%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRA002+1 : 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 : n007.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 85.70s 11.30s
% Output : CNFRefutation 85.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 131 ( 12 unt; 0 def)
% Number of atoms : 607 ( 204 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 753 ( 277 ~; 363 |; 78 &)
% ( 7 <=>; 25 =>; 1 <=; 2 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 291 ( 42 sgn 111 !; 9 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
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(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(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(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/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(edge_ends_are_vertices,axiom,
! [X1] :
( edge(X1)
=> ( vertex(tail_of(X1))
& vertex(head_of(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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(precedes_properties,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( ( sequential(X7,X8)
<~> ? [X9] :
( precedes(X9,X8,X4)
& sequential(X7,X9) ) )
& on_path(X8,X4)
& on_path(X7,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
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(graph_has_them_all,axiom,
! [X11,X12] : less_or_equal(number_of_in(X11,X12),number_of_in(X11,graph)),
file('/export/starexec/sandbox/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,
( 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,
! [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_17,plain,
! [X16,X17,X18,X19,X20,X21,X22] :
( ( shortest_path(X20,X21,X22)
| X20 = X21
| ~ path(X20,X21,X22)
| ~ less_or_equal(length_of(X22),length_of(esk4_3(X20,X21,X22))) )
& ( shortest_path(X20,X21,X22)
| X20 = X21
| ~ path(X20,X21,X22)
| path(X20,X21,esk4_3(X20,X21,X22)) )
& ( ~ shortest_path(X16,X17,X18)
| less_or_equal(length_of(X18),length_of(X19))
| ~ path(X16,X17,X19) )
& ( ~ shortest_path(X16,X17,X18)
| X16 != X17 )
& ( ~ shortest_path(X16,X17,X18)
| path(X16,X17,X18) ) ),
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_18,negated_conjecture,
( ~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph))
& shortest_path(esk2_0,esk3_0,esk1_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_19,plain,
! [X41,X42] :
( ( ~ complete
| X41 = X42
| ~ vertex(X42)
| ~ vertex(X41)
| X42 = tail_of(esk7_2(X41,X42))
| X41 = tail_of(esk7_2(X41,X42)) )
& ( ~ complete
| X41 = X42
| ~ vertex(X42)
| ~ vertex(X41)
| X42 = tail_of(esk7_2(X41,X42))
| X42 = head_of(esk7_2(X41,X42)) )
& ( ~ complete
| X41 = X42
| ~ vertex(X42)
| ~ vertex(X41)
| X41 = head_of(esk7_2(X41,X42))
| X41 = tail_of(esk7_2(X41,X42)) )
& ( ~ complete
| X41 = X42
| ~ vertex(X42)
| ~ vertex(X41)
| X41 = head_of(esk7_2(X41,X42))
| X42 = head_of(esk7_2(X41,X42)) )
& ( ~ complete
| X41 = X42
| ~ vertex(X42)
| ~ vertex(X41)
| X41 != tail_of(esk7_2(X41,X42))
| X42 != head_of(esk7_2(X41,X42))
| X42 != tail_of(esk7_2(X41,X42))
| X41 != head_of(esk7_2(X41,X42)) )
& ( ~ complete
| X41 = X42
| ~ vertex(X42)
| ~ vertex(X41)
| edge(esk7_2(X41,X42)) ) ),
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])])])])])]) ).
fof(c_0_20,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_21,plain,
! [X49,X50,X51,X52,X53,X54] :
( ( ~ path(X50,X51,X49)
| precedes(X52,X53,X49)
| ~ on_path(X53,X49)
| ~ on_path(X52,X49)
| ~ precedes(X54,X53,X49)
| ~ sequential(X52,X54) )
& ( ~ path(X50,X51,X49)
| precedes(X52,X53,X49)
| ~ on_path(X53,X49)
| ~ on_path(X52,X49)
| ~ sequential(X52,X53) ) ),
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_16])])])])]) ).
