%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRA002+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:31:28 PM UTC 2026
% Result : Theorem 7.52s 1.55s
% Output : CNFRefutation 7.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 96 ( 13 unt; 0 def)
% Number of atoms : 363 ( 107 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 423 ( 156 ~; 180 |; 61 &)
% ( 5 <=>; 20 =>; 1 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 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 : 223 ( 31 sgn 111 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
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/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(sequential_pairs_and_triangles,axiom,
! [X4,X2,X3] :
( ( ! [X7,X8] :
( ( sequential(X7,X8)
& on_path(X8,X4)
& on_path(X7,X4) )
=> ? [X9] : triangle(X7,X8,X9) )
& path(X2,X3,X4) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(back_edge,lemma,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( precedes(X7,X8,X4)
& shortest_path(X2,X3,X4) )
=> ? [X9] :
( head_of(X9) = tail_of(X7)
& tail_of(X9) = head_of(X8)
& edge(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',back_edge) ).
fof(sequential_defn,axiom,
! [X7,X8] :
( sequential(X7,X8)
<=> ( head_of(X7) = tail_of(X8)
& X7 != X8
& edge(X8)
& edge(X7) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
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/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(c_0_13,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_14,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_15,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_13])])])])])])]) ).
fof(c_0_16,negated_conjecture,
( ~ less_or_equal(minus(length_of(esk10_0),n1),number_of_in(triangles,graph))
& shortest_path(esk11_0,esk12_0,esk10_0)
& complete ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_17,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_18,plain,
! [X76,X77,X78,X81] :
( ( number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76)
| ~ path(X77,X78,X76)
| ~ triangle(esk7_1(X76),esk8_1(X76),X81) )
& ( number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76)
| ~ path(X77,X78,X76)
| sequential(esk7_1(X76),esk8_1(X76)) )
& ( number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76)
| ~ path(X77,X78,X76)
| on_path(esk8_1(X76),X76) )
& ( number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76)
| ~ path(X77,X78,X76)
| on_path(esk7_1(X76),X76) ) ),
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)],[sequential_pairs_and_triangles])])])])])])]) ).
cnf(c_0_19,plain,
( ~ shortest_path(X1,X2,X3)
| path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
shortest_path(esk11_0,esk12_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,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_17])])])])]) ).
cnf(c_0_22,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk8_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
path(esk11_0,esk12_0,esk10_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,lemma,
! [X84,X85,X86,X87,X88] :
( ( ~ complete
| ~ precedes(X86,X87,X88)
| ~ shortest_path(X84,X85,X88)
| head_of(esk9_4(X84,X85,X86,X87)) = tail_of(X86) )
& ( ~ complete
| ~ precedes(X86,X87,X88)
| ~ shortest_path(X84,X85,X88)
| tail_of(esk9_4(X84,X85,X86,X87)) = head_of(X87) )
& ( ~ complete
| ~ precedes(X86,X87,X88)
| ~ shortest_path(X84,X85,X88)
| edge(esk9_4(X84,X85,X86,X87)) ) ),
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)],[back_edge])])])])])])]) ).
cnf(c_0_25,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_21]) ).
cnf(c_0_26,negated_conjecture,
( on_path(esk8_1(esk10_0),esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk7_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| sequential(esk7_1(X1),esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,lemma,
( ~ complete
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
( ~ path(X2,X3,esk10_0)
| ~ on_path(X1,esk10_0)
| ~ sequential(X1,esk8_1(esk10_0))
| precedes(X1,esk8_1(esk10_0),esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( on_path(esk7_1(esk10_0),esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_33,negated_conjecture,
( sequential(esk7_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_28,c_0_23]) ).
cnf(c_0_34,lemma,
( ~ complete
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| edge(esk9_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_35,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_36,lemma,
( ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| head_of(esk9_4(X1,X2,X3,X4)) = tail_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_37,negated_conjecture,
( ~ path(X1,X2,esk10_0)
| precedes(esk7_1(esk10_0),esk8_1(esk10_0),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_31,c_0_32]),c_0_33]) ).
