%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA005+1 : TPTP v9.2.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 : 300s
% DateTime : Tue May 5 04:22:55 PM UTC 2026
% Result : Theorem 0.29s 1.61s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 86)
% Comments :
%------------------------------------------------------------------------------
fof(path_properties,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> ( vertex(X2)
& vertex(X3)
& ? [X1] :
( edge(X1)
& X2 = tail_of(X1)
& ( ( X3 = head_of(X1)
& X4 = path_cons(X1,empty) )
<~> ? [X5] :
( path(head_of(X1),X3,X5)
& X4 = path_cons(X1,X5) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',path_properties) ).
fof(precedes_properties,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
<~> ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(precedes_defn,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
<= ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(shortest_path_properties,axiom,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( ~ ? [X9] :
( tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) )
& ~ precedes(X8,X7,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(path_defn,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
<= ( vertex(X2)
& vertex(X3)
& ? [X1] :
( edge(X1)
& X2 = tail_of(X1)
& ( ( X3 = head_of(X1)
& X4 = path_cons(X1,empty) )
| ? [X5] :
( path(head_of(X1),X3,X5)
& X4 = path_cons(X1,X5) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',path_defn) ).
fof(complete_properties,axiom,
( complete
=> ! [X2,X3] :
( ( vertex(X2)
& vertex(X3)
& X2 != X3 )
=> ? [X1] :
( edge(X1)
& ( ( X2 = head_of(X1)
& X3 = tail_of(X1) )
<~> ( X3 = head_of(X1)
& X2 = tail_of(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
fof(no_short_cut_edge,conjecture,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ~ ? [X9] :
( edge(X9)
& tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_short_cut_edge) ).
fof(in_path_properties,axiom,
! [X2,X3,X4,X6] :
( ( path(X2,X3,X4)
& in_path(X6,X4) )
=> ( vertex(X6)
& ? [X1] :
( on_path(X1,X4)
& ( X6 = head_of(X1)
| X6 = tail_of(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',in_path_properties) ).
fof(shortest_path_defn,axiom,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( path(X2,X3,X10)
& X2 != X3
& ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(sequential_pairs_and_triangles,axiom,
! [X4,X2,X3] :
( ( path(X2,X3,X4)
& ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(triangle_defn,axiom,
! [X7,X8,X9] :
( triangle(X7,X8,X9)
<=> ( edge(X7)
& edge(X8)
& edge(X9)
& sequential(X7,X8)
& sequential(X8,X9)
& sequential(X9,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(on_path_properties,axiom,
! [X2,X3,X4,X1] :
( ( path(X2,X3,X4)
& on_path(X1,X4) )
=> ( edge(X1)
& in_path(head_of(X1),X4)
& in_path(tail_of(X1),X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(path_length_sequential_pairs,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> number_of_in(sequential_pairs,X4) = minus(length_of(X4),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(length_defn,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> length_of(X4) = number_of_in(edges,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_defn) ).
fof(graph_has_them_all,axiom,
! [X11,X12] : less_or_equal(number_of_in(X11,X12),number_of_in(X11,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(edge_ends_are_vertices,axiom,
! [X1] :
( edge(X1)
=> ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
fof(i_0_18,plain,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> ( vertex(X2)
& vertex(X3)
& ? [X1] :
( edge(X1)
& X2 = tail_of(X1)
& ~ ( ( X3 = head_of(X1)
& X4 = path_cons(X1,empty) )
<=> ? [X5] :
( path(head_of(X1),X3,X5)
& X4 = path_cons(X1,X5) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[path_properties]) ).
fof(i_0_19,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( on_path(X7,X4)
& on_path(X8,X4)
& ~ ( sequential(X7,X8)
<=> ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[precedes_properties]) ).
fof(i_0_20,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) )
=> precedes(X7,X8,X4) ) ),
inference(fof_simplification,[status(thm)],[precedes_defn]) ).
