TSTP Solution File: GRA008+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n018.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 07:15:23 EDT 2022

% Result   : Theorem 13.95s 3.19s
% Output   : CNFRefutation 13.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   25
% Syntax   : Number of clauses     :  101 (  26 unt;  33 nHn; 101 RR)
%            Number of literals    :  298 (  97 equ; 161 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   2 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  171 (  60 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_35,plain,
    ( on_path(X1,X2)
    | ~ path(X3,X4,X2)
    | ~ precedes(X5,X1,X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_35) ).

cnf(i_0_44,negated_conjecture,
    precedes(esk8_0,esk9_0,esk10_0),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_44) ).

cnf(i_0_55,plain,
    ( path(X1,X2,X3)
    | ~ shortest_path(X1,X2,X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_55) ).

cnf(i_0_45,negated_conjecture,
    shortest_path(esk6_0,esk7_0,esk10_0),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_45) ).

cnf(i_0_36,plain,
    ( on_path(X1,X2)
    | ~ path(X3,X4,X2)
    | ~ precedes(X1,X5,X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_36) ).

cnf(i_0_57,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/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_57) ).

cnf(i_0_16,plain,
    ( in_path(head_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_16) ).

cnf(i_0_15,plain,
    ( in_path(tail_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_15) ).

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-5t21ax_7/input.p',i_0_2) ).

cnf(i_0_46,negated_conjecture,
    complete,
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_46) ).

cnf(i_0_41,plain,
    ( edge(X1)
    | ~ sequential(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_41) ).

cnf(i_0_43,negated_conjecture,
    sequential(esk8_0,esk9_0),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_43) ).

cnf(i_0_12,plain,
    ( vertex(X1)
    | ~ in_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_12) ).

cnf(i_0_7,plain,
    ( vertex(tail_of(X1))
    | ~ edge(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_7) ).

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-5t21ax_7/input.p',i_0_4) ).

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-5t21ax_7/input.p',i_0_1) ).

cnf(i_0_37,plain,
    ( X1 = X2
    | sequential(X1,X2)
    | tail_of(X2) != head_of(X1)
    | ~ edge(X2)
    | ~ edge(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_37) ).

cnf(i_0_14,plain,
    ( head_of(X1) != tail_of(X1)
    | ~ edge(X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_14) ).

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-5t21ax_7/input.p',i_0_6) ).

cnf(i_0_58,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-5t21ax_7/input.p',i_0_58) ).

cnf(i_0_40,plain,
    ( edge(X1)
    | ~ sequential(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_40) ).

cnf(i_0_42,negated_conjecture,
    ~ triangle(esk8_0,esk9_0,X1),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_42) ).

cnf(i_0_38,plain,
    ( tail_of(X1) = head_of(X2)
    | ~ sequential(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_38) ).

cnf(i_0_56,plain,
    ( ~ precedes(X1,X2,X3)
    | ~ precedes(X2,X1,X3)
    | ~ shortest_path(X4,X5,X3) ),
    file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_56) ).

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/sandbox2/tmp/enigma-theBenchmark.p-5t21ax_7/input.p',i_0_31) ).

cnf(c_0_84,plain,
    ( on_path(X1,X2)
    | ~ path(X3,X4,X2)
    | ~ precedes(X5,X1,X2) ),
    i_0_35 ).

cnf(c_0_85,negated_conjecture,
    precedes(esk8_0,esk9_0,esk10_0),
    i_0_44 ).

cnf(c_0_86,plain,
    ( path(X1,X2,X3)
    | ~ shortest_path(X1,X2,X3) ),
    i_0_55 ).

cnf(c_0_87,negated_conjecture,
    shortest_path(esk6_0,esk7_0,esk10_0),
    i_0_45 ).

cnf(c_0_88,plain,
    ( on_path(X1,X2)
    | ~ path(X3,X4,X2)
    | ~ precedes(X1,X5,X2) ),
    i_0_36 ).

cnf(c_0_89,negated_conjecture,
    ( on_path(esk9_0,esk10_0)
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_90,negated_conjecture,
    path(esk6_0,esk7_0,esk10_0),
    inference(spm,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_91,negated_conjecture,
    ( on_path(esk8_0,esk10_0)
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_88,c_0_85]) ).

