%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA002+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 : n022.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 04:22:54 PM UTC 2026
% Result : Theorem 15.34s 10.17s
% Output : CNFRefutation 15.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 90 ( 12 unt; 0 def)
% Number of atoms : 350 ( 97 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 423 ( 163 ~; 182 |; 56 &)
% ( 3 <=>; 18 =>; 1 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 226 ( 27 sgn 104 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maximal_path_length,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> less_or_equal(minus(length_of(X4),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
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(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(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(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(back_edge,lemma,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ? [X9] :
( edge(X9)
& tail_of(X9) = head_of(X8)
& head_of(X9) = tail_of(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
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(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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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(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(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(c_0_13,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> less_or_equal(minus(length_of(X4),n1),number_of_in(triangles,graph)) ) ),
inference(assume_negation,[status(cth)],[maximal_path_length]) ).
fof(c_0_14,plain,
! [X127,X128,X129,X130,X131,X132,X133] :
( ( path(X127,X128,X129)
| ~ shortest_path(X127,X128,X129) )
& ( X127 != X128
| ~ shortest_path(X127,X128,X129) )
& ( ~ path(X127,X128,X130)
| less_or_equal(length_of(X129),length_of(X130))
| ~ shortest_path(X127,X128,X129) )
& ( path(X131,X132,esk6_3(X131,X132,X133))
| ~ path(X131,X132,X133)
| X131 = X132
| shortest_path(X131,X132,X133) )
& ( ~ less_or_equal(length_of(X133),length_of(esk6_3(X131,X132,X133)))
| ~ path(X131,X132,X133)
| X131 = X132
| shortest_path(X131,X132,X133) ) ),
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_15,negated_conjecture,
( complete
& shortest_path(esk11_0,esk12_0,esk10_0)
& ~ less_or_equal(minus(length_of(esk10_0),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X103,X104,X105,X106] :
( ( edge(X106)
| ~ path(X103,X104,X105)
| ~ on_path(X106,X105) )
& ( in_path(head_of(X106),X105)
| ~ path(X103,X104,X105)
| ~ on_path(X106,X105) )
& ( in_path(tail_of(X106),X105)
| ~ path(X103,X104,X105)
| ~ on_path(X106,X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
cnf(c_0_17,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
shortest_path(esk11_0,esk12_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X150,X151,X152,X155] :
( ( on_path(esk7_1(X150),X150)
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) )
& ( on_path(esk8_1(X150),X150)
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) )
& ( sequential(esk7_1(X150),esk8_1(X150))
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) )
& ( ~ triangle(esk7_1(X150),esk8_1(X150),X155)
| ~ path(X151,X152,X150)
| number_of_in(sequential_pairs,X150) = number_of_in(triangles,X150) ) ),
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(c_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(c_0_21,lemma,
! [X158,X159,X160,X161,X162] :
( ( edge(esk9_4(X158,X159,X160,X161))
| ~ shortest_path(X158,X159,X162)
| ~ precedes(X160,X161,X162)
| ~ complete )
& ( tail_of(esk9_4(X158,X159,X160,X161)) = head_of(X161)
| ~ shortest_path(X158,X159,X162)
| ~ precedes(X160,X161,X162)
| ~ complete )
& ( head_of(esk9_4(X158,X159,X160,X161)) = tail_of(X160)
| ~ shortest_path(X158,X159,X162)
| ~ precedes(X160,X161,X162)
| ~ complete ) ),
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)],[back_edge])])])])])]) ).
cnf(c_0_22,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
path(esk11_0,esk12_0,esk10_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,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)],[c_0_19]) ).