cnf(c_0_22,plain,
( ~ shortest_path(X1,X2,X3)
| path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
shortest_path(esk2_0,esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X26,X27,X28,X31] :
( ( number_of_in(sequential_pairs,X26) = number_of_in(triangles,X26)
| ~ path(X27,X28,X26)
| ~ triangle(esk5_1(X26),esk6_1(X26),X31) )
& ( number_of_in(sequential_pairs,X26) = number_of_in(triangles,X26)
| ~ path(X27,X28,X26)
| sequential(esk5_1(X26),esk6_1(X26)) )
& ( number_of_in(sequential_pairs,X26) = number_of_in(triangles,X26)
| ~ path(X27,X28,X26)
| on_path(esk6_1(X26),X26) )
& ( number_of_in(sequential_pairs,X26) = number_of_in(triangles,X26)
| ~ path(X27,X28,X26)
| on_path(esk5_1(X26),X26) ) ),
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_25,plain,
( ~ complete
| ~ vertex(X1)
| ~ vertex(X2)
| X2 = X1
| X2 = head_of(esk7_2(X2,X1))
| X1 = head_of(esk7_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X63] :
( ( ~ edge(X63)
| vertex(tail_of(X63)) )
& ( ~ edge(X63)
| vertex(head_of(X63)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])])]) ).
fof(c_0_28,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]) ).
fof(c_0_29,plain,
! [X35,X36,X37,X38,X39,X40] :
( ( ~ precedes(X37,X38,X39)
| ~ shortest_path(X35,X36,X39)
| ~ precedes(X38,X37,X39) )
& ( ~ precedes(X37,X38,X39)
| ~ shortest_path(X35,X36,X39)
| head_of(X40) != head_of(X38)
| tail_of(X40) != tail_of(X37) ) ),
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_20])])])])]) ).
cnf(c_0_30,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_31,negated_conjecture,
path(esk2_0,esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( ~ vertex(X2)
| ~ vertex(X1)
| X2 = X1
| head_of(esk7_2(X1,X2)) = X1
| head_of(esk7_2(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_34,plain,
( ~ edge(X1)
| vertex(head_of(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X47,X48] :
( ( sequential(X47,X48)
| head_of(X47) != tail_of(X48)
| X47 = X48
| ~ edge(X48)
| ~ edge(X47) )
& ( ~ sequential(X47,X48)
| head_of(X47) = tail_of(X48) )
& ( ~ sequential(X47,X48)
| X47 != X48 )
& ( ~ sequential(X47,X48)
| edge(X48) )
& ( ~ sequential(X47,X48)
| edge(X47) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
cnf(c_0_36,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| sequential(esk5_1(X1),esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,plain,
( ~ complete
| ~ vertex(X2)
| ~ vertex(X1)
| X1 = X2
| X2 = tail_of(esk7_2(X1,X2))
| X1 = tail_of(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
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_29]) ).
cnf(c_0_39,negated_conjecture,
( ~ on_path(X1,esk1_0)
| ~ on_path(X2,esk1_0)
| ~ sequential(X1,X2)
| precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
( on_path(esk6_1(esk1_0),esk1_0)
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_41,plain,
( ~ edge(X1)
| ~ vertex(X2)
| X2 = head_of(X1)
| head_of(esk7_2(head_of(X1),X2)) = X2
| head_of(esk7_2(head_of(X1),X2)) = head_of(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
( ~ edge(X1)
| vertex(tail_of(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_43,plain,
( ~ sequential(X2,X1)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( sequential(esk5_1(esk1_0),esk6_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_45,plain,
( ~ complete
| ~ vertex(X1)
| ~ vertex(X2)
| X2 = X1
| X1 = tail_of(esk7_2(X2,X1))
| X1 = head_of(esk7_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_46,plain,
( ~ complete
| ~ vertex(X2)
| ~ vertex(X1)
| X1 = X2
| edge(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_47,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| X1 = X2
| tail_of(esk7_2(X1,X2)) = X2
| tail_of(esk7_2(X1,X2)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_26])]) ).
cnf(c_0_48,negated_conjecture,
( ~ precedes(X3,X2,esk1_0)
| tail_of(X1) != tail_of(X3)
| head_of(X1) != head_of(X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_49,negated_conjecture,
( ~ on_path(X1,esk1_0)
| ~ sequential(X1,esk6_1(esk1_0))
| precedes(X1,esk6_1(esk1_0),esk1_0)
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_50,plain,
( ~ path(X2,X3,X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_51,plain,
( ~ edge(X2)
| ~ edge(X1)
| tail_of(X2) = head_of(X1)
| head_of(esk7_2(head_of(X1),tail_of(X2))) = head_of(X1)
| head_of(esk7_2(head_of(X1),tail_of(X2))) = tail_of(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_52,negated_conjecture,
( edge(esk6_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,plain,
( ~ sequential(X1,X2)
| edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_54,plain,
( head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1)
| sequential(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_55,plain,
( ~ vertex(X2)
| ~ vertex(X1)
| X2 = X1
| head_of(esk7_2(X1,X2)) = X2
| tail_of(esk7_2(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_26])]) ).
