%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA009+2 : 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 : n010.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 04:22:56 PM UTC 2026
% Result : Theorem 11.96s 7.64s
% Output : CNFRefutation 11.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 104 ( 16 unt; 0 def)
% Number of atoms : 452 ( 145 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 559 ( 211 ~; 248 |; 74 &)
% ( 4 <=>; 20 =>; 1 <=; 1 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 202 ( 15 sgn 90 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complete_means_path_means_stuff_means_triangles,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_path_means_stuff_means_triangles) ).
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(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(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(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(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(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(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(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(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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(c_0_11,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ) ),
inference(assume_negation,[status(cth)],[complete_means_path_means_stuff_means_triangles]) ).
fof(c_0_12,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(c_0_13,negated_conjecture,
! [X160] :
( complete
& shortest_path(esk10_0,esk11_0,esk9_0)
& on_path(esk12_0,esk9_0)
& on_path(esk13_0,esk9_0)
& sequential(esk12_0,esk13_0)
& ~ triangle(esk12_0,esk13_0,X160) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_14,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(c_0_15,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(c_0_16,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(c_0_17,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])])])]) ).
cnf(c_0_18,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,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(c_0_21,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)],[c_0_14])])])]) ).
fof(c_0_22,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)],[c_0_15])])])]) ).
fof(c_0_23,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)],[c_0_16])])])])]) ).
cnf(c_0_24,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
path(esk10_0,esk11_0,esk9_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( in_path(tail_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( in_path(head_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,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)],[c_0_21]) ).
cnf(c_0_29,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)],[c_0_22]) ).
cnf(c_0_30,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)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_32,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
( in_path(tail_of(X1),esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_34,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)],[c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( in_path(head_of(X1),esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_36,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_37,negated_conjecture,
( precedes(X1,X2,esk9_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_38,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_30,c_0_31])]) ).
cnf(c_0_39,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
( tail_of(esk1_2(X1,X2)) = X1
| head_of(esk1_2(X1,X2)) = X1
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_31])]) ).
cnf(c_0_41,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)],[c_0_23]) ).
cnf(c_0_42,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_43,negated_conjecture,
on_path(esk13_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_44,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_45,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ sequential(X3,X2)
| ~ on_path(X2,esk9_0)
| ~ on_path(X3,esk9_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
| tail_of(esk1_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ on_path(X2,esk9_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
on_path(esk12_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_48,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(X2))) = X1
| head_of(esk1_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ on_path(X2,esk9_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_49,plain,
( tail_of(esk1_2(X1,X2)) = X2
| head_of(esk1_2(X1,X2)) = X2
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_31])]) ).
cnf(c_0_50,negated_conjecture,
vertex(head_of(esk13_0)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_51,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])])]) ).
fof(c_0_52,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])])]) ).
cnf(c_0_53,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_31])]) ).
cnf(c_0_54,negated_conjecture,
( head_of(X1) != head_of(esk13_0)
| tail_of(X1) != tail_of(X2)
| ~ sequential(X2,esk13_0)
| ~ on_path(X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_55,negated_conjecture,
sequential(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_56,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk1_2(X1,tail_of(esk12_0))) = X1
| X1 = tail_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_57,negated_conjecture,
( head_of(esk1_2(X1,tail_of(esk12_0))) = X1
| tail_of(esk1_2(X1,tail_of(esk12_0))) = X1
| X1 = tail_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_58,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),X1)) = X1
| head_of(esk1_2(head_of(esk13_0),X1)) = X1
| X1 = head_of(esk13_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,negated_conjecture,
( X1 = tail_of(X2)
| edge(esk1_2(X1,tail_of(X2)))
| ~ on_path(X2,esk9_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_39]) ).
fof(c_0_62,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])])]) ).
cnf(c_0_63,negated_conjecture,
( head_of(X1) != head_of(esk13_0)
| tail_of(X1) != tail_of(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_47])]) ).
cnf(c_0_64,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_50]) ).
cnf(c_0_65,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_50]) ).
cnf(c_0_66,negated_conjecture,
( head_of(esk1_2(head_of(esk13_0),tail_of(X1))) = tail_of(X1)
| tail_of(esk1_2(head_of(esk13_0),tail_of(X1))) = tail_of(X1)
| tail_of(X1) = head_of(esk13_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_60,c_0_55]) ).
cnf(c_0_68,negated_conjecture,
( X1 = tail_of(esk12_0)
| edge(esk1_2(X1,tail_of(esk12_0)))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_47]) ).
cnf(c_0_69,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)],[c_0_62]) ).
