TSTP Solution File: GRA008+2 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n024.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 8.61s 2.67s
% Output   : CNFRefutation 8.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   53 (  21 unt;   8 nHn;  53 RR)
%            Number of literals    :  124 (  33 equ;  70 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   2 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-4 aty)
%            Number of variables   :   83 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(i_0_1,lemma,
    ( head_of(esk1_4(X1,X2,X3,X4)) = tail_of(X3)
    | ~ complete
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_1) ).

cnf(i_0_49,negated_conjecture,
    complete,
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_49) ).

cnf(i_0_3,lemma,
    ( edge(esk1_4(X1,X2,X3,X4))
    | ~ complete
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_3) ).

cnf(i_0_47,negated_conjecture,
    precedes(esk9_0,esk10_0,esk11_0),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_47) ).

cnf(i_0_48,negated_conjecture,
    shortest_path(esk7_0,esk8_0,esk11_0),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_48) ).

cnf(i_0_2,lemma,
    ( tail_of(esk1_4(X1,X2,X3,X4)) = head_of(X4)
    | ~ complete
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_2) ).

cnf(i_0_40,plain,
    ( X1 = X2
    | sequential(X1,X2)
    | head_of(X1) != tail_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_40) ).

cnf(i_0_44,plain,
    ( edge(X1)
    | ~ sequential(X1,X2) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_44) ).

cnf(i_0_46,negated_conjecture,
    sequential(esk9_0,esk10_0),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_46) ).

cnf(i_0_61,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-g05e0uoy/lgb.p',i_0_61) ).

cnf(i_0_43,plain,
    ( edge(X1)
    | ~ sequential(X2,X1) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_43) ).

cnf(i_0_45,negated_conjecture,
    ~ triangle(esk9_0,esk10_0,X1),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_45) ).

cnf(i_0_41,plain,
    ( head_of(X1) = tail_of(X2)
    | ~ sequential(X1,X2) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_41) ).

cnf(i_0_17,plain,
    ( tail_of(X1) != head_of(X1)
    | ~ edge(X1) ),
    file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-g05e0uoy/lgb.p',i_0_17) ).

cnf(c_0_76,lemma,
    ( head_of(esk1_4(X1,X2,X3,X4)) = tail_of(X3)
    | ~ complete
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    i_0_1 ).

cnf(c_0_77,negated_conjecture,
    complete,
    i_0_49 ).

cnf(c_0_78,lemma,
    ( edge(esk1_4(X1,X2,X3,X4))
    | ~ complete
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    i_0_3 ).

cnf(c_0_79,lemma,
    ( head_of(esk1_4(X1,X2,X3,X4)) = tail_of(X3)
    | ~ precedes(X3,X4,X5)
    | ~ shortest_path(X1,X2,X5) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).

cnf(c_0_80,negated_conjecture,
    precedes(esk9_0,esk10_0,esk11_0),
    i_0_47 ).

cnf(c_0_81,lemma,
    ( edge(esk1_4(X1,X2,X3,X4))
    | ~ precedes(X3,X4,X5)
    | ~ shortest_path(X1,X2,X5) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_77])]) ).

cnf(c_0_82,negated_conjecture,
    ( head_of(esk1_4(X1,X2,esk9_0,esk10_0)) = tail_of(esk9_0)
    | ~ shortest_path(X1,X2,esk11_0) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_83,negated_conjecture,
    shortest_path(esk7_0,esk8_0,esk11_0),
    i_0_48 ).

cnf(c_0_84,negated_conjecture,
    ( edge(esk1_4(X1,X2,esk9_0,esk10_0))
    | ~ shortest_path(X1,X2,esk11_0) ),
    inference(spm,[status(thm)],[c_0_81,c_0_80]) ).

cnf(c_0_85,lemma,
    ( tail_of(esk1_4(X1,X2,X3,X4)) = head_of(X4)
    | ~ complete
    | ~ shortest_path(X1,X2,X5)
    | ~ precedes(X3,X4,X5) ),
    i_0_2 ).

cnf(c_0_86,plain,
    ( X1 = X2
    | sequential(X1,X2)
    | head_of(X1) != tail_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    i_0_40 ).

cnf(c_0_87,negated_conjecture,
    head_of(esk1_4(esk7_0,esk8_0,esk9_0,esk10_0)) = tail_of(esk9_0),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_88,negated_conjecture,
    edge(esk1_4(esk7_0,esk8_0,esk9_0,esk10_0)),
    inference(spm,[status(thm)],[c_0_84,c_0_83]) ).

cnf(c_0_89,plain,
    ( edge(X1)
    | ~ sequential(X1,X2) ),
    i_0_44 ).

cnf(c_0_90,negated_conjecture,
    sequential(esk9_0,esk10_0),
    i_0_46 ).

cnf(c_0_91,lemma,
    ( tail_of(esk1_4(X1,X2,X3,X4)) = head_of(X4)
    | ~ precedes(X3,X4,X5)
    | ~ shortest_path(X1,X2,X5) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_77])]) ).

cnf(c_0_92,plain,
    ( triangle(X1,X2,X3)
    | ~ edge(X3)
    | ~ edge(X2)
    | ~ edge(X1)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2) ),
    i_0_61 ).

cnf(c_0_93,plain,
    ( esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = X1
    | sequential(esk1_4(esk7_0,esk8_0,esk9_0,esk10_0),X1)
    | tail_of(esk9_0) != tail_of(X1)
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).

