%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA006+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 : n019.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 4.01s 3.28s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 16 unt; 0 def)
% Number of atoms : 435 ( 158 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 543 ( 200 ~; 234 |; 80 &)
% ( 5 <=>; 20 =>; 1 <=; 3 <~>)
% 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 : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 200 ( 24 sgn 97 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(edge_some_way,conjecture,
( complete
=> ! [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) )
<~> ? [X9] :
( edge(X9)
& tail_of(X9) = head_of(X8)
& head_of(X9) = tail_of(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_some_way) ).
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(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(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(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(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(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(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) = tail_of(X7)
& head_of(X9) = head_of(X8) )
<=> ? [X9] :
( edge(X9)
& tail_of(X9) = head_of(X8)
& head_of(X9) = tail_of(X7) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[edge_some_way])]) ).
fof(c_0_10,plain,
! [X125,X126,X127,X128,X129,X130,X131] :
( ( path(X125,X126,X127)
| ~ shortest_path(X125,X126,X127) )
& ( X125 != X126
| ~ shortest_path(X125,X126,X127) )
& ( ~ path(X125,X126,X128)
| less_or_equal(length_of(X127),length_of(X128))
| ~ shortest_path(X125,X126,X127) )
& ( path(X129,X130,esk6_3(X129,X130,X131))
| ~ path(X129,X130,X131)
| X129 = X130
| shortest_path(X129,X130,X131) )
& ( ~ less_or_equal(length_of(X131),length_of(esk6_3(X129,X130,X131)))
| ~ path(X129,X130,X131)
| X129 = X130
| shortest_path(X129,X130,X131) ) ),
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,
! [X161,X163] :
( complete
& shortest_path(esk9_0,esk10_0,esk13_0)
& precedes(esk11_0,esk12_0,esk13_0)
& ( edge(esk14_0)
| ~ edge(X161)
| tail_of(X161) != tail_of(esk11_0)
| head_of(X161) != head_of(esk12_0) )
& ( tail_of(esk14_0) = head_of(esk12_0)
| ~ edge(X161)
| tail_of(X161) != tail_of(esk11_0)
| head_of(X161) != head_of(esk12_0) )
& ( head_of(esk14_0) = tail_of(esk11_0)
| ~ edge(X161)
| tail_of(X161) != tail_of(esk11_0)
| head_of(X161) != head_of(esk12_0) )
& ( edge(esk15_0)
| ~ edge(X163)
| tail_of(X163) != head_of(esk12_0)
| head_of(X163) != tail_of(esk11_0) )
& ( tail_of(esk15_0) = tail_of(esk11_0)
| ~ edge(X163)
| tail_of(X163) != head_of(esk12_0)
| head_of(X163) != tail_of(esk11_0) )
& ( head_of(esk15_0) = head_of(esk12_0)
| ~ edge(X163)
| tail_of(X163) != head_of(esk12_0)
| head_of(X163) != tail_of(esk11_0) ) ),
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_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,
! [X105,X106,X107,X108] :
( ( vertex(X108)
| ~ path(X105,X106,X107)
| ~ in_path(X108,X107) )
& ( on_path(esk4_4(X105,X106,X107,X108),X107)
| ~ path(X105,X106,X107)
| ~ in_path(X108,X107) )
& ( X108 = head_of(esk4_4(X105,X106,X107,X108))
| X108 = tail_of(esk4_4(X105,X106,X107,X108))
| ~ path(X105,X106,X107)
| ~ in_path(X108,X107) ) ),
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,
! [X101,X102,X103,X104] :
( ( edge(X104)
| ~ path(X101,X102,X103)
| ~ on_path(X104,X103) )
& ( in_path(head_of(X104),X103)
| ~ path(X101,X102,X103)
| ~ on_path(X104,X103) )
& ( in_path(tail_of(X104),X103)
| ~ path(X101,X102,X103)
| ~ on_path(X104,X103) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
fof(c_0_17,plain,
! [X118,X119,X120,X121,X122,X123] :
( ( on_path(X121,X118)
| ~ precedes(X121,X122,X118)
| ~ path(X119,X120,X118) )
& ( on_path(X122,X118)
| ~ precedes(X121,X122,X118)
| ~ path(X119,X120,X118) )
& ( ~ sequential(X121,X122)
| ~ sequential(X121,X123)
| ~ precedes(X123,X122,X118)
| ~ precedes(X121,X122,X118)
| ~ path(X119,X120,X118) )
& ( sequential(X121,esk5_3(X118,X121,X122))
| sequential(X121,X122)
| ~ precedes(X121,X122,X118)
| ~ path(X119,X120,X118) )
& ( precedes(esk5_3(X118,X121,X122),X122,X118)
| sequential(X121,X122)
| ~ precedes(X121,X122,X118)
| ~ path(X119,X120,X118) ) ),
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(tail_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(X1,X3,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]) ).