cnf(c_0_56,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| edge(esk7_2(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_26])]) ).
cnf(c_0_57,plain,
( ~ edge(X2)
| ~ vertex(X1)
| X1 = tail_of(X2)
| tail_of(esk7_2(X1,tail_of(X2))) = X1
| tail_of(esk7_2(X1,tail_of(X2))) = tail_of(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
fof(c_0_58,plain,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
inference(fof_simplification,[status(thm)],[no_loops]) ).
cnf(c_0_59,negated_conjecture,
( ~ on_path(X2,esk1_0)
| ~ sequential(X2,esk6_1(esk1_0))
| tail_of(X1) != tail_of(X2)
| head_of(X1) != head_of(esk6_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_60,negated_conjecture,
( on_path(esk5_1(esk1_0),esk1_0)
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_31]) ).
cnf(c_0_61,negated_conjecture,
( ~ edge(X1)
| tail_of(X1) = head_of(esk6_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(X1))) = tail_of(X1)
| head_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(X1))) = head_of(esk6_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( edge(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_44]) ).
fof(c_0_63,plain,
! [X44,X45,X46] :
( ( triangle(X44,X45,X46)
| ~ sequential(X46,X44)
| ~ sequential(X45,X46)
| ~ sequential(X44,X45)
| ~ edge(X46)
| ~ edge(X45)
| ~ edge(X44) )
& ( ~ triangle(X44,X45,X46)
| sequential(X46,X44) )
& ( ~ triangle(X44,X45,X46)
| sequential(X45,X46) )
& ( ~ triangle(X44,X45,X46)
| sequential(X44,X45) )
& ( ~ triangle(X44,X45,X46)
| edge(X46) )
& ( ~ triangle(X44,X45,X46)
| edge(X45) )
& ( ~ triangle(X44,X45,X46)
| edge(X44) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])])]) ).
cnf(c_0_64,plain,
( ~ edge(X2)
| ~ vertex(X1)
| sequential(esk7_2(X1,tail_of(X2)),X2)
| tail_of(X2) = X1
| esk7_2(X1,tail_of(X2)) = X2
| tail_of(esk7_2(X1,tail_of(X2))) = tail_of(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55])]),c_0_56]),c_0_42]) ).
cnf(c_0_65,plain,
( ~ edge(X1)
| ~ edge(X2)
| head_of(X1) = tail_of(X2)
| tail_of(esk7_2(head_of(X1),tail_of(X2))) = tail_of(X2)
| tail_of(esk7_2(head_of(X1),tail_of(X2))) = head_of(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_34]) ).
fof(c_0_66,plain,
! [X62] :
( head_of(X62) != tail_of(X62)
| ~ edge(X62) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
cnf(c_0_67,negated_conjecture,
( tail_of(X1) != tail_of(esk5_1(esk1_0))
| head_of(X1) != head_of(esk6_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_44]),c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| head_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0)))) = head_of(esk6_1(esk1_0))
| head_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0)))) = tail_of(esk5_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,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_63]) ).
cnf(c_0_70,plain,
( ~ edge(X1)
| ~ edge(X2)
| sequential(esk7_2(tail_of(X1),tail_of(X2)),X2)
| tail_of(X2) = tail_of(X1)
| esk7_2(tail_of(X1),tail_of(X2)) = X2
| tail_of(esk7_2(tail_of(X1),tail_of(X2))) = tail_of(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_42]) ).
cnf(c_0_71,negated_conjecture,
( ~ edge(X1)
| head_of(X1) = tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| tail_of(esk7_2(head_of(X1),tail_of(esk5_1(esk1_0)))) = head_of(X1)
| tail_of(esk7_2(head_of(X1),tail_of(esk5_1(esk1_0)))) = tail_of(esk5_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_62]) ).
cnf(c_0_72,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( tail_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0)))) != tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| head_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0)))) = tail_of(esk5_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( ~ path(X3,X4,X1)
| ~ triangle(esk5_1(X1),esk6_1(X1),X2)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_75,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_69,c_0_53]),c_0_53]),c_0_53]) ).