cnf(c_0_38,lemma,
( ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| edge(esk9_4(X1,X2,X3,X4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_30])]) ).
fof(c_0_39,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_40,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_35])])])]) ).
cnf(c_0_41,negated_conjecture,
( ~ precedes(X1,X2,esk10_0)
| head_of(esk9_4(esk11_0,esk12_0,X1,X2)) = tail_of(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_20]) ).
cnf(c_0_42,negated_conjecture,
( precedes(esk7_1(esk10_0),esk8_1(esk10_0),esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_43,negated_conjecture,
( ~ precedes(X1,X2,esk10_0)
| edge(esk9_4(esk11_0,esk12_0,X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_20]) ).
cnf(c_0_44,plain,
( ~ on_path(X1,X4)
| ~ path(X2,X3,X4)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,lemma,
( ~ complete
| ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_46,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_47,plain,
( head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1)
| sequential(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| head_of(esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0))) = tail_of(esk7_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( edge(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) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( ~ path(X1,X2,esk10_0)
| edge(esk7_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_51,lemma,
( ~ precedes(X3,X4,X5)
| ~ shortest_path(X1,X2,X5)
| tail_of(esk9_4(X1,X2,X3,X4)) = head_of(X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_30])]) ).
cnf(c_0_52,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_46]) ).
cnf(c_0_53,plain,
( ~ sequential(X1,X2)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,negated_conjecture,
( ~ edge(X1)
| tail_of(X1) != tail_of(esk7_1(esk10_0))
| sequential(esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)),X1)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( edge(esk7_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_56,negated_conjecture,
( ~ precedes(X1,X2,esk10_0)
| tail_of(esk9_4(esk11_0,esk12_0,X1,X2)) = head_of(X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_20]) ).
cnf(c_0_57,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_52,c_0_53]),c_0_53]),c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( sequential(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)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_54]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| tail_of(esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0))) = head_of(esk8_1(esk10_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_42]) ).
cnf(c_0_60,negated_conjecture,
( ~ path(X1,X2,esk10_0)
| edge(esk8_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_26]) ).
cnf(c_0_61,negated_conjecture,
( ~ sequential(esk7_1(esk10_0),X1)
| ~ sequential(X1,esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)))
| triangle(esk7_1(esk10_0),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)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( ~ edge(X1)
| head_of(esk8_1(esk10_0)) != head_of(X1)
| sequential(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)
| X1 = esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_59]),c_0_49]) ).
cnf(c_0_63,negated_conjecture,
( edge(esk8_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_23]) ).
fof(c_0_64,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]) ).
fof(c_0_65,plain,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
inference(fof_simplification,[status(thm)],[no_loops]) ).
cnf(c_0_66,negated_conjecture,
( ~ sequential(esk8_1(esk10_0),esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)))
| triangle(esk7_1(esk10_0),esk8_1(esk10_0),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)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_33]) ).
cnf(c_0_67,negated_conjecture,
( sequential(esk8_1(esk10_0),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)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk8_1(esk10_0) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_62]),c_0_63]) ).
fof(c_0_68,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_64])])])])]) ).
fof(c_0_69,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_65])])]) ).
cnf(c_0_70,plain,
( ~ path(X3,X4,X1)
| ~ triangle(esk7_1(X1),esk8_1(X1),X2)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_71,negated_conjecture,
( triangle(esk7_1(esk10_0),esk8_1(esk10_0),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)
| 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) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,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_68]) ).
fof(c_0_73,plain,
! [X70,X71,X72] :
( length_of(X72) = number_of_in(edges,X72)
| ~ path(X70,X71,X72) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[length_defn])])]) ).
cnf(c_0_74,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( ~ path(X1,X2,esk10_0)
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| 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) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( ~ precedes(X3,X2,esk10_0)
| tail_of(X1) != tail_of(X3)
| head_of(X1) != head_of(X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_20]) ).