fof(i_0_21,plain,
! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ( ~ ? [X9] :
( tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) )
& ~ precedes(X8,X7,X4) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_properties]) ).
fof(i_0_22,plain,
! [X2,X3,X4] :
( ( vertex(X2)
& vertex(X3)
& ? [X1] :
( edge(X1)
& X2 = tail_of(X1)
& ( ( X3 = head_of(X1)
& X4 = path_cons(X1,empty) )
| ? [X5] :
( path(head_of(X1),X3,X5)
& X4 = path_cons(X1,X5) ) ) ) )
=> path(X2,X3,X4) ),
inference(fof_simplification,[status(thm)],[path_defn]) ).
fof(i_0_23,plain,
( complete
=> ! [X2,X3] :
( ( vertex(X2)
& vertex(X3)
& X2 != X3 )
=> ? [X1] :
( edge(X1)
& ~ ( ( X2 = head_of(X1)
& X3 = tail_of(X1) )
<=> ( X3 = head_of(X1)
& X2 = tail_of(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[complete_properties]) ).
fof(i_0_24,negated_conjecture,
~ ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ~ ? [X9] :
( edge(X9)
& tail_of(X9) = tail_of(X7)
& head_of(X9) = head_of(X8) ) ),
inference(assume_negation,[status(cth)],[no_short_cut_edge]) ).
fof(i_0_25,plain,
! [X104,X105,X106,X107] :
( ( vertex(X107)
| ~ path(X104,X105,X106)
| ~ in_path(X107,X106) )
& ( on_path(esk4_4(X104,X105,X106,X107),X106)
| ~ path(X104,X105,X106)
| ~ in_path(X107,X106) )
& ( X107 = head_of(esk4_4(X104,X105,X106,X107))
| X107 = tail_of(esk4_4(X104,X105,X106,X107))
| ~ path(X104,X105,X106)
| ~ in_path(X107,X106) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])]) ).
fof(i_0_26,plain,
! [X94,X95,X96,X98] :
( ( vertex(X94)
| ~ path(X94,X95,X96) )
& ( vertex(X95)
| ~ path(X94,X95,X96) )
& ( edge(esk2_3(X94,X95,X96))
| ~ path(X94,X95,X96) )
& ( X94 = tail_of(esk2_3(X94,X95,X96))
| ~ path(X94,X95,X96) )
& ( X95 != head_of(esk2_3(X94,X95,X96))
| X96 != path_cons(esk2_3(X94,X95,X96),empty)
| ~ path(head_of(esk2_3(X94,X95,X96)),X95,X98)
| X96 != path_cons(esk2_3(X94,X95,X96),X98)
| ~ path(X94,X95,X96) )
& ( path(head_of(esk2_3(X94,X95,X96)),X95,esk3_3(X94,X95,X96))
| X95 = head_of(esk2_3(X94,X95,X96))
| ~ path(X94,X95,X96) )
& ( X96 = path_cons(esk2_3(X94,X95,X96),esk3_3(X94,X95,X96))
| X95 = head_of(esk2_3(X94,X95,X96))
| ~ path(X94,X95,X96) )
& ( path(head_of(esk2_3(X94,X95,X96)),X95,esk3_3(X94,X95,X96))
| X96 = path_cons(esk2_3(X94,X95,X96),empty)
| ~ path(X94,X95,X96) )
& ( X96 = path_cons(esk2_3(X94,X95,X96),esk3_3(X94,X95,X96))
| X96 = path_cons(esk2_3(X94,X95,X96),empty)
| ~ path(X94,X95,X96) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])])])])]) ).
