%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRA009+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:31:30 PM UTC 2026
% Result : Theorem 0.22s 15.43s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 98 ( 21 unt; 0 def)
% Number of atoms : 422 ( 127 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 518 ( 194 ~; 218 |; 77 &)
% ( 6 <=>; 21 =>; 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 : 201 ( 33 sgn 95 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(precedes_defn,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
<= ( ( ? [X9] :
( precedes(X9,X8,X4)
& sequential(X7,X9) )
| sequential(X7,X8) )
& on_path(X8,X4)
& on_path(X7,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(complete_means_path_means_stuff_means_triangles,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> ! [X7,X8] :
( ( sequential(X7,X8)
& on_path(X8,X4)
& on_path(X7,X4) )
=> ? [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)
<=> ( ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) )
& X2 != X3
& path(X2,X3,X10) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(complete_properties,axiom,
( complete
=> ! [X2,X3] :
( ( X2 != X3
& vertex(X3)
& vertex(X2) )
=> ? [X1] :
( ( ( X3 = tail_of(X1)
& X2 = head_of(X1) )
<~> ( X2 = tail_of(X1)
& X3 = head_of(X1) ) )
& edge(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
fof(on_path_properties,axiom,
! [X2,X3,X4,X1] :
( ( on_path(X1,X4)
& path(X2,X3,X4) )
=> ( in_path(tail_of(X1),X4)
& in_path(head_of(X1),X4)
& edge(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(shortest_path_properties,axiom,
! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ( ~ precedes(X8,X7,X4)
& ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7) ) ) ),
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(in_path_properties,axiom,
! [X2,X3,X4,X6] :
( ( in_path(X6,X4)
& path(X2,X3,X4) )
=> ( ? [X1] :
( ( X6 = tail_of(X1)
| X6 = head_of(X1) )
& on_path(X1,X4) )
& vertex(X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',in_path_properties) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( head_of(X7) = tail_of(X8)
& X7 != X8
& edge(X8)
& edge(X7) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(triangle_defn,axiom,
! [X7,X8,X9] :
( triangle(X7,X8,X9)
<=> ( sequential(X9,X7)
& sequential(X8,X9)
& sequential(X7,X8)
& edge(X9)
& edge(X8)
& edge(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(c_0_10,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( ( ( ? [X9] :
( precedes(X9,X8,X4)
& sequential(X7,X9) )
| sequential(X7,X8) )
& on_path(X8,X4)
& on_path(X7,X4) )
=> precedes(X7,X8,X4) ) ),
inference(fof_simplification,[status(thm)],[precedes_defn]) ).
fof(c_0_11,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> ! [X7,X8] :
( ( sequential(X7,X8)
& on_path(X8,X4)
& on_path(X7,X4) )
=> ? [X9] : triangle(X7,X8,X9) ) ) ),
inference(assume_negation,[status(cth)],[complete_means_path_means_stuff_means_triangles]) ).
fof(c_0_12,plain,
! [X2,X3,X10] :
( shortest_path(X2,X3,X10)
<=> ( ! [X4] :
( path(X2,X3,X4)
=> less_or_equal(length_of(X10),length_of(X4)) )
& X2 != X3
& path(X2,X3,X10) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_defn]) ).
fof(c_0_13,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ path(X41,X42,X40)
| precedes(X43,X44,X40)
| ~ on_path(X44,X40)
| ~ on_path(X43,X40)
| ~ precedes(X45,X44,X40)
| ~ sequential(X43,X45) )
& ( ~ path(X41,X42,X40)
| precedes(X43,X44,X40)
| ~ on_path(X44,X40)
| ~ on_path(X43,X40)
| ~ sequential(X43,X44) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_14,negated_conjecture,
! [X89] :
( ~ triangle(esk12_0,esk13_0,X89)
& sequential(esk12_0,esk13_0)
& on_path(esk13_0,esk9_0)
& on_path(esk12_0,esk9_0)
& shortest_path(esk10_0,esk11_0,esk9_0)
& complete ),
inference(fof_nnf,[status(thm)],[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_15,plain,
( complete
=> ! [X2,X3] :
( ( X2 != X3
& vertex(X3)
& vertex(X2) )
=> ? [X1] :
( ~ ( ( X3 = tail_of(X1)
& X2 = head_of(X1) )
<=> ( X2 = tail_of(X1)
& X3 = head_of(X1) ) )
& edge(X1) ) ) ),
inference(fof_simplification,[status(thm)],[complete_properties]) ).