fof(c_0_25,plain,
! [X114,X115,X116,X117,X118,X119] :
( ( ~ sequential(X117,X118)
| ~ on_path(X117,X114)
| ~ on_path(X118,X114)
| precedes(X117,X118,X114)
| ~ path(X115,X116,X114) )
& ( ~ sequential(X117,X119)
| ~ precedes(X119,X118,X114)
| ~ on_path(X117,X114)
| ~ on_path(X118,X114)
| precedes(X117,X118,X114)
| ~ path(X115,X116,X114) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_26,lemma,
( edge(esk9_4(X1,X2,X3,X4))
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_28,plain,
! [X112,X113] :
( ( edge(X112)
| ~ sequential(X112,X113) )
& ( edge(X113)
| ~ sequential(X112,X113) )
& ( X112 != X113
| ~ sequential(X112,X113) )
& ( head_of(X112) = tail_of(X113)
| ~ sequential(X112,X113) )
& ( ~ edge(X112)
| ~ edge(X113)
| X112 = X113
| head_of(X112) != tail_of(X113)
| sequential(X112,X113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
cnf(c_0_29,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| on_path(esk7_1(esk10_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_31,lemma,
( head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,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_25]) ).
cnf(c_0_33,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)],[c_0_19]) ).
cnf(c_0_34,lemma,
( edge(esk9_4(X1,X2,X3,X4))
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_35,lemma,
( tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_36,plain,
! [X141,X142,X143] :
( ( edge(X141)
| ~ triangle(X141,X142,X143) )
& ( edge(X142)
| ~ triangle(X141,X142,X143) )
& ( edge(X143)
| ~ triangle(X141,X142,X143) )
& ( sequential(X141,X142)
| ~ triangle(X141,X142,X143) )
& ( sequential(X142,X143)
| ~ triangle(X141,X142,X143) )
& ( sequential(X143,X141)
| ~ triangle(X141,X142,X143) )
& ( ~ edge(X141)
| ~ edge(X142)
| ~ edge(X143)
| ~ sequential(X141,X142)
| ~ sequential(X142,X143)
| ~ sequential(X143,X141)
| triangle(X141,X142,X143) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])]) ).
cnf(c_0_37,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| edge(esk7_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,lemma,
( head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_27])]) ).
cnf(c_0_40,negated_conjecture,
( precedes(X1,X2,esk10_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk10_0)
| ~ on_path(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_41,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| on_path(esk8_1(esk10_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_42,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)],[c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( edge(esk9_4(esk11_0,esk12_0,X1,X2))
| ~ precedes(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_44,lemma,
( tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_27])]) ).
cnf(c_0_45,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_36]) ).
cnf(c_0_46,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_47,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| X1 = esk7_1(esk10_0)
| sequential(X1,esk7_1(esk10_0))
| tail_of(esk7_1(esk10_0)) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( head_of(esk9_4(esk11_0,esk12_0,X1,X2)) = tail_of(X1)
| ~ precedes(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_49,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| precedes(X1,esk8_1(esk10_0),esk10_0)
| ~ sequential(X1,esk8_1(esk10_0))
| ~ on_path(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| sequential(esk7_1(esk10_0),esk8_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_51,negated_conjecture,
( X1 = esk9_4(esk11_0,esk12_0,X2,X3)
| sequential(X1,esk9_4(esk11_0,esk12_0,X2,X3))
| tail_of(esk9_4(esk11_0,esk12_0,X2,X3)) != head_of(X1)
| ~ precedes(X2,X3,esk10_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( tail_of(esk9_4(esk11_0,esk12_0,X1,X2)) = head_of(X2)
| ~ precedes(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_18]) ).
cnf(c_0_53,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)],[c_0_19]) ).
cnf(c_0_54,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_45,c_0_46]),c_0_46]),c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( esk9_4(esk11_0,esk12_0,X1,X2) = esk7_1(esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| sequential(esk9_4(esk11_0,esk12_0,X1,X2),esk7_1(esk10_0))
| tail_of(esk7_1(esk10_0)) != tail_of(X1)
| ~ precedes(X1,X2,esk10_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_43]) ).
cnf(c_0_56,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| precedes(esk7_1(esk10_0),esk8_1(esk10_0),esk10_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_30]) ).
