (701 2) math:integerQuotient 2104. + } { + (3 701) math:product 2103 . + (2103 1) math:sum 2104. + }) log:ifThenElseIn (() 1)}] + skolem:lemma717 + [ a r:Fact; r:gives {(701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (701 (2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (701 2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma706 a r:Inference; + r:gives { + 728 :collatz (1 (728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (728 2) math:remainder 0. + } { + (728 2) math:integerQuotient 364. + } { + (3 728) math:product _:sk_0. + (_:sk_0 1) math:sum 364. + }) log:ifThenElseIn (() 1)}] + skolem:lemma533 + [ a r:Fact; r:gives {(728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (728 (364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma707 a r:Inference; + r:gives { + 755 :collatz (1 (755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (755 2) math:remainder 0. + } { + (755 2) math:integerQuotient 2266. + } { + (3 755) math:product 2265 . + (2265 1) math:sum 2266. + }) log:ifThenElseIn (() 1)}] + skolem:lemma718 + [ a r:Fact; r:gives {(755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (755 (2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (755 2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma708 a r:Inference; + r:gives { + 782 :collatz (1 (782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (782 2) math:remainder 0. + } { + (782 2) math:integerQuotient 391. + } { + (3 782) math:product _:sk_0. + (_:sk_0 1) math:sum 391. + }) log:ifThenElseIn (() 1)}] + skolem:lemma719 + [ a r:Fact; r:gives {(782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (782 (391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (782 391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma709 a r:Inference; + r:gives { + 796 :collatz (1 (796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (796 2) math:remainder 0. + } { + (796 2) math:integerQuotient 398. + } { + (3 796) math:product _:sk_0. + (_:sk_0 1) math:sum 398. + }) log:ifThenElseIn (() 1)}] + skolem:lemma720 + [ a r:Fact; r:gives {(796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (796 (398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (796 398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma710 a r:Inference; + r:gives { + 809 :collatz (1 (809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (809 2) math:remainder 0. + } { + (809 2) math:integerQuotient 2428. + } { + (3 809) math:product 2427 . + (2427 1) math:sum 2428. + }) log:ifThenElseIn (() 1)}] + skolem:lemma721 + [ a r:Fact; r:gives {(809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (809 (2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (809 2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma711 a r:Inference; + r:gives { + 836 :collatz (1 (836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (836 2) math:remainder 0. + } { + (836 2) math:integerQuotient 418. + } { + (3 836) math:product _:sk_0. + (_:sk_0 1) math:sum 418. + }) log:ifThenElseIn (() 1)}] + skolem:lemma542 + [ a r:Fact; r:gives {(836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (836 (418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma712 a r:Inference; + r:gives { + 850 :collatz (1 (850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (850 2) math:remainder 0. + } { + (850 2) math:integerQuotient 425. + } { + (3 850) math:product _:sk_0. + (_:sk_0 1) math:sum 425. + }) log:ifThenElseIn (() 1)}] + skolem:lemma722 + [ a r:Fact; r:gives {(850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (850 (425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma713 a r:Inference; + r:gives { + 863 :collatz (1 (863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (863 2) math:remainder 0. + } { + (863 2) math:integerQuotient 2590. + } { + (3 863) math:product 2589 . + (2589 1) math:sum 2590. + }) log:ifThenElseIn (() 1)}] + skolem:lemma723 + [ a r:Fact; r:gives {(863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (863 (2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (863 2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma714 a r:Inference; + r:gives { + 1780 :collatz (1 (1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1780 2) math:remainder 0. + } { + (1780 2) math:integerQuotient 890. + } { + (3 1780) math:product _:sk_0. + (_:sk_0 1) math:sum 890. + }) log:ifThenElseIn (() 1)}] + skolem:lemma724 + [ a r:Fact; r:gives {(1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1780 (890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma715 a r:Inference; + r:gives { + 1942 :collatz (1 (1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1942 2) math:remainder 0. + } { + (1942 2) math:integerQuotient 971. + } { + (3 1942) math:product _:sk_0. + (_:sk_0 1) math:sum 971. + }) log:ifThenElseIn (() 1)}] + skolem:lemma725 + [ a r:Fact; r:gives {(1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1942 (971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1942 971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma716 a r:Inference; + r:gives { + 337 :collatz (1 (337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (337 2) math:remainder 0. + } { + (337 2) math:integerQuotient 1012. + } { + (3 337) math:product 1011 . + (1011 1) math:sum 1012. + }) log:ifThenElseIn (() 1)}] + skolem:lemma726 + [ a r:Fact; r:gives {(337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (337 (1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1011]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma717 a r:Inference; + r:gives { + 2104 :collatz (1 (2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2104 2) math:remainder 0. + } { + (2104 2) math:integerQuotient 1052. + } { + (3 2104) math:product _:sk_0. + (_:sk_0 1) math:sum 1052. + }) log:ifThenElseIn (() 1)}] + skolem:lemma727 + [ a r:Fact; r:gives {(2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2104 (1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2104 1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma718 a r:Inference; + r:gives { + 2266 :collatz (1 (2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2266 2) math:remainder 0. + } { + (2266 2) math:integerQuotient 1133. + } { + (3 2266) math:product _:sk_0. + (_:sk_0 1) math:sum 1133. + }) log:ifThenElseIn (() 1)}] + skolem:lemma728 + [ a r:Fact; r:gives {(2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2266 (1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2266 1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma719 a r:Inference; + r:gives { + 391 :collatz (1 (391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (391 2) math:remainder 0. + } { + (391 2) math:integerQuotient 1174. + } { + (3 391) math:product 1173 . + (1173 1) math:sum 1174. + }) log:ifThenElseIn (() 1)}] + skolem:lemma729 + [ a r:Fact; r:gives {(391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (391 (1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (391 1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma720 a r:Inference; + r:gives { + 398 :collatz (1 (398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (398 2) math:remainder 0. + } { + (398 2) math:integerQuotient 199. + } { + (3 398) math:product _:sk_0. + (_:sk_0 1) math:sum 199. + }) log:ifThenElseIn (() 1)}] + skolem:lemma456 + [ a r:Fact; r:gives {(398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (398 (199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (398 199 598 299 898 449 1348 674 337 1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma721 a r:Inference; + r:gives { + 2428 :collatz (1 (2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2428 2) math:remainder 0. + } { + (2428 2) math:integerQuotient 1214. + } { + (3 2428) math:product _:sk_0. + (_:sk_0 1) math:sum 1214. + }) log:ifThenElseIn (() 1)}] + skolem:lemma730 + [ a r:Fact; r:gives {(2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2428 (1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2428 1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma722 a r:Inference; + r:gives { + 425 :collatz (1 (425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (425 2) math:remainder 0. + } { + (425 2) math:integerQuotient 1276. + } { + (3 425) math:product 1275 . + (1275 1) math:sum 1276. + }) log:ifThenElseIn (() 1)}] + skolem:lemma731 + [ a r:Fact; r:gives {(425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (425 (1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma723 a r:Inference; + r:gives { + 2590 :collatz (1 (2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2590 2) math:remainder 0. + } { + (2590 2) math:integerQuotient 1295. + } { + (3 2590) math:product _:sk_0. + (_:sk_0 1) math:sum 1295. + }) log:ifThenElseIn (() 1)}] + skolem:lemma732 + [ a r:Fact; r:gives {(2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (2590 (1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2590 1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma724 a r:Inference; + r:gives { + 890 :collatz (1 (890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (890 2) math:remainder 0. + } { + (890 2) math:integerQuotient 445. + } { + (3 890) math:product _:sk_0. + (_:sk_0 1) math:sum 445. + }) log:ifThenElseIn (() 1)}] + skolem:lemma733 + [ a r:Fact; r:gives {(890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (890 (445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma725 a r:Inference; + r:gives { + 971 :collatz (1 (971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (971 2) math:remainder 0. + } { + (971 2) math:integerQuotient 2914. + } { + (3 971) math:product 2913 . + (2913 1) math:sum 2914. + }) log:ifThenElseIn (() 1)}] + skolem:lemma734 + [ a r:Fact; r:gives {(971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (971 (2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (971 2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma726 a r:Inference; + r:gives { + 1012 :collatz (1 (1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1012 2) math:remainder 0. + } { + (1012 2) math:integerQuotient 506. + } { + (3 1012) math:product _:sk_0. + (_:sk_0 1) math:sum 506. + }) log:ifThenElseIn (() 1)}] + skolem:lemma735 + [ a r:Fact; r:gives {(1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1012 (506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma727 a r:Inference; + r:gives { + 1052 :collatz (1 (1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1052 2) math:remainder 0. + } { + (1052 2) math:integerQuotient 526. + } { + (3 1052) math:product _:sk_0. + (_:sk_0 1) math:sum 526. + }) log:ifThenElseIn (() 1)}] + skolem:lemma560 + [ a r:Fact; r:gives {(1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1052 (526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1052 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma728 a r:Inference; + r:gives { + 1133 :collatz (1 (1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1133 2) math:remainder 0. + } { + (1133 2) math:integerQuotient 3400. + } { + (3 1133) math:product 3399 . + (3399 1) math:sum 3400. + }) log:ifThenElseIn (() 1)}] + skolem:lemma736 + [ a r:Fact; r:gives {(1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1133 (3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1133 3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma729 a r:Inference; + r:gives { + 1174 :collatz (1 (1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1174 2) math:remainder 0. + } { + (1174 2) math:integerQuotient 