TSTP Solution File: GRA012+1 by Enigma---0.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : GRA012+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 07:15:24 EDT 2022
% Result : Theorem 63.15s 9.34s
% Output : CNFRefutation 63.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 26
% Syntax : Number of clauses : 124 ( 19 unt; 57 nHn; 124 RR)
% Number of literals : 444 ( 180 equ; 252 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 221 ( 68 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_20,plain,
( minus(length_of(X1),n1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_20) ).
cnf(i_0_50,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_50) ).
cnf(i_0_61,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_61) ).
cnf(i_0_17,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_17) ).
cnf(i_0_45,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk6_1(X1),X1)
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_45) ).
cnf(i_0_60,negated_conjecture,
minus(length_of(esk9_0),n1) != number_of_in(triangles,esk9_0),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_60) ).
cnf(i_0_4,plain,
( X1 = X2
| head_of(esk1_2(X2,X1)) = X2
| head_of(esk1_2(X2,X1)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_4) ).
cnf(i_0_62,negated_conjecture,
complete,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_62) ).
cnf(i_0_31,plain,
( precedes(X1,X2,X3)
| ~ on_path(X2,X3)
| ~ on_path(X1,X3)
| ~ sequential(X1,X2)
| ~ path(X4,X5,X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_31) ).
cnf(i_0_44,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk7_1(X1),X1)
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_44) ).
cnf(i_0_7,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_7) ).
cnf(i_0_1,plain,
( X1 = X2
| tail_of(esk1_2(X1,X2)) = X2
| tail_of(esk1_2(X1,X2)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_1) ).
cnf(i_0_52,plain,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,X4)
| ~ shortest_path(X5,X6,X4) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_52) ).
cnf(i_0_8,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_8) ).
cnf(i_0_53,plain,
( triangle(X1,X2,X3)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_53) ).
cnf(i_0_41,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_41) ).
cnf(i_0_42,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1)
| ~ triangle(esk6_1(X1),esk7_1(X1),X4) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_42) ).
cnf(i_0_43,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| sequential(esk6_1(X1),esk7_1(X1))
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_43) ).
cnf(i_0_2,plain,
( X1 = X2
| head_of(esk1_2(X2,X1)) = X1
| tail_of(esk1_2(X2,X1)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_2) ).
cnf(i_0_14,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_14) ).
cnf(i_0_37,plain,
( X1 = X2
| sequential(X1,X2)
| tail_of(X2) != head_of(X1)
| ~ edge(X2)
| ~ edge(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_37) ).
cnf(i_0_40,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_40) ).
cnf(i_0_6,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_6) ).
cnf(i_0_38,plain,
( tail_of(X1) = head_of(X2)
| ~ sequential(X2,X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_38) ).
cnf(i_0_51,plain,
( ~ precedes(X1,X2,X3)
| ~ precedes(X2,X1,X3)
| ~ shortest_path(X4,X5,X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_51) ).
cnf(i_0_3,plain,
( X1 = X2
| head_of(esk1_2(X1,X2)) = X1
| tail_of(esk1_2(X1,X2)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-znh271vr/lgb.p',i_0_3) ).
cnf(c_0_89,plain,
( minus(length_of(X1),n1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1) ),
i_0_20 ).
cnf(c_0_90,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
i_0_50 ).
cnf(c_0_91,plain,
( minus(length_of(X1),n1) = number_of_in(sequential_pairs,X1)
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_92,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
i_0_61 ).
cnf(c_0_93,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
i_0_17 ).
cnf(c_0_94,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk6_1(X1),X1)
| ~ path(X2,X3,X1) ),
i_0_45 ).
cnf(c_0_95,negated_conjecture,
minus(length_of(esk9_0),n1) != number_of_in(triangles,esk9_0),
i_0_60 ).
cnf(c_0_96,negated_conjecture,
minus(length_of(esk9_0),n1) = number_of_in(sequential_pairs,esk9_0),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,plain,
( X1 = X2
| head_of(esk1_2(X2,X1)) = X2
| head_of(esk1_2(X2,X1)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
i_0_4 ).
cnf(c_0_98,negated_conjecture,
complete,
i_0_62 ).
cnf(c_0_99,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_90]) ).
cnf(c_0_100,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk6_1(X1),X1)
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_90]) ).