fof(c_0_16,plain,
! [X29,X30,X31,X32] :
( ( ~ on_path(X32,X31)
| ~ path(X29,X30,X31)
| in_path(tail_of(X32),X31) )
& ( ~ on_path(X32,X31)
| ~ path(X29,X30,X31)
| in_path(head_of(X32),X31) )
& ( ~ on_path(X32,X31)
| ~ path(X29,X30,X31)
| edge(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])])]) ).
fof(c_0_17,plain,
! [X53,X54,X55,X56,X57,X58,X59] :
( ( shortest_path(X57,X58,X59)
| X57 = X58
| ~ path(X57,X58,X59)
| ~ less_or_equal(length_of(X59),length_of(esk6_3(X57,X58,X59))) )
& ( shortest_path(X57,X58,X59)
| X57 = X58
| ~ path(X57,X58,X59)
| path(X57,X58,esk6_3(X57,X58,X59)) )
& ( ~ shortest_path(X53,X54,X55)
| less_or_equal(length_of(X55),length_of(X56))
| ~ path(X53,X54,X56) )
& ( ~ shortest_path(X53,X54,X55)
| X53 != X54 )
& ( ~ shortest_path(X53,X54,X55)
| path(X53,X54,X55) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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,
! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ( ~ precedes(X8,X7,X4)
& ~ ? [X9] :
( head_of(X9) = head_of(X8)
& tail_of(X9) = tail_of(X7) ) ) ),
inference(fof_simplification,[status(thm)],[shortest_path_properties]) ).
cnf(c_0_19,plain,
( ~ path(X4,X5,X3)
| ~ on_path(X2,X3)
| ~ on_path(X1,X3)
| ~ sequential(X1,X2)
| precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
on_path(esk13_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
inference(fof_simplification,[status(thm)],[no_loops]) ).
fof(c_0_22,plain,
! [X15,X16] :
( ( ~ complete
| X15 = X16
| ~ vertex(X16)
| ~ vertex(X15)
| X16 = tail_of(esk1_2(X15,X16))
| X15 = tail_of(esk1_2(X15,X16)) )
& ( ~ complete
| X15 = X16
| ~ vertex(X16)
| ~ vertex(X15)
| X16 = tail_of(esk1_2(X15,X16))
| X16 = head_of(esk1_2(X15,X16)) )
& ( ~ complete
| X15 = X16
| ~ vertex(X16)
| ~ vertex(X15)
| X15 = head_of(esk1_2(X15,X16))
| X15 = tail_of(esk1_2(X15,X16)) )
& ( ~ complete
| X15 = X16
| ~ vertex(X16)
| ~ vertex(X15)
| X15 = head_of(esk1_2(X15,X16))
| X16 = head_of(esk1_2(X15,X16)) )
& ( ~ complete
| X15 = X16
| ~ vertex(X16)
| ~ vertex(X15)
| X15 != tail_of(esk1_2(X15,X16))
| X16 != head_of(esk1_2(X15,X16))
| X16 != tail_of(esk1_2(X15,X16))
| X15 != head_of(esk1_2(X15,X16)) )
& ( ~ complete
| X15 = X16
| ~ vertex(X16)
| ~ vertex(X15)
| edge(esk1_2(X15,X16)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])]) ).