fof(i_0_27,plain,
! [X124,X125,X126,X127,X128,X129,X130] :
( ( path(X124,X125,X126)
| ~ shortest_path(X124,X125,X126) )
& ( X124 != X125
| ~ shortest_path(X124,X125,X126) )
& ( ~ path(X124,X125,X127)
| less_or_equal(length_of(X126),length_of(X127))
| ~ shortest_path(X124,X125,X126) )
& ( path(X128,X129,esk6_3(X128,X129,X130))
| ~ path(X128,X129,X130)
| X128 = X129
| shortest_path(X128,X129,X130) )
& ( ~ less_or_equal(length_of(X130),length_of(esk6_3(X128,X129,X130)))
| ~ path(X128,X129,X130)
| X128 = X129
| shortest_path(X128,X129,X130) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[shortest_path_defn])])])])])]) ).
fof(i_0_28,plain,
! [X117,X118,X119,X120,X121,X122] :
( ( on_path(X120,X117)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( on_path(X121,X117)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( ~ sequential(X120,X121)
| ~ sequential(X120,X122)
| ~ precedes(X122,X121,X117)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( sequential(X120,esk5_3(X117,X120,X121))
| sequential(X120,X121)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( precedes(esk5_3(X117,X120,X121),X121,X117)
| sequential(X120,X121)
| ~ precedes(X120,X121,X117)
| ~ path(X118,X119,X117) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_19])])])])])]) ).
fof(i_0_29,plain,
! [X111,X112,X113,X114,X115,X116] :
( ( ~ sequential(X114,X115)
| ~ on_path(X114,X111)
| ~ on_path(X115,X111)
| precedes(X114,X115,X111)
| ~ path(X112,X113,X111) )
& ( ~ sequential(X114,X116)
| ~ precedes(X116,X115,X111)
| ~ on_path(X114,X111)
| ~ on_path(X115,X111)
| precedes(X114,X115,X111)
| ~ path(X112,X113,X111) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_20])])])]) ).
fof(i_0_30,plain,
! [X132,X133,X134,X135,X136,X137] :
( ( tail_of(X137) != tail_of(X134)
| head_of(X137) != head_of(X135)
| ~ shortest_path(X132,X133,X136)
| ~ precedes(X134,X135,X136) )
& ( ~ precedes(X135,X134,X136)
| ~ shortest_path(X132,X133,X136)
| ~ precedes(X134,X135,X136) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_21])])])]) ).
fof(i_0_31,plain,
! [X147,X148,X149,X152] :
( ( on_path(esk7_1(X147),X147)
| ~ path(X148,X149,X147)
| number_of_in(sequential_pairs,X147) = number_of_in(triangles,X147) )
& ( on_path(esk8_1(X147),X147)
| ~ path(X148,X149,X147)
| number_of_in(sequential_pairs,X147) = number_of_in(triangles,X147) )
& ( sequential(esk7_1(X147),esk8_1(X147))
| ~ path(X148,X149,X147)
| number_of_in(sequential_pairs,X147) = number_of_in(triangles,X147) )
& ( ~ triangle(esk7_1(X147),esk8_1(X147),X152)
| ~ path(X148,X149,X147)
| number_of_in(sequential_pairs,X147) = number_of_in(triangles,X147) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_pairs_and_triangles])])])])])]) ).
fof(i_0_32,plain,
! [X89,X90,X91,X92,X93] :
( ( X90 != head_of(X92)
| X91 != path_cons(X92,empty)
| ~ edge(X92)
| X89 != tail_of(X92)
| ~ vertex(X89)
| ~ vertex(X90)
| path(X89,X90,X91) )
& ( ~ path(head_of(X92),X90,X93)
| X91 != path_cons(X92,X93)
| ~ edge(X92)
| X89 != tail_of(X92)
| ~ vertex(X89)
| ~ vertex(X90)
| path(X89,X90,X91) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_22])])])]) ).