cnf(c_0_101,negated_conjecture,
number_of_in(triangles,esk9_0) != number_of_in(sequential_pairs,esk9_0),
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,plain,
( precedes(X1,X2,X3)
| ~ on_path(X2,X3)
| ~ on_path(X1,X3)
| ~ sequential(X1,X2)
| ~ path(X4,X5,X3) ),
i_0_31 ).
cnf(c_0_103,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk7_1(X1),X1)
| ~ path(X2,X3,X1) ),
i_0_44 ).
cnf(c_0_104,plain,
( head_of(esk1_2(X1,X2)) = X2
| head_of(esk1_2(X1,X2)) = X1
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_105,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
i_0_7 ).
cnf(c_0_106,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_99,c_0_92]) ).
cnf(c_0_107,negated_conjecture,
on_path(esk6_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_92]),c_0_101]) ).
cnf(c_0_108,plain,
( precedes(X1,X2,X3)
| ~ sequential(X1,X2)
| ~ on_path(X2,X3)
| ~ on_path(X1,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(spm,[status(thm)],[c_0_102,c_0_90]) ).
cnf(c_0_109,plain,
( X1 = X2
| tail_of(esk1_2(X1,X2)) = X2
| tail_of(esk1_2(X1,X2)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
i_0_1 ).
cnf(c_0_110,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk7_1(X1),X1)
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_90]) ).
cnf(c_0_111,plain,
( head_of(esk1_2(tail_of(X1),X2)) = tail_of(X1)
| head_of(esk1_2(tail_of(X1),X2)) = X2
| X2 = tail_of(X1)
| ~ edge(X1)
| ~ vertex(X2) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,negated_conjecture,
edge(esk6_1(esk9_0)),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,X4)
| ~ shortest_path(X5,X6,X4) ),
i_0_52 ).
cnf(c_0_114,negated_conjecture,
( precedes(X1,X2,esk9_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_108,c_0_92]) ).
cnf(c_0_115,plain,
( tail_of(esk1_2(X1,X2)) = X1
| tail_of(esk1_2(X1,X2)) = X2
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_98])]) ).
cnf(c_0_116,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
i_0_8 ).
cnf(c_0_117,negated_conjecture,
on_path(esk7_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_92]),c_0_101]) ).
cnf(c_0_118,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),X1)) = tail_of(esk6_1(esk9_0))
| head_of(esk1_2(tail_of(esk6_1(esk9_0)),X1)) = X1
| X1 = tail_of(esk6_1(esk9_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,plain,
( triangle(X1,X2,X3)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
i_0_53 ).
cnf(c_0_120,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
i_0_41 ).
cnf(c_0_121,plain,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ sequential(X3,X2)
| ~ on_path(X2,esk9_0)
| ~ on_path(X3,esk9_0)
| ~ shortest_path(X4,X5,esk9_0) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_122,plain,
( tail_of(esk1_2(X1,head_of(X2))) = head_of(X2)
| tail_of(esk1_2(X1,head_of(X2))) = X1
| X1 = head_of(X2)
| ~ edge(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,negated_conjecture,
edge(esk7_1(esk9_0)),
inference(spm,[status(thm)],[c_0_106,c_0_117]) ).
cnf(c_0_124,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(X1))) = tail_of(esk6_1(esk9_0))
| head_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(X1))) = head_of(X1)
| head_of(X1) = tail_of(esk6_1(esk9_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_116]) ).
cnf(c_0_125,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1)
| ~ triangle(esk6_1(X1),esk7_1(X1),X4) ),
i_0_42 ).
cnf(c_0_126,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_119,c_0_120]),c_0_120]),c_0_120]) ).
cnf(c_0_127,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| sequential(esk6_1(X1),esk7_1(X1))
| ~ path(X2,X3,X1) ),
i_0_43 ).
cnf(c_0_128,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ sequential(X3,X2)
| ~ on_path(X2,esk9_0)
| ~ on_path(X3,esk9_0) ),
inference(spm,[status(thm)],[c_0_121,c_0_92]) ).
cnf(c_0_129,plain,
( X1 = X2
| head_of(esk1_2(X2,X1)) = X1
| tail_of(esk1_2(X2,X1)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
i_0_2 ).
