%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : GRA011+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n023.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 : 600s
% DateTime : Sat Jul 16 07:15:24 EDT 2022
% Result : Theorem 87.40s 12.40s
% Output : CNFRefutation 87.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 102 ( 20 unt; 0 def)
% Number of atoms : 432 ( 146 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 546 ( 216 ~; 247 |; 62 &)
% ( 3 <=>; 16 =>; 1 <=; 1 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 204 ( 29 sgn 88 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(triangles_and_sequential_pairs,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
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(sequential_pairs_and_triangles,axiom,
! [X4,X2,X3] :
( ( path(X2,X3,X4)
& ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(precedes_defn,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
<= ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
| ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(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(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(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(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(edge_ends_are_vertices,axiom,
! [X1] :
( edge(X1)
=> ( vertex(head_of(X1))
& vertex(tail_of(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
fof(triangle_defn,axiom,
! [X7,X8,X9] :
( triangle(X7,X8,X9)
<=> ( edge(X7)
& edge(X8)
& edge(X9)
& sequential(X7,X8)
& sequential(X8,X9)
& sequential(X9,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(path_length_sequential_pairs,axiom,
! [X2,X3,X4] :
( path(X2,X3,X4)
=> number_of_in(sequential_pairs,X4) = minus(length_of(X4),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(c_0_13,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
inference(assume_negation,[status(cth)],[triangles_and_sequential_pairs]) ).
fof(c_0_14,plain,
! [X53,X54,X55,X56,X57,X58,X59] :
( ( path(X53,X54,X55)
| ~ shortest_path(X53,X54,X55) )
& ( X53 != X54
| ~ shortest_path(X53,X54,X55) )
& ( ~ path(X53,X54,X56)
| less_or_equal(length_of(X55),length_of(X56))
| ~ shortest_path(X53,X54,X55) )
& ( path(X57,X58,esk6_3(X57,X58,X59))
| ~ path(X57,X58,X59)
| X57 = X58
| shortest_path(X57,X58,X59) )
& ( ~ less_or_equal(length_of(X59),length_of(esk6_3(X57,X58,X59)))
| ~ path(X57,X58,X59)
| X57 = X58
| shortest_path(X57,X58,X59) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[shortest_path_defn])])])])])]) ).
fof(c_0_15,negated_conjecture,
( complete
& shortest_path(esk10_0,esk11_0,esk9_0)
& number_of_in(sequential_pairs,esk9_0) != number_of_in(triangles,esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X76,X77,X78,X81] :
( ( on_path(esk7_1(X76),X76)
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
& ( on_path(esk8_1(X76),X76)
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
& ( sequential(esk7_1(X76),esk8_1(X76))
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) )
& ( ~ triangle(esk7_1(X76),esk8_1(X76),X81)
| ~ path(X77,X78,X76)
| number_of_in(sequential_pairs,X76) = number_of_in(triangles,X76) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_pairs_and_triangles])])])])])]) ).
cnf(c_0_17,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ sequential(X43,X44)
| ~ on_path(X43,X40)
| ~ on_path(X44,X40)
| precedes(X43,X44,X40)
| ~ path(X41,X42,X40) )
& ( ~ sequential(X43,X45)
| ~ precedes(X45,X44,X40)
| ~ on_path(X43,X40)
| ~ on_path(X44,X40)
| precedes(X43,X44,X40)
| ~ path(X41,X42,X40) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[precedes_defn])])])])]) ).
fof(c_0_20,plain,
! [X38,X39] :
( ( edge(X38)
| ~ sequential(X38,X39) )
& ( edge(X39)
| ~ sequential(X38,X39) )
& ( X38 != X39
| ~ sequential(X38,X39) )
& ( head_of(X38) = tail_of(X39)
| ~ sequential(X38,X39) )
& ( ~ edge(X38)
| ~ edge(X39)
| X38 = X39
| head_of(X38) != tail_of(X39)
| sequential(X38,X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])]) ).
