From 2042c3b50b52503ef060a2e6ca7b1844960a4f34 Mon Sep 17 00:00:00 2001 From: josd Date: Wed, 8 Jan 2025 15:57:51 +0100 Subject: [PATCH] fixing within_scope(Context, -1) which should be used in backward rules --- RELEASE | 1 + VERSION | 2 +- eye.pl | 3 +- eye.zip | Bin 108972 -> 109023 bytes reasoning/goldbach/goldbach-proof.n3 | 1944 +++++++++++--------------- reasoning/goldbach/goldbach.n3 | 10 +- 6 files changed, 786 insertions(+), 1174 deletions(-) diff --git a/RELEASE b/RELEASE index cb273de88..99604b79e 100644 --- a/RELEASE +++ b/RELEASE @@ -1,5 +1,6 @@ EYE release +v11.4.2 (2025-01-08) fixing within_scope(Context, -1) which should be used in backward rules v11.4.1 (2025-01-07) improving --explain v11.4.0 (2025-01-06) dropping --plus and using --n3p instead v11.3.0 (2025-01-05) introducing eye --plus to run prolog with bottom-up steps diff --git a/VERSION b/VERSION index a6e5b12f9..3a3e396b1 100644 --- a/VERSION +++ b/VERSION @@ -1 +1 @@ -11.4.1 +11.4.2 diff --git a/eye.pl b/eye.pl index 9fda7373c..0944363cc 100644 --- a/eye.pl +++ b/eye.pl @@ -22,7 +22,7 @@ :- catch(use_module(library(process)), _, true). :- catch(use_module(library(http/http_open)), _, true). -version_info('EYE v11.4.1 (2025-01-07)'). +version_info('EYE v11.4.2 (2025-01-08)'). license_info('MIT License @@ -377,6 +377,7 @@ ; format(user_error, 'starting ~w [msec cputime] ~w [msec walltime]~n', [T0, T1]), flush_output(user_error) ), + assertz(recursion(-1)), nb_setval(entail_mode, false), nb_setval(exit_code, 0), nb_setval(indentation, 0), diff --git a/eye.zip b/eye.zip index 8cd93279b7c4b543ec0cded8ea644e3d82b44b18..72b86e099aefa69259479aad3a48142e446ba466 100644 GIT binary patch delta 56221 zcmV)TK(W89(+1zu1`SY40|W{H00000I)5mU4H^e;l744zl76u+h6N3hcqm%9wswOb z(EtEhlfeZRfAocZXY_@BXLWcB009K(0{{R7=mP)%#5`$p8#l7w`75w-r8xAGq7EmU zD6;Cw6lHUxt4PXTKS#wH4l(4!b9oL?+DiGizwQR+#tcc>si)nTL!i6SXf*l)hCj02 z4u7p5*)X8=;8;Mos6&tyY)X}KJzv449Ze>>-F?0Epb8+AaKaL!gy3)Qtq-@mqkI$Hz1(C^zomW=X1A+ 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r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma93 a r:Extraction; r:gives { @@ -1412,10 +1415,13 @@ skolem:lemma94 a r:Inference; r:evidence ( [ a r:Fact; r:gives {13 math:greaterThan 3}] [ a r:Fact; r:gives {(13 2) math:remainder 1}] - skolem:lemma126 + [ a r:Fact; r:gives {({ + 13 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma95 a r:Inference; r:gives { @@ -1424,10 +1430,13 @@ skolem:lemma95 a r:Inference; r:evidence ( [ a r:Fact; r:gives {29 math:greaterThan 3}] [ a r:Fact; r:gives {(29 2) math:remainder 1}] - skolem:lemma127 + [ a r:Fact; r:gives {({ + 29 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 29]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma96 a r:Inference; r:gives { @@ -1436,10 +1445,13 @@ skolem:lemma96 a r:Inference; r:evidence ( [ a r:Fact; r:gives {61 math:greaterThan 3}] [ a r:Fact; r:gives {(61 2) math:remainder 1}] - skolem:lemma128 + [ a r:Fact; r:gives {({ + 61 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 61]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma97 a r:Inference; r:gives { @@ -1452,7 +1464,7 @@ skolem:lemma97 a r:Inference; ); 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_0"]; r:boundTo 3]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. skolem:lemma98 a r:Inference; r:gives { @@ -1460,8 +1472,8 @@ skolem:lemma98 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 128}] - skolem:lemma130 - skolem:lemma131 + skolem:lemma126 + skolem:lemma127 ); 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 128]; @@ -1487,7 +1499,7 @@ skolem:lemma100 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {(256 5) math:difference 251}] - skolem:lemma132 + skolem:lemma128 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 251]; @@ -1502,10 +1514,13 @@ skolem:lemma101 a r:Inference; r:evidence ( [ a r:Fact; r:gives {509 math:greaterThan 3}] [ a r:Fact; r:gives {(509 2) math:remainder 1}] - skolem:lemma133 + [ a r:Fact; r:gives {({ + 509 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 509]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma102 a r:Inference; r:gives { @@ -1514,10 +1529,13 @@ skolem:lemma102 a r:Inference; r:evidence ( [ a r:Fact; r:gives {1021 math:greaterThan 3}] [ a r:Fact; r:gives {(1021 2) math:remainder 1}] - skolem:lemma134 + [ a r:Fact; r:gives {({ + 1021 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1021]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma103 a r:Inference; r:gives { @@ -1525,8 +1543,8 @@ skolem:lemma103 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 2048}] - skolem:lemma130 - skolem:lemma135 + skolem:lemma126 + skolem:lemma129 ); 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 2048]; @@ -1541,10 +1559,13 @@ skolem:lemma104 a r:Inference; r:evidence ( [ a r:Fact; r:gives {4093 math:greaterThan 3}] [ a r:Fact; r:gives {(4093 2) math:remainder 1}] - skolem:lemma136 + [ a r:Fact; r:gives {({ + 4093 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4093]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma105 a r:Inference; r:gives { @@ -1552,8 +1573,8 @@ skolem:lemma105 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 8192}] + skolem:lemma126 skolem:lemma130 - skolem:lemma137 ); 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 8192]; @@ -1568,10 +1589,13 @@ skolem:lemma106 a r:Inference; r:evidence ( [ a r:Fact; r:gives {16381 math:greaterThan 3}] [ a r:Fact; r:gives {(16381 2) math:remainder 1}] - skolem:lemma138 + [ a r:Fact; r:gives {({ + 16381 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16381]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma107 a r:Inference; r:gives { @@ -1579,8 +1603,8 @@ skolem:lemma107 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 32768}] - skolem:lemma130 - skolem:lemma139 + skolem:lemma126 + skolem:lemma131 ); 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 32768]; @@ -1594,8 +1618,8 @@ skolem:lemma108 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 65536}] - skolem:lemma130 - skolem:lemma140 + skolem:lemma126 + skolem:lemma132 ); 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 65536]; @@ -1609,8 +1633,8 @@ skolem:lemma109 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 131072}] - skolem:lemma130 - skolem:lemma141 + skolem:lemma126 + skolem:lemma133 ); 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 131072]; @@ -1624,7 +1648,7 @@ skolem:lemma110 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {(262144 5) math:difference 262139}] - skolem:lemma142 + skolem:lemma134 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 262139]; @@ -1638,8 +1662,8 @@ skolem:lemma111 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 524288}] - skolem:lemma130 - skolem:lemma143 + skolem:lemma126 + skolem:lemma135 ); 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 524288]; @@ -1654,10 +1678,13 @@ skolem:lemma112 a r:Inference; r:evidence ( [ a r:Fact; r:gives {1048573 math:greaterThan 3}] [ a r:Fact; r:gives {(1048573 2) math:remainder 1}] - skolem:lemma144 + [ a r:Fact; r:gives {({ + 1048573 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1048573]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma113 a r:Inference; r:gives { @@ -1665,8 +1692,8 @@ skolem:lemma113 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 2097152}] - skolem:lemma130 - skolem:lemma145 + skolem:lemma126 + skolem:lemma136 ); 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 2097152]; @@ -1681,10 +1708,13 @@ skolem:lemma114 a r:Inference; r:evidence ( [ a r:Fact; r:gives {4194301 math:greaterThan 3}] [ a r:Fact; r:gives {(4194301 2) math:remainder 1}] - skolem:lemma146 + [ a r:Fact; r:gives {({ + 4194301 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4194301]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma115 a r:Inference; r:gives { @@ -1692,8 +1722,8 @@ skolem:lemma115 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 8388608}] - skolem:lemma130 - skolem:lemma147 + skolem:lemma126 + skolem:lemma137 ); 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 8388608]; @@ -1708,10 +1738,13 @@ skolem:lemma116 a r:Inference; r:evidence ( [ a r:Fact; r:gives {16777213 math:greaterThan 3}] [ a r:Fact; r:gives {(16777213 2) math:remainder 1}] - skolem:lemma148 + [ a r:Fact; r:gives {({ + 16777213 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16777213]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma117 a r:Inference; r:gives { @@ -1719,8 +1752,8 @@ skolem:lemma117 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 33554432}] - skolem:lemma130 - skolem:lemma149 + skolem:lemma126 + skolem:lemma138 ); 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 33554432]; @@ -1734,7 +1767,7 @@ skolem:lemma118 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {(67108864 5) math:difference 67108859}] - skolem:lemma150 + skolem:lemma139 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 67108859]; @@ -1748,8 +1781,8 @@ skolem:lemma119 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 134217728}] - skolem:lemma130 - skolem:lemma151 + skolem:lemma126 + skolem:lemma140 ); 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 134217728]; @@ -1763,8 +1796,8 @@ skolem:lemma120 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 268435456}] - skolem:lemma130 - skolem:lemma152 + skolem:lemma126 + skolem:lemma141 ); 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 268435456]; @@ -1779,10 +1812,13 @@ skolem:lemma121 a r:Inference; r:evidence ( [ a r:Fact; r:gives {536870909 math:greaterThan 3}] [ a r:Fact; r:gives {(536870909 2) math:remainder 1}] - skolem:lemma153 + [ a r:Fact; r:gives {({ + 536870909 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 536870909]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. skolem:lemma122 a r:Inference; r:gives { @@ -1790,8 +1826,8 @@ skolem:lemma122 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 1073741824}] - skolem:lemma130 - skolem:lemma154 + skolem:lemma126 + skolem:lemma142 ); 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 1073741824]; @@ -1805,8 +1841,8 @@ skolem:lemma123 a r:Inference; }; r:evidence ( [ a r:Fact; r:gives {5 math:lessThan 2147483648}] - skolem:lemma130 - skolem:lemma155 + skolem:lemma126 + skolem:lemma143 ); 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 2147483648]; @@ -1814,63 +1850,21 @@ skolem:lemma123 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2147483629)]; r:rule skolem:lemma99. -skolem:lemma124 a r:Inference; - r:gives { - 5 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma125 a r:Extraction; +skolem:lemma124 a r:Extraction; r:gives { - @forAll var:x_0. { + @forAll var:x_0, var:x_1. { true :is_prime var:x_0. } <= { var:x_0 math:greaterThan 3 . (var:x_0 2) math:remainder 1 . - var:x_0 :not_has_factor 3. + ({ + var:x_0 :has_factor 3. + } false true) log:ifThenElseIn (var:x_1 -1). }. }; r:because [ a r:Parsing; r:source ]. -skolem:lemma126 a r:Inference; - r:gives { - 13 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma127 a r:Inference; - r:gives { - 29 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma128 a r:Inference; - r:gives { - 61 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma129 a r:Extraction; +skolem:lemma125 a r:Extraction; r:gives { @forAll var:x_0, var:x_1. { var:x_0 :next_prime var:x_1. @@ -1882,27 +1876,27 @@ skolem:lemma129 a r:Extraction; }; r:because [ a r:Parsing; r:source ]. -skolem:lemma130 a r:Inference; +skolem:lemma126 a r:Inference; r:gives { 5 :next_prime 7 . }; r:evidence ( [ a r:Fact; r:gives {(5 2) math:sum 7}] - skolem:lemma157 + skolem:lemma144 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 5]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma131 a r:Inference; +skolem:lemma127 a r:Inference; r:gives { 128 :goldb ((19 109) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 128}] - skolem:lemma158 - skolem:lemma159 + skolem:lemma145 + skolem:lemma146 ); 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 128]; @@ -1910,48 +1904,29 @@ skolem:lemma131 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 109)]; r:rule skolem:lemma99. -skolem:lemma132 a r:Inference; +skolem:lemma128 a r:Inference; r:gives { true :is_prime 251 . }; r:evidence ( [ a r:Fact; r:gives {251 math:greaterThan 3}] [ a r:Fact; r:gives {(251 2) math:remainder 1}] - skolem:lemma160 + [ a r:Fact; r:gives {({ + 251 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 251]; - r:rule skolem:lemma125. - -skolem:lemma133 a r:Inference; - r:gives { - 509 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 509]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma134 a r:Inference; - r:gives { - 1021 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1021]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma135 a r:Inference; +skolem:lemma129 a r:Inference; r:gives { 2048 :goldb ((19 2029) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 2048}] - skolem:lemma158 - skolem:lemma161 + skolem:lemma145 + skolem:lemma147 ); 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 2048]; @@ -1959,25 +1934,14 @@ skolem:lemma135 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2029)]; r:rule skolem:lemma99. -skolem:lemma136 a r:Inference; - r:gives { - 4093 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4093]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma137 a r:Inference; +skolem:lemma130 a r:Inference; r:gives { 8192 :goldb ((13 8179) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 8192}] - skolem:lemma158 - skolem:lemma162 + skolem:lemma145 + skolem:lemma148 ); 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 8192]; @@ -1985,25 +1949,14 @@ skolem:lemma137 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (13 8179)]; r:rule skolem:lemma99. -skolem:lemma138 a r:Inference; - r:gives { - 16381 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16381]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma139 a r:Inference; +skolem:lemma131 a r:Inference; r:gives { 32768 :goldb ((19 32749) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 32768}] - skolem:lemma158 - skolem:lemma163 + skolem:lemma145 + skolem:lemma149 ); 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 32768]; @@ -2011,14 +1964,14 @@ skolem:lemma139 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 32749)]; r:rule skolem:lemma99. -skolem:lemma140 a r:Inference; +skolem:lemma132 a r:Inference; r:gives { 65536 :goldb ((17 65519) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 65536}] - skolem:lemma158 - skolem:lemma164 + skolem:lemma145 + skolem:lemma150 ); 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 65536]; @@ -2026,14 +1979,14 @@ skolem:lemma140 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (17 65519)]; r:rule skolem:lemma99. -skolem:lemma141 a r:Inference; +skolem:lemma133 a r:Inference; r:gives { 131072 :goldb ((13 131059) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 131072}] - skolem:lemma158 - skolem:lemma165 + skolem:lemma145 + skolem:lemma151 ); 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 131072]; @@ -2041,26 +1994,29 @@ skolem:lemma141 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (13 131059)]; r:rule skolem:lemma99. -skolem:lemma142 a r:Inference; +skolem:lemma134 a r:Inference; r:gives { true :is_prime 262139 . }; r:evidence ( [ a r:Fact; r:gives {262139 math:greaterThan 3}] [ a r:Fact; r:gives {(262139 2) math:remainder 1}] - skolem:lemma166 + [ a r:Fact; r:gives {({ + 262139 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 262139]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma143 a r:Inference; +skolem:lemma135 a r:Inference; r:gives { 524288 :goldb ((19 524269) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 524288}] - skolem:lemma158 - skolem:lemma167 + skolem:lemma145 + skolem:lemma152 ); 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 524288]; @@ -2068,25 +2024,14 @@ skolem:lemma143 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 524269)]; r:rule skolem:lemma99. -skolem:lemma144 a r:Inference; - r:gives { - 1048573 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1048573]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma145 a r:Inference; +skolem:lemma136 a r:Inference; r:gives { 2097152 :goldb ((19 2097133) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 2097152}] - skolem:lemma158 - skolem:lemma168 + skolem:lemma145 + skolem:lemma153 ); 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 2097152]; @@ -2094,25 +2039,14 @@ skolem:lemma145 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2097133)]; r:rule skolem:lemma99. -skolem:lemma146 a r:Inference; - r:gives { - 4194301 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4194301]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma147 a r:Inference; +skolem:lemma137 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 8388608}] - skolem:lemma158 - skolem:lemma169 + skolem:lemma145 + skolem:lemma154 ); 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 8388608]; @@ -2120,25 +2054,14 @@ skolem:lemma147 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; r:rule skolem:lemma99. -skolem:lemma148 a r:Inference; - r:gives { - 16777213 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16777213]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma149 a r:Inference; +skolem:lemma138 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 33554432}] - skolem:lemma158 - skolem:lemma170 + skolem:lemma145 + skolem:lemma155 ); 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 33554432]; @@ -2146,26 +2069,29 @@ skolem:lemma149 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma150 a r:Inference; +skolem:lemma139 a r:Inference; r:gives { true :is_prime 67108859 . }; r:evidence ( [ a r:Fact; r:gives {67108859 math:greaterThan 3}] [ a r:Fact; r:gives {(67108859 2) math:remainder 1}] - skolem:lemma171 + [ a r:Fact; r:gives {({ + 67108859 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 67108859]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma151 a r:Inference; +skolem:lemma140 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 134217728}] - skolem:lemma158 - skolem:lemma172 + skolem:lemma145 + skolem:lemma156 ); 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 134217728]; @@ -2173,14 +2099,14 @@ skolem:lemma151 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma152 a r:Inference; +skolem:lemma141 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 268435456}] - skolem:lemma158 - skolem:lemma173 + skolem:lemma145 + skolem:lemma157 ); 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 268435456]; @@ -2188,25 +2114,14 @@ skolem:lemma152 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma153 a r:Inference; - r:gives { - 536870909 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 536870909]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma154 a r:Inference; +skolem:lemma142 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 1073741824}] + skolem:lemma145 skolem:lemma158 - skolem:lemma174 ); 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 1073741824]; @@ -2214,14 +2129,14 @@ skolem:lemma154 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma155 a r:Inference; +skolem:lemma143 a r:Inference; r:gives { 2147483648 :goldb ((19 2147483629) 7). }; r:evidence ( [ a r:Fact; r:gives {7 math:lessThan 2147483648}] - skolem:lemma158 - skolem:lemma175 + skolem:lemma145 + skolem:lemma159 ); 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 2147483648]; @@ -2229,47 +2144,42 @@ skolem:lemma155 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2147483629)]; r:rule skolem:lemma99. -skolem:lemma156 a r:Extraction; - r:gives { - @forSome var:x_0, var:x_1. { - var:x_0 :not_has_factor var:x_1. - } <= true. - }; - r:because [ a r:Parsing; r:source ]. - -skolem:lemma157 a r:Inference; +skolem:lemma144 a r:Inference; r:gives { true :is_prime 7 . }; r:evidence ( [ a r:Fact; r:gives {7 math:greaterThan 3}] [ a r:Fact; r:gives {(7 2) math:remainder 1}] - skolem:lemma176 + [ a r:Fact; r:gives {({ + 7 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma158 a r:Inference; +skolem:lemma145 a r:Inference; r:gives { 7 :next_prime 11 . }; r:evidence ( [ a r:Fact; r:gives {(7 2) math:sum 9}] - skolem:lemma177 + skolem:lemma160 ); 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_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 11]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma159 a r:Inference; +skolem:lemma146 a r:Inference; r:gives { 128 :goldb ((19 109) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 128}] - skolem:lemma179 - skolem:lemma180 + skolem:lemma162 + skolem:lemma163 ); 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 128]; @@ -2277,25 +2187,14 @@ skolem:lemma159 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 109)]; r:rule skolem:lemma99. -skolem:lemma160 a r:Inference; - r:gives { - 251 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma161 a r:Inference; +skolem:lemma147 a r:Inference; r:gives { 2048 :goldb ((19 2029) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 2048}] - skolem:lemma179 - skolem:lemma181 + skolem:lemma162 + skolem:lemma164 ); 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 2048]; @@ -2303,14 +2202,14 @@ skolem:lemma161 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2029)]; r:rule skolem:lemma99. -skolem:lemma162 a r:Inference; +skolem:lemma148 a r:Inference; r:gives { 8192 :goldb ((13 8179) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 8192}] - skolem:lemma179 - skolem:lemma182 + skolem:lemma162 + skolem:lemma165 ); 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 8192]; @@ -2318,14 +2217,14 @@ skolem:lemma162 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (13 8179)]; r:rule skolem:lemma99. -skolem:lemma163 a r:Inference; +skolem:lemma149 a r:Inference; r:gives { 32768 :goldb ((19 32749) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 32768}] - skolem:lemma179 - skolem:lemma183 + skolem:lemma162 + skolem:lemma166 ); 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 32768]; @@ -2333,14 +2232,14 @@ skolem:lemma163 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 32749)]; r:rule skolem:lemma99. -skolem:lemma164 a r:Inference; +skolem:lemma150 a r:Inference; r:gives { 65536 :goldb ((17 65519) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 65536}] - skolem:lemma179 - skolem:lemma184 + skolem:lemma162 + skolem:lemma167 ); 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 65536]; @@ -2348,14 +2247,14 @@ skolem:lemma164 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (17 65519)]; r:rule skolem:lemma99. -skolem:lemma165 a r:Inference; +skolem:lemma151 a r:Inference; r:gives { 131072 :goldb ((13 131059) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 131072}] - skolem:lemma179 - skolem:lemma185 + skolem:lemma162 + skolem:lemma168 ); 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 131072]; @@ -2363,25 +2262,14 @@ skolem:lemma165 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (13 131059)]; r:rule skolem:lemma99. -skolem:lemma166 a r:Inference; - r:gives { - 262139 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 262139]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma167 a r:Inference; +skolem:lemma152 a r:Inference; r:gives { 524288 :goldb ((19 524269) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 524288}] - skolem:lemma179 - skolem:lemma186 + skolem:lemma162 + skolem:lemma169 ); 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 524288]; @@ -2389,14 +2277,14 @@ skolem:lemma167 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 524269)]; r:rule skolem:lemma99. -skolem:lemma168 a r:Inference; +skolem:lemma153 a r:Inference; r:gives { 2097152 :goldb ((19 2097133) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 2097152}] - skolem:lemma179 - skolem:lemma187 + skolem:lemma162 + skolem:lemma170 ); 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 2097152]; @@ -2404,14 +2292,14 @@ skolem:lemma168 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2097133)]; r:rule skolem:lemma99. -skolem:lemma169 a r:Inference; +skolem:lemma154 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 8388608}] - skolem:lemma179 - skolem:lemma188 + skolem:lemma162 + skolem:lemma171 ); 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 8388608]; @@ -2419,14 +2307,14 @@ skolem:lemma169 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; r:rule skolem:lemma99. -skolem:lemma170 a r:Inference; +skolem:lemma155 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 33554432}] - skolem:lemma179 - skolem:lemma189 + skolem:lemma162 + skolem:lemma172 ); 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 33554432]; @@ -2434,25 +2322,14 @@ skolem:lemma170 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma171 a r:Inference; - r:gives { - 67108859 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 67108859]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma172 a r:Inference; +skolem:lemma156 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 134217728}] - skolem:lemma179 - skolem:lemma190 + skolem:lemma162 + skolem:lemma173 ); 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 134217728]; @@ -2460,14 +2337,14 @@ skolem:lemma172 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma173 a r:Inference; +skolem:lemma157 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 268435456}] - skolem:lemma179 - skolem:lemma191 + skolem:lemma162 + skolem:lemma174 ); 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 268435456]; @@ -2475,14 +2352,14 @@ skolem:lemma173 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma174 a r:Inference; +skolem:lemma158 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 1073741824}] - skolem:lemma179 - skolem:lemma192 + skolem:lemma162 + skolem:lemma175 ); 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 1073741824]; @@ -2490,14 +2367,14 @@ skolem:lemma174 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma175 a r:Inference; +skolem:lemma159 a r:Inference; r:gives { 2147483648 :goldb ((19 2147483629) 11). }; r:evidence ( [ a r:Fact; r:gives {11 math:lessThan 2147483648}] - skolem:lemma179 - skolem:lemma193 + skolem:lemma162 + skolem:lemma176 ); 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 2147483648]; @@ -2505,31 +2382,20 @@ skolem:lemma175 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2147483629)]; r:rule skolem:lemma99. -skolem:lemma176 a r:Inference; - r:gives { - 7 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma177 a r:Inference; +skolem:lemma160 a r:Inference; r:gives { 9 :next_prime 11 . }; r:evidence ( [ a r:Fact; r:gives {(9 2) math:sum 11}] - skolem:lemma194 + skolem:lemma177 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 9]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma178 a r:Extraction; +skolem:lemma161 a r:Extraction; r:gives { @forAll var:x_0, var:x_1, var:x_2. { var:x_0 :next_prime var:x_2. @@ -2540,7 +2406,7 @@ skolem:lemma178 a r:Extraction; }; r:because [ a r:Parsing; r:source ]. -skolem:lemma179 a r:Inference; +skolem:lemma162 a r:Inference; r:gives { 11 :next_prime 13 . }; @@ -2551,16 +2417,16 @@ skolem:lemma179 a r:Inference; ); 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_0"]; r:boundTo 11]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma180 a r:Inference; +skolem:lemma163 a r:Inference; r:gives { 128 :goldb ((19 109) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 128}] - skolem:lemma195 - skolem:lemma196 + skolem:lemma178 + skolem:lemma179 ); 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 128]; @@ -2568,14 +2434,14 @@ skolem:lemma180 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 109)]; r:rule skolem:lemma99. -skolem:lemma181 a r:Inference; +skolem:lemma164 a r:Inference; r:gives { 2048 :goldb ((19 2029) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 2048}] - skolem:lemma195 - skolem:lemma197 + skolem:lemma178 + skolem:lemma180 ); 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 2048]; @@ -2583,13 +2449,13 @@ skolem:lemma181 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2029)]; r:rule skolem:lemma99. -skolem:lemma182 a r:Inference; +skolem:lemma165 a r:Inference; r:gives { 8192 :goldb ((13 8179) 13). }; r:evidence ( [ a r:Fact; r:gives {(8192 13) math:difference 8179}] - skolem:lemma198 + skolem:lemma181 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8179]; @@ -2597,14 +2463,14 @@ skolem:lemma182 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 13]; r:rule skolem:lemma93. -skolem:lemma183 a r:Inference; +skolem:lemma166 a r:Inference; r:gives { 32768 :goldb ((19 32749) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 32768}] - skolem:lemma195 - skolem:lemma199 + skolem:lemma178 + skolem:lemma182 ); 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 32768]; @@ -2612,14 +2478,14 @@ skolem:lemma183 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 32749)]; r:rule skolem:lemma99. -skolem:lemma184 a r:Inference; +skolem:lemma167 a r:Inference; r:gives { 65536 :goldb ((17 65519) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 65536}] - skolem:lemma195 - skolem:lemma200 + skolem:lemma178 + skolem:lemma183 ); 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 65536]; @@ -2627,13 +2493,13 @@ skolem:lemma184 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (17 65519)]; r:rule skolem:lemma99. -skolem:lemma185 a r:Inference; +skolem:lemma168 a r:Inference; r:gives { 131072 :goldb ((13 131059) 13). }; r:evidence ( [ a r:Fact; r:gives {(131072 13) math:difference 131059}] - skolem:lemma201 + skolem:lemma184 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 131059]; @@ -2641,14 +2507,14 @@ skolem:lemma185 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 13]; r:rule skolem:lemma93. -skolem:lemma186 a r:Inference; +skolem:lemma169 a r:Inference; r:gives { 524288 :goldb ((19 524269) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 524288}] - skolem:lemma195 - skolem:lemma202 + skolem:lemma178 + skolem:lemma185 ); 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 524288]; @@ -2656,14 +2522,14 @@ skolem:lemma186 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 524269)]; r:rule skolem:lemma99. -skolem:lemma187 a r:Inference; +skolem:lemma170 a r:Inference; r:gives { 2097152 :goldb ((19 2097133) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 2097152}] - skolem:lemma195 - skolem:lemma203 + skolem:lemma178 + skolem:lemma186 ); 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 2097152]; @@ -2671,14 +2537,14 @@ skolem:lemma187 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2097133)]; r:rule skolem:lemma99. -skolem:lemma188 a r:Inference; +skolem:lemma171 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 8388608}] - skolem:lemma195 - skolem:lemma204 + skolem:lemma178 + skolem:lemma187 ); 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 8388608]; @@ -2686,14 +2552,14 @@ skolem:lemma188 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; r:rule skolem:lemma99. -skolem:lemma189 a r:Inference; +skolem:lemma172 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 33554432}] - skolem:lemma195 - skolem:lemma205 + skolem:lemma178 + skolem:lemma188 ); 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 33554432]; @@ -2701,14 +2567,14 @@ skolem:lemma189 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma190 a r:Inference; +skolem:lemma173 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 134217728}] - skolem:lemma195 - skolem:lemma206 + skolem:lemma178 + skolem:lemma189 ); 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 134217728]; @@ -2716,14 +2582,14 @@ skolem:lemma190 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma191 a r:Inference; +skolem:lemma174 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 268435456}] - skolem:lemma195 - skolem:lemma207 + skolem:lemma178 + skolem:lemma190 ); 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 268435456]; @@ -2731,14 +2597,14 @@ skolem:lemma191 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma192 a r:Inference; +skolem:lemma175 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 1073741824}] - skolem:lemma195 - skolem:lemma208 + skolem:lemma178 + skolem:lemma191 ); 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 1073741824]; @@ -2746,14 +2612,14 @@ skolem:lemma192 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma193 a r:Inference; +skolem:lemma176 a r:Inference; r:gives { 2147483648 :goldb ((19 2147483629) 13). }; r:evidence ( [ a r:Fact; r:gives {13 math:lessThan 2147483648}] - skolem:lemma195 - skolem:lemma209 + skolem:lemma178 + skolem:lemma192 ); 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 2147483648]; @@ -2761,39 +2627,42 @@ skolem:lemma193 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2147483629)]; r:rule skolem:lemma99. -skolem:lemma194 a r:Inference; +skolem:lemma177 a r:Inference; r:gives { true :is_prime 11 . }; r:evidence ( [ a r:Fact; r:gives {11 math:greaterThan 3}] [ a r:Fact; r:gives {(11 2) math:remainder 1}] - skolem:lemma210 + [ a r:Fact; r:gives {({ + 11 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 11]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma195 a r:Inference; +skolem:lemma178 a r:Inference; r:gives { 13 :next_prime 17 . }; r:evidence ( [ a r:Fact; r:gives {(13 2) math:sum 15}] - skolem:lemma211 + skolem:lemma193 ); 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_0"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 17]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma196 a r:Inference; +skolem:lemma179 a r:Inference; r:gives { 128 :goldb ((19 109) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 128}] - skolem:lemma212 - skolem:lemma213 + skolem:lemma194 + skolem:lemma195 ); 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 128]; @@ -2801,14 +2670,14 @@ skolem:lemma196 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 109)]; r:rule skolem:lemma99. -skolem:lemma197 a r:Inference; +skolem:lemma180 a r:Inference; r:gives { 2048 :goldb ((19 2029) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 2048}] - skolem:lemma212 - skolem:lemma214 + skolem:lemma194 + skolem:lemma196 ); 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 2048]; @@ -2816,26 +2685,29 @@ skolem:lemma197 