TSTP Solution File: GRA002+1 by Enigma---0.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : GRA002+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n027.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 07:15:22 EDT 2022
% Result : Theorem 13.55s 3.07s
% Output : CNFRefutation 13.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 29
% Syntax : Number of clauses : 148 ( 15 unt; 72 nHn; 146 RR)
% Number of literals : 548 ( 244 equ; 275 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 275 ( 88 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_12,plain,
( vertex(X1)
| ~ in_path(X1,X2)
| ~ path(X3,X4,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_12) ).
cnf(i_0_53,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_53) ).
cnf(i_0_19,plain,
( in_path(head_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_19) ).
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/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_1) ).
cnf(i_0_16,negated_conjecture,
complete,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_16) ).
cnf(i_0_15,negated_conjecture,
shortest_path(esk4_0,esk5_0,esk3_0),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_15) ).
cnf(i_0_7,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_7) ).
cnf(i_0_47,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk10_1(X1),X1)
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_47) ).
cnf(i_0_20,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_20) ).
cnf(i_0_23,plain,
( minus(length_of(X1),n1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_23) ).
cnf(i_0_18,plain,
( in_path(tail_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_18) ).
cnf(i_0_34,plain,
( precedes(X1,X2,X3)
| ~ on_path(X2,X3)
| ~ on_path(X1,X3)
| ~ sequential(X1,X2)
| ~ path(X4,X5,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_34) ).
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/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_4) ).
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/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_2) ).
cnf(i_0_6,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_6) ).
cnf(i_0_8,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_8) ).
cnf(i_0_14,negated_conjecture,
~ less_or_equal(minus(length_of(esk3_0),n1),number_of_in(triangles,graph)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_14) ).
cnf(i_0_48,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk9_1(X1),X1)
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_48) ).
cnf(i_0_56,plain,
( triangle(X1,X2,X3)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_56) ).
cnf(i_0_44,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_44) ).
cnf(i_0_55,plain,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ shortest_path(X4,X5,X6)
| ~ precedes(X3,X2,X6) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_55) ).
cnf(i_0_17,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_17) ).
cnf(i_0_9,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_9) ).
cnf(i_0_45,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1)
| ~ triangle(esk9_1(X1),esk10_1(X1),X4) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_45) ).
cnf(i_0_46,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| sequential(esk9_1(X1),esk10_1(X1))
| ~ path(X2,X3,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_46) ).
cnf(i_0_40,plain,
( X1 = X2
| sequential(X1,X2)
| tail_of(X2) != head_of(X1)
| ~ edge(X2)
| ~ edge(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_40) ).
cnf(i_0_43,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_43) ).
cnf(i_0_54,plain,
( ~ shortest_path(X1,X2,X3)
| ~ precedes(X4,X5,X3)
| ~ precedes(X5,X4,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_54) ).
cnf(i_0_41,plain,
( tail_of(X1) = head_of(X2)
| ~ sequential(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-bkz4kru4/lgb.p',i_0_41) ).
cnf(c_0_86,plain,
( vertex(X1)
| ~ in_path(X1,X2)
| ~ path(X3,X4,X2) ),
i_0_12 ).
cnf(c_0_87,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
i_0_53 ).
cnf(c_0_88,plain,
( in_path(head_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
i_0_19 ).
cnf(c_0_89,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_90,negated_conjecture,
complete,
i_0_16 ).
cnf(c_0_91,plain,
( vertex(X1)
| ~ in_path(X1,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,negated_conjecture,
shortest_path(esk4_0,esk5_0,esk3_0),
i_0_15 ).
cnf(c_0_93,plain,
( in_path(head_of(X1),X2)
| ~ on_path(X1,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_87]) ).
cnf(c_0_94,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_89,c_0_90])]) ).
cnf(c_0_95,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
i_0_7 ).
cnf(c_0_96,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
( in_path(head_of(X1),esk3_0)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_92]) ).
cnf(c_0_98,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk10_1(X1),X1)
| ~ path(X2,X3,X1) ),
i_0_47 ).
cnf(c_0_99,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
i_0_20 ).
cnf(c_0_100,plain,
( minus(length_of(X1),n1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1) ),
i_0_23 ).
cnf(c_0_101,plain,
( in_path(tail_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
i_0_18 ).