cnf(c_0_21,plain,
( sequential(esk7_1(X1),esk8_1(X1))
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
path(esk10_0,esk11_0,esk9_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
number_of_in(sequential_pairs,esk9_0) != number_of_in(triangles,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_24,plain,
! [X33,X34,X35,X36] :
( ( vertex(X36)
| ~ path(X33,X34,X35)
| ~ in_path(X36,X35) )
& ( on_path(esk4_4(X33,X34,X35,X36),X35)
| ~ path(X33,X34,X35)
| ~ in_path(X36,X35) )
& ( X36 = head_of(esk4_4(X33,X34,X35,X36))
| X36 = tail_of(esk4_4(X33,X34,X35,X36))
| ~ path(X33,X34,X35)
| ~ in_path(X36,X35) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[in_path_properties])])])]) ).
fof(c_0_25,plain,
! [X29,X30,X31,X32] :
( ( edge(X32)
| ~ path(X29,X30,X31)
| ~ on_path(X32,X31) )
& ( in_path(head_of(X32),X31)
| ~ path(X29,X30,X31)
| ~ on_path(X32,X31) )
& ( in_path(tail_of(X32),X31)
| ~ path(X29,X30,X31)
| ~ on_path(X32,X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
fof(c_0_26,plain,
! [X61,X62,X63,X64,X65,X66] :
( ( tail_of(X66) != tail_of(X63)
| head_of(X66) != head_of(X64)
| ~ shortest_path(X61,X62,X65)
| ~ precedes(X63,X64,X65) )
& ( ~ precedes(X64,X63,X65)
| ~ shortest_path(X61,X62,X65)
| ~ precedes(X63,X64,X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[shortest_path_properties])])])])]) ).
cnf(c_0_27,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_19]) ).
cnf(c_0_28,plain,
( on_path(esk8_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_29,plain,
! [X15,X16] :
( ( edge(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X15 != head_of(esk1_2(X15,X16))
| X16 != tail_of(esk1_2(X15,X16))
| X16 != head_of(esk1_2(X15,X16))
| X15 != tail_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X16 = head_of(esk1_2(X15,X16))
| X15 = head_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X15 = tail_of(esk1_2(X15,X16))
| X15 = head_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X16 = head_of(esk1_2(X15,X16))
| X16 = tail_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete )
& ( X15 = tail_of(esk1_2(X15,X16))
| X16 = tail_of(esk1_2(X15,X16))
| ~ vertex(X15)
| ~ vertex(X16)
| X15 = X16
| ~ complete ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[complete_properties])])])])])]) ).
fof(c_0_30,plain,
! [X14] :
( ( vertex(head_of(X14))
| ~ edge(X14) )
& ( vertex(tail_of(X14))
| ~ edge(X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])]) ).
cnf(c_0_31,plain,
( edge(X1)
| ~ sequential(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
sequential(esk7_1(esk9_0),esk8_1(esk9_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_33,plain,
( vertex(X1)
| ~ path(X2,X3,X4)
| ~ in_path(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( in_path(tail_of(X1),X2)
| ~ path(X3,X4,X2)
| ~ on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,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_26]) ).
cnf(c_0_36,negated_conjecture,
( precedes(X1,X2,esk9_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_37,negated_conjecture,
on_path(esk8_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_23]) ).
cnf(c_0_38,plain,
( X1 = tail_of(esk1_2(X1,X2))
| X2 = tail_of(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_40,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
edge(esk8_1(esk9_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_42,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_43,negated_conjecture,
( in_path(tail_of(X1),esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_44,plain,
( on_path(esk7_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_45,plain,
! [X67,X68,X69] :
( ( edge(X67)
| ~ triangle(X67,X68,X69) )
& ( edge(X68)
| ~ triangle(X67,X68,X69) )
& ( edge(X69)
| ~ triangle(X67,X68,X69) )
& ( sequential(X67,X68)
| ~ triangle(X67,X68,X69) )
& ( sequential(X68,X69)
| ~ triangle(X67,X68,X69) )
& ( sequential(X69,X67)
| ~ triangle(X67,X68,X69) )
& ( ~ edge(X67)
| ~ edge(X68)
| ~ edge(X69)
| ~ sequential(X67,X68)
| ~ sequential(X68,X69)
| ~ sequential(X69,X67)
| triangle(X67,X68,X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])]) ).
fof(c_0_46,plain,
! [X73,X74,X75] :
( ~ path(X73,X74,X75)
| number_of_in(sequential_pairs,X75) = minus(length_of(X75),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
cnf(c_0_47,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X1) != tail_of(X3)
| ~ precedes(X3,X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_48,negated_conjecture,
( precedes(X1,esk8_1(esk9_0),esk9_0)
| ~ sequential(X1,esk8_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,plain,
( tail_of(esk1_2(X1,X2)) = X1
| tail_of(esk1_2(X1,X2)) = X2
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_50,negated_conjecture,
vertex(head_of(esk8_1(esk9_0))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
on_path(esk7_1(esk9_0),esk9_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_22]),c_0_23]) ).