cnf(c_0_57,negated_conjecture,
( X1 = esk9_4(esk11_0,esk12_0,X2,X3)
| sequential(X1,esk9_4(esk11_0,esk12_0,X2,X3))
| head_of(X3) != head_of(X1)
| ~ precedes(X2,X3,esk10_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_58,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]) ).
cnf(c_0_59,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ sequential(X2,esk7_1(X1))
| ~ sequential(esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_42]) ).
cnf(c_0_60,negated_conjecture,
( esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| sequential(esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)),esk7_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( X1 = esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| sequential(X1,esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)))
| head_of(esk8_1(esk10_0)) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| edge(esk8_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
fof(c_0_63,plain,
! [X135,X136,X137,X138,X139,X140] :
( ( tail_of(X140) != tail_of(X137)
| head_of(X140) != head_of(X138)
| ~ shortest_path(X135,X136,X139)
| ~ precedes(X137,X138,X139) )
& ( ~ precedes(X138,X137,X139)
| ~ shortest_path(X135,X136,X139)
| ~ precedes(X137,X138,X139) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
fof(c_0_64,plain,
! [X87] :
( ~ edge(X87)
| head_of(X87) != tail_of(X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).
cnf(c_0_65,negated_conjecture,
( esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| ~ sequential(esk8_1(esk10_0),esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)))
| ~ path(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk8_1(esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| sequential(esk8_1(esk10_0),esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0))) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_61]),c_0_62]) ).
cnf(c_0_67,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_63]) ).
fof(c_0_68,plain,
! [X144,X145,X146] :
( ~ path(X144,X145,X146)
| length_of(X146) = number_of_in(edges,X146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[length_defn])]) ).
cnf(c_0_69,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk8_1(esk10_0)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| ~ path(X1,X2,esk10_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,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_67,c_0_18]) ).
cnf(c_0_72,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_73,plain,
! [X147,X148,X149] :
( ~ path(X147,X148,X149)
| number_of_in(sequential_pairs,X149) = minus(length_of(X149),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
cnf(c_0_74,plain,
( length_of(X3) = number_of_in(edges,X3)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( head_of(esk9_4(esk11_0,esk12_0,X1,X2)) != head_of(X2)
| ~ precedes(X1,X2,esk10_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_52]),c_0_43]) ).
cnf(c_0_76,negated_conjecture,
( esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk8_1(esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_70,c_0_23]) ).
cnf(c_0_77,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| head_of(X1) != head_of(esk8_1(esk10_0))
| tail_of(X1) != tail_of(esk7_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_56]) ).
cnf(c_0_78,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| tail_of(esk8_1(esk10_0)) = head_of(esk7_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_72,c_0_50]) ).
cnf(c_0_79,plain,
( number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,negated_conjecture,
length_of(esk10_0) = number_of_in(edges,esk10_0),
inference(spm,[status(thm)],[c_0_74,c_0_23]) ).
fof(c_0_81,plain,
! [X156,X157] : less_or_equal(number_of_in(X156,X157),number_of_in(X156,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_82,negated_conjecture,
( esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_56]) ).
cnf(c_0_83,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| tail_of(esk7_1(esk10_0)) != head_of(esk7_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
~ less_or_equal(minus(length_of(esk10_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_85,negated_conjecture,
minus(number_of_in(edges,esk10_0),n1) = number_of_in(sequential_pairs,esk10_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_23]),c_0_80]) ).
cnf(c_0_86,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_87,negated_conjecture,
number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_82]),c_0_56]),c_0_83]) ).
cnf(c_0_88,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk10_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_80]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA002+2 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.11 % 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 : n022.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 18:16:06 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 15.34/10.17 % Version : CSE_E---1.7
% 15.34/10.17 % Problem : theBenchmark.p
% 15.34/10.17 % SZS status Theorem for theBenchmark.p
% 15.34/10.17 % SZS output start CNFRefutation
% See solution above
% 15.42/10.23 % Total time : 7.383s
%------------------------------------------------------------------------------