cnf(c_0_130,negated_conjecture,
( tail_of(esk1_2(X1,head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk1_2(X1,head_of(esk7_1(esk9_0)))) = X1
| X1 = head_of(esk7_1(esk9_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_131,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
i_0_14 ).
cnf(c_0_132,negated_conjecture,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| head_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = tail_of(esk6_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_133,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ sequential(X2,esk6_1(X1))
| ~ sequential(esk7_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_134,plain,
( X1 = X2
| sequential(X1,X2)
| tail_of(X2) != head_of(X1)
| ~ edge(X2)
| ~ edge(X1) ),
i_0_37 ).
cnf(c_0_135,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
i_0_40 ).
cnf(c_0_136,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
i_0_6 ).
cnf(c_0_137,negated_conjecture,
( head_of(X1) != head_of(esk7_1(esk9_0))
| tail_of(X1) != tail_of(X2)
| ~ sequential(X2,esk7_1(esk9_0))
| ~ on_path(X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_128,c_0_117]) ).
cnf(c_0_138,plain,
( tail_of(esk1_2(X1,X2)) = X2
| head_of(esk1_2(X1,X2)) = X2
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_98])]) ).
cnf(c_0_139,plain,
( tail_of(esk1_2(tail_of(X1),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk1_2(tail_of(X1),head_of(esk7_1(esk9_0)))) = tail_of(X1)
| tail_of(X1) = head_of(esk7_1(esk9_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_105]) ).
cnf(c_0_140,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) != tail_of(esk6_1(esk9_0))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_141,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| X2 = esk6_1(X1)
| tail_of(esk6_1(X1)) != head_of(X2)
| ~ edge(esk6_1(X1))
| ~ sequential(esk7_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]) ).
cnf(c_0_142,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),tail_of(X1))) = tail_of(esk6_1(esk9_0))
| head_of(esk1_2(tail_of(esk6_1(esk9_0)),tail_of(X1))) = tail_of(X1)
| tail_of(X1) = tail_of(esk6_1(esk9_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_105]) ).
cnf(c_0_143,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_98])]) ).
cnf(c_0_144,plain,
( tail_of(esk1_2(X1,head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| head_of(esk7_1(esk9_0)) = X1
| tail_of(esk1_2(X1,head_of(esk7_1(esk9_0)))) != tail_of(X2)
| ~ vertex(head_of(esk7_1(esk9_0)))
| ~ vertex(X1)
| ~ sequential(X2,esk7_1(esk9_0))
| ~ on_path(X2,esk9_0) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138])]) ).
cnf(c_0_145,negated_conjecture,
( tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = tail_of(esk6_1(esk9_0))
| tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_139,c_0_112]) ).
cnf(c_0_146,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| sequential(esk6_1(X1),esk7_1(X1))
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_90]) ).
cnf(c_0_147,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| vertex(tail_of(esk6_1(esk9_0)))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_116,c_0_132]) ).
cnf(c_0_148,plain,
( tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| vertex(head_of(esk7_1(esk9_0)))
| tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) != tail_of(esk6_1(esk9_0))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_116,c_0_140]) ).
cnf(c_0_149,negated_conjecture,
( tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) != tail_of(esk6_1(esk9_0))
| tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) != tail_of(X1)
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0))))
| ~ sequential(X1,esk7_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_137,c_0_140]) ).
cnf(c_0_150,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| esk7_1(X1) = X2
| X2 = esk6_1(X1)
| tail_of(esk6_1(X1)) != head_of(X2)
| tail_of(X2) != head_of(esk7_1(X1))
| ~ edge(esk6_1(X1))
| ~ edge(esk7_1(X1))
| ~ edge(X2)
| ~ path(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_141,c_0_134]) ).
cnf(c_0_151,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),tail_of(esk1_2(X1,X2)))) = tail_of(esk1_2(X1,X2))
| head_of(esk1_2(tail_of(esk6_1(esk9_0)),tail_of(esk1_2(X1,X2)))) = tail_of(esk6_1(esk9_0))
| tail_of(esk1_2(X1,X2)) = tail_of(esk6_1(esk9_0))
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_152,plain,
( tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) != tail_of(X1)
| ~ vertex(head_of(esk7_1(esk9_0)))
| ~ vertex(tail_of(esk6_1(esk9_0)))
| ~ sequential(X1,esk7_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_153,negated_conjecture,
sequential(esk6_1(esk9_0),esk7_1(esk9_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_92]),c_0_101]) ).