cnf(c_0_23,plain,
( ~ on_path(X1,X2)
| ~ path(X3,X4,X2)
| in_path(tail_of(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
on_path(esk12_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( ~ shortest_path(X1,X2,X3)
| path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_27,plain,
! [X61,X62,X63,X64,X65,X66] :
( ( ~ precedes(X63,X64,X65)
| ~ shortest_path(X61,X62,X65)
| ~ precedes(X64,X63,X65) )
& ( ~ precedes(X63,X64,X65)
| ~ shortest_path(X61,X62,X65)
| head_of(X66) != head_of(X64)
| tail_of(X66) != tail_of(X63) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
cnf(c_0_28,negated_conjecture,
( ~ path(X2,X3,esk9_0)
| ~ on_path(X1,esk9_0)
| ~ sequential(X1,esk13_0)
| precedes(X1,esk13_0,esk9_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
sequential(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_30,plain,
! [X13] :
( head_of(X13) != tail_of(X13)
| ~ edge(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_31,plain,
( ~ complete
| ~ vertex(X2)
| ~ vertex(X1)
| X1 = X2
| X2 = tail_of(esk1_2(X1,X2))
| X1 = tail_of(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,plain,
( ~ complete
| ~ vertex(X2)
| ~ vertex(X1)
| X1 = X2
| edge(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_34,plain,
! [X33,X34,X35,X36] :
( ( ~ in_path(X36,X35)
| ~ path(X33,X34,X35)
| X36 = tail_of(esk4_4(X33,X34,X35,X36))
| X36 = head_of(esk4_4(X33,X34,X35,X36)) )
& ( ~ in_path(X36,X35)
| ~ path(X33,X34,X35)
| on_path(esk4_4(X33,X34,X35,X36),X35) )
& ( ~ in_path(X36,X35)
| ~ path(X33,X34,X35)
| vertex(X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ path(X1,X2,esk9_0)
| in_path(tail_of(esk12_0),esk9_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_36,negated_conjecture,
path(esk10_0,esk11_0,esk9_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,plain,
( ~ on_path(X1,X2)
| ~ path(X3,X4,X2)
| in_path(head_of(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_38,plain,
( ~ precedes(X2,X3,X6)
| ~ shortest_path(X4,X5,X6)
| head_of(X1) != head_of(X3)
| tail_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,negated_conjecture,
( ~ path(X1,X2,esk9_0)
| precedes(esk12_0,esk13_0,esk9_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_29])]) ).
cnf(c_0_40,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| X1 = X2
| tail_of(esk1_2(X1,X2)) = X2
| tail_of(esk1_2(X1,X2)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_42,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| edge(esk1_2(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_32])]) ).
cnf(c_0_43,plain,
( ~ complete
| ~ vertex(X1)
| ~ vertex(X2)
| X2 = X1
| X2 = head_of(esk1_2(X2,X1))
| X1 = head_of(esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_44,plain,
( ~ in_path(X1,X4)
| ~ path(X2,X3,X4)
| vertex(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,negated_conjecture,
in_path(tail_of(esk12_0),esk9_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( ~ path(X1,X2,esk9_0)
| in_path(head_of(esk13_0),esk9_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_20]) ).
cnf(c_0_47,negated_conjecture,
( ~ precedes(X3,X2,esk9_0)
| tail_of(X1) != tail_of(X3)
| head_of(X1) != head_of(X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_48,negated_conjecture,
precedes(esk12_0,esk13_0,esk9_0),
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
cnf(c_0_49,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| head_of(esk1_2(X1,X2)) != X2
| X1 = X2
| tail_of(esk1_2(X1,X2)) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_50,plain,
( ~ vertex(X2)
| ~ vertex(X1)
| X2 = X1
| head_of(esk1_2(X1,X2)) = X1
| head_of(esk1_2(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_32])]) ).
cnf(c_0_51,negated_conjecture,
( ~ path(X1,X2,esk9_0)
| vertex(tail_of(esk12_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
in_path(head_of(esk13_0),esk9_0),
inference(spm,[status(thm)],[c_0_46,c_0_36]) ).
fof(c_0_53,plain,
! [X7,X8] :
( sequential(X7,X8)
<=> ( head_of(X7) = tail_of(X8)
& X7 != X8
& edge(X8)
& edge(X7) ) ),
inference(fof_simplification,[status(thm)],[sequential_defn]) ).
cnf(c_0_54,negated_conjecture,
( tail_of(X1) != tail_of(esk12_0)
| head_of(X1) != head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| X1 = X2
| tail_of(esk1_2(X1,X2)) = X1
| head_of(esk1_2(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
vertex(tail_of(esk12_0)),
inference(spm,[status(thm)],[c_0_51,c_0_36]) ).
cnf(c_0_57,negated_conjecture,
( ~ path(X1,X2,esk9_0)
| vertex(head_of(esk13_0)) ),
inference(spm,[status(thm)],[c_0_44,c_0_52]) ).