587. + } { + (3 1174) math:product _:sk_0. + (_:sk_0 1) math:sum 587. + }) log:ifThenElseIn (() 1)}] + skolem:lemma737 + [ a r:Fact; r:gives {(1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1174 (587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1174 587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma730 a r:Inference; + r:gives { + 1214 :collatz (1 (1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1214 2) math:remainder 0. + } { + (1214 2) math:integerQuotient 607. + } { + (3 1214) math:product _:sk_0. + (_:sk_0 1) math:sum 607. + }) log:ifThenElseIn (() 1)}] + skolem:lemma738 + [ a r:Fact; r:gives {(1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1214 (607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1214 607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma731 a r:Inference; + r:gives { + 1276 :collatz (1 (1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1276 2) math:remainder 0. + } { + (1276 2) math:integerQuotient 638. + } { + (3 1276) math:product _:sk_0. + (_:sk_0 1) math:sum 638. + }) log:ifThenElseIn (() 1)}] + skolem:lemma739 + [ a r:Fact; r:gives {(1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1276 (638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma732 a r:Inference; + r:gives { + 1295 :collatz (1 (1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1295 2) math:remainder 0. + } { + (1295 2) math:integerQuotient 3886. + } { + (3 1295) math:product 3885 . + (3885 1) math:sum 3886. + }) log:ifThenElseIn (() 1)}] + skolem:lemma740 + [ a r:Fact; r:gives {(1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1295 (3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1295 3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma733 a r:Inference; + r:gives { + 445 :collatz (1 (445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (445 2) math:remainder 0. + } { + (445 2) math:integerQuotient 1336. + } { + (3 445) math:product 1335 . + (1335 1) math:sum 1336. + }) log:ifThenElseIn (() 1)}] + skolem:lemma741 + [ a r:Fact; r:gives {(445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (445 (1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma734 a r:Inference; + r:gives { + 2914 :collatz (1 (2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2914 2) math:remainder 0. + } { + (2914 2) math:integerQuotient 1457. + } { + (3 2914) math:product _:sk_0. + (_:sk_0 1) math:sum 1457. + }) log:ifThenElseIn (() 1)}] + skolem:lemma742 + [ a r:Fact; r:gives {(2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (2914 (1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2914 1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma735 a r:Inference; + r:gives { + 506 :collatz (1 (506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (506 2) math:remainder 0. + } { + (506 2) math:integerQuotient 253. + } { + (3 506) math:product _:sk_0. + (_:sk_0 1) math:sum 253. + }) log:ifThenElseIn (() 1)}] + skolem:lemma510 + [ a r:Fact; r:gives {(506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (506 (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (506 253 760 380 190 95 286 143 430 215 646 323 970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma736 a r:Inference; + r:gives { + 3400 :collatz (1 (3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (3400 2) math:remainder 0. + } { + (3400 2) math:integerQuotient 1700. + } { + (3 3400) math:product _:sk_0. + (_:sk_0 1) math:sum 1700. + }) log:ifThenElseIn (() 1)}] + skolem:lemma743 + [ a r:Fact; r:gives {(3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (3400 (1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3400 1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma737 a r:Inference; + r:gives { + 587 :collatz (1 (587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (587 2) math:remainder 0. + } { + (587 2) math:integerQuotient 1762. + } { + (3 587) math:product 1761 . + (1761 1) math:sum 1762. + }) log:ifThenElseIn (() 1)}] + skolem:lemma744 + [ a r:Fact; r:gives {(587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (587 (1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (587 1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma738 a r:Inference; + r:gives { + 607 :collatz (1 (607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (607 2) math:remainder 0. + } { + (607 2) math:integerQuotient 1822. + } { + (3 607) math:product 1821 . + (1821 1) math:sum 1822. + }) log:ifThenElseIn (() 1)}] + skolem:lemma745 + [ a r:Fact; r:gives {(607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (607 (1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (607 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma739 a r:Inference; + r:gives { + 638 :collatz (1 (638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (638 2) math:remainder 0. + } { + (638 2) math:integerQuotient 319. + } { + (3 638) math:product _:sk_0. + (_:sk_0 1) math:sum 319. + }) log:ifThenElseIn (() 1)}] + skolem:lemma746 + [ a r:Fact; r:gives {(638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (638 (319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma740 a r:Inference; + r:gives { + 3886 :collatz (1 (3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (3886 2) math:remainder 0. + } { + (3886 2) math:integerQuotient 1943. + } { + (3 3886) math:product _:sk_0. + (_:sk_0 1) math:sum 1943. + }) log:ifThenElseIn (() 1)}] + skolem:lemma747 + [ a r:Fact; r:gives {(3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (3886 (1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3886 1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma741 a r:Inference; + r:gives { + 1336 :collatz (1 (1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1336 2) math:remainder 