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_34 ).
cnf(c_0_103,plain,
( tail_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
| tail_of(esk1_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_105,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk10_1(X1),X1)
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_87]) ).
cnf(c_0_106,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_107,plain,
( edge(X1)
| ~ on_path(X1,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_99,c_0_87]) ).
cnf(c_0_108,plain,
( minus(length_of(X1),n1) = number_of_in(sequential_pairs,X1)
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_87]) ).
cnf(c_0_109,plain,
( in_path(tail_of(X1),X2)
| ~ on_path(X1,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_87]) ).
cnf(c_0_110,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_87]) ).
cnf(c_0_111,negated_conjecture,
( tail_of(esk1_2(head_of(X1),tail_of(X2))) = head_of(X1)
| tail_of(esk1_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| head_of(X1) = tail_of(X2)
| ~ edge(X2)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| on_path(esk10_1(esk3_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_105,c_0_92]) ).
cnf(c_0_113,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_114,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
i_0_6 ).
cnf(c_0_115,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_106,c_0_90])]) ).
cnf(c_0_116,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
i_0_8 ).
cnf(c_0_117,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_107,c_0_92]) ).
cnf(c_0_118,negated_conjecture,
~ less_or_equal(minus(length_of(esk3_0),n1),number_of_in(triangles,graph)),
i_0_14 ).
cnf(c_0_119,negated_conjecture,
minus(length_of(esk3_0),n1) = number_of_in(sequential_pairs,esk3_0),
inference(spm,[status(thm)],[c_0_108,c_0_92]) ).
cnf(c_0_120,negated_conjecture,
( in_path(tail_of(X1),esk3_0)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_109,c_0_92]) ).
cnf(c_0_121,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk9_1(X1),X1)
| ~ path(X2,X3,X1) ),
i_0_48 ).
cnf(c_0_122,plain,
( triangle(X1,X2,X3)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
i_0_56 ).
cnf(c_0_123,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
i_0_44 ).
cnf(c_0_124,plain,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ shortest_path(X4,X5,X6)
| ~ precedes(X3,X2,X6) ),
i_0_55 ).
cnf(c_0_125,negated_conjecture,
( precedes(X1,X2,esk3_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk3_0)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_110,c_0_92]) ).
cnf(c_0_126,negated_conjecture,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_127,plain,
( head_of(esk1_2(X1,X2)) = X2
| tail_of(esk1_2(X1,X2)) = X2
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_90])]) ).
cnf(c_0_128,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_90])]) ).
cnf(c_0_129,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
i_0_17 ).
cnf(c_0_130,plain,
( head_of(esk1_2(head_of(X1),X2)) = head_of(X1)
| head_of(esk1_2(head_of(X1),X2)) = X2
| X2 = head_of(X1)
| ~ vertex(X2)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_131,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
i_0_9 ).
cnf(c_0_132,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| edge(esk10_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_117,c_0_112]) ).
cnf(c_0_133,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk3_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_134,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_96,c_0_120]) ).
cnf(c_0_135,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| on_path(esk9_1(X1),X1)
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_87]) ).
cnf(c_0_136,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ path(X2,X3,X1)
| ~ triangle(esk9_1(X1),esk10_1(X1),X4) ),
i_0_45 ).
cnf(c_0_137,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_122,c_0_123]),c_0_123]),c_0_123]) ).
cnf(c_0_138,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| sequential(esk9_1(X1),esk10_1(X1))
| ~ path(X2,X3,X1) ),
i_0_46 ).
cnf(c_0_139,plain,
( tail_of(X1) != tail_of(X2)
| head_of(X1) != head_of(X3)
| ~ sequential(X2,X3)
| ~ on_path(X3,esk3_0)
| ~ on_path(X2,esk3_0)
| ~ shortest_path(X4,X5,esk3_0) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_140,plain,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = X1
| head_of(esk1_2(X2,X1)) = X1
| X1 = head_of(esk10_1(esk3_0))
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_141,plain,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) != tail_of(X1)
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_126]) ).
cnf(c_0_142,plain,
( head_of(esk1_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| head_of(esk1_2(head_of(X1),tail_of(X2))) = head_of(X1)
| tail_of(X2) = head_of(X1)
| ~ edge(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[c_0_130,c_0_95]) ).
cnf(c_0_143,plain,
edge(esk10_1(esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_133]) ).
cnf(c_0_144,plain,
( tail_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
| tail_of(esk1_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ vertex(X1)
| ~ on_path(X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_134]) ).