cnf(c_0_92,plain,
    ( head_of(X1) != head_of(X2)
    | tail_of(X1) != tail_of(X3)
    | ~ precedes(X3,X2,X4)
    | ~ shortest_path(X5,X6,X4) ),
    i_0_57 ).

cnf(c_0_93,plain,
    ( in_path(head_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    i_0_16 ).

cnf(c_0_94,negated_conjecture,
    on_path(esk9_0,esk10_0),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_95,plain,
    ( in_path(tail_of(X1),X2)
    | ~ on_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    i_0_15 ).

cnf(c_0_96,negated_conjecture,
    on_path(esk8_0,esk10_0),
    inference(spm,[status(thm)],[c_0_91,c_0_90]) ).

cnf(c_0_97,negated_conjecture,
    ( head_of(X1) != head_of(X2)
    | tail_of(X1) != tail_of(X3)
    | ~ precedes(X3,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_92,c_0_87]) ).

cnf(c_0_98,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_99,negated_conjecture,
    complete,
    i_0_46 ).

cnf(c_0_100,plain,
    ( in_path(head_of(esk9_0),esk10_0)
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_101,plain,
    ( in_path(tail_of(esk8_0),esk10_0)
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_102,negated_conjecture,
    ( head_of(X1) != head_of(esk9_0)
    | tail_of(X1) != tail_of(esk8_0) ),
    inference(spm,[status(thm)],[c_0_97,c_0_85]) ).

cnf(c_0_103,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_98,c_0_99])]) ).

cnf(c_0_104,plain,
    ( edge(X1)
    | ~ sequential(X1,X2) ),
    i_0_41 ).

cnf(c_0_105,negated_conjecture,
    sequential(esk8_0,esk9_0),
    i_0_43 ).

cnf(c_0_106,plain,
    ( vertex(X1)
    | ~ in_path(X1,X2)
    | ~ path(X3,X4,X2) ),
    i_0_12 ).

cnf(c_0_107,negated_conjecture,
    in_path(head_of(esk9_0),esk10_0),
    inference(spm,[status(thm)],[c_0_100,c_0_90]) ).

cnf(c_0_108,negated_conjecture,
    in_path(tail_of(esk8_0),esk10_0),
    inference(spm,[status(thm)],[c_0_101,c_0_90]) ).

cnf(c_0_109,plain,
    ( head_of(esk1_2(X1,tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) = X1
    | head_of(esk1_2(X1,tail_of(esk8_0))) != head_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(X1) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103])]) ).

cnf(c_0_110,plain,
    ( vertex(tail_of(X1))
    | ~ edge(X1) ),
    i_0_7 ).

cnf(c_0_111,negated_conjecture,
    edge(esk8_0),
    inference(spm,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_112,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_113,plain,
    ( vertex(head_of(esk9_0))
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_106,c_0_107]) ).

cnf(c_0_114,plain,
    ( vertex(tail_of(esk8_0))
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_106,c_0_108]) ).

cnf(c_0_115,plain,
    ( head_of(esk1_2(X1,tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) = X1
    | head_of(esk1_2(X1,tail_of(esk8_0))) != head_of(esk9_0)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111])]) ).

cnf(c_0_116,plain,
    ( head_of(esk1_2(X1,X2)) = X1
    | head_of(esk1_2(X1,X2)) = X2
    | X2 = X1
    | ~ vertex(X1)
    | ~ vertex(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_99])]) ).

cnf(c_0_117,negated_conjecture,
    vertex(head_of(esk9_0)),
    inference(spm,[status(thm)],[c_0_113,c_0_90]) ).

cnf(c_0_118,negated_conjecture,
    vertex(tail_of(esk8_0)),
    inference(spm,[status(thm)],[c_0_114,c_0_90]) ).

cnf(c_0_119,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_120,plain,
    ( X1 = X2
    | sequential(X1,X2)
    | tail_of(X2) != head_of(X1)
    | ~ edge(X2)
    | ~ edge(X1) ),
    i_0_37 ).

cnf(c_0_121,plain,
    ( head_of(esk1_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) = head_of(esk9_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116])]),c_0_117]),c_0_118])]) ).

cnf(c_0_122,plain,
    ( head_of(X1) != tail_of(X1)
    | ~ edge(X1) ),
    i_0_14 ).