fof(i_0_33,plain,
! [X138,X139,X140] :
( ( edge(X138)
| ~ triangle(X138,X139,X140) )
& ( edge(X139)
| ~ triangle(X138,X139,X140) )
& ( edge(X140)
| ~ triangle(X138,X139,X140) )
& ( sequential(X138,X139)
| ~ triangle(X138,X139,X140) )
& ( sequential(X139,X140)
| ~ triangle(X138,X139,X140) )
& ( sequential(X140,X138)
| ~ triangle(X138,X139,X140) )
& ( ~ edge(X138)
| ~ edge(X139)
| ~ edge(X140)
| ~ sequential(X138,X139)
| ~ sequential(X139,X140)
| ~ sequential(X140,X138)
| triangle(X138,X139,X140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])]) ).
fof(i_0_34,plain,
! [X100,X101,X102,X103] :
( ( edge(X103)
| ~ path(X100,X101,X102)
| ~ on_path(X103,X102) )
& ( in_path(head_of(X103),X102)
| ~ path(X100,X101,X102)
| ~ on_path(X103,X102) )
& ( in_path(tail_of(X103),X102)
| ~ path(X100,X101,X102)
| ~ on_path(X103,X102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
fof(i_0_35,plain,
! [X144,X145,X146] :
( ~ path(X144,X145,X146)
| number_of_in(sequential_pairs,X146) = minus(length_of(X146),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
fof(i_0_36,plain,
! [X141,X142,X143] :
( ~ path(X141,X142,X143)
| length_of(X143) = number_of_in(edges,X143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[length_defn])]) ).
fof(i_0_37,plain,
! [X86,X87] :
( ( edge(esk1_2(X86,X87))
| ~ vertex(X86)
| ~ vertex(X87)
| X86 = X87
| ~ complete )
& ( X86 != head_of(esk1_2(X86,X87))
| X87 != tail_of(esk1_2(X86,X87))
| X87 != head_of(esk1_2(X86,X87))
| X86 != tail_of(esk1_2(X86,X87))
| ~ vertex(X86)
| ~ vertex(X87)
| X86 = X87
| ~ complete )
& ( X87 = head_of(esk1_2(X86,X87))
| X86 = head_of(esk1_2(X86,X87))
| ~ vertex(X86)
| ~ vertex(X87)
| X86 = X87
| ~ complete )
& ( X86 = tail_of(esk1_2(X86,X87))
| X86 = head_of(esk1_2(X86,X87))
| ~ vertex(X86)
| ~ vertex(X87)
| X86 = X87
| ~ complete )
& ( X87 = head_of(esk1_2(X86,X87))
| X87 = tail_of(esk1_2(X86,X87))
| ~ vertex(X86)
| ~ vertex(X87)
| X86 = X87
| ~ complete )
& ( X86 = tail_of(esk1_2(X86,X87))
| X87 = tail_of(esk1_2(X86,X87))
| ~ vertex(X86)
| ~ vertex(X87)
| X86 = X87
| ~ complete ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_23])])])])]) ).
fof(i_0_38,plain,
! [X153,X154] : less_or_equal(number_of_in(X153,X154),number_of_in(X153,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
fof(i_0_39,negated_conjecture,
( shortest_path(esk9_0,esk10_0,esk13_0)
& precedes(esk11_0,esk12_0,esk13_0)
& edge(esk14_0)
& tail_of(esk14_0) = tail_of(esk11_0)
& head_of(esk14_0) = head_of(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_24])])]) ).
fof(i_0_40,plain,
! [X109,X110] :
( ( edge(X109)
| ~ sequential(X109,X110) )
& ( edge(X110)
| ~ sequential(X109,X110) )
& ( X109 != X110
| ~ sequential(X109,X110) )
& ( head_of(X109) = tail_of(X110)
| ~ sequential(X109,X110) )
& ( ~ edge(X109)
| ~ edge(X110)
| X109 = X110
| head_of(X109) != tail_of(X110)
| sequential(X109,X110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
fof(i_0_41,plain,
! [X84] :
( ~ edge(X84)
| head_of(X84) != tail_of(X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).
fof(i_0_42,plain,
! [X85] :
( ( vertex(head_of(X85))
| ~ edge(X85) )
& ( vertex(tail_of(X85))
| ~ edge(X85) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])]) ).