cnf(c_0_77,plain,
( ~ sequential(X1,X2)
| head_of(X1) = tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_78,plain,
( ~ path(X1,X2,X3)
| length_of(X3) = number_of_in(edges,X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_79,plain,
! [X73,X74,X75] :
( number_of_in(sequential_pairs,X75) = minus(length_of(X75),n1)
| ~ path(X73,X74,X75) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])])]) ).
cnf(c_0_80,negated_conjecture,
( head_of(esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0))) != head_of(esk8_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_74,c_0_59]),c_0_49]) ).
cnf(c_0_81,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| 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) ),
inference(spm,[status(thm)],[c_0_75,c_0_23]) ).
cnf(c_0_82,negated_conjecture,
( tail_of(X1) != tail_of(esk7_1(esk10_0))
| head_of(X1) != head_of(esk8_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_76,c_0_42]) ).
cnf(c_0_83,negated_conjecture,
( tail_of(esk8_1(esk10_0)) = head_of(esk7_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_33]) ).
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_16]) ).
cnf(c_0_85,negated_conjecture,
length_of(esk10_0) = number_of_in(edges,esk10_0),
inference(spm,[status(thm)],[c_0_78,c_0_23]) ).
cnf(c_0_86,plain,
( ~ path(X1,X2,X3)
| number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
fof(c_0_87,plain,
! [X82,X83] : less_or_equal(number_of_in(X82,X83),number_of_in(X82,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_88,negated_conjecture,
( number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0)
| esk9_4(esk11_0,esk12_0,esk7_1(esk10_0),esk8_1(esk10_0)) = esk7_1(esk10_0) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( tail_of(esk7_1(esk10_0)) != head_of(esk7_1(esk10_0))
| number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
~ less_or_equal(minus(number_of_in(edges,esk10_0),n1),number_of_in(triangles,graph)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,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_86,c_0_23]),c_0_85]) ).
cnf(c_0_92,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_93,negated_conjecture,
number_of_in(triangles,esk10_0) = number_of_in(sequential_pairs,esk10_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_88]),c_0_89]) ).
cnf(c_0_94,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk10_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA002+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 18:20:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 7.52/1.55 % Version: 3.5.1
% 7.52/1.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.52/1.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.52/1.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.52/1.55 % Starting new_bool_3 with 300s (1) cores
% 7.52/1.55 % Starting new_bool_1 with 300s (1) cores
% 7.52/1.55 % Starting sh5l with 300s (1) cores
% 7.52/1.55 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4114360 completed with status 0
% 7.52/1.55 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.52/1.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.52/1.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.52/1.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.52/1.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.52/1.55 % No SInE strategy applied
% 7.52/1.55 % Search class: FGHSF-FFMF32-SFFFFFNN
% 7.52/1.55 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 7.52/1.55 % Starting SubtermCWHack with 151s (1) cores
% 7.52/1.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 7.52/1.55 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 7.52/1.55 % Starting new_bool_3 with 151s (1) cores
% 7.52/1.55 % Starting new_bool_1 with 146s (1) cores
% 7.52/1.55 % new_bool_3 with pid 4114370 completed with status 0
% 7.52/1.55 % Result found by new_bool_3
% 7.52/1.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.52/1.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.52/1.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.52/1.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.52/1.55 % No SInE strategy applied
% 7.52/1.55 % Search class: FGHSF-FFMF32-SFFFFFNN
% 7.52/1.55 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 7.52/1.55 % Starting SubtermCWHack with 151s (1) cores
% 7.52/1.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 901s (1) cores
% 7.52/1.55 % Starting G-E--_107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y with 151s (1) cores
% 7.52/1.55 % Starting new_bool_3 with 151s (1) cores
% 7.52/1.55 % Preprocessing time : 0.002 s
% 7.52/1.55 % Presaturation interreduction done
% 7.52/1.55
% 7.52/1.55 % Proof found!