cnf(c_0_145,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| on_path(esk9_1(esk3_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_135,c_0_92]) ).
cnf(c_0_146,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ sequential(X2,esk9_1(X1))
| ~ sequential(esk10_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]) ).
cnf(c_0_147,plain,
( X1 = X2
| sequential(X1,X2)
| tail_of(X2) != head_of(X1)
| ~ edge(X2)
| ~ edge(X1) ),
i_0_40 ).
cnf(c_0_148,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
i_0_43 ).
cnf(c_0_149,negated_conjecture,
( tail_of(X1) != tail_of(X2)
| head_of(X1) != head_of(X3)
| ~ sequential(X2,X3)
| ~ on_path(X3,esk3_0)
| ~ on_path(X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_139,c_0_92]) ).
cnf(c_0_150,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| sequential(esk9_1(X1),esk10_1(X1))
| ~ shortest_path(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_138,c_0_87]) ).
cnf(c_0_151,negated_conjecture,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = head_of(esk10_1(esk3_0))
| tail_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = X1
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| head_of(esk1_2(head_of(X2),X1)) = X1
| X1 = head_of(esk10_1(esk3_0))
| X1 = head_of(X2)
| ~ vertex(X1)
| ~ on_path(X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_140,c_0_104]) ).
cnf(c_0_152,plain,
( head_of(esk1_2(head_of(X1),X2)) = head_of(X1)
| head_of(esk1_2(head_of(X1),X2)) = X2
| X2 = head_of(X1)
| ~ vertex(X2)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_115,c_0_104]) ).
cnf(c_0_153,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| vertex(head_of(esk10_1(esk3_0)))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) != tail_of(X1)
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_141]) ).
cnf(c_0_154,plain,
( head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_155,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(esk9_1(esk3_0)))) = tail_of(esk9_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk1_2(X1,tail_of(esk9_1(esk3_0)))) = X1
| X1 = tail_of(esk9_1(esk3_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_156,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| X2 = esk9_1(X1)
| head_of(X2) != tail_of(esk9_1(X1))
| ~ sequential(esk10_1(X1),X2)
| ~ edge(esk9_1(X1))
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
cnf(c_0_157,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| head_of(X1) != head_of(esk10_1(esk3_0))
| tail_of(X1) != tail_of(X2)
| ~ sequential(X2,esk10_1(esk3_0))
| ~ on_path(X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_149,c_0_112]) ).
cnf(c_0_158,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| sequential(esk9_1(esk3_0),esk10_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_150,c_0_92]) ).
cnf(c_0_159,negated_conjecture,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = head_of(esk10_1(esk3_0))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = X1
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = X1
| X1 = head_of(esk10_1(esk3_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_112]) ).
cnf(c_0_160,negated_conjecture,
( head_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| head_of(esk1_2(head_of(esk10_1(esk3_0)),X1)) = X1
| X1 = head_of(esk10_1(esk3_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_152,c_0_112]) ).
cnf(c_0_161,plain,
( head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| vertex(head_of(esk10_1(esk3_0)))
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_162,plain,
( tail_of(esk1_2(head_of(X1),tail_of(esk9_1(esk3_0)))) = tail_of(esk9_1(esk3_0))
| tail_of(esk1_2(head_of(X1),tail_of(esk9_1(esk3_0)))) = head_of(X1)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| head_of(X1) = tail_of(esk9_1(esk3_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_116]) ).
cnf(c_0_163,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| esk10_1(X1) = X2
| X2 = esk9_1(X1)
| head_of(X2) != tail_of(esk9_1(X1))
| head_of(esk10_1(X1)) != tail_of(X2)
| ~ edge(esk9_1(X1))
| ~ edge(esk10_1(X1))
| ~ edge(X2)
| ~ path(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_156,c_0_147]) ).
cnf(c_0_164,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| head_of(X1) != head_of(esk10_1(esk3_0))
| tail_of(X1) != tail_of(esk9_1(esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_145]),c_0_158]) ).
cnf(c_0_165,negated_conjecture,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_159,c_0_134]) ).
cnf(c_0_166,negated_conjecture,
( head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_160,c_0_134]) ).
cnf(c_0_167,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| vertex(head_of(esk10_1(esk3_0)))
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_161]) ).
cnf(c_0_168,plain,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) = head_of(esk10_1(esk3_0))
| tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) = tail_of(esk9_1(esk3_0))
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0) ),
inference(spm,[status(thm)],[c_0_162,c_0_143]) ).