cnf(c_0_123,plain,
    ( tail_of(esk1_2(X1,X2)) = X2
    | tail_of(esk1_2(X1,X2)) = X1
    | X1 = X2
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_99])]) ).

cnf(c_0_124,plain,
    ( X1 = X2
    | edge(esk1_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    i_0_6 ).

cnf(c_0_125,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = X1
    | tail_of(esk8_0) = head_of(esk9_0)
    | sequential(esk1_2(head_of(esk9_0),tail_of(esk8_0)),X1)
    | tail_of(X1) != tail_of(esk8_0)
    | ~ edge(esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[c_0_120,c_0_121]) ).

cnf(c_0_126,plain,
    ( tail_of(esk1_2(X1,X2)) = X1
    | X1 = X2
    | head_of(esk1_2(X1,X2)) != X2
    | ~ edge(esk1_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_122,c_0_123]) ).

cnf(c_0_127,plain,
    ( X1 = X2
    | edge(esk1_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_99])]) ).

cnf(c_0_128,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | tail_of(esk8_0) = head_of(esk9_0)
    | sequential(esk1_2(head_of(esk9_0),tail_of(esk8_0)),esk8_0)
    | ~ edge(esk1_2(head_of(esk9_0),tail_of(esk8_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_125]),c_0_111])]) ).

cnf(c_0_129,plain,
    ( tail_of(esk1_2(X1,X2)) = X1
    | X1 = X2
    | head_of(esk1_2(X1,X2)) != X2
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[c_0_126,c_0_127]) ).

cnf(c_0_130,plain,
    ( triangle(X1,X2,X3)
    | ~ edge(X3)
    | ~ edge(X2)
    | ~ edge(X1)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2) ),
    i_0_58 ).

cnf(c_0_131,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | tail_of(esk8_0) = head_of(esk9_0)
    | sequential(esk1_2(head_of(esk9_0),tail_of(esk8_0)),esk8_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_127]),c_0_118]),c_0_117])]) ).

cnf(c_0_132,plain,
    ( tail_of(esk1_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
    | tail_of(esk8_0) = head_of(esk9_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_121]),c_0_118]),c_0_117])]) ).

cnf(c_0_133,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | tail_of(esk8_0) = head_of(esk9_0)
    | triangle(esk8_0,X1,esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(X1)
    | ~ sequential(X1,esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ sequential(esk8_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_111])]) ).

cnf(c_0_134,plain,
    ( edge(X1)
    | ~ sequential(X2,X1) ),
    i_0_40 ).

cnf(c_0_135,plain,
    ( X1 = esk1_2(head_of(esk9_0),tail_of(esk8_0))
    | tail_of(esk8_0) = head_of(esk9_0)
    | sequential(X1,esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[c_0_120,c_0_132]) ).

cnf(c_0_136,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | tail_of(esk8_0) = head_of(esk9_0)
    | triangle(esk8_0,X1,esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(X1)
    | ~ sequential(X1,esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ sequential(esk8_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_127]),c_0_118]),c_0_117])]) ).

cnf(c_0_137,negated_conjecture,
    edge(esk9_0),
    inference(spm,[status(thm)],[c_0_134,c_0_105]) ).

cnf(c_0_138,negated_conjecture,
    ~ triangle(esk8_0,esk9_0,X1),
    i_0_42 ).

cnf(c_0_139,plain,
    ( X1 = esk1_2(head_of(esk9_0),tail_of(esk8_0))
    | tail_of(esk8_0) = head_of(esk9_0)
    | sequential(X1,esk1_2(head_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_127]),c_0_118]),c_0_117])]) ).

cnf(c_0_140,plain,
    ( tail_of(X1) = head_of(X2)
    | ~ sequential(X2,X1) ),
    i_0_38 ).

cnf(c_0_141,negated_conjecture,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | tail_of(esk8_0) = head_of(esk9_0)
    | ~ sequential(esk9_0,esk1_2(head_of(esk9_0),tail_of(esk8_0))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_105]),c_0_137])]),c_0_138]) ).

cnf(c_0_142,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk9_0
    | tail_of(esk8_0) = head_of(esk9_0)
    | sequential(esk9_0,esk1_2(head_of(esk9_0),tail_of(esk8_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_139]),c_0_137])]) ).

cnf(c_0_143,negated_conjecture,
    tail_of(esk9_0) = head_of(esk8_0),
    inference(spm,[status(thm)],[c_0_140,c_0_105]) ).