cnf(c_0_70,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_71,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( tail_of(esk12_0) = head_of(esk13_0)
| edge(esk1_2(head_of(esk13_0),tail_of(esk12_0))) ),
inference(spm,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_74,negated_conjecture,
~ triangle(esk12_0,esk13_0,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_75,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_69,c_0_60]),c_0_60]),c_0_60]) ).
cnf(c_0_76,negated_conjecture,
( X1 = esk12_0
| sequential(X1,esk12_0)
| tail_of(esk12_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_67]) ).
cnf(c_0_77,negated_conjecture,
( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( X1 = esk1_2(head_of(esk13_0),tail_of(esk12_0))
| tail_of(esk12_0) = head_of(esk13_0)
| sequential(X1,esk1_2(head_of(esk13_0),tail_of(esk12_0)))
| tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_73]) ).
cnf(c_0_79,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_80,plain,
! [X84] :
( ~ edge(X84)
| head_of(X84) != tail_of(X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).
cnf(c_0_81,negated_conjecture,
( ~ sequential(X1,esk12_0)
| ~ sequential(esk13_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_55])]) ).
cnf(c_0_82,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
| tail_of(esk12_0) = head_of(esk13_0)
| sequential(esk1_2(head_of(esk13_0),tail_of(esk12_0)),esk12_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_73]) ).
cnf(c_0_83,negated_conjecture,
( X1 = esk1_2(head_of(esk13_0),tail_of(esk12_0))
| tail_of(esk12_0) = head_of(esk13_0)
| sequential(X1,esk1_2(head_of(esk13_0),tail_of(esk12_0)))
| head_of(esk13_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_71]) ).
cnf(c_0_84,negated_conjecture,
edge(esk13_0),
inference(spm,[status(thm)],[c_0_79,c_0_55]) ).
cnf(c_0_85,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_86,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_87,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
| tail_of(esk12_0) = head_of(esk13_0)
| ~ sequential(esk13_0,esk1_2(head_of(esk13_0),tail_of(esk12_0))) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk13_0
| tail_of(esk12_0) = head_of(esk13_0)
| sequential(esk13_0,esk1_2(head_of(esk13_0),tail_of(esk12_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_83]),c_0_84])]) ).
cnf(c_0_89,negated_conjecture,
( ~ precedes(X1,X2,esk9_0)
| ~ precedes(X2,X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_85,c_0_19]) ).
cnf(c_0_90,negated_conjecture,
( tail_of(esk12_0) = head_of(esk13_0)
| head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_71]),c_0_73]) ).
cnf(c_0_91,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk13_0
| esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( ~ precedes(X1,X2,esk9_0)
| ~ sequential(X2,X1)
| ~ on_path(X1,esk9_0)
| ~ on_path(X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_89,c_0_37]) ).
cnf(c_0_93,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_94,negated_conjecture,
( ~ sequential(X1,X2)
| ~ sequential(X2,X1)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_92,c_0_37]) ).
cnf(c_0_95,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_96,negated_conjecture,
tail_of(esk12_0) = head_of(esk13_0),
inference(spm,[status(thm)],[c_0_71,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( ~ sequential(X1,esk13_0)
| ~ sequential(esk13_0,X1)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_43]) ).
cnf(c_0_98,negated_conjecture,
tail_of(esk13_0) = head_of(esk12_0),
inference(spm,[status(thm)],[c_0_95,c_0_55]) ).
cnf(c_0_99,negated_conjecture,
( X1 = esk12_0
| sequential(X1,esk12_0)
| head_of(esk13_0) != head_of(X1)
| ~ edge(X1) ),
inference(rw,[status(thm)],[c_0_76,c_0_96]) ).
cnf(c_0_100,negated_conjecture,
~ sequential(esk13_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_47]),c_0_55])]) ).
cnf(c_0_101,negated_conjecture,
head_of(esk13_0) != head_of(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_98]),c_0_84])]) ).
cnf(c_0_102,negated_conjecture,
esk13_0 = esk12_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_99]),c_0_84])]),c_0_100]) ).
cnf(c_0_103,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA009+2 : 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
% 0.14/0.32 % Computer : n010.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:06:21 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 11.96/7.64 % Version : CSE_E---1.7
% 11.96/7.64 % Problem : theBenchmark.p
% 11.96/7.64 % SZS status Theorem for theBenchmark.p
% 11.96/7.64 % SZS output start CNFRefutation
% See solution above
% 11.96/7.69 % Total time : 5.368s
%------------------------------------------------------------------------------