fof(c_0_58,plain,
! [X38,X39] :
( ( sequential(X38,X39)
| head_of(X38) != tail_of(X39)
| X38 = X39
| ~ edge(X39)
| ~ edge(X38) )
& ( ~ sequential(X38,X39)
| head_of(X38) = tail_of(X39) )
& ( ~ sequential(X38,X39)
| X38 != X39 )
& ( ~ sequential(X38,X39)
| edge(X39) )
& ( ~ sequential(X38,X39)
| edge(X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
cnf(c_0_59,negated_conjecture,
( ~ vertex(X1)
| head_of(esk1_2(tail_of(esk12_0),X1)) != head_of(esk13_0)
| tail_of(esk12_0) = X1
| head_of(esk1_2(tail_of(esk12_0),X1)) = tail_of(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55])]),c_0_56])]) ).
cnf(c_0_60,negated_conjecture,
vertex(head_of(esk13_0)),
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_61,plain,
( head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1)
| sequential(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( tail_of(esk12_0) = head_of(esk13_0)
| head_of(esk1_2(tail_of(esk12_0),head_of(esk13_0))) = tail_of(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_50]),c_0_56])])]),c_0_60])]) ).
cnf(c_0_63,plain,
( ~ sequential(X1,X2)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_64,plain,
! [X67,X68,X69] :
( ( triangle(X67,X68,X69)
| ~ sequential(X69,X67)
| ~ sequential(X68,X69)
| ~ sequential(X67,X68)
| ~ edge(X69)
| ~ edge(X68)
| ~ edge(X67) )
& ( ~ triangle(X67,X68,X69)
| sequential(X69,X67) )
& ( ~ triangle(X67,X68,X69)
| sequential(X68,X69) )
& ( ~ triangle(X67,X68,X69)
| sequential(X67,X68) )
& ( ~ triangle(X67,X68,X69)
| edge(X69) )
& ( ~ triangle(X67,X68,X69)
| edge(X68) )
& ( ~ triangle(X67,X68,X69)
| edge(X67) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])])]) ).
cnf(c_0_65,negated_conjecture,
( ~ edge(X1)
| ~ edge(esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| tail_of(X1) != tail_of(esk12_0)
| sequential(esk1_2(tail_of(esk12_0),head_of(esk13_0)),X1)
| tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = X1 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_63,c_0_29]) ).
cnf(c_0_67,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| head_of(esk1_2(X1,X2)) != X1
| X1 = X2
| tail_of(esk1_2(X1,X2)) = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_68,plain,
( ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1)
| triangle(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( ~ edge(esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| sequential(esk1_2(tail_of(esk12_0),head_of(esk13_0)),esk12_0)
| tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk12_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_65]),c_0_66])]) ).
cnf(c_0_70,negated_conjecture,
( tail_of(esk12_0) = head_of(esk13_0)
| tail_of(esk1_2(tail_of(esk12_0),head_of(esk13_0))) = head_of(esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_62]),c_0_60]),c_0_56])]) ).
cnf(c_0_71,plain,
( ~ sequential(X1,X2)
| ~ sequential(X2,X3)
| ~ sequential(X3,X1)
| triangle(X1,X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_68,c_0_63]),c_0_63]),c_0_63]) ).
cnf(c_0_72,negated_conjecture,
( sequential(esk1_2(tail_of(esk12_0),head_of(esk13_0)),esk12_0)
| tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk12_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_42]),c_0_60]),c_0_56])]) ).
cnf(c_0_73,negated_conjecture,
( ~ edge(X1)
| ~ edge(esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| head_of(esk13_0) != head_of(X1)
| sequential(X1,esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| tail_of(esk12_0) = head_of(esk13_0)
| X1 = esk1_2(tail_of(esk12_0),head_of(esk13_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_70]) ).
cnf(c_0_74,plain,
( ~ sequential(X2,X1)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_75,negated_conjecture,
( ~ sequential(esk12_0,X1)
| ~ sequential(X1,esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| triangle(esk12_0,X1,esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk12_0 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
~ triangle(esk12_0,esk13_0,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_77,negated_conjecture,
( ~ edge(X1)
| head_of(esk13_0) != head_of(X1)
| sequential(X1,esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| tail_of(esk12_0) = head_of(esk13_0)
| X1 = esk1_2(tail_of(esk12_0),head_of(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_42]),c_0_60]),c_0_56])]) ).
cnf(c_0_78,negated_conjecture,
edge(esk13_0),
inference(spm,[status(thm)],[c_0_74,c_0_29]) ).