cnf(c_0_53,plain,
( triangle(X1,X2,X3)
| ~ edge(X1)
| ~ edge(X2)
| ~ edge(X3)
| ~ sequential(X1,X2)
| ~ sequential(X2,X3)
| ~ sequential(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_55,plain,
( number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1)
| ~ path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( head_of(X1) != head_of(esk8_1(esk9_0))
| tail_of(X1) != tail_of(X2)
| ~ sequential(X2,esk8_1(esk9_0))
| ~ on_path(X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_57,negated_conjecture,
( tail_of(esk1_2(X1,head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk1_2(X1,head_of(esk8_1(esk9_0)))) = X1
| X1 = head_of(esk8_1(esk9_0))
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,negated_conjecture,
vertex(tail_of(esk7_1(esk9_0))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ triangle(esk7_1(X1),esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_60,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53,c_0_54]),c_0_54]),c_0_54]) ).
cnf(c_0_61,plain,
( X1 = X2
| sequential(X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| head_of(X1) != tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_62,negated_conjecture,
number_of_in(sequential_pairs,esk9_0) = minus(length_of(esk9_0),n1),
inference(spm,[status(thm)],[c_0_55,c_0_22]) ).
cnf(c_0_63,plain,
( edge(esk1_2(X1,X2))
| X1 = X2
| ~ vertex(X1)
| ~ vertex(X2)
| ~ complete ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_64,plain,
! [X13] :
( ~ edge(X13)
| head_of(X13) != tail_of(X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).
cnf(c_0_65,negated_conjecture,
( head_of(X1) != head_of(esk8_1(esk9_0))
| tail_of(X1) != tail_of(esk7_1(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_32]),c_0_52])]) ).
cnf(c_0_66,negated_conjecture,
( tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = tail_of(esk7_1(esk9_0))
| tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ sequential(X2,esk7_1(X1))
| ~ sequential(esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_21]) ).
cnf(c_0_68,negated_conjecture,
( esk8_1(esk9_0) = X1
| sequential(esk8_1(esk9_0),X1)
| tail_of(X1) != head_of(esk8_1(esk9_0))
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_69,negated_conjecture,
number_of_in(triangles,esk9_0) != minus(length_of(esk9_0),n1),
inference(rw,[status(thm)],[c_0_23,c_0_62]) ).
cnf(c_0_70,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_39])]) ).
cnf(c_0_71,plain,
( ~ edge(X1)
| head_of(X1) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) != head_of(esk8_1(esk9_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( esk8_1(esk9_0) = X1
| tail_of(X1) != head_of(esk8_1(esk9_0))
| ~ sequential(X1,esk7_1(esk9_0))
| ~ path(X2,X3,esk9_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_62]),c_0_69]),c_0_54]) ).
cnf(c_0_74,plain,
( esk1_2(X1,X2) = X3
| X1 = X2
| sequential(esk1_2(X1,X2),X3)
| tail_of(X3) != head_of(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
edge(esk7_1(esk9_0)),
inference(spm,[status(thm)],[c_0_54,c_0_32]) ).
cnf(c_0_76,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_29]) ).
cnf(c_0_77,negated_conjecture,
( tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) != head_of(esk8_1(esk9_0))
| ~ edge(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( esk1_2(X1,X2) = esk7_1(esk9_0)
| esk8_1(esk9_0) = esk1_2(X1,X2)
| X1 = X2
| tail_of(esk1_2(X1,X2)) != head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) != head_of(esk1_2(X1,X2))
| ~ path(X3,X4,esk9_0)
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_79,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_29]) ).
cnf(c_0_80,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_76,c_0_39])]) ).
cnf(c_0_81,negated_conjecture,
( tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0))
| head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) != head_of(esk8_1(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_70]),c_0_50]),c_0_58])]) ).
cnf(c_0_82,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_83,negated_conjecture,
( esk8_1(esk9_0) = esk1_2(X1,X2)
| esk1_2(X1,X2) = esk7_1(esk9_0)
| X1 = X2
| tail_of(esk1_2(X1,X2)) != head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) != head_of(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_22]) ).