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2029)]; r:rule skolem:lemma99. -skolem:lemma198 a r:Inference; +skolem:lemma181 a r:Inference; r:gives { true :is_prime 8179 . }; r:evidence ( [ a r:Fact; r:gives {8179 math:greaterThan 3}] [ a r:Fact; r:gives {(8179 2) math:remainder 1}] - skolem:lemma215 + [ a r:Fact; r:gives {({ + 8179 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8179]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma199 a r:Inference; +skolem:lemma182 a r:Inference; r:gives { 32768 :goldb ((19 32749) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 32768}] - skolem:lemma212 - skolem:lemma216 + skolem:lemma194 + skolem:lemma197 ); 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 32768]; @@ -2843,13 +2715,13 @@ skolem:lemma199 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 32749)]; r:rule skolem:lemma99. -skolem:lemma200 a r:Inference; +skolem:lemma183 a r:Inference; r:gives { 65536 :goldb ((17 65519) 17). }; r:evidence ( [ a r:Fact; r:gives {(65536 17) math:difference 65519}] - skolem:lemma217 + skolem:lemma198 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 65519]; @@ -2857,26 +2729,29 @@ skolem:lemma200 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 17]; r:rule skolem:lemma93. -skolem:lemma201 a r:Inference; +skolem:lemma184 a r:Inference; r:gives { true :is_prime 131059 . }; r:evidence ( [ a r:Fact; r:gives {131059 math:greaterThan 3}] [ a r:Fact; r:gives {(131059 2) math:remainder 1}] - skolem:lemma218 + [ a r:Fact; r:gives {({ + 131059 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 131059]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma202 a r:Inference; +skolem:lemma185 a r:Inference; r:gives { 524288 :goldb ((19 524269) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 524288}] - skolem:lemma212 - skolem:lemma219 + skolem:lemma194 + skolem:lemma199 ); 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 524288]; @@ -2884,14 +2759,14 @@ skolem:lemma202 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 524269)]; r:rule skolem:lemma99. -skolem:lemma203 a r:Inference; +skolem:lemma186 a r:Inference; r:gives { 2097152 :goldb ((19 2097133) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 2097152}] - skolem:lemma212 - skolem:lemma220 + skolem:lemma194 + skolem:lemma200 ); 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 2097152]; @@ -2899,14 +2774,14 @@ skolem:lemma203 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2097133)]; r:rule skolem:lemma99. -skolem:lemma204 a r:Inference; +skolem:lemma187 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 8388608}] - skolem:lemma212 - skolem:lemma221 + skolem:lemma194 + skolem:lemma201 ); 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 8388608]; @@ -2914,14 +2789,14 @@ skolem:lemma204 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; r:rule skolem:lemma99. -skolem:lemma205 a r:Inference; +skolem:lemma188 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 33554432}] - skolem:lemma212 - skolem:lemma222 + skolem:lemma194 + skolem:lemma202 ); 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 33554432]; @@ -2929,14 +2804,14 @@ skolem:lemma205 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma206 a r:Inference; +skolem:lemma189 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 134217728}] - skolem:lemma212 - skolem:lemma223 + skolem:lemma194 + skolem:lemma203 ); 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 134217728]; @@ -2944,14 +2819,14 @@ skolem:lemma206 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma207 a r:Inference; +skolem:lemma190 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 268435456}] - skolem:lemma212 - skolem:lemma224 + skolem:lemma194 + skolem:lemma204 ); 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 268435456]; @@ -2959,14 +2834,14 @@ skolem:lemma207 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma208 a r:Inference; +skolem:lemma191 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 1073741824}] - skolem:lemma212 - skolem:lemma225 + skolem:lemma194 + skolem:lemma205 ); 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 1073741824]; @@ -2974,14 +2849,14 @@ skolem:lemma208 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma209 a r:Inference; +skolem:lemma192 a r:Inference; r:gives { 2147483648 :goldb ((19 2147483629) 17). }; r:evidence ( [ a r:Fact; r:gives {17 math:lessThan 2147483648}] - skolem:lemma212 - skolem:lemma226 + skolem:lemma194 + skolem:lemma206 ); 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 2147483648]; @@ -2989,50 +2864,39 @@ skolem:lemma209 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (19 2147483629)]; r:rule skolem:lemma99. -skolem:lemma210 a r:Inference; - r:gives { - 11 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma211 a r:Inference; +skolem:lemma193 a r:Inference; r:gives { 15 :next_prime 17 . }; r:evidence ( [ a r:Fact; r:gives {(15 2) math:sum 17}] - skolem:lemma227 + skolem:lemma207 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 15]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma212 a r:Inference; +skolem:lemma194 a r:Inference; r:gives { 17 :next_prime 19 . }; r:evidence ( [ a r:Fact; r:gives {(17 2) math:sum 19}] - skolem:lemma228 + skolem:lemma208 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 17]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma213 a r:Inference; +skolem:lemma195 a r:Inference; r:gives { 128 :goldb ((19 109) 19). }; r:evidence ( [ a r:Fact; r:gives {(128 19) math:difference 109}] - skolem:lemma229 + skolem:lemma209 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 109]; @@ -3040,13 +2904,13 @@ skolem:lemma213 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; r:rule skolem:lemma93. -skolem:lemma214 a r:Inference; +skolem:lemma196 a r:Inference; r:gives { 2048 :goldb ((19 2029) 19). }; r:evidence ( [ a r:Fact; r:gives {(2048 19) math:difference 2029}] - skolem:lemma230 + skolem:lemma210 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2029]; @@ -3054,24 +2918,13 @@ skolem:lemma214 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; r:rule skolem:lemma93. -skolem:lemma215 a r:Inference; - r:gives { - 8179 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8179]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma216 a r:Inference; +skolem:lemma197 a r:Inference; r:gives { 32768 :goldb ((19 32749) 19). }; r:evidence ( [ a r:Fact; r:gives {(32768 19) math:difference 32749}] - skolem:lemma231 + skolem:lemma211 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 32749]; @@ -3079,36 +2932,28 @@ skolem:lemma216 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; r:rule skolem:lemma93. -skolem:lemma217 a r:Inference; +skolem:lemma198 a r:Inference; r:gives { true :is_prime 65519 . }; r:evidence ( [ a r:Fact; r:gives {65519 math:greaterThan 3}] [ a r:Fact; r:gives {(65519 2) math:remainder 1}] - skolem:lemma232 + [ a r:Fact; r:gives {({ + 65519 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 65519]; - r:rule skolem:lemma125. - -skolem:lemma218 a r:Inference; - r:gives { - 131059 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 131059]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma219 a r:Inference; +skolem:lemma199 a r:Inference; r:gives { 524288 :goldb ((19 524269) 19). }; r:evidence ( [ a r:Fact; r:gives {(524288 19) math:difference 524269}] - skolem:lemma233 + skolem:lemma212 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 524269]; @@ -3116,13 +2961,13 @@ skolem:lemma219 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; r:rule skolem:lemma93. -skolem:lemma220 a r:Inference; +skolem:lemma200 a r:Inference; r:gives { 2097152 :goldb ((19 2097133) 19). }; r:evidence ( [ a r:Fact; r:gives {(2097152 19) math:difference 2097133}] - skolem:lemma234 + skolem:lemma213 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2097133]; @@ -3130,14 +2975,14 @@ skolem:lemma220 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; r:rule skolem:lemma93. -skolem:lemma221 a r:Inference; +skolem:lemma201 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 19). }; r:evidence ( [ a r:Fact; r:gives {19 math:lessThan 8388608}] - skolem:lemma235 - skolem:lemma236 + skolem:lemma214 + skolem:lemma215 ); 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 8388608]; @@ -3145,14 +2990,14 @@ skolem:lemma221 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; r:rule skolem:lemma99. -skolem:lemma222 a r:Inference; +skolem:lemma202 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 19). }; r:evidence ( [ a r:Fact; r:gives {19 math:lessThan 33554432}] - skolem:lemma235 - skolem:lemma237 + skolem:lemma214 + skolem:lemma216 ); 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 33554432]; @@ -3160,14 +3005,14 @@ skolem:lemma222 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma223 a r:Inference; +skolem:lemma203 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 19). }; r:evidence ( [ a r:Fact; r:gives {19 math:lessThan 134217728}] - skolem:lemma235 - skolem:lemma238 + skolem:lemma214 + skolem:lemma217 ); 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 134217728]; @@ -3175,14 +3020,14 @@ skolem:lemma223 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma224 a r:Inference; +skolem:lemma204 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 19). }; r:evidence ( [ a r:Fact; r:gives {19 math:lessThan 268435456}] - skolem:lemma235 - skolem:lemma239 + skolem:lemma214 + skolem:lemma218 ); 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 268435456]; @@ -3190,14 +3035,14 @@ skolem:lemma224 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma225 a r:Inference; +skolem:lemma205 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 19). }; r:evidence ( [ a r:Fact; r:gives {19 math:lessThan 1073741824}] - skolem:lemma235 - skolem:lemma240 + skolem:lemma214 + skolem:lemma219 ); 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 1073741824]; @@ -3205,13 +3050,13 @@ skolem:lemma225 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma226 a r:Inference; +skolem:lemma206 a r:Inference; r:gives { 2147483648 :goldb ((19 2147483629) 19). }; r:evidence ( [ a r:Fact; r:gives {(2147483648 19) math:difference 2147483629}] - skolem:lemma241 + skolem:lemma220 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2147483629]; @@ -3219,122 +3064,132 @@ skolem:lemma226 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 19]; r:rule skolem:lemma93. -skolem:lemma227 a r:Inference; +skolem:lemma207 a r:Inference; r:gives { true :is_prime 17 . }; r:evidence ( [ a r:Fact; r:gives {17 math:greaterThan 3}] [ a r:Fact; r:gives {(17 2) math:remainder 1}] - skolem:lemma242 + [ a r:Fact; r:gives {({ + 17 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 17]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma228 a r:Inference; +skolem:lemma208 a r:Inference; r:gives { true :is_prime 19 . }; r:evidence ( [ a r:Fact; r:gives {19 math:greaterThan 3}] [ a r:Fact; r:gives {(19 2) math:remainder 1}] - skolem:lemma243 + [ a r:Fact; r:gives {({ + 19 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 19]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma229 a r:Inference; +skolem:lemma209 a r:Inference; r:gives { true :is_prime 109 . }; r:evidence ( [ a r:Fact; r:gives {109 math:greaterThan 3}] [ a r:Fact; r:gives {(109 2) math:remainder 1}] - skolem:lemma244 + [ a r:Fact; r:gives {({ + 109 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 