cnf(c_0_76,negated_conjecture,
( ~ edge(X1)
| sequential(esk7_2(tail_of(X1),tail_of(esk5_1(esk1_0))),esk5_1(esk1_0))
| tail_of(esk5_1(esk1_0)) = tail_of(X1)
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| esk7_2(tail_of(X1),tail_of(esk5_1(esk1_0))) = esk5_1(esk1_0)
| tail_of(esk7_2(tail_of(X1),tail_of(esk5_1(esk1_0)))) = tail_of(esk5_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_62]) ).
cnf(c_0_77,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| tail_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0)))) = tail_of(esk5_1(esk1_0))
| tail_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0)))) = head_of(esk6_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_52]) ).
cnf(c_0_78,negated_conjecture,
( ~ edge(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))))
| tail_of(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0)))) != tail_of(esk5_1(esk1_0))
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_79,plain,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( ~ ( sequential(X7,X8)
<=> ? [X9] :
( precedes(X9,X8,X4)
& sequential(X7,X9) ) )
& on_path(X8,X4)
& on_path(X7,X4) ) ) ),
inference(fof_simplification,[status(thm)],[precedes_properties]) ).
cnf(c_0_80,plain,
( ~ path(X3,X4,X1)
| ~ sequential(esk6_1(X1),X2)
| ~ sequential(X2,esk5_1(X1))
| number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_36]) ).
cnf(c_0_81,negated_conjecture,
( ~ edge(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))))
| sequential(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))),esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) = esk5_1(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( ~ edge(X1)
| ~ edge(esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))))
| head_of(esk6_1(esk1_0)) != head_of(X1)
| sequential(X1,esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))))
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| X1 = esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_77]),c_0_78]) ).
fof(c_0_83,plain,
! [X55,X56,X57,X58,X59,X60] :
( ( ~ path(X56,X57,X55)
| ~ precedes(X58,X59,X55)
| sequential(X58,X59)
| precedes(esk8_3(X55,X58,X59),X59,X55) )
& ( ~ path(X56,X57,X55)
| ~ precedes(X58,X59,X55)
| sequential(X58,X59)
| sequential(X58,esk8_3(X55,X58,X59)) )
& ( ~ path(X56,X57,X55)
| ~ precedes(X58,X59,X55)
| ~ precedes(X60,X59,X55)
| ~ sequential(X58,X60)
| ~ sequential(X58,X59) )
& ( ~ path(X56,X57,X55)
| ~ precedes(X58,X59,X55)
| on_path(X59,X55) )
& ( ~ path(X56,X57,X55)
| ~ precedes(X58,X59,X55)
| on_path(X58,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_79])])])])])])]) ).
cnf(c_0_84,negated_conjecture,
( ~ path(X1,X2,esk1_0)
| ~ sequential(esk6_1(esk1_0),esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) = esk5_1(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_43]) ).
cnf(c_0_85,negated_conjecture,
( ~ edge(X1)
| ~ vertex(head_of(esk6_1(esk1_0)))
| ~ vertex(tail_of(esk5_1(esk1_0)))
| head_of(esk6_1(esk1_0)) != head_of(X1)
| sequential(X1,esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| X1 = esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_82,c_0_56]) ).
cnf(c_0_86,plain,
( ~ sequential(X1,X2)
| head_of(X1) = tail_of(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_87,plain,
( ~ path(X4,X5,X1)
| ~ precedes(X2,X3,X1)
| sequential(X2,X3)
| precedes(esk8_3(X1,X2,X3),X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_88,plain,
( ~ complete
| ~ vertex(X2)
| ~ vertex(X1)
| X1 = X2
| X1 = head_of(esk7_2(X1,X2))
| X1 = tail_of(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_89,negated_conjecture,
( ~ vertex(head_of(esk6_1(esk1_0)))
| ~ vertex(tail_of(esk5_1(esk1_0)))
| ~ path(X1,X2,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) = esk5_1(esk1_0)
| esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) = esk6_1(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_52]) ).
cnf(c_0_90,negated_conjecture,
( head_of(esk5_1(esk1_0)) = tail_of(esk6_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_86,c_0_44]) ).
cnf(c_0_91,plain,
( ~ path(X4,X5,X2)
| ~ precedes(X1,X3,X2)
| on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( ~ precedes(X1,X2,esk1_0)
| sequential(X1,X2)
| precedes(esk8_3(esk1_0,X1,X2),X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_87,c_0_31]) ).