cnf(i_0_43,plain,
( X1 = head_of(esk4_4(X2,X3,X4,X1))
| X1 = tail_of(esk4_4(X2,X3,X4,X1))
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_44,plain,
( X1 != head_of(esk2_3(X2,X1,X3))
| X3 != path_cons(esk2_3(X2,X1,X3),empty)
| ~ path(head_of(esk2_3(X2,X1,X3)),X1,X4)
| X3 != path_cons(esk2_3(X2,X1,X3),X4)
| ~ path(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_45,plain,
( on_path(esk4_4(X1,X2,X3,X4),X3)
| ~ path(X1,X2,X3)
| ~ in_path(X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_46,plain,
( path(head_of(esk2_3(X1,X2,X3)),X2,esk3_3(X1,X2,X3))
| X3 = path_cons(esk2_3(X1,X2,X3),empty)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_47,plain,
( path(head_of(esk2_3(X1,X2,X3)),X2,esk3_3(X1,X2,X3))
| X2 = head_of(esk2_3(X1,X2,X3))
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_48,plain,
( X2 = X3
| shortest_path(X2,X3,X1)
| ~ less_or_equal(length_of(X1),length_of(esk6_3(X2,X3,X1)))
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_49,plain,
( X1 = path_cons(esk2_3(X2,X3,X1),esk3_3(X2,X3,X1))
| X1 = path_cons(esk2_3(X2,X3,X1),empty)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_50,plain,
( X1 = path_cons(esk2_3(X2,X3,X1),esk3_3(X2,X3,X1))
| X3 = head_of(esk2_3(X2,X3,X1))
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_51,plain,
( precedes(esk5_3(X1,X2,X3),X3,X1)
| sequential(X2,X3)
| ~ precedes(X2,X3,X1)
| ~ path(X4,X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_52,plain,
( sequential(X1,esk5_3(X2,X1,X3))
| sequential(X1,X3)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_53,plain,
( path(X1,X2,esk6_3(X1,X2,X3))
| X1 = X2
| shortest_path(X1,X2,X3)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_54,plain,
( ~ sequential(X1,X2)
| ~ sequential(X1,X3)
| ~ precedes(X3,X2,X4)
| ~ precedes(X1,X2,X4)
| ~ path(X5,X6,X4) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_55,plain,
( precedes(X1,X3,X4)
| ~ sequential(X1,X2)
| ~ precedes(X2,X3,X4)
| ~ on_path(X1,X4)
| ~ on_path(X3,X4)
| ~ path(X5,X6,X4) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_56,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_57,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ triangle(esk7_1(X1),esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_58,plain,
( precedes(X1,X2,X3)
| ~ sequential(X1,X2)
| ~ on_path(X1,X3)
| ~ on_path(X2,X3)
| ~ path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_59,plain,
( path(X5,X2,X4)
| ~ path(head_of(X1),X2,X3)
| X4 != path_cons(X1,X3)
| ~ edge(X1)
| X5 != tail_of(X1)
| ~ vertex(X5)
| ~ vertex(X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_60,plain,
( less_or_equal(length_of(X4),length_of(X3))
| ~ path(X1,X2,X3)
| ~ shortest_path(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_61,plain,
( tail_of(X1) != tail_of(X2)
| head_of(X1) != head_of(X3)
| ~ shortest_path(X4,X5,X6)
| ~ precedes(X2,X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_62,plain,
( X1 = tail_of(esk2_3(X1,X2,X3))
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_63,plain,
( edge(esk2_3(X1,X2,X3))
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_64,plain,
( on_path(X1,X2)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_65,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_66,plain,
( triangle(X1,X2,X3)
| ~ edge(X1)
| ~ edge(X2)
| ~ edge(X3)
| ~ sequential(X1,X2)
| ~ sequential(X2,X3)
| ~ sequential(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_67,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_68,plain,
( sequential(esk7_1(X1),esk8_1(X1))
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_69,plain,
( on_path(esk8_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_70,plain,
( on_path(esk7_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_71,plain,
( in_path(tail_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_72,plain,
( in_path(head_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_73,plain,