% 7.52/1.55 % SZS status Theorem
% 7.52/1.55 % SZS output start CNFRefutation
% See solution above
% 7.52/1.55 % Parsed axioms : 19
% 7.52/1.55 % Removed by relevancy pruning/SinE : 0
% 7.52/1.55 % Initial clauses : 65
% 7.52/1.55 % Removed in clause preprocessing : 1
% 7.52/1.55 % Initial clauses in saturation : 64
% 7.52/1.55 % Processed clauses : 3060
% 7.52/1.55 % ...of these trivial : 2
% 7.52/1.55 % ...subsumed : 1281
% 7.52/1.55 % ...remaining for further processing : 1777
% 7.52/1.55 % Other redundant clauses eliminated : 309
% 7.52/1.55 % Clauses deleted for lack of memory : 0
% 7.52/1.55 % Backward-subsumed : 262
% 7.52/1.55 % Backward-rewritten : 720
% 7.52/1.55 % Generated clauses : 17930
% 7.52/1.55 % ...of the previous two non-redundant : 16939
% 7.52/1.55 % ...aggressively subsumed : 0
% 7.52/1.55 % Contextual simplify-reflections : 380
% 7.52/1.55 % Paramodulations : 17598
% 7.52/1.55 % Factorizations : 13
% 7.52/1.55 % NegExts : 0
% 7.52/1.55 % Equation resolutions : 322
% 7.52/1.55 % Disequality decompositions : 0
% 7.52/1.55 % Total rewrite steps : 2196
% 7.52/1.55 % ...of those cached : 2178
% 7.52/1.55 % Propositional unsat checks : 0
% 7.52/1.55 % Propositional check models : 0
% 7.52/1.55 % Propositional check unsatisfiable : 0
% 7.52/1.55 % Propositional clauses : 0
% 7.52/1.55 % Propositional clauses after purity: 0
% 7.52/1.55 % Propositional unsat core size : 0
% 7.52/1.55 % Propositional preprocessing time : 0.000
% 7.52/1.55 % Propositional encoding time : 0.000
% 7.52/1.55 % Propositional solver time : 0.000
% 7.52/1.55 % Success case prop preproc time : 0.000
% 7.52/1.55 % Success case prop encoding time : 0.000
% 7.52/1.55 % Success case prop solver time : 0.000
% 7.52/1.55 % Current number of processed clauses : 727
% 7.52/1.55 % Positive orientable unit clauses : 21
% 7.52/1.55 % Positive unorientable unit clauses: 0
% 7.52/1.55 % Negative unit clauses : 7
% 7.52/1.55 % Non-unit-clauses : 699
% 7.52/1.55 % Current number of unprocessed clauses: 13938
% 7.52/1.55 % ...number of literals in the above : 106308
% 7.52/1.55 % Current number of archived formulas : 0
% 7.52/1.55 % Current number of archived clauses : 1046
% 7.52/1.55 % Clause-clause subsumption calls (NU) : 206574
% 7.52/1.55 % Rec. Clause-clause subsumption calls : 73736
% 7.52/1.55 % Non-unit clause-clause subsumptions : 1896
% 7.52/1.55 % Unit Clause-clause subsumption calls : 296
% 7.52/1.55 % Rewrite failures with RHS unbound : 0
% 7.52/1.55 % BW rewrite match attempts : 13
% 7.52/1.55 % BW rewrite match successes : 3
% 7.52/1.55 % Condensation attempts : 0
% 7.52/1.55 % Condensation successes : 0
% 7.52/1.55 % Termbank termtop insertions : 1057431
% 7.52/1.55 % Search garbage collected termcells : 1254
% 7.52/1.55
% 7.52/1.55 % -------------------------------------------------
% 7.52/1.55 % User time : 1.032 s
% 7.52/1.55 % System time : 0.026 s
% 7.52/1.55 % Total time : 1.058 s
% 7.52/1.55 % Maximum resident set size: 3672 pages
% 7.52/1.55
% 7.52/1.55 % -------------------------------------------------
% 7.52/1.55 % User time : 4.388 s
% 7.52/1.55 % System time : 0.141 s
% 7.52/1.55 % Total time : 4.530 s
% 7.52/1.55 % Maximum resident set size: 4864 pages
% 7.52/1.55 % E exiting
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