cnf(c_0_93,plain,
( ~ vertex(X1)
| ~ vertex(X2)
| X1 = X2
| head_of(esk7_2(X1,X2)) = X1
| tail_of(esk7_2(X1,X2)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_26])]) ).
cnf(c_0_94,negated_conjecture,
( ~ vertex(head_of(esk6_1(esk1_0)))
| ~ vertex(tail_of(esk5_1(esk1_0)))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) = esk6_1(esk1_0)
| esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) = esk5_1(esk1_0) ),
inference(spm,[status(thm)],[c_0_89,c_0_31]) ).
cnf(c_0_95,negated_conjecture,
( tail_of(esk6_1(esk1_0)) != tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_90]),c_0_62]) ).
cnf(c_0_96,plain,
( ~ precedes(X2,X1,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_97,negated_conjecture,
( ~ path(X3,X4,esk1_0)
| ~ precedes(X1,X2,esk1_0)
| on_path(esk8_3(esk1_0,X1,X2),esk1_0)
| sequential(X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,plain,
( ~ path(X5,X6,X4)
| ~ on_path(X3,X4)
| ~ on_path(X1,X4)
| ~ precedes(X2,X3,X4)
| ~ sequential(X1,X2)
| precedes(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_99,plain,
( ~ path(X4,X5,X2)
| ~ precedes(X3,X1,X2)
| on_path(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_100,negated_conjecture,
( ~ vertex(X1)
| ~ vertex(head_of(esk6_1(esk1_0)))
| tail_of(esk7_2(head_of(esk6_1(esk1_0)),X1)) != tail_of(esk5_1(esk1_0))
| head_of(esk6_1(esk1_0)) = X1
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| tail_of(esk7_2(head_of(esk6_1(esk1_0)),X1)) = head_of(esk6_1(esk1_0)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_93])]) ).
cnf(c_0_101,negated_conjecture,
( ~ vertex(tail_of(esk5_1(esk1_0)))
| ~ vertex(head_of(esk6_1(esk1_0)))
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| esk7_2(head_of(esk6_1(esk1_0)),tail_of(esk5_1(esk1_0))) = esk5_1(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_94]),c_0_95]) ).
cnf(c_0_102,negated_conjecture,
( ~ precedes(X2,X1,esk1_0)
| ~ precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_96,c_0_23]) ).
cnf(c_0_103,negated_conjecture,
( ~ precedes(X1,X2,esk1_0)
| on_path(esk8_3(esk1_0,X1,X2),esk1_0)
| sequential(X1,X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_31]) ).
cnf(c_0_104,plain,
( ~ path(X5,X6,X3)
| ~ on_path(X1,X3)
| ~ sequential(X1,X4)
| ~ precedes(X4,X2,X3)
| precedes(X1,X2,X3) ),
inference(csr,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
( ~ vertex(tail_of(esk5_1(esk1_0)))
| ~ vertex(head_of(esk6_1(esk1_0)))
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,negated_conjecture,
( ~ precedes(X1,X2,esk1_0)
| ~ precedes(X2,esk8_3(esk1_0,X1,X2),esk1_0)
| sequential(X1,X2) ),
inference(spm,[status(thm)],[c_0_102,c_0_92]) ).
cnf(c_0_107,negated_conjecture,
( ~ on_path(X1,esk1_0)
| ~ sequential(X1,esk8_3(esk1_0,X2,X3))
| ~ precedes(X2,X3,esk1_0)
| sequential(X2,X3)
| precedes(X1,esk8_3(esk1_0,X2,X3),esk1_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_103]) ).
cnf(c_0_108,plain,
( ~ path(X4,X5,X2)
| ~ precedes(X1,X3,X2)
| sequential(X1,X3)
| sequential(X1,esk8_3(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_109,plain,
( ~ sequential(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_110,negated_conjecture,
( ~ on_path(X1,esk1_0)
| ~ sequential(X1,X3)
| ~ precedes(X3,X2,esk1_0)
| precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_31]) ).
cnf(c_0_111,negated_conjecture,
( ~ vertex(tail_of(esk5_1(esk1_0)))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_34]),c_0_52]) ).