( number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_74,plain,
( path(X4,X1,X3)
| X1 != head_of(X2)
| X3 != path_cons(X2,empty)
| ~ edge(X2)
| X4 != tail_of(X2)
| ~ vertex(X4)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_75,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_76,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_77,plain,
( length_of(X3) = number_of_in(edges,X3)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_78,plain,
( sequential(X1,X2)
| ~ triangle(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_79,plain,
( sequential(X1,X2)
| ~ triangle(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_80,plain,
( sequential(X1,X2)
| ~ triangle(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_81,plain,
( vertex(X1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_82,plain,
( vertex(X1)
| ~ path(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_83,plain,
( edge(X1)
| ~ triangle(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_84,plain,
( edge(X1)
| ~ triangle(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_85,plain,
( edge(X1)
| ~ triangle(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_86,plain,
( X1 != X2
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_87,plain,
( X1 = tail_of(esk1_2(X1,X2))
| X1 = head_of(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_88,plain,
( X1 = head_of(esk1_2(X2,X1))
| X1 = tail_of(esk1_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_89,plain,
( X1 = tail_of(esk1_2(X1,X2))
| X2 = tail_of(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_90,plain,
( X1 = head_of(esk1_2(X2,X1))
| X2 = head_of(esk1_2(X2,X1))
| X2 = X1
| ~ vertex(X2)
| ~ vertex(X1)
| ~ complete ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_91,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_92,negated_conjecture,
shortest_path(esk9_0,esk10_0,esk13_0),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_93,negated_conjecture,
precedes(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_94,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_95,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_96,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_97,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_98,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_99,plain,
( X1 != X2
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_100,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_101,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_102,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_103,negated_conjecture,
tail_of(esk14_0) = tail_of(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_104,negated_conjecture,
head_of(esk14_0) = head_of(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_105,negated_conjecture,
edge(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_106,axiom,
X1 = X1 ).
cnf(i_0_107,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_108,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_109,axiom,
( X1 != X2
| head_of(X1) = head_of(X2) ) ).
cnf(i_0_110,axiom,
( X1 != X2
| number_of_in(X1,X3) = number_of_in(X2,X3) ) ).
cnf(i_0_111,axiom,
( X1 != X2
| number_of_in(X3,X1) = number_of_in(X3,X2) ) ).
cnf(i_0_112,axiom,
( X1 != X2
| minus(X1,X3) = minus(X2,X3) ) ).
cnf(i_0_113,axiom,
( X1 != X2
| minus(X3,X1) = minus(X3,X2) ) ).
cnf(i_0_114,axiom,
( X1 != X2
| tail_of(X1) = tail_of(X2) ) ).
cnf(i_0_115,axiom,
( X1 != X2
| path_cons(X1,X3) = path_cons(X2,X3) ) ).
cnf(i_0_116,axiom,
( X1 != X2
| path_cons(X3,X1) = path_cons(X3,X2) ) ).
cnf(i_0_117,axiom,
( X1 != X2
| length_of(X1) = length_of(X2) ) ).
cnf(i_0_118,axiom,
( X1 != X2
| ~ path(X1,X3,X4)
| path(X2,X3,X4) ) ).
cnf(i_0_119,axiom,
( X1 != X2
| ~ path(X3,X1,X4)
| path(X3,X2,X4) ) ).
cnf(i_0_120,axiom,
( X1 != X2
| ~ path(X3,X4,X1)
| path(X3,X4,X2) ) ).
cnf(i_0_121,axiom,
( X1 != X2
| ~ vertex(X1)
| vertex(X2) ) ).
