%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA007+2 : TPTP v9.2.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 2.41s 2.07s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 16 unt; 0 def)
% Number of atoms : 381 ( 114 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 472 ( 175 ~; 199 |; 71 &)
% ( 4 <=>; 20 =>; 1 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 196 ( 24 sgn 96 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(back_edge,conjecture,
( 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/sandbox2/benchmark/theBenchmark.p',back_edge) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_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/sandbox2/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/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( edge(X7)
& edge(X8)
& X7 != X8
& head_of(X7) = tail_of(X8) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(c_0_9,negated_conjecture,
~ ( 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) ) ) ),
inference(assume_negation,[status(cth)],[back_edge]) ).
fof(c_0_10,plain,
! [X130,X131,X132,X133,X134,X135,X136] :
( ( path(X130,X131,X132)
| ~ shortest_path(X130,X131,X132) )
& ( X130 != X131
| ~ shortest_path(X130,X131,X132) )
& ( ~ path(X130,X131,X133)
| less_or_equal(length_of(X132),length_of(X133))
| ~ shortest_path(X130,X131,X132) )
& ( path(X134,X135,esk6_3(X134,X135,X136))
| ~ path(X134,X135,X136)
| X134 = X135
| shortest_path(X134,X135,X136) )
& ( ~ less_or_equal(length_of(X136),length_of(esk6_3(X134,X135,X136)))
| ~ path(X134,X135,X136)
| X134 = X135
| shortest_path(X134,X135,X136) ) ),
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_11,negated_conjecture,
! [X172] :
( complete
& shortest_path(esk9_0,esk10_0,esk13_0)
& precedes(esk11_0,esk12_0,esk13_0)
& ( ~ edge(X172)
| tail_of(X172) != head_of(esk12_0)
| head_of(X172) != tail_of(esk11_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_12,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(c_0_13,plain,
! [X110,X111,X112,X113] :
( ( vertex(X113)
| ~ path(X110,X111,X112)
| ~ in_path(X113,X112) )
& ( on_path(esk4_4(X110,X111,X112,X113),X112)
| ~ path(X110,X111,X112)
| ~ in_path(X113,X112) )
& ( X113 = head_of(esk4_4(X110,X111,X112,X113))
| X113 = tail_of(esk4_4(X110,X111,X112,X113))
| ~ path(X110,X111,X112)
| ~ in_path(X113,X112) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])]) ).
cnf(c_0_14,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
shortest_path(esk9_0,esk10_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X106,X107,X108,X109] :
( ( edge(X109)
| ~ path(X106,X107,X108)
| ~ on_path(X109,X108) )
& ( in_path(head_of(X109),X108)
| ~ path(X106,X107,X108)
| ~ on_path(X109,X108) )
& ( in_path(tail_of(X109),X108)
| ~ path(X106,X107,X108)
| ~ on_path(X109,X108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
fof(c_0_17,plain,
! [X123,X124,X125,X126,X127,X128] :
( ( on_path(X126,X123)
| ~ precedes(X126,X127,X123)
| ~ path(X124,X125,X123) )
& ( on_path(X127,X123)
| ~ precedes(X126,X127,X123)
| ~ path(X124,X125,X123) )
& ( ~ sequential(X126,X127)
| ~ sequential(X126,X128)
| ~ precedes(X128,X127,X123)
| ~ precedes(X126,X127,X123)
| ~ path(X124,X125,X123) )
& ( sequential(X126,esk5_3(X123,X126,X127))
| sequential(X126,X127)
| ~ precedes(X126,X127,X123)
| ~ path(X124,X125,X123) )
& ( precedes(esk5_3(X123,X126,X127),X127,X123)
| sequential(X126,X127)
| ~ precedes(X126,X127,X123)
| ~ path(X124,X125,X123) ) ),
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)],[c_0_12])])])])])]) ).
fof(c_0_18,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]) ).
cnf(c_0_19,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
path(esk9_0,esk10_0,esk13_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( in_path(head_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
precedes(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_24,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_25,plain,
! [X92,X93] :
( ( edge(esk1_2(X92,X93))
| ~ vertex(X92)
| ~ vertex(X93)
| X92 = X93
| ~ complete )
& ( X92 != head_of(esk1_2(X92,X93))
| X93 != tail_of(esk1_2(X92,X93))
| X93 != head_of(esk1_2(X92,X93))
| X92 != tail_of(esk1_2(X92,X93))
| ~ vertex(X92)
| ~ vertex(X93)
| X92 = X93
| ~ complete )
& ( X93 = head_of(esk1_2(X92,X93))
| X92 = head_of(esk1_2(X92,X93))
| ~ vertex(X92)
| ~ vertex(X93)
| X92 = X93
| ~ complete )
& ( X92 = tail_of(esk1_2(X92,X93))
| X92 = head_of(esk1_2(X92,X93))
| ~ vertex(X92)
| ~ vertex(X93)
| X92 = X93
| ~ complete )
& ( X93 = head_of(esk1_2(X92,X93))
| X93 = tail_of(esk1_2(X92,X93))
| ~ vertex(X92)
| ~ vertex(X93)
| X92 = X93
| ~ complete )
& ( X92 = tail_of(esk1_2(X92,X93))
| X93 = tail_of(esk1_2(X92,X93))
| ~ vertex(X92)
| ~ vertex(X93)
| X92 = X93
| ~ 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_18])])])])]) ).
