%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRA002+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n027.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 07:16:06 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 11 unt; 0 def)
% Number of atoms : 340 ( 82 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 431 ( 173 ~; 186 |; 52 &)
% ( 3 <=>; 15 =>; 1 <=; 1 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-4 aty)
% Number of variables : 225 ( 35 sgn 96 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',maximal_path_length) ).
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(back_edge,lemma,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4) )
=> ? [X9] :
( edge(X9)
& tail_of(X9) = head_of(X8)
& head_of(X9) = tail_of(X7) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',back_edge) ).
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_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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sequential_pairs_and_triangles) ).
fof(precedes_properties,axiom,
! [X4,X2,X3] :
( path(X2,X3,X4)
=> ! [X7,X8] :
( precedes(X7,X8,X4)
=> ( on_path(X7,X4)
& on_path(X8,X4)
& ( sequential(X7,X8)
<~> ? [X9] :
( sequential(X7,X9)
& precedes(X9,X8,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',triangle_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(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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',graph_has_them_all) ).
fof(c_0_12,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_13,plain,
! [X11,X12,X13,X14,X11,X12,X13] :
( ( path(X11,X12,X13)
| ~ shortest_path(X11,X12,X13) )
& ( X11 != X12
| ~ shortest_path(X11,X12,X13) )
& ( ~ path(X11,X12,X14)
| less_or_equal(length_of(X13),length_of(X14))
| ~ shortest_path(X11,X12,X13) )
& ( path(X11,X12,esk4_3(X11,X12,X13))
| ~ path(X11,X12,X13)
| X11 = X12
| shortest_path(X11,X12,X13) )
& ( ~ less_or_equal(length_of(X13),length_of(esk4_3(X11,X12,X13)))
| ~ path(X11,X12,X13)
| X11 = X12
| shortest_path(X11,X12,X13) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[shortest_path_defn])])])])])])]) ).
fof(c_0_14,negated_conjecture,
( complete
& shortest_path(esk2_0,esk3_0,esk1_0)
& ~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
fof(c_0_15,lemma,
! [X10,X11,X12,X13,X14] :
( ( edge(esk7_4(X10,X11,X12,X13))
| ~ shortest_path(X10,X11,X14)
| ~ precedes(X12,X13,X14)
| ~ complete )
& ( tail_of(esk7_4(X10,X11,X12,X13)) = head_of(X13)
| ~ shortest_path(X10,X11,X14)
| ~ precedes(X12,X13,X14)
| ~ complete )
& ( head_of(esk7_4(X10,X11,X12,X13)) = tail_of(X12)
| ~ shortest_path(X10,X11,X14)
| ~ precedes(X12,X13,X14)
| ~ complete ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[back_edge])])])])])])]) ).
fof(c_0_16,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( ~ sequential(X13,X14)
| ~ on_path(X13,X10)
| ~ on_path(X14,X10)
| precedes(X13,X14,X10)
| ~ path(X11,X12,X10) )
& ( ~ sequential(X13,X15)
| ~ precedes(X15,X14,X10)
| ~ on_path(X13,X10)
| ~ on_path(X14,X10)
| precedes(X13,X14,X10)
| ~ path(X11,X12,X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[precedes_defn])])])])])])]) ).
cnf(c_0_17,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
shortest_path(esk2_0,esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X10,X11,X12,X15] :
( ( on_path(esk5_1(X10),X10)
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) )
& ( on_path(esk6_1(X10),X10)
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) )
& ( sequential(esk5_1(X10),esk6_1(X10))
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) )
& ( ~ triangle(esk5_1(X10),esk6_1(X10),X15)
| ~ path(X11,X12,X10)
| number_of_in(sequential_pairs,X10) = number_of_in(triangles,X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_pairs_and_triangles])])])])])])]) ).
cnf(c_0_20,lemma,
( head_of(esk7_4(X4,X5,X1,X2)) = tail_of(X1)
| ~ complete
| ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,lemma,
( edge(esk7_4(X4,X5,X1,X2))
| ~ complete
| ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( on_path(X13,X10)
| ~ precedes(X13,X14,X10)
| ~ path(X11,X12,X10) )
& ( on_path(X14,X10)
| ~ precedes(X13,X14,X10)
| ~ path(X11,X12,X10) )
& ( ~ sequential(X13,X14)
| ~ sequential(X13,X15)
| ~ precedes(X15,X14,X10)
| ~ precedes(X13,X14,X10)
| ~ path(X11,X12,X10) )
& ( sequential(X13,esk9_3(X10,X13,X14))
| sequential(X13,X14)
| ~ precedes(X13,X14,X10)
| ~ path(X11,X12,X10) )
& ( precedes(esk9_3(X10,X13,X14),X14,X10)
| sequential(X13,X14)
| ~ precedes(X13,X14,X10)
| ~ path(X11,X12,X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[precedes_properties])])])])])])])]) ).