cnf(i_0_122,axiom,
( X1 != X2
| ~ in_path(X1,X3)
| in_path(X2,X3) ) ).
cnf(i_0_123,axiom,
( X1 != X2
| ~ in_path(X3,X1)
| in_path(X3,X2) ) ).
cnf(i_0_124,axiom,
( X1 != X2
| ~ on_path(X1,X3)
| on_path(X2,X3) ) ).
cnf(i_0_125,axiom,
( X1 != X2
| ~ on_path(X3,X1)
| on_path(X3,X2) ) ).
cnf(i_0_126,axiom,
( X1 != X2
| ~ shortest_path(X1,X3,X4)
| shortest_path(X2,X3,X4) ) ).
cnf(i_0_127,axiom,
( X1 != X2
| ~ shortest_path(X3,X1,X4)
| shortest_path(X3,X2,X4) ) ).
cnf(i_0_128,axiom,
( X1 != X2
| ~ shortest_path(X3,X4,X1)
| shortest_path(X3,X4,X2) ) ).
cnf(i_0_129,axiom,
( X1 != X2
| ~ less_or_equal(X1,X3)
| less_or_equal(X2,X3) ) ).
cnf(i_0_130,axiom,
( X1 != X2
| ~ less_or_equal(X3,X1)
| less_or_equal(X3,X2) ) ).
cnf(i_0_131,axiom,
( X1 != X2
| ~ precedes(X1,X3,X4)
| precedes(X2,X3,X4) ) ).
cnf(i_0_132,axiom,
( X1 != X2
| ~ precedes(X3,X1,X4)
| precedes(X3,X2,X4) ) ).
cnf(i_0_133,axiom,
( X1 != X2
| ~ precedes(X3,X4,X1)
| precedes(X3,X4,X2) ) ).
cnf(i_0_134,axiom,
( X1 != X2
| ~ sequential(X1,X3)
| sequential(X2,X3) ) ).
cnf(i_0_135,axiom,
( X1 != X2
| ~ sequential(X3,X1)
| sequential(X3,X2) ) ).
cnf(i_0_136,axiom,
( X1 != X2
| ~ triangle(X1,X3,X4)
| triangle(X2,X3,X4) ) ).
cnf(i_0_137,axiom,
( X1 != X2
| ~ triangle(X3,X1,X4)
| triangle(X3,X2,X4) ) ).
cnf(i_0_138,axiom,
( X1 != X2
| ~ triangle(X3,X4,X1)
| triangle(X3,X4,X2) ) ).
cnf(i_0_139,axiom,
( X1 != X2
| ~ edge(X1)
| edge(X2) ) ).
cnf(i_0_106_001,axiom,
X1 = X1 ).
cnf(i_0_107_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_108_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_109_004,axiom,
( X1 != X2
| head_of(X1) = head_of(X2) ) ).
cnf(i_0_110_005,axiom,
( X1 != X2
| number_of_in(X1,X3) = number_of_in(X2,X3) ) ).
cnf(i_0_111_006,axiom,
( X1 != X2
| number_of_in(X3,X1) = number_of_in(X3,X2) ) ).
cnf(i_0_112_007,axiom,
( X1 != X2
| minus(X1,X3) = minus(X2,X3) ) ).
cnf(i_0_113_008,axiom,
( X1 != X2
| minus(X3,X1) = minus(X3,X2) ) ).
cnf(i_0_114_009,axiom,
( X1 != X2
| tail_of(X1) = tail_of(X2) ) ).
cnf(i_0_115_010,axiom,
( X1 != X2
| path_cons(X1,X3) = path_cons(X2,X3) ) ).
cnf(i_0_116_011,axiom,
( X1 != X2
| path_cons(X3,X1) = path_cons(X3,X2) ) ).
cnf(i_0_117_012,axiom,
( X1 != X2
| length_of(X1) = length_of(X2) ) ).