cnf(c_0_79,plain,
( ~ sequential(X1,X2)
| head_of(X1) = tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_80,negated_conjecture,
( ~ sequential(esk13_0,esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk12_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_29]),c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( sequential(esk13_0,esk1_2(tail_of(esk12_0),head_of(esk13_0)))
| tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk13_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_78])]) ).
cnf(c_0_82,negated_conjecture,
tail_of(esk13_0) = head_of(esk12_0),
inference(spm,[status(thm)],[c_0_79,c_0_29]) ).
cnf(c_0_83,negated_conjecture,
( tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk12_0
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk13_0 ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_84,negated_conjecture,
head_of(esk13_0) != head_of(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_82]),c_0_78])]) ).
cnf(c_0_85,negated_conjecture,
tail_of(esk12_0) != head_of(esk12_0),
inference(spm,[status(thm)],[c_0_54,c_0_82]) ).
cnf(c_0_86,plain,
( ~ precedes(X2,X1,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_87,negated_conjecture,
( tail_of(esk12_0) = head_of(esk13_0)
| esk1_2(tail_of(esk12_0),head_of(esk13_0)) = esk12_0 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_83]),c_0_82]),c_0_82]),c_0_60]),c_0_56])]),c_0_84]),c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( ~ precedes(X2,X1,esk9_0)
| ~ precedes(X1,X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_86,c_0_26]) ).
cnf(c_0_89,negated_conjecture,
tail_of(esk12_0) = head_of(esk13_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_87]),c_0_56]),c_0_60])]),c_0_85]),c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( ~ path(X2,X3,esk9_0)
| ~ on_path(X1,esk9_0)
| ~ sequential(X1,esk12_0)
| precedes(X1,esk12_0,esk9_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_91,negated_conjecture,
~ precedes(esk13_0,esk12_0,esk9_0),
inference(spm,[status(thm)],[c_0_88,c_0_48]) ).
cnf(c_0_92,negated_conjecture,
( ~ edge(X1)
| head_of(esk13_0) != head_of(X1)
| sequential(X1,esk12_0)
| X1 = esk12_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_89]),c_0_66])]) ).
cnf(c_0_93,negated_conjecture,
( ~ path(X1,X2,esk9_0)
| ~ sequential(esk13_0,esk12_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_20]),c_0_91]) ).
cnf(c_0_94,negated_conjecture,
( sequential(esk13_0,esk12_0)
| esk13_0 = esk12_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_92]),c_0_78])]) ).
cnf(c_0_95,negated_conjecture,
( ~ path(X1,X2,esk9_0)
| esk13_0 = esk12_0 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_96,negated_conjecture,
esk13_0 = esk12_0,
inference(spm,[status(thm)],[c_0_95,c_0_36]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA009+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/15.31 % CPULimit : 300
% 0.10/15.31 % WCLimit : 300
% 0.10/15.31 % DateTime : Sun Sep 20 18:23:55 UTC 2026
% 0.10/15.31 % CPUTime :
% 0.10/15.31 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/15.36 Running first-order theorem proving
% 0.10/15.36 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/15.43 % Version: 3.5.1
% 0.22/15.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/15.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/15.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/15.43 % Starting new_bool_3 with 300s (1) cores
% 0.22/15.43 % Starting new_bool_1 with 300s (1) cores
% 0.22/15.43 % Starting sh5l with 300s (1) cores
% 0.22/15.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3256282 completed with status 0
% 0.22/15.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/15.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/15.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/15.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/15.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/15.43 % No SInE strategy applied
% 0.22/15.43 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.22/15.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/15.43 % Starting SubtermCWHack with 136s (1) cores
% 0.22/15.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/15.43 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.22/15.43 % Starting new_bool_3 with 136s (1) cores
% 0.22/15.43 % Starting new_bool_1 with 136s (1) cores
% 0.22/15.43 % new_bool_3 with pid 3256291 completed with status 0
% 0.22/15.43 % Result found by new_bool_3
% 0.22/15.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/15.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/15.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/15.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/15.43 % No SInE strategy applied
% 0.22/15.43 % Search class: FGHSF-FFMS32-SFFFFFNN
% 0.22/15.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/15.43 % Starting SubtermCWHack with 136s (1) cores
% 0.22/15.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/15.43 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.22/15.43 % Starting new_bool_3 with 136s (1) cores
% 0.22/15.43 % Preprocessing time : 0.002 s
% 0.22/15.43 % Presaturation interreduction done
% 0.22/15.43
% 0.22/15.43 % Proof found!