cnf(c_0_169,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| X2 = esk9_1(X1)
| esk10_1(X1) = X2
| head_of(X2) != tail_of(esk9_1(X1))
| head_of(esk10_1(X1)) != tail_of(X2)
| ~ edge(esk9_1(X1))
| ~ edge(esk10_1(X1))
| ~ edge(X2)
| ~ shortest_path(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_163,c_0_87]) ).
cnf(c_0_170,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| edge(esk9_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_117,c_0_145]) ).
cnf(c_0_171,negated_conjecture,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| tail_of(X1) != tail_of(esk9_1(esk3_0))
| ~ on_path(X1,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166]) ).
cnf(c_0_172,negated_conjecture,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) != head_of(esk10_1(esk3_0))
| tail_of(X1) != tail_of(esk9_1(esk3_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_164,c_0_126]) ).
cnf(c_0_173,plain,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) = head_of(esk10_1(esk3_0))
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| vertex(head_of(esk10_1(esk3_0)))
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_174,plain,
( ~ shortest_path(X1,X2,X3)
| ~ precedes(X4,X5,X3)
| ~ precedes(X5,X4,X3) ),
i_0_54 ).
cnf(c_0_175,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| esk10_1(esk3_0) = X1
| X1 = esk9_1(esk3_0)
| head_of(X1) != tail_of(esk9_1(esk3_0))
| tail_of(X1) != head_of(esk10_1(esk3_0))
| ~ edge(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_92]),c_0_143])]),c_0_170]) ).
cnf(c_0_176,plain,
( head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| tail_of(X1) != tail_of(esk9_1(esk3_0))
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)))
| ~ on_path(X1,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_171]),c_0_166]) ).
cnf(c_0_177,plain,
( head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) = tail_of(X1)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| tail_of(X1) != tail_of(esk9_1(esk3_0))
| ~ vertex(head_of(esk10_1(esk3_0)))
| ~ edge(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_172]),c_0_95]),c_0_154]) ).
cnf(c_0_178,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| vertex(head_of(esk10_1(esk3_0)))
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) ),
inference(spm,[status(thm)],[c_0_95,c_0_173]) ).
cnf(c_0_179,plain,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| head_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) != tail_of(esk9_1(esk3_0))
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) ),
inference(spm,[status(thm)],[c_0_129,c_0_168]) ).
cnf(c_0_180,plain,
( ~ precedes(X1,X2,esk3_0)
| ~ sequential(X2,X1)
| ~ on_path(X1,esk3_0)
| ~ on_path(X2,esk3_0)
| ~ shortest_path(X3,X4,esk3_0) ),
inference(spm,[status(thm)],[c_0_174,c_0_125]) ).
cnf(c_0_181,negated_conjecture,
( esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)) = esk9_1(esk3_0)
| esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)) = esk10_1(esk3_0)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(X1) = head_of(esk10_1(esk3_0))
| tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1))) != head_of(esk10_1(esk3_0))
| tail_of(X1) != tail_of(esk9_1(esk3_0))
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(X1)))
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_182,plain,
( tail_of(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) = head_of(esk10_1(esk3_0))
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_168]),c_0_178]),c_0_179]) ).
cnf(c_0_183,negated_conjecture,
( ~ sequential(X1,X2)
| ~ sequential(X2,X1)
| ~ on_path(X2,esk3_0)
| ~ on_path(X1,esk3_0)
| ~ shortest_path(X3,X4,esk3_0) ),
inference(spm,[status(thm)],[c_0_180,c_0_125]) ).
cnf(c_0_184,plain,
( esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0))) = esk10_1(esk3_0)
| esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0))) = esk9_1(esk3_0)
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| ~ edge(esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_145]) ).
cnf(c_0_185,negated_conjecture,
( ~ sequential(X1,X2)
| ~ sequential(X2,X1)
| ~ on_path(X2,esk3_0)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_183,c_0_92]) ).
cnf(c_0_186,plain,
( esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0))) = esk9_1(esk3_0)
| esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0))) = esk10_1(esk3_0)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| ~ vertex(tail_of(esk9_1(esk3_0)))
| ~ vertex(head_of(esk10_1(esk3_0))) ),
inference(spm,[status(thm)],[c_0_184,c_0_128]) ).