cnf(c_0_26,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( in_path(head_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( on_path(esk12_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( in_path(tail_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,plain,
( on_path(X1,X2)
| ~ precedes(X1,X3,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_31,plain,
! [X138,X139,X140,X141,X142,X143] :
( ( tail_of(X143) != tail_of(X140)
| head_of(X143) != head_of(X141)
| ~ shortest_path(X138,X139,X142)
| ~ precedes(X140,X141,X142) )
& ( ~ precedes(X141,X140,X142)
| ~ shortest_path(X138,X139,X142)
| ~ precedes(X140,X141,X142) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_32,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_25]) ).
cnf(c_0_33,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_34,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
on_path(esk12_0,esk13_0),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_36,negated_conjecture,
( in_path(tail_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_37,negated_conjecture,
( on_path(esk11_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_38,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)],[c_0_25]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,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_32,c_0_33])]) ).
cnf(c_0_41,negated_conjecture,
vertex(head_of(esk12_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
on_path(esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_44,plain,
( head_of(esk1_2(X1,X2)) = X2
| head_of(esk1_2(X1,X2)) = X1
| X2 = X1
| ~ vertex(X1)
| ~ vertex(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_33])]) ).
cnf(c_0_45,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_46,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_15]) ).
cnf(c_0_47,negated_conjecture,
( tail_of(esk1_2(head_of(esk12_0),X1)) = X1
| head_of(esk1_2(head_of(esk12_0),X1)) = X1
| X1 = head_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
vertex(tail_of(esk11_0)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),X1)) = head_of(esk12_0)
| head_of(esk1_2(head_of(esk12_0),X1)) = X1
| X1 = head_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_50,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_33])]) ).
cnf(c_0_51,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_25]) ).
cnf(c_0_52,negated_conjecture,
( head_of(X1) != head_of(esk12_0)
| tail_of(X1) != tail_of(esk11_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_53,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
| tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
| head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( X1 = tail_of(esk11_0)
| edge(esk1_2(X1,tail_of(esk11_0)))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
fof(c_0_56,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]) ).
cnf(c_0_57,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_58,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_51,c_0_33])]) ).
cnf(c_0_59,negated_conjecture,
( ~ edge(X1)
| tail_of(X1) != head_of(esk12_0)
| head_of(X1) != tail_of(esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_60,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = tail_of(esk11_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| edge(esk1_2(head_of(esk12_0),tail_of(esk11_0))) ),
inference(spm,[status(thm)],[c_0_55,c_0_41]) ).
fof(c_0_62,plain,
! [X117,X118,X119,X120,X121,X122] :
( ( ~ sequential(X120,X121)
| ~ on_path(X120,X117)
| ~ on_path(X121,X117)
| precedes(X120,X121,X117)
| ~ path(X118,X119,X117) )
& ( ~ sequential(X120,X122)
| ~ precedes(X122,X121,X117)
| ~ on_path(X120,X117)
| ~ on_path(X121,X117)
| precedes(X120,X121,X117)
| ~ path(X118,X119,X117) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
fof(c_0_63,plain,
! [X115,X116] :
( ( edge(X115)
| ~ sequential(X115,X116) )
& ( edge(X116)
| ~ sequential(X115,X116) )
& ( X115 != X116
| ~ sequential(X115,X116) )
& ( head_of(X115) = tail_of(X116)
| ~ sequential(X115,X116) )
& ( ~ edge(X115)
| ~ edge(X116)
| X115 = X116
| head_of(X115) != tail_of(X116)
| sequential(X115,X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
cnf(c_0_64,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_65,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(esk11_0))) = X1
| head_of(esk1_2(X1,tail_of(esk11_0))) = X1
| X1 = tail_of(esk11_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_48]) ).
cnf(c_0_66,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| tail_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) != head_of(esk12_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_67,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_62]) ).
cnf(c_0_68,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_69,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_70,negated_conjecture,
edge(esk11_0),
inference(spm,[status(thm)],[c_0_64,c_0_43]) ).
cnf(c_0_71,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_41]),c_0_66]) ).
cnf(c_0_72,negated_conjecture,
( precedes(X1,X2,esk13_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_20]) ).
cnf(c_0_73,negated_conjecture,
( ~ precedes(X1,X2,esk13_0)
| ~ precedes(X2,X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_15]) ).
cnf(c_0_74,negated_conjecture,
( X1 = esk11_0
| sequential(X1,esk11_0)
| tail_of(esk11_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
tail_of(esk11_0) = head_of(esk12_0),
inference(spm,[status(thm)],[c_0_60,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( precedes(X1,esk11_0,esk13_0)
| ~ sequential(X1,esk11_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_43]) ).
cnf(c_0_77,negated_conjecture,
~ precedes(esk12_0,esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_73,c_0_23]) ).
cnf(c_0_78,negated_conjecture,
( X1 = esk11_0
| sequential(X1,esk11_0)
| head_of(esk12_0) != head_of(X1)
| ~ edge(X1) ),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_80,negated_conjecture,
~ sequential(esk12_0,esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_35]),c_0_77]) ).
cnf(c_0_81,negated_conjecture,
head_of(esk12_0) != head_of(esk11_0),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_82,negated_conjecture,
esk12_0 = esk11_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_78]),c_0_79])]),c_0_80]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA007+2 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n011.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % 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 18:07:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.41/2.07 % Version : CSE_E---1.7
% 2.41/2.07 % Problem : theBenchmark.p
% 2.41/2.07 % SZS status Theorem for theBenchmark.p
% 2.41/2.07 % SZS output start CNFRefutation
% See solution above
% 2.41/2.08 % Total time : 1.372s
%------------------------------------------------------------------------------