cnf(c_0_154,plain,
( tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| vertex(tail_of(esk6_1(esk9_0)))
| tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) != head_of(esk7_1(esk9_0))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_131,c_0_147]) ).
cnf(c_0_155,negated_conjecture,
( tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| vertex(head_of(esk7_1(esk9_0)))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_148,c_0_145]) ).
cnf(c_0_156,negated_conjecture,
( tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) != tail_of(X1)
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0))))
| ~ sequential(X1,esk7_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_149,c_0_145]) ).
cnf(c_0_157,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| X2 = esk6_1(X1)
| esk7_1(X1) = X2
| tail_of(esk6_1(X1)) != head_of(X2)
| tail_of(X2) != head_of(esk7_1(X1))
| ~ edge(esk6_1(X1))
| ~ edge(esk7_1(X1))
| ~ edge(X2)
| ~ shortest_path(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_150,c_0_90]) ).
cnf(c_0_158,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),tail_of(esk1_2(X1,X2)))) = tail_of(esk6_1(esk9_0))
| tail_of(esk1_2(X1,X2)) = tail_of(esk6_1(esk9_0))
| X1 = X2
| tail_of(esk1_2(tail_of(esk6_1(esk9_0)),tail_of(esk1_2(X1,X2)))) != tail_of(esk1_2(X1,X2))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),tail_of(esk1_2(X1,X2))))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_131,c_0_151]) ).
cnf(c_0_159,plain,
( tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ vertex(head_of(esk7_1(esk9_0)))
| ~ vertex(tail_of(esk6_1(esk9_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_152]),c_0_153]),c_0_107])]) ).
cnf(c_0_160,plain,
( tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| vertex(tail_of(esk6_1(esk9_0)))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_145]),c_0_154]) ).
cnf(c_0_161,plain,
( tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| vertex(head_of(esk7_1(esk9_0)))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_105,c_0_155]) ).
cnf(c_0_162,negated_conjecture,
( tail_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = head_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_156]),c_0_153]),c_0_107])]) ).
cnf(c_0_163,plain,
( tail_of(X1) = head_of(X2)
| ~ sequential(X2,X1) ),
i_0_38 ).
cnf(c_0_164,plain,
( ~ precedes(X1,X2,X3)
| ~ precedes(X2,X1,X3)
| ~ shortest_path(X4,X5,X3) ),
i_0_51 ).
cnf(c_0_165,negated_conjecture,
( esk7_1(esk9_0) = X1
| X1 = esk6_1(esk9_0)
| tail_of(esk6_1(esk9_0)) != head_of(X1)
| tail_of(X1) != head_of(esk7_1(esk9_0))
| ~ edge(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_92]),c_0_112]),c_0_123])]),c_0_101]) ).
cnf(c_0_166,plain,
( head_of(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) = tail_of(esk6_1(esk9_0))
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_160]),c_0_161]),c_0_162]) ).
cnf(c_0_167,plain,
head_of(esk6_1(esk9_0)) = tail_of(esk7_1(esk9_0)),
inference(spm,[status(thm)],[c_0_163,c_0_153]) ).
cnf(c_0_168,plain,
( ~ precedes(X1,X2,esk9_0)
| ~ sequential(X2,X1)
| ~ on_path(X1,esk9_0)
| ~ on_path(X2,esk9_0)
| ~ shortest_path(X3,X4,esk9_0) ),
inference(spm,[status(thm)],[c_0_164,c_0_114]) ).
cnf(c_0_169,negated_conjecture,
( esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0))) = esk6_1(esk9_0)
| esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ edge(esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_162]) ).
cnf(c_0_170,plain,
( head_of(esk7_1(esk9_0)) != tail_of(esk7_1(esk9_0))
| tail_of(esk6_1(esk9_0)) != tail_of(X1)
| ~ sequential(X1,esk7_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_137,c_0_167]) ).