cnf(c_0_112,negated_conjecture,
( ~ on_path(X2,esk1_0)
| ~ sequential(X2,esk8_3(esk1_0,X1,X2))
| ~ precedes(X1,X2,esk1_0)
| sequential(X1,X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
( ~ precedes(X1,X2,esk1_0)
| sequential(X1,X2)
| sequential(X1,esk8_3(esk1_0,X1,X2)) ),
inference(spm,[status(thm)],[c_0_108,c_0_31]) ).
cnf(c_0_114,plain,
~ sequential(X1,X1),
inference(er,[status(thm)],[c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( ~ on_path(X2,esk1_0)
| ~ on_path(X1,esk1_0)
| ~ sequential(X1,X2)
| ~ sequential(X2,esk6_1(esk1_0))
| precedes(X1,esk6_1(esk1_0),esk1_0)
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(spm,[status(thm)],[c_0_110,c_0_49]) ).
cnf(c_0_116,negated_conjecture,
( head_of(esk6_1(esk1_0)) = tail_of(esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_42]),c_0_62]) ).
cnf(c_0_117,negated_conjecture,
( ~ on_path(X1,esk1_0)
| ~ precedes(X1,X1,esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( ~ on_path(X1,esk1_0)
| ~ sequential(X1,esk5_1(esk1_0))
| precedes(X1,esk6_1(esk1_0),esk1_0)
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_44]),c_0_60]) ).
fof(c_0_119,plain,
! [X32,X33,X34] :
( number_of_in(sequential_pairs,X34) = minus(length_of(X34),n1)
| ~ path(X32,X33,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])])]) ).
cnf(c_0_120,negated_conjecture,
( ~ edge(X1)
| tail_of(X1) != tail_of(esk5_1(esk1_0))
| sequential(esk6_1(esk1_0),X1)
| esk6_1(esk1_0) = X1
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_116]),c_0_52]) ).
cnf(c_0_121,negated_conjecture,
( ~ sequential(esk6_1(esk1_0),esk5_1(esk1_0))
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_40]) ).
cnf(c_0_122,plain,
( ~ path(X1,X2,X3)
| number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
fof(c_0_123,plain,
! [X24,X25] : less_or_equal(number_of_in(X24,X25),number_of_in(X24,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_124,negated_conjecture,
( esk6_1(esk1_0) = esk5_1(esk1_0)
| number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_120]),c_0_62]),c_0_121]) ).
cnf(c_0_125,negated_conjecture,
~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_126,negated_conjecture,
minus(length_of(esk1_0),n1) = number_of_in(sequential_pairs,esk1_0),
inference(spm,[status(thm)],[c_0_122,c_0_31]) ).
cnf(c_0_127,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_128,negated_conjecture,
number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_124]),c_0_114]) ).
cnf(c_0_129,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk1_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA002+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 18:14:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 85.70/11.30 % Version: 3.5.1
% 85.70/11.30 % Preprocessing class: FSMSSMSSSSSNFFN.
% 85.70/11.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.70/11.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 85.70/11.30 % Starting new_bool_3 with 300s (1) cores
% 85.70/11.30 % Starting new_bool_1 with 300s (1) cores
% 85.70/11.30 % Starting sh5l with 300s (1) cores
% 85.70/11.30 % new_bool_1 with pid 3290892 completed with status 0
% 85.70/11.30 % Result found by new_bool_1
% 85.70/11.30 % Preprocessing class: FSMSSMSSSSSNFFN.
% 85.70/11.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.70/11.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 85.70/11.30 % Starting new_bool_3 with 300s (1) cores
% 85.70/11.30 % Starting new_bool_1 with 300s (1) cores
% 85.70/11.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 85.70/11.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 85.70/11.30 % Search class: FGHSF-FFMF31-SFFFFFNN
% 85.70/11.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 85.70/11.30 % Starting SubtermCWHack with 31s (1) cores
% 85.70/11.30 % SubtermCWHack with pid 3290894 completed with status 0
% 85.70/11.30 % Result found by SubtermCWHack
% 85.70/11.30 % Preprocessing class: FSMSSMSSSSSNFFN.
% 85.70/11.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.70/11.30 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 85.70/11.30 % Starting new_bool_3 with 300s (1) cores
% 85.70/11.30 % Starting new_bool_1 with 300s (1) cores
% 85.70/11.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 85.70/11.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 85.70/11.30 % Search class: FGHSF-FFMF31-SFFFFFNN
% 85.70/11.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 85.70/11.30 % Starting SubtermCWHack with 31s (1) cores
% 85.70/11.30 % Preprocessing time : 0.001 s
% 85.70/11.30
% 85.70/11.30 % Proof found!