0. + } { + (1336 2) math:integerQuotient 668. + } { + (3 1336) math:product _:sk_0. + (_:sk_0 1) math:sum 668. + }) log:ifThenElseIn (() 1)}] + skolem:lemma748 + [ a r:Fact; r:gives {(1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1336 (668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma742 a r:Inference; + r:gives { + 1457 :collatz (1 (1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1457 2) math:remainder 0. + } { + (1457 2) math:integerQuotient 4372. + } { + (3 1457) math:product 4371 . + (4371 1) math:sum 4372. + }) log:ifThenElseIn (() 1)}] + skolem:lemma749 + [ a r:Fact; r:gives {(1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1457 (4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1457 4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma743 a r:Inference; + r:gives { + 1700 :collatz (1 (1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1700 2) math:remainder 0. + } { + (1700 2) math:integerQuotient 850. + } { + (3 1700) math:product _:sk_0. + (_:sk_0 1) math:sum 850. + }) log:ifThenElseIn (() 1)}] + skolem:lemma712 + [ a r:Fact; r:gives {(1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1700 (850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1700 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma744 a r:Inference; + r:gives { + 1762 :collatz (1 (1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1762 2) math:remainder 0. + } { + (1762 2) math:integerQuotient 881. + } { + (3 1762) math:product _:sk_0. + (_:sk_0 1) math:sum 881. + }) log:ifThenElseIn (() 1)}] + skolem:lemma750 + [ a r:Fact; r:gives {(1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1762 (881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1762 881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma745 a r:Inference; + r:gives { + 1822 :collatz (1 (1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1822 2) math:remainder 0. + } { + (1822 2) math:integerQuotient 911. + } { + (3 1822) math:product _:sk_0. + (_:sk_0 1) math:sum 911. + }) log:ifThenElseIn (() 1)}] + skolem:lemma751 + [ a r:Fact; r:gives {(1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1822 (911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma746 a r:Inference; + r:gives { + 319 :collatz (1 (319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (319 2) math:remainder 0. + } { + (319 2) math:integerQuotient 958. + } { + (3 319) math:product 957 . + (957 1) math:sum 958. + }) log:ifThenElseIn (() 1)}] + skolem:lemma752 + [ a r:Fact; r:gives {(319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (319 (958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma747 a r:Inference; + r:gives { + 1943 :collatz (1 (1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1943 2) math:remainder 0. + } { + (1943 2) math:integerQuotient 5830. + } { + (3 1943) math:product 5829 . + (5829 1) math:sum 5830. + }) log:ifThenElseIn (() 1)}] + skolem:lemma753 + [ a r:Fact; r:gives {(1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1943 (5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1943 5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma748 a r:Inference; + r:gives { + 668 :collatz (1 (668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (668 2) math:remainder 0. + } { + (668 2) math:integerQuotient 334. + } { + (3 668) math:product _:sk_0. + (_:sk_0 1) math:sum 334. + }) log:ifThenElseIn (() 1)}] + skolem:lemma528 + [ a r:Fact; r:gives {(668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (668 (334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma749 a r:Inference; + r:gives { + 4372 :collatz (1 (4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (4372 2) math:remainder 0. + } { + (4372 2) math:integerQuotient 2186. + } { + (3 4372) math:product _:sk_0. + (_:sk_0 1) math:sum 2186. + }) log:ifThenElseIn (() 1)}] + skolem:lemma754 + [ a r:Fact; r:gives {(4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (4372 (2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4372 2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma750 a r:Inference; + r:gives { + 881 :collatz (1 (881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (881 2) math:remainder 0. + } { + (881 2) math:integerQuotient 2644. + } { + (3 881) math:product 2643 . + (2643 1) math:sum 2644. + }) log:ifThenElseIn (() 1)}] + skolem:lemma755 + [ a r:Fact; r:gives {(881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (881 (2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (881 2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma751 a r:Inference; + r:gives { + 911 :collatz (1 (911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (911 2) math:remainder 0. + } { + (911 2) math:integerQuotient 2734. + } { + (3 911) math:product 2733 . + (2733 1) math:sum 2734. + }) log:ifThenElseIn (() 1)}] + skolem:lemma756 + [ a r:Fact; r:gives {(911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (911 (2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma752 a r:Inference; + r:gives { + 958 :collatz (1 (958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (958 2) math:remainder 0. + } { + (958 2) math:integerQuotient 479. + } { + (3 958) math:product _:sk_0. + (_:sk_0 1) math:sum 479. + }) log:ifThenElseIn (() 1)}] + skolem:lemma757 + [ a r:Fact; r:gives {(958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (958 (479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma753 a r:Inference; + r:gives { + 5830 :collatz (1 (5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (5830 2) math:remainder 0. + } { + (5830 2) math:integerQuotient 2915. + } { + (3 5830) math:product _:sk_0. + (_:sk_0 1) math:sum 2915. + }) log:ifThenElseIn (() 1)}] + skolem:lemma758 + [ a r:Fact; r:gives {(5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (5830 (2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (5830 2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma754 a r:Inference; + r:gives { + 2186 :collatz (1 (2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2186 2) math:remainder 0. + } { + (2186 2) math:integerQuotient 1093. + } { + (3 2186) math:product _:sk_0. + (_:sk_0 1) math:sum 1093. + }) log:ifThenElseIn (() 1)}] + skolem:lemma759 + [ a r:Fact; r:gives {(2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (2186 (1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2186 1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma755 a r:Inference; + r:gives { + 2644 :collatz (1 (2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2644 2) math:remainder 0. + } { + (2644 2) math:integerQuotient 1322. + } { + (3 2644) math:product _:sk_0. + (_:sk_0 1) math:sum 1322. + }) log:ifThenElseIn (() 1)}] + skolem:lemma760 + [ a r:Fact; r:gives {(2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2644 (1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2644 1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma756 a r:Inference; + r:gives { + 2734 :collatz (1 (2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2734 2) math:remainder 0. + } { + (2734 2) math:integerQuotient 1367. + } { + (3 2734) math:product _:sk_0. + (_:sk_0 1) math:sum 1367. + }) log:ifThenElseIn (() 1)}] + skolem:lemma761 + [ a r:Fact; r:gives {(2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2734 (1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma757 a r:Inference; + r:gives { + 479 :collatz (1 (479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (479 2) math:remainder 0. + } { + (479 2) math:integerQuotient 1438. + } { + (3 479) math:product 1437 . + (1437 1) math:sum 1438. + }) log:ifThenElseIn (() 1)}] + skolem:lemma762 + [ a r:Fact; r:gives {(479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (479 (1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma758 a r:Inference; + r:gives { + 2915 :collatz (1 (2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2915 2) math:remainder 0. + } { + (2915 2) math:integerQuotient 8746. + } { + (3 2915) math:product 8745 . + (8745 1) math:sum 8746. + }) log:ifThenElseIn (() 1)}] + skolem:lemma763 + [ a r:Fact; r:gives {(2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (2915 (8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2915 8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma759 a r:Inference; + r:gives { + 1093 :collatz (1 (1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1093 2) math:remainder 0. + } { + (1093 2) math:integerQuotient 3280. + } { + (3 1093) math:product 3279 . + (3279 1) math:sum 3280. + }) log:ifThenElseIn (() 1)}] + skolem:lemma764 + [ a r:Fact; r:gives {(1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1093 (3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1093 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma760 a r:Inference; + r:gives { + 1322 :collatz (1 (1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1322 2) math:remainder 0. + } { + (1322 2) math:integerQuotient 661. + } { + (3 1322) math:product _:sk_0. + (_:sk_0 1) math:sum 661. + }) log:ifThenElseIn (() 1)}] + skolem:lemma765 + [ a r:Fact; r:gives {(1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1322 (661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1322 661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma761 a r:Inference; + r:gives { + 1367 :collatz (1 (1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1367 2) math:remainder 0. + } { + (1367 2) math:integerQuotient 4102. + } { + (3 1367) math:product 4101 . + (4101 1) math:sum 4102. + }) log:ifThenElseIn (() 1)}] + skolem:lemma766 + [ a r:Fact; r:gives {(1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1367 (4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma762 a r:Inference; + r:gives { + 1438 :collatz (1 (1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1438 2) math:remainder 0. + } { + (1438 2) math:integerQuotient 719. + } { + (3 1438) math:product _:sk_0. + (_:sk_0 1) math:sum 719. + }) log:ifThenElseIn (() 1)}] + skolem:lemma767 + [ a r:Fact; r:gives {(1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1438 (719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma763 a r:Inference; + r:gives { + 8746 :collatz (1 (8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (8746 2) math:remainder 0. + } { + (8746 2) math:integerQuotient 4373. + } { + (3 8746) math:product _:sk_0. + (_:sk_0 1) math:sum 4373. + }) log:ifThenElseIn (() 1)}] + skolem:lemma768 + [ a r:Fact; r:gives {(8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (8746 (4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (8746 4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma764 a r:Inference; + r:gives { + 3280 :collatz (1 (3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (3280 2) math:remainder 0. + } { + (3280 2) math:integerQuotient 1640. + } { + (3 3280) math:product _:sk_0. + (_:sk_0 1) math:sum 1640. + }) log:ifThenElseIn (() 1)}] + skolem:lemma769 + [ a r:Fact; r:gives {(3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (3280 (1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma765 a r:Inference; + r:gives { + 661 :collatz (1 (661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (661 2) math:remainder 0. + } { + (661 2) math:integerQuotient 1984. + } { + (3 661) math:product 1983 . + (1983 1) math:sum 1984. + }) log:ifThenElseIn (() 1)}] + skolem:lemma770 + [ a r:Fact; r:gives {(661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (661 (1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (661 