cnf(c_0_171,negated_conjecture,
( ~ sequential(X1,X2)
| ~ sequential(X2,X1)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0)
| ~ shortest_path(X3,X4,esk9_0) ),
inference(spm,[status(thm)],[c_0_168,c_0_114]) ).
cnf(c_0_172,plain,
( X1 = X2
| head_of(esk1_2(X1,X2)) = X1
| tail_of(esk1_2(X1,X2)) = X1
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
i_0_3 ).
cnf(c_0_173,plain,
( esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0))) = esk7_1(esk9_0)
| esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0))) = esk6_1(esk9_0)
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ vertex(head_of(esk7_1(esk9_0)))
| ~ vertex(tail_of(esk6_1(esk9_0))) ),
inference(spm,[status(thm)],[c_0_169,c_0_143]) ).
cnf(c_0_174,plain,
head_of(esk7_1(esk9_0)) != tail_of(esk7_1(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_170]),c_0_153]),c_0_107])]) ).
cnf(c_0_175,negated_conjecture,
( ~ sequential(X1,X2)
| ~ sequential(X2,X1)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_171,c_0_92]) ).
cnf(c_0_176,plain,
( tail_of(esk1_2(X1,X2)) = X1
| head_of(esk1_2(X1,X2)) = X1
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_98])]) ).
cnf(c_0_177,plain,
( esk1_2(tail_of(esk6_1(esk9_0)),head_of(esk7_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ vertex(tail_of(esk6_1(esk9_0)))
| ~ vertex(head_of(esk7_1(esk9_0))) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_173]),c_0_167]),c_0_174]) ).
cnf(c_0_178,plain,
tail_of(esk6_1(esk9_0)) != tail_of(esk7_1(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_167]),c_0_112])]) ).
cnf(c_0_179,negated_conjecture,
( ~ sequential(X1,esk6_1(esk9_0))
| ~ sequential(esk6_1(esk9_0),X1)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_175,c_0_107]) ).
cnf(c_0_180,plain,
( tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ vertex(head_of(esk7_1(esk9_0)))
| ~ vertex(tail_of(esk6_1(esk9_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_178]) ).
cnf(c_0_181,plain,
( X1 = esk6_1(esk9_0)
| tail_of(esk6_1(esk9_0)) != head_of(X1)
| ~ sequential(esk6_1(esk9_0),X1)
| ~ on_path(X1,esk9_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_134]),c_0_112])]),c_0_135]) ).
cnf(c_0_182,plain,
( tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0))
| ~ vertex(head_of(esk7_1(esk9_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_105]),c_0_112])]) ).
cnf(c_0_183,plain,
( esk6_1(esk9_0) = esk7_1(esk9_0)
| tail_of(esk6_1(esk9_0)) != head_of(esk7_1(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_153]),c_0_117])]) ).
cnf(c_0_184,plain,
tail_of(esk6_1(esk9_0)) = head_of(esk7_1(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_116]),c_0_123])]) ).
cnf(c_0_185,plain,
esk6_1(esk9_0) = esk7_1(esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_184])]) ).
cnf(c_0_186,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185]),c_0_174]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRA012+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 03:03:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 # ENIGMATIC: Selected SinE mode:
% 0.18/0.44 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.18/0.44 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.18/0.44 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 63.15/9.34 # ENIGMATIC: Solved by autoschedule-lgb:
% 63.15/9.34 # No SInE strategy applied
% 63.15/9.34 # Trying AutoSched0 for 150 seconds
% 63.15/9.34 # AutoSched0-Mode selected heuristic G_E___207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 63.15/9.34 # and selection function SelectMaxLComplexAvoidPosPred.
% 63.15/9.34 #
% 63.15/9.34 # Preprocessing time : 0.023 s
% 63.15/9.34
% 63.15/9.34 # Proof found!
% 63.15/9.34 # SZS status Theorem
% 63.15/9.34 # SZS output start CNFRefutation
% See solution above
% 63.15/9.34 # Training examples: 0 positive, 0 negative
% 63.15/9.34
% 63.15/9.34 # -------------------------------------------------
% 63.15/9.34 # User time : 6.671 s
% 63.15/9.34 # System time : 0.093 s
% 63.15/9.34 # Total time : 6.764 s
% 63.15/9.34 # Maximum resident set size: 7128 pages
% 63.15/9.34
%------------------------------------------------------------------------------