cnf(c_0_24,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_25,plain,
( on_path(X1,X2)
| ~ precedes(X3,X1,X2)
| ~ path(X4,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_26,plain,
! [X87,X88] :
( ( edge(esk1_2(X87,X88))
| ~ vertex(X87)
| ~ vertex(X88)
| X87 = X88
| ~ complete )
& ( X87 != head_of(esk1_2(X87,X88))
| X88 != tail_of(esk1_2(X87,X88))
| X88 != head_of(esk1_2(X87,X88))
| X87 != tail_of(esk1_2(X87,X88))
| ~ vertex(X87)
| ~ vertex(X88)
| X87 = X88
| ~ complete )
& ( X88 = head_of(esk1_2(X87,X88))
| X87 = head_of(esk1_2(X87,X88))
| ~ vertex(X87)
| ~ vertex(X88)
| X87 = X88
| ~ complete )
& ( X87 = tail_of(esk1_2(X87,X88))
| X87 = head_of(esk1_2(X87,X88))
| ~ vertex(X87)
| ~ vertex(X88)
| X87 = X88
| ~ complete )
& ( X88 = head_of(esk1_2(X87,X88))
| X88 = tail_of(esk1_2(X87,X88))
| ~ vertex(X87)
| ~ vertex(X88)
| X87 = X88
| ~ complete )
& ( X87 = tail_of(esk1_2(X87,X88))
| X88 = tail_of(esk1_2(X87,X88))
| ~ vertex(X87)
| ~ vertex(X88)
| X87 = X88
| ~ 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_27,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( in_path(tail_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( on_path(esk11_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_30,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_31,negated_conjecture,
( in_path(head_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( on_path(esk12_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_33,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
on_path(esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
fof(c_0_37,plain,
! [X133,X134,X135,X136,X137,X138] :
( ( tail_of(X138) != tail_of(X135)
| head_of(X138) != head_of(X136)
| ~ shortest_path(X133,X134,X137)
| ~ precedes(X135,X136,X137) )
& ( ~ precedes(X136,X135,X137)
| ~ shortest_path(X133,X134,X137)
| ~ precedes(X135,X136,X137) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_38,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_26]) ).
cnf(c_0_39,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
on_path(esk12_0,esk13_0),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_41,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_26]) ).
cnf(c_0_42,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_43,negated_conjecture,
vertex(tail_of(esk11_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,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_37]) ).
cnf(c_0_45,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_38,c_0_34])]) ).
cnf(c_0_46,negated_conjecture,
vertex(head_of(esk12_0)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,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_41,c_0_34])]) ).
cnf(c_0_48,negated_conjecture,
( X1 = tail_of(esk11_0)
| edge(esk1_2(X1,tail_of(esk11_0)))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,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_44,c_0_15]) ).
cnf(c_0_50,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_45,c_0_46]) ).
cnf(c_0_51,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_47,c_0_46]) ).
cnf(c_0_52,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_26]) ).
cnf(c_0_53,negated_conjecture,
( tail_of(esk15_0) = tail_of(esk11_0)
| ~ 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_54,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_48,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( head_of(X1) != head_of(esk12_0)
| tail_of(X1) != tail_of(esk11_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_23]) ).
cnf(c_0_56,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_50,c_0_43]) ).
cnf(c_0_57,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_51,c_0_43]) ).