cnf(i_0_118_013,axiom,
( X1 != X2
| ~ path(X1,X3,X4)
| path(X2,X3,X4) ) ).
cnf(i_0_119_014,axiom,
( X1 != X2
| ~ path(X3,X1,X4)
| path(X3,X2,X4) ) ).
cnf(i_0_120_015,axiom,
( X1 != X2
| ~ path(X3,X4,X1)
| path(X3,X4,X2) ) ).
cnf(i_0_121_016,axiom,
( X1 != X2
| ~ vertex(X1)
| vertex(X2) ) ).
cnf(i_0_122_017,axiom,
( X1 != X2
| ~ in_path(X1,X3)
| in_path(X2,X3) ) ).
cnf(i_0_123_018,axiom,
( X1 != X2
| ~ in_path(X3,X1)
| in_path(X3,X2) ) ).
cnf(i_0_124_019,axiom,
( X1 != X2
| ~ on_path(X1,X3)
| on_path(X2,X3) ) ).
cnf(i_0_125_020,axiom,
( X1 != X2
| ~ on_path(X3,X1)
| on_path(X3,X2) ) ).
cnf(i_0_126_021,axiom,
( X1 != X2
| ~ shortest_path(X1,X3,X4)
| shortest_path(X2,X3,X4) ) ).
cnf(i_0_127_022,axiom,
( X1 != X2
| ~ shortest_path(X3,X1,X4)
| shortest_path(X3,X2,X4) ) ).
cnf(i_0_128_023,axiom,
( X1 != X2
| ~ shortest_path(X3,X4,X1)
| shortest_path(X3,X4,X2) ) ).
cnf(i_0_129_024,axiom,
( X1 != X2
| ~ less_or_equal(X1,X3)
| less_or_equal(X2,X3) ) ).
cnf(i_0_130_025,axiom,
( X1 != X2
| ~ less_or_equal(X3,X1)
| less_or_equal(X3,X2) ) ).
cnf(i_0_131_026,axiom,
( X1 != X2
| ~ precedes(X1,X3,X4)
| precedes(X2,X3,X4) ) ).
cnf(i_0_132_027,axiom,
( X1 != X2
| ~ precedes(X3,X1,X4)
| precedes(X3,X2,X4) ) ).
cnf(i_0_133_028,axiom,
( X1 != X2
| ~ precedes(X3,X4,X1)
| precedes(X3,X4,X2) ) ).
cnf(i_0_134_029,axiom,
( X1 != X2
| ~ sequential(X1,X3)
| sequential(X2,X3) ) ).
cnf(i_0_135_030,axiom,
( X1 != X2
| ~ sequential(X3,X1)
| sequential(X3,X2) ) ).
cnf(i_0_136_031,axiom,
( X1 != X2
| ~ triangle(X1,X3,X4)
| triangle(X2,X3,X4) ) ).
cnf(i_0_137_032,axiom,
( X1 != X2
| ~ triangle(X3,X1,X4)
| triangle(X3,X2,X4) ) ).
cnf(i_0_138_033,axiom,
( X1 != X2
| ~ triangle(X3,X4,X1)
| triangle(X3,X4,X2) ) ).
cnf(i_0_139_034,axiom,
( X1 != X2
| ~ edge(X1)
| edge(X2) ) ).
cnf(i_0_140,plain,
~ shortest_path(X1,X1,X2),
inference(equality_inference,[],[86]) ).
cnf(i_0_141,plain,
~ sequential(X1,X1),
inference(equality_inference,[],[99]) ).
cnf(i_0_142,plain,
$false,
inference(scs_inference,[],[i_0_103,i_0_104,i_0_92,i_0_93,i_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA005+1 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:07:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.29/1.61 % Version : CSE_E---1.7
% 0.29/1.61 % Problem : theBenchmark.p
% 0.29/1.61 % SZS status Theorem for theBenchmark.p
% 0.29/1.61 % SZS output start CNFRefutation
% See solution above
% 0.29/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------