% 0.22/15.43 % SZS status Theorem
% 0.22/15.43 % SZS output start CNFRefutation
% See solution above
% 0.22/15.43 % Parsed axioms : 18
% 0.22/15.43 % Removed by relevancy pruning/SinE : 0
% 0.22/15.43 % Initial clauses : 65
% 0.22/15.43 % Removed in clause preprocessing : 1
% 0.22/15.43 % Initial clauses in saturation : 64
% 0.22/15.43 % Processed clauses : 382
% 0.22/15.43 % ...of these trivial : 1
% 0.22/15.43 % ...subsumed : 40
% 0.22/15.43 % ...remaining for further processing : 341
% 0.22/15.43 % Other redundant clauses eliminated : 51
% 0.22/15.43 % Clauses deleted for lack of memory : 0
% 0.22/15.43 % Backward-subsumed : 15
% 0.22/15.43 % Backward-rewritten : 96
% 0.22/15.43 % Generated clauses : 815
% 0.22/15.43 % ...of the previous two non-redundant : 687
% 0.22/15.43 % ...aggressively subsumed : 0
% 0.22/15.43 % Contextual simplify-reflections : 22
% 0.22/15.43 % Paramodulations : 756
% 0.22/15.43 % Factorizations : 5
% 0.22/15.43 % NegExts : 0
% 0.22/15.43 % Equation resolutions : 57
% 0.22/15.43 % Disequality decompositions : 0
% 0.22/15.43 % Total rewrite steps : 504
% 0.22/15.43 % ...of those cached : 464
% 0.22/15.43 % Propositional unsat checks : 0
% 0.22/15.43 % Propositional check models : 0
% 0.22/15.43 % Propositional check unsatisfiable : 0
% 0.22/15.43 % Propositional clauses : 0
% 0.22/15.43 % Propositional clauses after purity: 0
% 0.22/15.43 % Propositional unsat core size : 0
% 0.22/15.43 % Propositional preprocessing time : 0.000
% 0.22/15.43 % Propositional encoding time : 0.000
% 0.22/15.43 % Propositional solver time : 0.000
% 0.22/15.43 % Success case prop preproc time : 0.000
% 0.22/15.43 % Success case prop encoding time : 0.000
% 0.22/15.43 % Success case prop solver time : 0.000
% 0.22/15.43 % Current number of processed clauses : 162
% 0.22/15.43 % Positive orientable unit clauses : 41
% 0.22/15.43 % Positive unorientable unit clauses: 0
% 0.22/15.43 % Negative unit clauses : 3
% 0.22/15.43 % Non-unit-clauses : 118
% 0.22/15.43 % Current number of unprocessed clauses: 391
% 0.22/15.43 % ...number of literals in the above : 1762
% 0.22/15.43 % Current number of archived formulas : 0
% 0.22/15.43 % Current number of archived clauses : 175
% 0.22/15.43 % Clause-clause subsumption calls (NU) : 4966
% 0.22/15.43 % Rec. Clause-clause subsumption calls : 2002
% 0.22/15.43 % Non-unit clause-clause subsumptions : 63
% 0.22/15.43 % Unit Clause-clause subsumption calls : 167
% 0.22/15.43 % Rewrite failures with RHS unbound : 0
% 0.22/15.43 % BW rewrite match attempts : 41
% 0.22/15.43 % BW rewrite match successes : 23
% 0.22/15.43 % Condensation attempts : 0
% 0.22/15.43 % Condensation successes : 0
% 0.22/15.43 % Termbank termtop insertions : 25348
% 0.22/15.43 % Search garbage collected termcells : 1234
% 0.22/15.43
% 0.22/15.43 % -------------------------------------------------
% 0.22/15.43 % User time : 0.042 s
% 0.22/15.43 % System time : 0.010 s
% 0.22/15.43 % Total time : 0.052 s
% 0.22/15.43 % Maximum resident set size: 3668 pages
% 0.22/15.43
% 0.22/15.43 % -------------------------------------------------
% 0.22/15.43 % User time : 0.213 s
% 0.22/15.43 % System time : 0.027 s
% 0.22/15.43 % Total time : 0.241 s
% 0.22/15.43 % Maximum resident set size: 4608 pages
% 0.22/15.43 % E exiting
%------------------------------------------------------------------------------