1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma766 a r:Inference; + r:gives { + 4102 :collatz (1 (4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (4102 2) math:remainder 0. + } { + (4102 2) math:integerQuotient 2051. + } { + (3 4102) math:product _:sk_0. + (_:sk_0 1) math:sum 2051. + }) log:ifThenElseIn (() 1)}] + skolem:lemma771 + [ a r:Fact; r:gives {(4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (4102 (2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma767 a r:Inference; + r:gives { + 719 :collatz (1 (719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (719 2) math:remainder 0. + } { + (719 2) math:integerQuotient 2158. + } { + (3 719) math:product 2157 . + (2157 1) math:sum 2158. + }) log:ifThenElseIn (() 1)}] + skolem:lemma772 + [ a r:Fact; r:gives {(719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (719 (2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma768 a r:Inference; + r:gives { + 4373 :collatz (1 (4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (4373 2) math:remainder 0. + } { + (4373 2) math:integerQuotient 13120. + } { + (3 4373) math:product 13119 . + (13119 1) math:sum 13120. + }) log:ifThenElseIn (() 1)}] + skolem:lemma773 + [ a r:Fact; r:gives {(4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (4373 (13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 13120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 13119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4373 13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma769 a r:Inference; + r:gives { + 1640 :collatz (1 (1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1640 2) math:remainder 0. + } { + (1640 2) math:integerQuotient 820. + } { + (3 1640) math:product _:sk_0. + (_:sk_0 1) math:sum 820. + }) log:ifThenElseIn (() 1)}] + skolem:lemma774 + [ a r:Fact; r:gives {(1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (1640 (820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma770 a r:Inference; + r:gives { + 1984 :collatz (1 (1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1984 2) math:remainder 0. + } { + (1984 2) math:integerQuotient 992. + } { + (3 1984) math:product _:sk_0. + (_:sk_0 1) math:sum 992. + }) log:ifThenElseIn (() 1)}] + skolem:lemma775 + [ a r:Fact; r:gives {(1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1984 (992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma771 a r:Inference; + r:gives { + 2051 :collatz (1 (2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2051 2) math:remainder 0. + } { + (2051 2) math:integerQuotient 6154. + } { + (3 2051) math:product 6153 . + (6153 1) math:sum 6154. + }) log:ifThenElseIn (() 1)}] + skolem:lemma776 + [ a r:Fact; r:gives {(2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2051 (6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma772 a r:Inference; + r:gives { + 2158 :collatz (1 (2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2158 2) math:remainder 0. + } { + (2158 2) math:integerQuotient 1079. + } { + (3 2158) math:product _:sk_0. + (_:sk_0 1) math:sum 1079. + }) log:ifThenElseIn (() 1)}] + skolem:lemma777 + [ a r:Fact; r:gives {(2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2158 (1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma773 a r:Inference; + r:gives { + 13120 :collatz (1 (13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (13120 2) math:remainder 0. + } { + (13120 2) math:integerQuotient 6560. + } { + (3 13120) math:product _:sk_0. + (_:sk_0 1) math:sum 6560. + }) log:ifThenElseIn (() 1)}] + skolem:lemma778 + [ a r:Fact; r:gives {(13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (13120 (6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (13120 6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma774 a r:Inference; + r:gives { + 820 :collatz (1 (820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (820 2) math:remainder 0. + } { + (820 2) math:integerQuotient 410. + } { + (3 820) math:product _:sk_0. + (_:sk_0 1) math:sum 410. + }) log:ifThenElseIn (() 1)}] + skolem:lemma779 + [ a r:Fact; r:gives {(820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (820 (410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma775 a r:Inference; + r:gives { + 992 :collatz (1 (992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (992 2) math:remainder 0. + } { + (992 2) math:integerQuotient 496. + } { + (3 992) math:product _:sk_0. + (_:sk_0 1) math:sum 496. + }) log:ifThenElseIn (() 1)}] + skolem:lemma555 + [ a r:Fact; r:gives {(992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (992 (496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma776 a r:Inference; + r:gives { + 6154 :collatz (1 (6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (6154 2) math:remainder 0. + } { + (6154 2) math:integerQuotient 3077. + } { + (3 6154) math:product _:sk_0. + (_:sk_0 1) math:sum 3077. + }) log:ifThenElseIn (() 1)}] + skolem:lemma780 + [ a r:Fact; r:gives {(6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (6154 (3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma777 a r:Inference; + r:gives { + 1079 :collatz (1 (1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1079 2) math:remainder 0. + } { + (1079 2) math:integerQuotient 3238. + } { + (3 1079) math:product 3237 . + (3237 1) math:sum 3238. + }) log:ifThenElseIn (() 1)}] + skolem:lemma781 + [ a r:Fact; r:gives {(1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1079 (3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma778 a r:Inference; + r:gives { + 6560 :collatz (1 (6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (6560 2) math:remainder 0. + } { + (6560 2) math:integerQuotient 3280. + } { + (3 6560) math:product _:sk_0. + (_:sk_0 