cnf(c_0_144,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk9_0
    | tail_of(esk8_0) = head_of(esk9_0) ),
    inference(spm,[status(thm)],[c_0_141,c_0_142]) ).

cnf(c_0_145,negated_conjecture,
    tail_of(esk8_0) != head_of(esk8_0),
    inference(spm,[status(thm)],[c_0_102,c_0_143]) ).

cnf(c_0_146,plain,
    ( ~ precedes(X1,X2,X3)
    | ~ precedes(X2,X1,X3)
    | ~ shortest_path(X4,X5,X3) ),
    i_0_56 ).

cnf(c_0_147,plain,
    ( esk1_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | tail_of(esk8_0) = head_of(esk9_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_144]),c_0_143]),c_0_117]),c_0_118])]),c_0_145]) ).

cnf(c_0_148,plain,
    head_of(esk9_0) != head_of(esk8_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_143]),c_0_137])]) ).

cnf(c_0_149,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_150,negated_conjecture,
    ( ~ precedes(X1,X2,esk10_0)
    | ~ precedes(X2,X1,esk10_0) ),
    inference(spm,[status(thm)],[c_0_146,c_0_87]) ).

cnf(c_0_151,plain,
    tail_of(esk8_0) = head_of(esk9_0),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_147]),c_0_117]),c_0_118])]),c_0_148]),c_0_145]) ).

cnf(c_0_152,plain,
    ( precedes(X1,esk8_0,esk10_0)
    | ~ on_path(X1,esk10_0)
    | ~ path(X2,X3,esk10_0)
    | ~ sequential(X1,esk8_0) ),
    inference(spm,[status(thm)],[c_0_149,c_0_96]) ).

cnf(c_0_153,negated_conjecture,
    ~ precedes(esk9_0,esk8_0,esk10_0),
    inference(spm,[status(thm)],[c_0_150,c_0_85]) ).

cnf(c_0_154,plain,
    ( X1 = esk8_0
    | sequential(X1,esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_151]),c_0_111])]) ).

cnf(c_0_155,negated_conjecture,
    ( ~ path(X1,X2,esk10_0)
    | ~ sequential(esk9_0,esk8_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_94]),c_0_153]) ).

cnf(c_0_156,plain,
    ( esk9_0 = esk8_0
    | sequential(esk9_0,esk8_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_154]),c_0_137])]) ).

cnf(c_0_157,negated_conjecture,
    ( esk9_0 = esk8_0
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[c_0_155,c_0_156]) ).

cnf(c_0_158,negated_conjecture,
    esk9_0 = esk8_0,
    inference(spm,[status(thm)],[c_0_157,c_0_90]) ).

cnf(c_0_159,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_158])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue May 31 03:05:59 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.45  # ENIGMATIC: Selected SinE mode:
% 0.20/0.46  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.20/0.46  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.20/0.46  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 13.95/3.19  # ENIGMATIC: Solved by Enigma+tptp-cade20-model03-h2e15+lgb-t150-d30-l6400-e0.15+coop-eprover66:
% 13.95/3.19  # ENIGMA: LightGBM model '/export/starexec/sandbox2/solver/bin/data/Enigma/tptp-cade20-model03-h2e15/lgb-t150-d30-l6400-e0.15/model.lgb' loaded. (hash_base: 32768; conj_feats: 37; version: 991; iters: 150)
% 13.95/3.19  # Preprocessing time       : 0.832 s
% 13.95/3.19  # Presaturation interreduction done
% 13.95/3.19  
% 13.95/3.19  # Proof found!
% 13.95/3.19  # SZS status Theorem
% 13.95/3.19  # SZS output start CNFRefutation
% See solution above
% 13.95/3.19  # Training examples: 0 positive, 0 negative
% 13.95/3.19  
% 13.95/3.19  # -------------------------------------------------
% 13.95/3.19  # User time                : 0.765 s
% 13.95/3.19  # System time              : 0.110 s
% 13.95/3.19  # Total time               : 0.875 s
% 13.95/3.19  # ...preprocessing         : 0.832 s
% 13.95/3.19  # ...main loop             : 0.042 s
% 13.95/3.19  # Maximum resident set size: 167292 pages
% 13.95/3.19  
%------------------------------------------------------------------------------