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

cnf(c_0_95,negated_conjecture,
    ( tail_of(esk1_4(X1,X2,esk9_0,esk10_0)) = head_of(esk10_0)
    | ~ shortest_path(X1,X2,esk11_0) ),
    inference(spm,[status(thm)],[c_0_91,c_0_80]) ).

cnf(c_0_96,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_92,c_0_89]),c_0_89]),c_0_89]) ).

cnf(c_0_97,plain,
    ( esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = esk9_0
    | sequential(esk1_4(esk7_0,esk8_0,esk9_0,esk10_0),esk9_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_93]),c_0_94])]) ).

cnf(c_0_98,negated_conjecture,
    tail_of(esk1_4(esk7_0,esk8_0,esk9_0,esk10_0)) = head_of(esk10_0),
    inference(spm,[status(thm)],[c_0_95,c_0_83]) ).

cnf(c_0_99,plain,
    ( edge(X1)
    | ~ sequential(X2,X1) ),
    i_0_43 ).

cnf(c_0_100,plain,
    ( esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = esk9_0
    | triangle(esk9_0,X1,esk1_4(esk7_0,esk8_0,esk9_0,esk10_0))
    | ~ sequential(X1,esk1_4(esk7_0,esk8_0,esk9_0,esk10_0))
    | ~ sequential(esk9_0,X1) ),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_101,negated_conjecture,
    ~ triangle(esk9_0,esk10_0,X1),
    i_0_45 ).

cnf(c_0_102,plain,
    ( X1 = esk1_4(esk7_0,esk8_0,esk9_0,esk10_0)
    | sequential(X1,esk1_4(esk7_0,esk8_0,esk9_0,esk10_0))
    | head_of(X1) != head_of(esk10_0)
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_98]),c_0_88])]) ).

cnf(c_0_103,negated_conjecture,
    edge(esk10_0),
    inference(spm,[status(thm)],[c_0_99,c_0_90]) ).

cnf(c_0_104,plain,
    ( head_of(X1) = tail_of(X2)
    | ~ sequential(X1,X2) ),
    i_0_41 ).

cnf(c_0_105,negated_conjecture,
    ( esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = esk9_0
    | ~ sequential(esk10_0,esk1_4(esk7_0,esk8_0,esk9_0,esk10_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_90]),c_0_101]) ).

cnf(c_0_106,plain,
    ( esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = esk10_0
    | sequential(esk10_0,esk1_4(esk7_0,esk8_0,esk9_0,esk10_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_102]),c_0_103])]) ).

cnf(c_0_107,plain,
    ( tail_of(X1) != head_of(X1)
    | ~ edge(X1) ),
    i_0_17 ).

cnf(c_0_108,negated_conjecture,
    tail_of(esk10_0) = head_of(esk9_0),
    inference(spm,[status(thm)],[c_0_104,c_0_90]) ).

cnf(c_0_109,plain,
    ( esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = esk10_0
    | esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = esk9_0 ),
    inference(spm,[status(thm)],[c_0_105,c_0_106]) ).

cnf(c_0_110,plain,
    head_of(esk10_0) != head_of(esk9_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_103])]) ).

cnf(c_0_111,plain,
    head_of(esk1_4(esk7_0,esk8_0,esk9_0,esk10_0)) != head_of(esk10_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_98]),c_0_88])]) ).

cnf(c_0_112,negated_conjecture,
    esk1_4(esk7_0,esk8_0,esk9_0,esk10_0) = esk9_0,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_109]),c_0_108]),c_0_110]) ).

cnf(c_0_113,plain,
    tail_of(esk9_0) != head_of(esk10_0),
    inference(rw,[status(thm)],[c_0_111,c_0_87]) ).

cnf(c_0_114,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_112]),c_0_113]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.08/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue May 31 00:57:08 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.46  # ENIGMATIC: Selected SinE mode:
% 0.21/0.47  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.21/0.47  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.21/0.47  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 8.61/2.67  # ENIGMATIC: Solved by autoschedule-lgb:
% 8.61/2.67  # No SInE strategy applied
% 8.61/2.67  # Trying AutoSched0 for 150 seconds
% 8.61/2.67  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 8.61/2.67  # and selection function SelectCQArNTNpEqFirst.
% 8.61/2.67  #
% 8.61/2.67  # Preprocessing time       : 0.024 s
% 8.61/2.67  # Presaturation interreduction done
% 8.61/2.67  
% 8.61/2.67  # Proof found!
% 8.61/2.67  # SZS status Theorem
% 8.61/2.67  # SZS output start CNFRefutation
% See solution above
% 8.61/2.67  # Training examples: 0 positive, 0 negative
% 8.61/2.67  
% 8.61/2.67  # -------------------------------------------------
% 8.61/2.67  # User time                : 0.066 s
% 8.61/2.67  # System time              : 0.006 s
% 8.61/2.67  # Total time               : 0.072 s
% 8.61/2.67  # Maximum resident set size: 7128 pages
% 8.61/2.67  
%------------------------------------------------------------------------------