1) math:sum 3280. + }) log:ifThenElseIn (() 1)}] + skolem:lemma764 + [ a r:Fact; r:gives {(6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (6560 (3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (6560 3280 1640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma779 a r:Inference; + r:gives { + 410 :collatz (1 (410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (410 2) math:remainder 0. + } { + (410 2) math:integerQuotient 205. + } { + (3 410) math:product _:sk_0. + (_:sk_0 1) math:sum 205. + }) log:ifThenElseIn (() 1)}] + skolem:lemma462 + [ a r:Fact; r:gives {(410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) list:firstRest (410 (205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma780 a r:Inference; + r:gives { + 3077 :collatz (1 (3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (3077 2) math:remainder 0. + } { + (3077 2) math:integerQuotient 9232. + } { + (3 3077) math:product 9231 . + (9231 1) math:sum 9232. + }) log:ifThenElseIn (() 1)}] + skolem:lemma782 + [ a r:Fact; r:gives {(3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (3077 (9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma781 a r:Inference; + r:gives { + 3238 :collatz (1 (3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (3238 2) math:remainder 0. + } { + (3238 2) math:integerQuotient 1619. + } { + (3 3238) math:product _:sk_0. + (_:sk_0 1) math:sum 1619. + }) log:ifThenElseIn (() 1)}] + skolem:lemma783 + [ a r:Fact; r:gives {(3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (3238 (1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma782 a r:Inference; + r:gives { + 9232 :collatz (1 (9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (9232 2) math:remainder 0. + } { + (9232 2) math:integerQuotient 4616. + } { + (3 9232) math:product _:sk_0. + (_:sk_0 1) math:sum 4616. + }) log:ifThenElseIn (() 1)}] + skolem:lemma784 + [ a r:Fact; r:gives {(9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (9232 (4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma783 a r:Inference; + r:gives { + 1619 :collatz (1 (1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1619 2) math:remainder 0. + } { + (1619 2) math:integerQuotient 4858. + } { + (3 1619) math:product 4857 . + (4857 1) math:sum 4858. + }) log:ifThenElseIn (() 1)}] + skolem:lemma785 + [ a r:Fact; r:gives {(1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1619 (4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma784 a r:Inference; + r:gives { + 4616 :collatz (1 (4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (4616 2) math:remainder 0. + } { + (4616 2) math:integerQuotient 2308. + } { + (3 4616) math:product _:sk_0. + (_:sk_0 1) math:sum 2308. + }) log:ifThenElseIn (() 1)}] + skolem:lemma786 + [ a r:Fact; r:gives {(4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (4616 (2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma785 a r:Inference; + r:gives { + 4858 :collatz (1 (4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (4858 2) math:remainder 0. + } { + (4858 2) math:integerQuotient 2429. + } { + (3 4858) math:product _:sk_0. + (_:sk_0 1) math:sum 2429. + }) log:ifThenElseIn (() 1)}] + skolem:lemma787 + [ a r:Fact; r:gives {(4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (4858 (2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma786 a r:Inference; + r:gives { + 2308 :collatz (1 (2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2308 2) math:remainder 0. + } { + (2308 2) math:integerQuotient 1154. + } { + (3 2308) math:product _:sk_0. + (_:sk_0 1) math:sum 1154. + }) log:ifThenElseIn (() 1)}] + skolem:lemma788 + [ a r:Fact; r:gives {(2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2308 (1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma787 a r:Inference; + r:gives { + 2429 :collatz (1 (2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (2429 2) math:remainder 0. + } { + (2429 2) math:integerQuotient 7288. + } { + (3 2429) math:product 7287 . + (7287 1) math:sum 7288. + }) log:ifThenElseIn (() 1)}] + skolem:lemma789 + [ a r:Fact; r:gives {(2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (2429 (7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma788 a r:Inference; + r:gives { + 1154 :collatz (1 (1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1154 2) math:remainder 0. + } { + (1154 2) math:integerQuotient 577. + } { + (3 1154) math:product _:sk_0. + (_:sk_0 1) math:sum 577. + }) log:ifThenElseIn (() 1)}] + skolem:lemma790 + [ a r:Fact; r:gives {(1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1154 (577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma789 a r:Inference; + r:gives { + 7288 :collatz (1 (7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (7288 2) math:remainder 0. + } { + (7288 2) math:integerQuotient 3644. + } { + (3 7288) math:product _:sk_0. + (_:sk_0 1) math:sum 3644. + }) log:ifThenElseIn (() 1)}] + skolem:lemma791 + [ a r:Fact; r:gives {(7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (7288 (3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma790 a r:Inference; + r:gives { + 577 :collatz (1 (577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (577 2) math:remainder 0. + } { + (577 2) math:integerQuotient 1732. + } { + (3 577) math:product 1731 . + (1731 1) math:sum 1732. + }) log:ifThenElseIn (() 1)}] + skolem:lemma792 + [ a r:Fact; r:gives {(577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (577 (1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma791 a r:Inference; + r:gives { + 3644 :collatz (1 (3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (3644 2) math:remainder 0. + } { + (3644 2) math:integerQuotient 1822. + } { + (3 3644) math:product _:sk_0. + (_:sk_0 1) math:sum 