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_52,c_0_34])]) ).
cnf(c_0_59,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| tail_of(esk15_0) = tail_of(esk11_0)
| 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))) != head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
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_55,c_0_56]),c_0_57]) ).
cnf(c_0_61,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_43]) ).
cnf(c_0_62,negated_conjecture,
( tail_of(esk15_0) = tail_of(esk11_0)
| 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(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( head_of(esk1_2(head_of(esk12_0),tail_of(esk11_0))) = head_of(esk12_0)
| tail_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_61,c_0_46]) ).
cnf(c_0_64,negated_conjecture,
( head_of(esk15_0) = head_of(esk12_0)
| ~ 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_65,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)
| tail_of(esk15_0) = tail_of(esk11_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_66,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_67,plain,
( edge(X1)
| ~ path(X2,X3,X4)
| ~ on_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_68,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| head_of(esk15_0) = head_of(esk12_0)
| 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))) != head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
cnf(c_0_69,negated_conjecture,
( tail_of(esk15_0) = tail_of(esk11_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_65]) ).
fof(c_0_70,plain,
! [X112,X113,X114,X115,X116,X117] :
( ( ~ sequential(X115,X116)
| ~ on_path(X115,X112)
| ~ on_path(X116,X112)
| precedes(X115,X116,X112)
| ~ path(X113,X114,X112) )
& ( ~ sequential(X115,X117)
| ~ precedes(X117,X116,X112)
| ~ on_path(X115,X112)
| ~ on_path(X116,X112)
| precedes(X115,X116,X112)
| ~ path(X113,X114,X112) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])]) ).
fof(c_0_71,plain,
! [X110,X111] :
( ( edge(X110)
| ~ sequential(X110,X111) )
& ( edge(X111)
| ~ sequential(X110,X111) )
& ( X110 != X111
| ~ sequential(X110,X111) )
& ( head_of(X110) = tail_of(X111)
| ~ sequential(X110,X111) )
& ( ~ edge(X110)
| ~ edge(X111)
| X110 = X111
| head_of(X110) != tail_of(X111)
| sequential(X110,X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
cnf(c_0_72,negated_conjecture,
( edge(X1)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_20]) ).
cnf(c_0_73,negated_conjecture,
( head_of(esk15_0) = head_of(esk12_0)
| 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(spm,[status(thm)],[c_0_68,c_0_60]) ).
cnf(c_0_74,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| head_of(esk15_0) != head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_69]) ).
cnf(c_0_75,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_70]) ).
cnf(c_0_76,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_77,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,negated_conjecture,
edge(esk11_0),
inference(spm,[status(thm)],[c_0_72,c_0_36]) ).
cnf(c_0_79,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_73,c_0_63]),c_0_74]) ).
cnf(c_0_80,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_75,c_0_20]) ).
cnf(c_0_81,negated_conjecture,
( ~ precedes(X1,X2,esk13_0)
| ~ precedes(X2,X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_76,c_0_15]) ).
cnf(c_0_82,negated_conjecture,
( X1 = esk11_0
| sequential(X1,esk11_0)
| tail_of(esk11_0) != head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
tail_of(esk11_0) = head_of(esk12_0),
inference(spm,[status(thm)],[c_0_60,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( precedes(X1,esk11_0,esk13_0)
| ~ sequential(X1,esk11_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_80,c_0_36]) ).
cnf(c_0_85,negated_conjecture,
~ precedes(esk12_0,esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_81,c_0_23]) ).
cnf(c_0_86,negated_conjecture,
( X1 = esk11_0
| sequential(X1,esk11_0)
| head_of(esk12_0) != head_of(X1)
| ~ edge(X1) ),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_72,c_0_40]) ).
cnf(c_0_88,negated_conjecture,
~ sequential(esk12_0,esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_40]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
head_of(esk12_0) != head_of(esk11_0),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_90,negated_conjecture,
esk12_0 = esk11_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_86]),c_0_87])]),c_0_88]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA006+1 : 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
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 18:05:44 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 4.01/3.28 % Version : CSE_E---1.7
% 4.01/3.28 % Problem : theBenchmark.p
% 4.01/3.28 % SZS status Theorem for theBenchmark.p
% 4.01/3.28 % SZS output start CNFRefutation
% See solution above
% 4.01/3.29 % Total time : 2.372s
%------------------------------------------------------------------------------