cnf(c_0_187,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| ~ sequential(X1,esk10_1(esk3_0))
| ~ sequential(esk10_1(esk3_0),X1)
| ~ on_path(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_185,c_0_112]) ).
cnf(c_0_188,plain,
( head_of(esk1_2(X1,tail_of(esk9_1(esk3_0)))) = tail_of(esk9_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk9_1(esk3_0)) = X1
| head_of(esk1_2(X1,tail_of(esk9_1(esk3_0)))) != head_of(esk10_1(esk3_0))
| ~ vertex(tail_of(esk9_1(esk3_0)))
| ~ vertex(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_127])]) ).
cnf(c_0_189,plain,
( esk1_2(head_of(esk10_1(esk3_0)),tail_of(esk9_1(esk3_0))) = esk10_1(esk3_0)
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| ~ vertex(tail_of(esk9_1(esk3_0)))
| ~ vertex(head_of(esk10_1(esk3_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_186]),c_0_170]) ).
cnf(c_0_190,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| ~ sequential(esk9_1(esk3_0),esk10_1(esk3_0))
| ~ sequential(esk10_1(esk3_0),esk9_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_187,c_0_145]) ).
cnf(c_0_191,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| ~ vertex(tail_of(esk9_1(esk3_0)))
| ~ vertex(head_of(esk10_1(esk3_0))) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
cnf(c_0_192,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| ~ sequential(esk10_1(esk3_0),esk9_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_190,c_0_158]) ).
cnf(c_0_193,negated_conjecture,
( tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0))
| number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| ~ vertex(head_of(esk10_1(esk3_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_134]),c_0_145]) ).
cnf(c_0_194,plain,
( tail_of(X1) = head_of(X2)
| ~ sequential(X2,X1) ),
i_0_41 ).
cnf(c_0_195,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| esk9_1(esk3_0) = esk10_1(esk3_0)
| tail_of(esk9_1(esk3_0)) != head_of(esk10_1(esk3_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_147]),c_0_143])]),c_0_170]) ).
cnf(c_0_196,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk9_1(esk3_0)) = head_of(esk10_1(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_116]),c_0_143])]) ).
cnf(c_0_197,negated_conjecture,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| head_of(esk9_1(esk3_0)) != head_of(esk10_1(esk3_0)) ),
inference(er,[status(thm)],[c_0_164]) ).
cnf(c_0_198,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| head_of(esk9_1(esk3_0)) = tail_of(esk10_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_194,c_0_158]) ).
cnf(c_0_199,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| esk9_1(esk3_0) = esk10_1(esk3_0) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_200,plain,
( number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0)
| tail_of(esk10_1(esk3_0)) != head_of(esk10_1(esk3_0)) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_201,plain,
esk9_1(esk3_0) = esk10_1(esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_199]),c_0_133]) ).
cnf(c_0_202,plain,
tail_of(esk10_1(esk3_0)) != head_of(esk10_1(esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_200]),c_0_133]) ).
cnf(c_0_203,plain,
number_of_in(triangles,esk3_0) = number_of_in(sequential_pairs,esk3_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_201]),c_0_202]) ).
cnf(c_0_204,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_203]),c_0_133]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA002+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 00:15:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 # ENIGMATIC: Selected SinE mode:
% 0.19/0.46 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.19/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.19/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 13.55/3.07 # ENIGMATIC: Solved by autoschedule-lgb:
% 13.55/3.07 # No SInE strategy applied
% 13.55/3.07 # Trying AutoSched0 for 150 seconds
% 13.55/3.07 # AutoSched0-Mode selected heuristic G_E___207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 13.55/3.07 # and selection function SelectMaxLComplexAvoidPosPred.
% 13.55/3.07 #
% 13.55/3.07 # Preprocessing time : 0.012 s
% 13.55/3.07
% 13.55/3.07 # Proof found!
% 13.55/3.07 # SZS status Theorem
% 13.55/3.07 # SZS output start CNFRefutation
% See solution above
% 13.55/3.07 # Training examples: 0 positive, 0 negative
% 13.55/3.07
% 13.55/3.07 # -------------------------------------------------
% 13.55/3.07 # User time : 0.742 s
% 13.55/3.07 # System time : 0.011 s
% 13.55/3.07 # Total time : 0.753 s
% 13.55/3.07 # Maximum resident set size: 7124 pages
% 13.55/3.07
%------------------------------------------------------------------------------