1822. + }) log:ifThenElseIn (() 1)}] + skolem:lemma745 + [ a r:Fact; r:gives {(3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (3644 (1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma792 a r:Inference; + r:gives { + 1732 :collatz (1 (1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1732 2) math:remainder 0. + } { + (1732 2) math:integerQuotient 866. + } { + (3 1732) math:product _:sk_0. + (_:sk_0 1) math:sum 866. + }) log:ifThenElseIn (() 1)}] + skolem:lemma793 + [ a r:Fact; r:gives {(1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1732 (866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma793 a r:Inference; + r:gives { + 866 :collatz (1 (866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (866 2) math:remainder 0. + } { + (866 2) math:integerQuotient 433. + } { + (3 866) math:product _:sk_0. + (_:sk_0 1) math:sum 433. + }) log:ifThenElseIn (() 1)}] + skolem:lemma794 + [ a r:Fact; r:gives {(866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (866 (433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma794 a r:Inference; + r:gives { + 433 :collatz (1 (433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (433 2) math:remainder 0. + } { + (433 2) math:integerQuotient 1300. + } { + (3 433) math:product 1299 . + (1299 1) math:sum 1300. + }) log:ifThenElseIn (() 1)}] + skolem:lemma795 + [ a r:Fact; r:gives {(433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (433 (1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma795 a r:Inference; + r:gives { + 1300 :collatz (1 (1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (1300 2) math:remainder 0. + } { + (1300 2) math:integerQuotient 650. + } { + (3 1300) math:product _:sk_0. + (_:sk_0 1) math:sum 650. + }) log:ifThenElseIn (() 1)}] + skolem:lemma796 + [ a r:Fact; r:gives {(1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (1300 (650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma796 a r:Inference; + r:gives { + 650 :collatz (1 (650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (650 2) math:remainder 0. + } { + (650 2) math:integerQuotient 325. + } { + (3 650) math:product _:sk_0. + (_:sk_0 1) math:sum 325. + }) log:ifThenElseIn (() 1)}] + skolem:lemma797 + [ a r:Fact; r:gives {(650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (650 (325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma797 a r:Inference; + r:gives { + 325 :collatz (1 (325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (325 2) math:remainder 0. + } { + (325 2) math:integerQuotient 976. + } { + (3 325) math:product 975 . + (975 1) math:sum 976. + }) log:ifThenElseIn (() 1)}] + skolem:lemma798 + [ a r:Fact; r:gives {(325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (325 (976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma798 a r:Inference; + r:gives { + 976 :collatz (1 (976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (976 2) math:remainder 0. + } { + (976 2) math:integerQuotient 488. + } { + (3 976) math:product _:sk_0. + (_:sk_0 1) math:sum 488. + }) log:ifThenElseIn (() 1)}] + skolem:lemma799 + [ a r:Fact; r:gives {(976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (976 (488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + +skolem:lemma799 a r:Inference; + r:gives { + 488 :collatz (1 (488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)). + }; + r:evidence ( + [ a r:Fact; r:gives {({ + (488 2) math:remainder 0. + } { + (488 2) math:integerQuotient 244. + } { + (3 488) math:product _:sk_0. + (_:sk_0 1) math:sum 244. + }) log:ifThenElseIn (() 1)}] + skolem:lemma501 + [ a r:Fact; r:gives {(488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1) list:firstRest (488 (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1))}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo [ a r:Existential; n3:nodeId "_:sk_0"]]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo (244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo (488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1)]; + r:rule skolem:lemma515. + diff --git a/reasoning/collatz/collatz-query.n3 b/reasoning/collatz/collatz-query.n3 new file mode 100644 index 000000000..468d766c1 --- /dev/null +++ b/reasoning/collatz/collatz-query.n3 @@ -0,0 +1,11 @@ +@prefix math: . +@prefix log: . +@prefix : . + +{ + 256 log:repeat ?N0. + (?N0 1) math:sum ?N. + ?N :collatz (1 ?M). +} => { + ?N :collatz (1 ?M). +}. diff --git a/reasoning/collatz/collatz.n3 b/reasoning/collatz/collatz.n3 new file mode 100644 index 000000000..87bed9f26 --- /dev/null +++ b/reasoning/collatz/collatz.n3 @@ -0,0 +1,17 @@ +@prefix math: . +@prefix list: . +@prefix log: . +@prefix : . + +{ ?N :collatz (?N (?N)) } <= { + true log:callWithCut true. +}. + +{ ?N0 :collatz (?N ?M)} <= { + ( { (?N0 2) math:remainder 0 } + { (?N0 2) math:integerQuotient ?N1 } + { ((3 ?N0)!math:product 1) math:sum ?N1 } + ) log:ifThenElseIn ?SCOPE. + ?N1 :collatz (?N ?J). + ?M list:firstRest (?N0 ?J). +}. diff --git a/reasoning/collatz/test b/reasoning/collatz/test new file mode 100755 index 000000000..2f1232ed6 --- /dev/null +++ b/reasoning/collatz/test @@ -0,0 +1,3 @@ +#!/bin/bash +eye --quiet --skolem-genid 8b98b360-9a70-4845-b52c-c675af60ad01 --wcache https://eyereasoner.github.io/eye/reasoning .. --nope https://eyereasoner.github.io/eye/reasoning/collatz/collatz.n3 --query https://eyereasoner.github.io/eye/reasoning/collatz/collatz-query.n3 --output collatz-answer.n3 +eye --quiet --skolem-genid 8b98b360-9a70-4845-b52c-c675af60ad01 --wcache https://eyereasoner.github.io/eye/reasoning .. https://eyereasoner.github.io/eye/reasoning/collatz/collatz.n3 --query https://eyereasoner.github.io/eye/reasoning/collatz/collatz-query.n3 --output collatz-proof.n3