cnf(c_0_84,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_79,c_0_39])]) ).
cnf(c_0_85,negated_conjecture,
( tail_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = head_of(esk8_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_66]),c_0_58]),c_0_50])]),c_0_81]) ).
cnf(c_0_86,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_87,negated_conjecture,
( ~ precedes(X1,X2,esk9_0)
| ~ precedes(X2,X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_18]) ).
cnf(c_0_88,negated_conjecture,
( esk1_2(X1,X2) = esk7_1(esk9_0)
| esk8_1(esk9_0) = esk1_2(X1,X2)
| head_of(esk1_2(X1,X2)) = X2
| X1 = X2
| tail_of(esk7_1(esk9_0)) != head_of(esk1_2(X1,X2))
| X2 != head_of(esk8_1(esk9_0))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_80]) ).
cnf(c_0_89,negated_conjecture,
( head_of(esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0)))) = tail_of(esk7_1(esk9_0))
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_50]),c_0_58])]) ).
cnf(c_0_90,negated_conjecture,
tail_of(esk8_1(esk9_0)) = head_of(esk7_1(esk9_0)),
inference(spm,[status(thm)],[c_0_86,c_0_32]) ).
cnf(c_0_91,negated_conjecture,
( ~ precedes(esk8_1(esk9_0),X1,esk9_0)
| ~ sequential(X1,esk8_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_87,c_0_48]) ).
cnf(c_0_92,negated_conjecture,
( precedes(X1,esk7_1(esk9_0),esk9_0)
| ~ sequential(X1,esk7_1(esk9_0))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_93,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk8_1(esk9_0)
| esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_50]),c_0_58])]) ).
cnf(c_0_94,negated_conjecture,
tail_of(esk7_1(esk9_0)) != head_of(esk7_1(esk9_0)),
inference(spm,[status(thm)],[c_0_65,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
~ sequential(esk8_1(esk9_0),esk7_1(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_32]),c_0_52]),c_0_37])]) ).
cnf(c_0_96,negated_conjecture,
( esk1_2(tail_of(esk7_1(esk9_0)),head_of(esk8_1(esk9_0))) = esk7_1(esk9_0)
| tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_93]),c_0_90]),c_0_50]),c_0_58])]),c_0_94]) ).
cnf(c_0_97,negated_conjecture,
head_of(esk8_1(esk9_0)) != head_of(esk7_1(esk9_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_90]),c_0_41])]) ).
cnf(c_0_98,negated_conjecture,
( esk8_1(esk9_0) = esk7_1(esk9_0)
| tail_of(esk7_1(esk9_0)) != head_of(esk8_1(esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_68]),c_0_75])]) ).
cnf(c_0_99,negated_conjecture,
tail_of(esk7_1(esk9_0)) = head_of(esk8_1(esk9_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_96]),c_0_58]),c_0_50])]),c_0_97]) ).
cnf(c_0_100,negated_conjecture,
esk8_1(esk9_0) = esk7_1(esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
cnf(c_0_101,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_100])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA011+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 23:28:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 # ENIGMATIC: Selected SinE mode:
% 0.19/0.46 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.19/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.19/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 87.40/12.40 # ENIGMATIC: Solved by autoschedule:
% 87.40/12.40 # No SInE strategy applied
% 87.40/12.40 # Trying AutoSched0 for 150 seconds
% 87.40/12.40 # AutoSched0-Mode selected heuristic G_E___107_C36_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 87.40/12.40 # and selection function SelectMaxLComplexAvoidPosPred.
% 87.40/12.40 #
% 87.40/12.40 # Preprocessing time : 0.028 s
% 87.40/12.40 # Presaturation interreduction done
% 87.40/12.40
% 87.40/12.40 # Proof found!
% 87.40/12.40 # SZS status Theorem
% 87.40/12.40 # SZS output start CNFRefutation
% See solution above
% 87.40/12.40 # Training examples: 0 positive, 0 negative
% 87.40/12.40
% 87.40/12.40 # -------------------------------------------------
% 87.40/12.40 # User time : 9.691 s
% 87.40/12.40 # System time : 0.216 s
% 87.40/12.40 # Total time : 9.907 s
% 87.40/12.40 # Maximum resident set size: 7120 pages
% 87.40/12.40
%------------------------------------------------------------------------------