% 85.70/11.30 % SZS status Theorem
% 85.70/11.30 % SZS output start CNFRefutation
% See solution above
% 85.70/11.30 % Parsed axioms : 18
% 85.70/11.30 % Removed by relevancy pruning/SinE : 5
% 85.70/11.30 % Initial clauses : 44
% 85.70/11.30 % Removed in clause preprocessing : 1
% 85.70/11.30 % Initial clauses in saturation : 43
% 85.70/11.30 % Processed clauses : 10541
% 85.70/11.30 % ...of these trivial : 67
% 85.70/11.30 % ...subsumed : 6485
% 85.70/11.30 % ...remaining for further processing : 3989
% 85.70/11.30 % Other redundant clauses eliminated : 1962
% 85.70/11.30 % Clauses deleted for lack of memory : 0
% 85.70/11.30 % Backward-subsumed : 1016
% 85.70/11.30 % Backward-rewritten : 2305
% 85.70/11.30 % Generated clauses : 371067
% 85.70/11.30 % ...of the previous two non-redundant : 336857
% 85.70/11.30 % ...aggressively subsumed : 0
% 85.70/11.30 % Contextual simplify-reflections : 1052
% 85.70/11.30 % Paramodulations : 368567
% 85.70/11.30 % Factorizations : 152
% 85.70/11.30 % NegExts : 0
% 85.70/11.30 % Equation resolutions : 2348
% 85.70/11.30 % Disequality decompositions : 0
% 85.70/11.30 % Total rewrite steps : 2344
% 85.70/11.30 % ...of those cached : 2339
% 85.70/11.30 % Propositional unsat checks : 0
% 85.70/11.30 % Propositional check models : 0
% 85.70/11.30 % Propositional check unsatisfiable : 0
% 85.70/11.30 % Propositional clauses : 0
% 85.70/11.30 % Propositional clauses after purity: 0
% 85.70/11.30 % Propositional unsat core size : 0
% 85.70/11.30 % Propositional preprocessing time : 0.000
% 85.70/11.30 % Propositional encoding time : 0.000
% 85.70/11.30 % Propositional solver time : 0.000
% 85.70/11.30 % Success case prop preproc time : 0.000
% 85.70/11.30 % Success case prop encoding time : 0.000
% 85.70/11.30 % Success case prop solver time : 0.000
% 85.70/11.30 % Current number of processed clauses : 666
% 85.70/11.30 % Positive orientable unit clauses : 6
% 85.70/11.30 % Positive unorientable unit clauses: 0
% 85.70/11.30 % Negative unit clauses : 3
% 85.70/11.30 % Non-unit-clauses : 657
% 85.70/11.30 % Current number of unprocessed clauses: 321105
% 85.70/11.30 % ...number of literals in the above : 4160448
% 85.70/11.30 % Current number of archived formulas : 0
% 85.70/11.30 % Current number of archived clauses : 3321
% 85.70/11.30 % Clause-clause subsumption calls (NU) : 2082950
% 85.70/11.30 % Rec. Clause-clause subsumption calls : 109101
% 85.70/11.30 % Non-unit clause-clause subsumptions : 7880
% 85.70/11.30 % Unit Clause-clause subsumption calls : 85
% 85.70/11.30 % Rewrite failures with RHS unbound : 0
% 85.70/11.30 % BW rewrite match attempts : 2
% 85.70/11.30 % BW rewrite match successes : 2
% 85.70/11.30 % Condensation attempts : 0
% 85.70/11.30 % Condensation successes : 0
% 85.70/11.30 % Termbank termtop insertions : 21609148
% 85.70/11.30 % Search garbage collected termcells : 934
% 85.70/11.30
% 85.70/11.30 % -------------------------------------------------
% 85.70/11.30 % User time : 10.432 s
% 85.70/11.30 % System time : 0.270 s
% 85.70/11.30 % Total time : 10.702 s
% 85.70/11.30 % Maximum resident set size: 3668 pages
% 85.70/11.30
% 85.70/11.30 % -------------------------------------------------
% 85.70/11.30 % User time : 10.434 s
% 85.70/11.30 % System time : 0.276 s
% 85.70/11.30 % Total time : 10.710 s
% 85.70/11.30 % Maximum resident set size: 4608 pages
% 85.70/11.30 % E exiting
%------------------------------------------------------------------------------