109]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma230 a r:Inference; +skolem:lemma210 a r:Inference; r:gives { true :is_prime 2029 . }; r:evidence ( [ a r:Fact; r:gives {2029 math:greaterThan 3}] [ a r:Fact; r:gives {(2029 2) math:remainder 1}] - skolem:lemma245 + [ a r:Fact; r:gives {({ + 2029 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2029]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma231 a r:Inference; +skolem:lemma211 a r:Inference; r:gives { true :is_prime 32749 . }; r:evidence ( [ a r:Fact; r:gives {32749 math:greaterThan 3}] [ a r:Fact; r:gives {(32749 2) math:remainder 1}] - skolem:lemma246 + [ a r:Fact; r:gives {({ + 32749 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 32749]; - r:rule skolem:lemma125. - -skolem:lemma232 a r:Inference; - r:gives { - 65519 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 65519]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma233 a r:Inference; +skolem:lemma212 a r:Inference; r:gives { true :is_prime 524269 . }; r:evidence ( [ a r:Fact; r:gives {524269 math:greaterThan 3}] [ a r:Fact; r:gives {(524269 2) math:remainder 1}] - skolem:lemma247 + [ a r:Fact; r:gives {({ + 524269 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 524269]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma234 a r:Inference; +skolem:lemma213 a r:Inference; r:gives { true :is_prime 2097133 . }; r:evidence ( [ a r:Fact; r:gives {2097133 math:greaterThan 3}] [ a r:Fact; r:gives {(2097133 2) math:remainder 1}] - skolem:lemma248 + [ a r:Fact; r:gives {({ + 2097133 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2097133]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma235 a r:Inference; +skolem:lemma214 a r:Inference; r:gives { 19 :next_prime 23 . }; r:evidence ( [ a r:Fact; r:gives {(19 2) math:sum 21}] - skolem:lemma249 + skolem:lemma221 ); 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_0"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 23]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma236 a r:Inference; +skolem:lemma215 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 23). }; r:evidence ( [ a r:Fact; r:gives {23 math:lessThan 8388608}] - skolem:lemma250 - skolem:lemma251 + skolem:lemma222 + skolem:lemma223 ); 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 8388608]; @@ -3342,14 +3197,14 @@ skolem:lemma236 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; r:rule skolem:lemma99. -skolem:lemma237 a r:Inference; +skolem:lemma216 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 23). }; r:evidence ( [ a r:Fact; r:gives {23 math:lessThan 33554432}] - skolem:lemma250 - skolem:lemma252 + skolem:lemma222 + skolem:lemma224 ); 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 33554432]; @@ -3357,14 +3212,14 @@ skolem:lemma237 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma238 a r:Inference; +skolem:lemma217 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 23). }; r:evidence ( [ a r:Fact; r:gives {23 math:lessThan 134217728}] - skolem:lemma250 - skolem:lemma253 + skolem:lemma222 + skolem:lemma225 ); 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 134217728]; @@ -3372,14 +3227,14 @@ skolem:lemma238 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma239 a r:Inference; +skolem:lemma218 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 23). }; r:evidence ( [ a r:Fact; r:gives {23 math:lessThan 268435456}] - skolem:lemma250 - skolem:lemma254 + skolem:lemma222 + skolem:lemma226 ); 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 268435456]; @@ -3387,14 +3242,14 @@ skolem:lemma239 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma240 a r:Inference; +skolem:lemma219 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 23). }; r:evidence ( [ a r:Fact; r:gives {23 math:lessThan 1073741824}] - skolem:lemma250 - skolem:lemma255 + skolem:lemma222 + skolem:lemma227 ); 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 1073741824]; @@ -3402,144 +3257,70 @@ skolem:lemma240 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma241 a r:Inference; +skolem:lemma220 a r:Inference; r:gives { true :is_prime 2147483629 . }; r:evidence ( [ a r:Fact; r:gives {2147483629 math:greaterThan 3}] [ a r:Fact; r:gives {(2147483629 2) math:remainder 1}] - skolem:lemma256 + [ a r:Fact; r:gives {({ + 2147483629 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2147483629]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma242 a r:Inference; +skolem:lemma221 a r:Inference; r:gives { - 17 :not_has_factor 3 . + 21 :next_prime 23 . }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {(21 2) math:sum 23}] + skolem:lemma228 + [ 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 17]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + 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_0"]; r:boundTo 21]; + r:rule skolem:lemma125. -skolem:lemma243 a r:Inference; +skolem:lemma222 a r:Inference; r:gives { - 19 :not_has_factor 3 . + 23 :next_prime 29 . }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {(23 2) math:sum 25}] + skolem:lemma229 ); - 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 3]; - r:rule skolem:lemma156. + 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_0"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 29]; + r:rule skolem:lemma161. -skolem:lemma244 a r:Inference; +skolem:lemma223 a r:Inference; r:gives { - 109 :not_has_factor 3 . + 8388608 :goldb ((37 8388571) 29). }; r:evidence ( - [ a r:Fact; r:gives true] + [ a r:Fact; r:gives {29 math:lessThan 8388608}] + skolem:lemma230 + skolem:lemma231 ); - 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 3]; - r:rule skolem:lemma156. + 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 8388608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; + r:rule skolem:lemma99. -skolem:lemma245 a r:Inference; +skolem:lemma224 a r:Inference; r:gives { - 2029 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2029]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma246 a r:Inference; - r:gives { - 32749 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 32749]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma247 a r:Inference; - r:gives { - 524269 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 524269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma248 a r:Inference; - r:gives { - 2097133 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2097133]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma249 a r:Inference; - r:gives { - 21 :next_prime 23 . - }; - r:evidence ( - [ a r:Fact; r:gives {(21 2) math:sum 23}] - skolem:lemma257 - [ a r:Fact; r:gives {true log:callWithCut true}] - ); - 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_0"]; r:boundTo 21]; - r:rule skolem:lemma129. - -skolem:lemma250 a r:Inference; - r:gives { - 23 :next_prime 29 . - }; - r:evidence ( - [ a r:Fact; r:gives {(23 2) math:sum 25}] - skolem:lemma258 - ); - 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_0"]; r:boundTo 23]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 29]; - r:rule skolem:lemma178. - -skolem:lemma251 a r:Inference; - r:gives { - 8388608 :goldb ((37 8388571) 29). - }; - r:evidence ( - [ a r:Fact; r:gives {29 math:lessThan 8388608}] - skolem:lemma259 - skolem:lemma260 - ); - 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 8388608]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 31]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; - r:rule skolem:lemma99. - -skolem:lemma252 a r:Inference; - r:gives { - 33554432 :goldb ((61 33554371) 29). + 33554432 :goldb ((61 33554371) 29). }; r:evidence ( [ a r:Fact; r:gives {29 math:lessThan 33554432}] - skolem:lemma259 - skolem:lemma261 + skolem:lemma230 + skolem:lemma232 ); 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 33554432]; @@ -3547,14 +3328,14 @@ skolem:lemma252 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma253 a r:Inference; +skolem:lemma225 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 29). }; r:evidence ( [ a r:Fact; r:gives {29 math:lessThan 134217728}] - skolem:lemma259 - skolem:lemma262 + skolem:lemma230 + skolem:lemma233 ); 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 134217728]; @@ -3562,14 +3343,14 @@ skolem:lemma253 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma254 a r:Inference; +skolem:lemma226 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 29). }; r:evidence ( [ a r:Fact; r:gives {29 math:lessThan 268435456}] - skolem:lemma259 - skolem:lemma263 + skolem:lemma230 + skolem:lemma234 ); 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 268435456]; @@ -3577,14 +3358,14 @@ skolem:lemma254 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma255 a r:Inference; +skolem:lemma227 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 29). }; r:evidence ( [ a r:Fact; r:gives {29 math:lessThan 1073741824}] - skolem:lemma259 - skolem:lemma264 + skolem:lemma230 + skolem:lemma235 ); 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 1073741824]; @@ -3592,63 +3373,55 @@ skolem:lemma255 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma256 a r:Inference; - r:gives { - 2147483629 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2147483629]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma257 a r:Inference; +skolem:lemma228 a r:Inference; r:gives { true :is_prime 23 . }; r:evidence ( [ a r:Fact; r:gives {23 math:greaterThan 3}] [ a r:Fact; r:gives {(23 2) math:remainder 1}] - skolem:lemma265 + [ a r:Fact; r:gives {({ + 23 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 23]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma258 a r:Inference; +skolem:lemma229 a r:Inference; r:gives { 25 :next_prime 29 . }; r:evidence ( [ a r:Fact; r:gives {(25 2) math:sum 27}] - skolem:lemma266 + skolem:lemma236 ); 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_0"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 29]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma259 a r:Inference; +skolem:lemma230 a r:Inference; r:gives { 29 :next_prime 31 . }; r:evidence ( [ a r:Fact; r:gives {(29 2) math:sum 31}] - skolem:lemma267 + skolem:lemma237 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 29]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma260 a r:Inference; +skolem:lemma231 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 31). }; r:evidence ( [ a r:Fact; r:gives {31 math:lessThan 8388608}] - skolem:lemma268 - skolem:lemma269 + skolem:lemma238 + skolem:lemma239 ); 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 8388608]; @@ -3656,14 +3429,14 @@ skolem:lemma260 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (37 8388571)]; r:rule skolem:lemma99. -skolem:lemma261 a r:Inference; +skolem:lemma232 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 31). }; r:evidence ( [ a r:Fact; r:gives {31 math:lessThan 33554432}] - skolem:lemma268 - skolem:lemma270 + skolem:lemma238 + skolem:lemma240 ); 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 33554432]; @@ -3671,14 +3444,14 @@ skolem:lemma261 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma262 a r:Inference; +skolem:lemma233 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 31). }; r:evidence ( [ a r:Fact; r:gives {31 math:lessThan 134217728}] - skolem:lemma268 - skolem:lemma271 + skolem:lemma238 + skolem:lemma241 ); 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 134217728]; @@ -3686,14 +3459,14 @@ skolem:lemma262 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma263 a r:Inference; +skolem:lemma234 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 31). }; r:evidence ( [ a r:Fact; r:gives {31 math:lessThan 268435456}] - skolem:lemma268 - skolem:lemma272 + skolem:lemma238 + skolem:lemma242 ); 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 268435456]; @@ -3701,14 +3474,14 @@ skolem:lemma263 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma264 a r:Inference; +skolem:lemma235 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 31). }; r:evidence ( [ a r:Fact; r:gives {31 math:lessThan 1073741824}] - skolem:lemma268 - skolem:lemma273 + skolem:lemma238 + skolem:lemma243 ); 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 1073741824]; @@ -3716,18 +3489,7 @@ skolem:lemma264 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma265 a r:Inference; - r:gives { - 23 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma266 a r:Inference; +skolem:lemma236 a r:Inference; r:gives { 27 :next_prime 29 . }; @@ -3738,40 +3500,43 @@ skolem:lemma266 a r:Inference; ); 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_0"]; r:boundTo 27]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma267 a r:Inference; +skolem:lemma237 a r:Inference; r:gives { true :is_prime 31 . }; r:evidence ( [ a r:Fact; r:gives {31 math:greaterThan 3}] [ a r:Fact; r:gives {(31 2) math:remainder 1}] - skolem:lemma274 + [ a r:Fact; r:gives {({ + 31 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 31]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma268 a r:Inference; +skolem:lemma238 a r:Inference; r:gives { 31 :next_prime 37 . }; r:evidence ( [ a r:Fact; r:gives {(31 2) math:sum 33}] - skolem:lemma275 + skolem:lemma244 ); 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_0"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 37]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma269 a r:Inference; +skolem:lemma239 a r:Inference; r:gives { 8388608 :goldb ((37 8388571) 37). }; r:evidence ( [ a r:Fact; r:gives {(8388608 37) math:difference 8388571}] - skolem:lemma276 + skolem:lemma245 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8388571]; @@ -3779,14 +3544,14 @@ skolem:lemma269 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 37]; r:rule skolem:lemma93. -skolem:lemma270 a r:Inference; +skolem:lemma240 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 37). }; r:evidence ( [ a r:Fact; r:gives {37 math:lessThan 33554432}] - skolem:lemma277 - skolem:lemma278 + skolem:lemma246 + skolem:lemma247 ); 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 33554432]; @@ -3794,14 +3559,14 @@ skolem:lemma270 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma271 a r:Inference; +skolem:lemma241 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 37). }; r:evidence ( [ a r:Fact; r:gives {37 math:lessThan 134217728}] - skolem:lemma277 - skolem:lemma279 + skolem:lemma246 + skolem:lemma248 ); 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 134217728]; @@ -3809,14 +3574,14 @@ skolem:lemma271 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma272 a r:Inference; +skolem:lemma242 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 37). }; r:evidence ( [ a r:Fact; r:gives {37 math:lessThan 268435456}] - skolem:lemma277 - skolem:lemma280 + skolem:lemma246 + skolem:lemma249 ); 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 268435456]; @@ -3824,14 +3589,14 @@ skolem:lemma272 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma273 a r:Inference; +skolem:lemma243 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 37). }; r:evidence ( [ a r:Fact; r:gives {37 math:lessThan 1073741824}] - skolem:lemma277 - skolem:lemma281 + skolem:lemma246 + skolem:lemma250 ); 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 1073741824]; @@ -3839,63 +3604,55 @@ skolem:lemma273 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (41 1073741783)]; r:rule skolem:lemma99. -skolem:lemma274 a r:Inference; - r:gives { - 31 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma275 a r:Inference; +skolem:lemma244 a r:Inference; r:gives { 33 :next_prime 37 . }; r:evidence ( [ a r:Fact; r:gives {(33 2) math:sum 35}] - skolem:lemma282 + skolem:lemma251 ); 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_0"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 37]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma276 a r:Inference; +skolem:lemma245 a r:Inference; r:gives { true :is_prime 8388571 . }; r:evidence ( [ a r:Fact; r:gives {8388571 math:greaterThan 3}] [ a r:Fact; r:gives {(8388571 2) math:remainder 1}] - skolem:lemma283 + [ a r:Fact; r:gives {({ + 8388571 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8388571]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma277 a r:Inference; +skolem:lemma246 a r:Inference; r:gives { 37 :next_prime 41 . }; r:evidence ( [ a r:Fact; r:gives {(37 2) math:sum 39}] - skolem:lemma284 + skolem:lemma252 ); 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_0"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 41]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma278 a r:Inference; +skolem:lemma247 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 41). }; r:evidence ( [ a r:Fact; r:gives {41 math:lessThan 33554432}] - skolem:lemma285 - skolem:lemma286 + skolem:lemma253 + skolem:lemma254 ); 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 33554432]; @@ -3903,14 +3660,14 @@ skolem:lemma278 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma279 a r:Inference; +skolem:lemma248 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 41). }; r:evidence ( [ a r:Fact; r:gives {41 math:lessThan 134217728}] - skolem:lemma285 - skolem:lemma287 + skolem:lemma253 + skolem:lemma255 ); 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 134217728]; @@ -3918,14 +3675,14 @@ skolem:lemma279 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma280 a r:Inference; +skolem:lemma249 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 41). }; r:evidence ( [ a r:Fact; r:gives {41 math:lessThan 268435456}] - skolem:lemma285 - skolem:lemma288 + skolem:lemma253 + skolem:lemma256 ); 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 268435456]; @@ -3933,13 +3690,13 @@ skolem:lemma280 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma281 a r:Inference; +skolem:lemma250 a r:Inference; r:gives { 1073741824 :goldb ((41 1073741783) 41). }; r:evidence ( [ a r:Fact; r:gives {(1073741824 41) math:difference 1073741783}] - skolem:lemma289 + skolem:lemma257 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1073741783]; @@ -3947,64 +3704,53 @@ skolem:lemma281 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 41]; r:rule skolem:lemma93. -skolem:lemma282 a r:Inference; +skolem:lemma251 a r:Inference; r:gives { 35 :next_prime 37 . }; r:evidence ( [ a r:Fact; r:gives {(35 2) math:sum 37}] - skolem:lemma290 + skolem:lemma258 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 35]; - r:rule skolem:lemma129. - -skolem:lemma283 a r:Inference; - r:gives { - 8388571 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8388571]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + r:rule skolem:lemma125. -skolem:lemma284 a r:Inference; +skolem:lemma252 a r:Inference; r:gives { 39 :next_prime 41 . }; r:evidence ( [ a r:Fact; r:gives {(39 2) math:sum 41}] - skolem:lemma291 + skolem:lemma259 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 39]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma285 a r:Inference; +skolem:lemma253 a r:Inference; r:gives { 41 :next_prime 43 . }; r:evidence ( [ a r:Fact; r:gives {(41 2) math:sum 43}] - skolem:lemma292 + skolem:lemma260 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 41]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma286 a r:Inference; +skolem:lemma254 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 43). }; r:evidence ( [ a r:Fact; r:gives {43 math:lessThan 33554432}] - skolem:lemma293 - skolem:lemma294 + skolem:lemma261 + skolem:lemma262 ); 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 33554432]; @@ -4012,14 +3758,14 @@ skolem:lemma286 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma287 a r:Inference; +skolem:lemma255 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 43). }; r:evidence ( [ a r:Fact; r:gives {43 math:lessThan 134217728}] - skolem:lemma293 - skolem:lemma295 + skolem:lemma261 + skolem:lemma263 ); 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 134217728]; @@ -4027,14 +3773,14 @@ skolem:lemma287 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma288 a r:Inference; +skolem:lemma256 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 43). }; r:evidence ( [ a r:Fact; r:gives {43 math:lessThan 268435456}] - skolem:lemma293 - skolem:lemma296 + skolem:lemma261 + skolem:lemma264 ); 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 268435456]; @@ -4042,75 +3788,87 @@ skolem:lemma288 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma289 a r:Inference; +skolem:lemma257 a r:Inference; r:gives { true :is_prime 1073741783 . }; r:evidence ( [ a r:Fact; r:gives {1073741783 math:greaterThan 3}] [ a r:Fact; r:gives {(1073741783 2) math:remainder 1}] - skolem:lemma297 + [ a r:Fact; r:gives {({ + 1073741783 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1073741783]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma290 a r:Inference; +skolem:lemma258 a r:Inference; r:gives { true :is_prime 37 . }; r:evidence ( [ a r:Fact; r:gives {37 math:greaterThan 3}] [ a r:Fact; r:gives {(37 2) math:remainder 1}] - skolem:lemma298 + [ a r:Fact; r:gives {({ + 37 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 37]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma291 a r:Inference; +skolem:lemma259 a r:Inference; r:gives { true :is_prime 41 . }; r:evidence ( [ a r:Fact; r:gives {41 math:greaterThan 3}] [ a r:Fact; r:gives {(41 2) math:remainder 1}] - skolem:lemma299 + [ a r:Fact; r:gives {({ + 41 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 41]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma292 a r:Inference; +skolem:lemma260 a r:Inference; r:gives { true :is_prime 43 . }; r:evidence ( [ a r:Fact; r:gives {43 math:greaterThan 3}] [ a r:Fact; r:gives {(43 2) math:remainder 1}] - skolem:lemma300 + [ a r:Fact; r:gives {({ + 43 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 43]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma293 a r:Inference; +skolem:lemma261 a r:Inference; r:gives { 43 :next_prime 47 . }; r:evidence ( [ a r:Fact; r:gives {(43 2) math:sum 45}] - skolem:lemma301 + skolem:lemma265 ); 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_0"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 47]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma294 a r:Inference; +skolem:lemma262 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 47). }; r:evidence ( [ a r:Fact; r:gives {47 math:lessThan 33554432}] - skolem:lemma302 - skolem:lemma303 + skolem:lemma266 + skolem:lemma267 ); 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 33554432]; @@ -4118,14 +3876,14 @@ skolem:lemma294 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma295 a r:Inference; +skolem:lemma263 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 47). }; r:evidence ( [ a r:Fact; r:gives {47 math:lessThan 134217728}] - skolem:lemma302 - skolem:lemma304 + skolem:lemma266 + skolem:lemma268 ); 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 134217728]; @@ -4133,99 +3891,55 @@ skolem:lemma295 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma296 a r:Inference; +skolem:lemma264 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 47). }; r:evidence ( [ a r:Fact; r:gives {47 math:lessThan 268435456}] - skolem:lemma302 - 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 268435456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 53]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; - r:rule skolem:lemma99. - -skolem:lemma297 a r:Inference; - r:gives { - 1073741783 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1073741783]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. - -skolem:lemma298 a r:Inference; - r:gives { - 37 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma299 a r:Inference; - r:gives { - 41 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma300 a r:Inference; - r:gives { - 43 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] + skolem:lemma266 + skolem:lemma269 ); - 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 3]; - r:rule skolem:lemma156. + 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 268435456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; + r:rule skolem:lemma99. -skolem:lemma301 a r:Inference; +skolem:lemma265 a r:Inference; r:gives { 45 :next_prime 47 . }; r:evidence ( [ a r:Fact; r:gives {(45 2) math:sum 47}] - skolem:lemma306 + skolem:lemma270 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 45]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma302 a r:Inference; +skolem:lemma266 a r:Inference; r:gives { 47 :next_prime 53 . }; r:evidence ( [ a r:Fact; r:gives {(47 2) math:sum 49}] - skolem:lemma307 + skolem:lemma271 ); 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_0"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 53]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma303 a r:Inference; +skolem:lemma267 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 53). }; r:evidence ( [ a r:Fact; r:gives {53 math:lessThan 33554432}] - skolem:lemma308 - skolem:lemma309 + skolem:lemma272 + skolem:lemma273 ); 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 33554432]; @@ -4233,14 +3947,14 @@ skolem:lemma303 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma304 a r:Inference; +skolem:lemma268 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 53). }; r:evidence ( [ a r:Fact; r:gives {53 math:lessThan 134217728}] - skolem:lemma308 - skolem:lemma310 + skolem:lemma272 + skolem:lemma274 ); 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 134217728]; @@ -4248,14 +3962,14 @@ skolem:lemma304 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma305 a r:Inference; +skolem:lemma269 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 53). }; r:evidence ( [ a r:Fact; r:gives {53 math:lessThan 268435456}] - skolem:lemma308 - skolem:lemma311 + skolem:lemma272 + skolem:lemma275 ); 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 268435456]; @@ -4263,52 +3977,55 @@ skolem:lemma305 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma306 a r:Inference; +skolem:lemma270 a r:Inference; r:gives { true :is_prime 47 . }; r:evidence ( [ a r:Fact; r:gives {47 math:greaterThan 3}] [ a r:Fact; r:gives {(47 2) math:remainder 1}] - skolem:lemma312 + [ a r:Fact; r:gives {({ + 47 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 47]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma307 a r:Inference; +skolem:lemma271 a r:Inference; r:gives { 49 :next_prime 53 . }; r:evidence ( [ a r:Fact; r:gives {(49 2) math:sum 51}] - skolem:lemma313 + skolem:lemma276 ); 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_0"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 53]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma308 a r:Inference; +skolem:lemma272 a r:Inference; r:gives { 53 :next_prime 59 . }; r:evidence ( [ a r:Fact; r:gives {(53 2) math:sum 55}] - skolem:lemma314 + skolem:lemma277 ); 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_0"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 59]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma309 a r:Inference; +skolem:lemma273 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 59). }; r:evidence ( [ a r:Fact; r:gives {59 math:lessThan 33554432}] - skolem:lemma315 - skolem:lemma316 + skolem:lemma278 + skolem:lemma279 ); 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 33554432]; @@ -4316,14 +4033,14 @@ skolem:lemma309 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (61 33554371)]; r:rule skolem:lemma99. -skolem:lemma310 a r:Inference; +skolem:lemma274 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 59). }; r:evidence ( [ a r:Fact; r:gives {59 math:lessThan 134217728}] - skolem:lemma315 - skolem:lemma317 + skolem:lemma278 + skolem:lemma280 ); 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 134217728]; @@ -4331,14 +4048,14 @@ skolem:lemma310 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma311 a r:Inference; +skolem:lemma275 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 59). }; r:evidence ( [ a r:Fact; r:gives {59 math:lessThan 268435456}] - skolem:lemma315 - skolem:lemma318 + skolem:lemma278 + skolem:lemma281 ); 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 268435456]; @@ -4346,44 +4063,33 @@ skolem:lemma311 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma312 a r:Inference; - r:gives { - 47 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma313 a r:Inference; +skolem:lemma276 a r:Inference; r:gives { 51 :next_prime 53 . }; r:evidence ( [ a r:Fact; r:gives {(51 2) math:sum 53}] - skolem:lemma319 + skolem:lemma282 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 51]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma314 a r:Inference; +skolem:lemma277 a r:Inference; r:gives { 55 :next_prime 59 . }; r:evidence ( [ a r:Fact; r:gives {(55 2) math:sum 57}] - skolem:lemma320 + skolem:lemma283 ); 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_0"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 59]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma315 a r:Inference; +skolem:lemma278 a r:Inference; r:gives { 59 :next_prime 61 . }; @@ -4394,15 +4100,15 @@ skolem:lemma315 a r:Inference; ); 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_0"]; r:boundTo 59]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma316 a r:Inference; +skolem:lemma279 a r:Inference; r:gives { 33554432 :goldb ((61 33554371) 61). }; r:evidence ( [ a r:Fact; r:gives {(33554432 61) math:difference 33554371}] - skolem:lemma321 + skolem:lemma284 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 33554371]; @@ -4410,14 +4116,14 @@ skolem:lemma316 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 61]; r:rule skolem:lemma93. -skolem:lemma317 a r:Inference; +skolem:lemma280 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 61). }; r:evidence ( [ a r:Fact; r:gives {61 math:lessThan 134217728}] - skolem:lemma322 - skolem:lemma323 + skolem:lemma285 + skolem:lemma286 ); 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 134217728]; @@ -4425,14 +4131,14 @@ skolem:lemma317 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma318 a r:Inference; +skolem:lemma281 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 61). }; r:evidence ( [ a r:Fact; r:gives {61 math:lessThan 268435456}] - skolem:lemma322 - skolem:lemma324 + skolem:lemma285 + skolem:lemma287 ); 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 268435456]; @@ -4440,64 +4146,70 @@ skolem:lemma318 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma319 a r:Inference; +skolem:lemma282 a r:Inference; r:gives { true :is_prime 53 . }; r:evidence ( [ a r:Fact; r:gives {53 math:greaterThan 3}] [ a r:Fact; r:gives {(53 2) math:remainder 1}] - skolem:lemma325 + [ a r:Fact; r:gives {({ + 53 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 53]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma320 a r:Inference; +skolem:lemma283 a r:Inference; r:gives { 57 :next_prime 59 . }; r:evidence ( [ a r:Fact; r:gives {(57 2) math:sum 59}] - skolem:lemma326 + skolem:lemma288 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 57]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma321 a r:Inference; +skolem:lemma284 a r:Inference; r:gives { true :is_prime 33554371 . }; r:evidence ( [ a r:Fact; r:gives {33554371 math:greaterThan 3}] [ a r:Fact; r:gives {(33554371 2) math:remainder 1}] - skolem:lemma327 + [ a r:Fact; r:gives {({ + 33554371 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 33554371]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma322 a r:Inference; +skolem:lemma285 a r:Inference; r:gives { 61 :next_prime 67 . }; r:evidence ( [ a r:Fact; r:gives {(61 2) math:sum 63}] - skolem:lemma328 + skolem:lemma289 ); 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_0"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 67]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma323 a r:Inference; +skolem:lemma286 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 67). }; r:evidence ( [ a r:Fact; r:gives {67 math:lessThan 134217728}] - skolem:lemma329 - skolem:lemma330 + skolem:lemma290 + skolem:lemma291 ); 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 134217728]; @@ -4505,14 +4217,14 @@ skolem:lemma323 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma324 a r:Inference; +skolem:lemma287 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 67). }; r:evidence ( [ a r:Fact; r:gives {67 math:lessThan 268435456}] - skolem:lemma329 - skolem:lemma331 + skolem:lemma290 + skolem:lemma292 ); 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 268435456]; @@ -4520,74 +4232,55 @@ skolem:lemma324 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma325 a r:Inference; - r:gives { - 53 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma326 a r:Inference; +skolem:lemma288 a r:Inference; r:gives { true :is_prime 59 . }; r:evidence ( [ a r:Fact; r:gives {59 math:greaterThan 3}] [ a r:Fact; r:gives {(59 2) math:remainder 1}] - skolem:lemma332 + [ a r:Fact; r:gives {({ + 59 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 59]; - r:rule skolem:lemma125. - -skolem:lemma327 a r:Inference; - r:gives { - 33554371 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 33554371]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma328 a r:Inference; +skolem:lemma289 a r:Inference; r:gives { 63 :next_prime 67 . }; r:evidence ( [ a r:Fact; r:gives {(63 2) math:sum 65}] - skolem:lemma333 + skolem:lemma293 ); 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_0"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 67]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma329 a r:Inference; +skolem:lemma290 a r:Inference; r:gives { 67 :next_prime 71 . }; r:evidence ( [ a r:Fact; r:gives {(67 2) math:sum 69}] - skolem:lemma334 + skolem:lemma294 ); 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_0"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 71]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma330 a r:Inference; +skolem:lemma291 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 71). }; r:evidence ( [ a r:Fact; r:gives {71 math:lessThan 134217728}] - skolem:lemma335 - skolem:lemma336 + skolem:lemma295 + skolem:lemma296 ); 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 134217728]; @@ -4595,14 +4288,14 @@ skolem:lemma330 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma331 a r:Inference; +skolem:lemma292 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 71). }; r:evidence ( [ a r:Fact; r:gives {71 math:lessThan 268435456}] - skolem:lemma335 - skolem:lemma337 + skolem:lemma295 + skolem:lemma297 ); 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 268435456]; @@ -4610,64 +4303,53 @@ skolem:lemma331 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma332 a r:Inference; - r:gives { - 59 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma333 a r:Inference; +skolem:lemma293 a r:Inference; r:gives { 65 :next_prime 67 . }; r:evidence ( [ a r:Fact; r:gives {(65 2) math:sum 67}] - skolem:lemma338 + skolem:lemma298 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 65]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma334 a r:Inference; +skolem:lemma294 a r:Inference; r:gives { 69 :next_prime 71 . }; r:evidence ( [ a r:Fact; r:gives {(69 2) math:sum 71}] - skolem:lemma339 + skolem:lemma299 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 69]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma335 a r:Inference; +skolem:lemma295 a r:Inference; r:gives { 71 :next_prime 73 . }; r:evidence ( [ a r:Fact; r:gives {(71 2) math:sum 73}] - skolem:lemma340 + skolem:lemma300 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 71]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma336 a r:Inference; +skolem:lemma296 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 73). }; r:evidence ( [ a r:Fact; r:gives {73 math:lessThan 134217728}] - skolem:lemma341 - skolem:lemma342 + skolem:lemma301 + skolem:lemma302 ); 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 134217728]; @@ -4675,14 +4357,14 @@ skolem:lemma336 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (79 134217649)]; r:rule skolem:lemma99. -skolem:lemma337 a r:Inference; +skolem:lemma297 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 73). }; r:evidence ( [ a r:Fact; r:gives {73 math:lessThan 268435456}] - skolem:lemma341 - skolem:lemma343 + skolem:lemma301 + skolem:lemma303 ); 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 268435456]; @@ -4690,62 +4372,71 @@ skolem:lemma337 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma338 a r:Inference; +skolem:lemma298 a r:Inference; r:gives { true :is_prime 67 . }; r:evidence ( [ a r:Fact; r:gives {67 math:greaterThan 3}] [ a r:Fact; r:gives {(67 2) math:remainder 1}] - skolem:lemma344 + [ a r:Fact; r:gives {({ + 67 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 67]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma339 a r:Inference; +skolem:lemma299 a r:Inference; r:gives { true :is_prime 71 . }; r:evidence ( [ a r:Fact; r:gives {71 math:greaterThan 3}] [ a r:Fact; r:gives {(71 2) math:remainder 1}] - skolem:lemma345 + [ a r:Fact; r:gives {({ + 71 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 71]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma340 a r:Inference; +skolem:lemma300 a r:Inference; r:gives { true :is_prime 73 . }; r:evidence ( [ a r:Fact; r:gives {73 math:greaterThan 3}] [ a r:Fact; r:gives {(73 2) math:remainder 1}] - skolem:lemma346 + [ a r:Fact; r:gives {({ + 73 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 73]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma341 a r:Inference; +skolem:lemma301 a r:Inference; r:gives { 73 :next_prime 79 . }; r:evidence ( [ a r:Fact; r:gives {(73 2) math:sum 75}] - skolem:lemma347 + skolem:lemma304 ); 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_0"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 79]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma342 a r:Inference; +skolem:lemma302 a r:Inference; r:gives { 134217728 :goldb ((79 134217649) 79). }; r:evidence ( [ a r:Fact; r:gives {(134217728 79) math:difference 134217649}] - skolem:lemma348 + skolem:lemma305 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 134217649]; @@ -4753,14 +4444,14 @@ skolem:lemma342 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 79]; r:rule skolem:lemma93. -skolem:lemma343 a r:Inference; +skolem:lemma303 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 79). }; r:evidence ( [ a r:Fact; r:gives {79 math:lessThan 268435456}] - skolem:lemma349 - skolem:lemma350 + skolem:lemma306 + skolem:lemma307 ); 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 268435456]; @@ -4768,85 +4459,55 @@ skolem:lemma343 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma344 a r:Inference; - r:gives { - 67 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma345 a r:Inference; - r:gives { - 71 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma346 a r:Inference; - r:gives { - 73 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma347 a r:Inference; +skolem:lemma304 a r:Inference; r:gives { 75 :next_prime 79 . }; r:evidence ( [ a r:Fact; r:gives {(75 2) math:sum 77}] - skolem:lemma351 + skolem:lemma308 ); 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_0"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 79]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma348 a r:Inference; +skolem:lemma305 a r:Inference; r:gives { true :is_prime 134217649 . }; r:evidence ( [ a r:Fact; r:gives {134217649 math:greaterThan 3}] [ a r:Fact; r:gives {(134217649 2) math:remainder 1}] - skolem:lemma352 + [ a r:Fact; r:gives {({ + 134217649 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 134217649]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma349 a r:Inference; +skolem:lemma306 a r:Inference; r:gives { 79 :next_prime 83 . }; r:evidence ( [ a r:Fact; r:gives {(79 2) math:sum 81}] - skolem:lemma353 + skolem:lemma309 ); 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_0"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 83]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma350 a r:Inference; +skolem:lemma307 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 83). }; r:evidence ( [ a r:Fact; r:gives {83 math:lessThan 268435456}] - skolem:lemma354 - skolem:lemma355 + skolem:lemma310 + skolem:lemma311 ); 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 268435456]; @@ -4854,63 +4515,52 @@ skolem:lemma350 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (89 268435367)]; r:rule skolem:lemma99. -skolem:lemma351 a r:Inference; +skolem:lemma308 a r:Inference; r:gives { 77 :next_prime 79 . }; r:evidence ( [ a r:Fact; r:gives {(77 2) math:sum 79}] - skolem:lemma356 + skolem:lemma312 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 77]; - r:rule skolem:lemma129. - -skolem:lemma352 a r:Inference; - r:gives { - 134217649 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 134217649]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + r:rule skolem:lemma125. -skolem:lemma353 a r:Inference; +skolem:lemma309 a r:Inference; r:gives { 81 :next_prime 83 . }; r:evidence ( [ a r:Fact; r:gives {(81 2) math:sum 83}] - skolem:lemma357 + skolem:lemma313 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 81]; - r:rule skolem:lemma129. + r:rule skolem:lemma125. -skolem:lemma354 a r:Inference; +skolem:lemma310 a r:Inference; r:gives { 83 :next_prime 89 . }; r:evidence ( [ a r:Fact; r:gives {(83 2) math:sum 85}] - skolem:lemma358 + skolem:lemma314 ); 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_0"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 89]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma355 a r:Inference; +skolem:lemma311 a r:Inference; r:gives { 268435456 :goldb ((89 268435367) 89). }; r:evidence ( [ a r:Fact; r:gives {(268435456 89) math:difference 268435367}] - skolem:lemma359 + skolem:lemma315 [ a r:Fact; r:gives {true log:callWithCut true}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 268435367]; @@ -4918,121 +4568,89 @@ skolem:lemma355 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 89]; r:rule skolem:lemma93. -skolem:lemma356 a r:Inference; +skolem:lemma312 a r:Inference; r:gives { true :is_prime 79 . }; r:evidence ( [ a r:Fact; r:gives {79 math:greaterThan 3}] [ a r:Fact; r:gives {(79 2) math:remainder 1}] - skolem:lemma360 + [ a r:Fact; r:gives {({ + 79 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 79]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma357 a r:Inference; +skolem:lemma313 a r:Inference; r:gives { true :is_prime 83 . }; r:evidence ( [ a r:Fact; r:gives {83 math:greaterThan 3}] [ a r:Fact; r:gives {(83 2) math:remainder 1}] - skolem:lemma361 + [ a r:Fact; r:gives {({ + 83 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 83]; - r:rule skolem:lemma125. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma358 a r:Inference; +skolem:lemma314 a r:Inference; r:gives { 85 :next_prime 89 . }; r:evidence ( [ a r:Fact; r:gives {(85 2) math:sum 87}] - skolem:lemma362 + skolem:lemma316 ); 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_0"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 89]; - r:rule skolem:lemma178. + r:rule skolem:lemma161. -skolem:lemma359 a r:Inference; +skolem:lemma315 a r:Inference; r:gives { true :is_prime 268435367 . }; r:evidence ( [ a r:Fact; r:gives {268435367 math:greaterThan 3}] [ a r:Fact; r:gives {(268435367 2) math:remainder 1}] - skolem:lemma363 + [ a r:Fact; r:gives {({ + 268435367 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 268435367]; - r:rule skolem:lemma125. - -skolem:lemma360 a r:Inference; - r:gives { - 79 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. - -skolem:lemma361 a r:Inference; - r:gives { - 83 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. -skolem:lemma362 a r:Inference; +skolem:lemma316 a r:Inference; r:gives { 87 :next_prime 89 . }; r:evidence ( [ a r:Fact; r:gives {(87 2) math:sum 89}] - skolem:lemma364 + skolem:lemma317 [ a r:Fact; r:gives {true log:callWithCut true}] ); 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_0"]; r:boundTo 87]; - r:rule skolem:lemma129. - -skolem:lemma363 a r:Inference; - r:gives { - 268435367 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 268435367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; - r:rule skolem:lemma156. + r:rule skolem:lemma125. -skolem:lemma364 a r:Inference; +skolem:lemma317 a r:Inference; r:gives { true :is_prime 89 . }; r:evidence ( [ a r:Fact; r:gives {89 math:greaterThan 3}] [ a r:Fact; r:gives {(89 2) math:remainder 1}] - skolem:lemma365 + [ a r:Fact; r:gives {({ + 89 :has_factor 3. + } false true) log:ifThenElseIn (() -1)}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 89]; - r:rule skolem:lemma125. - -skolem:lemma365 a r:Inference; - r:gives { - 89 :not_has_factor 3 . - }; - r:evidence ( - [ a r:Fact; r:gives true] - ); - 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 3]; - r:rule skolem:lemma156. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo ()]; + r:rule skolem:lemma124. diff --git a/reasoning/goldbach/goldbach.n3 b/reasoning/goldbach/goldbach.n3 index ccb97ba76..4ce506bab 100644 --- a/reasoning/goldbach/goldbach.n3 +++ b/reasoning/goldbach/goldbach.n3 @@ -39,17 +39,9 @@ true :is_prime 3. { true :is_prime ?P } <= { ?P math:greaterThan 3. (?P 2) math:remainder 1. - ?P :not_has_factor 3. + ({ ?P :has_factor 3 } false true) log:ifThenElseIn (?Context -1). }. -{ ?P :not_has_factor ?F } <= { - ?P :has_factor ?F. - true log:callWithCut true. - false log:call false. -}. - -{ ?P :not_has_factor ?F } <= true. - { ?N :has_factor ?L } <= { (?N ?L) math:remainder 0. true log:callWithCut true.