cnf(c_0_24,plain,
( precedes(X4,X5,X3)
| ~ path(X1,X2,X3)
| ~ on_path(X5,X3)
| ~ on_path(X4,X3)
| ~ sequential(X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
path(esk2_0,esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk6_1(X1),X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X10,X11,X12,X10,X11,X12] :
( ( edge(X10)
| ~ triangle(X10,X11,X12) )
& ( edge(X11)
| ~ triangle(X10,X11,X12) )
& ( edge(X12)
| ~ triangle(X10,X11,X12) )
& ( sequential(X10,X11)
| ~ triangle(X10,X11,X12) )
& ( sequential(X11,X12)
| ~ triangle(X10,X11,X12) )
& ( sequential(X12,X10)
| ~ triangle(X10,X11,X12) )
& ( ~ edge(X10)
| ~ edge(X11)
| ~ edge(X12)
| ~ sequential(X10,X11)
| ~ sequential(X11,X12)
| ~ sequential(X12,X10)
| triangle(X10,X11,X12) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[triangle_defn])])])])]) ).
fof(c_0_28,plain,
! [X9,X10,X9,X10] :
( ( edge(X9)
| ~ sequential(X9,X10) )
& ( edge(X10)
| ~ sequential(X9,X10) )
& ( X9 != X10
| ~ sequential(X9,X10) )
& ( head_of(X9) = tail_of(X10)
| ~ sequential(X9,X10) )
& ( ~ edge(X9)
| ~ edge(X10)
| X9 = X10
| head_of(X9) != tail_of(X10)
| sequential(X9,X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_defn])])])])]) ).
cnf(c_0_29,lemma,
( head_of(esk7_4(X1,X2,X3,X4)) = tail_of(X3)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_30,lemma,
( edge(esk7_4(X1,X2,X3,X4))
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_21])]) ).
cnf(c_0_31,plain,
( sequential(X4,X5)
| sequential(X4,esk9_3(X3,X4,X5))
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,lemma,
( tail_of(esk7_4(X4,X5,X1,X2)) = head_of(X2)
| ~ complete
| ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_33,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( tail_of(X15) != tail_of(X12)
| head_of(X15) != head_of(X13)
| ~ shortest_path(X10,X11,X14)
| ~ precedes(X12,X13,X14) )
& ( ~ precedes(X13,X12,X14)
| ~ shortest_path(X10,X11,X14)
| ~ precedes(X12,X13,X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[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_34,negated_conjecture,
( precedes(X1,X2,esk1_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk1_0)
| ~ on_path(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_35,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| on_path(esk6_1(esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_36,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| on_path(esk5_1(X1),X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| sequential(esk5_1(X1),esk6_1(X1))
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_38,plain,
( triangle(X1,X2,X3)
| ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ~ edge(X3)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,plain,
( sequential(X1,X2)
| X1 = X2
| head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,negated_conjecture,
( head_of(esk7_4(esk2_0,esk3_0,X1,X2)) = tail_of(X1)
| ~ precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_42,negated_conjecture,
( edge(esk7_4(esk2_0,esk3_0,X1,X2))
| ~ precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_43,negated_conjecture,
( sequential(X1,esk9_3(esk1_0,X1,X2))
| sequential(X1,X2)
| ~ precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_44,lemma,
( tail_of(esk7_4(X1,X2,X3,X4)) = head_of(X4)
| ~ shortest_path(X1,X2,X5)
| ~ precedes(X3,X4,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_21])]) ).
cnf(c_0_45,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| head_of(X6) != head_of(X2)
| tail_of(X6) != tail_of(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| precedes(X1,esk6_1(esk1_0),esk1_0)
| ~ sequential(X1,esk6_1(esk1_0))
| ~ on_path(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_47,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| on_path(esk5_1(esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_48,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| sequential(esk5_1(esk1_0),esk6_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_49,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1)
| ~ triangle(esk5_1(X1),esk6_1(X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_50,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_38,c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_51,negated_conjecture,
( esk7_4(esk2_0,esk3_0,X1,X2) = X3
| sequential(esk7_4(esk2_0,esk3_0,X1,X2),X3)
| tail_of(X3) != tail_of(X1)
| ~ precedes(X1,X2,esk1_0)
| ~ edge(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_52,negated_conjecture,
( edge(X1)
| ~ precedes(X1,X2,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_39]) ).
cnf(c_0_53,negated_conjecture,
( tail_of(esk7_4(esk2_0,esk3_0,X1,X2)) = head_of(X2)
| ~ precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_18]) ).
cnf(c_0_54,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X3) != tail_of(X2)
| ~ precedes(X3,X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_55,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| precedes(esk5_1(esk1_0),esk6_1(esk1_0),esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_56,plain,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ sequential(X2,esk5_1(X1))
| ~ sequential(esk6_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_37]) ).
cnf(c_0_57,negated_conjecture,
( esk7_4(esk2_0,esk3_0,X1,X2) = X1
| sequential(esk7_4(esk2_0,esk3_0,X1,X2),X1)
| ~ precedes(X1,X2,esk1_0) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_51]),c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( X1 = esk7_4(esk2_0,esk3_0,X2,X3)
| sequential(X1,esk7_4(esk2_0,esk3_0,X2,X3))
| head_of(X3) != head_of(X1)
| ~ precedes(X2,X3,esk1_0)
| ~ edge(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_53]),c_0_42]) ).
cnf(c_0_59,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(esk6_1(esk1_0)) != head_of(X1)
| tail_of(esk5_1(esk1_0)) != tail_of(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( esk7_4(esk2_0,esk3_0,esk5_1(X1),X2) = esk5_1(X1)
| number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ precedes(esk5_1(X1),X2,esk1_0)
| ~ sequential(esk6_1(X1),esk7_4(esk2_0,esk3_0,esk5_1(X1),X2))
| ~ path(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,negated_conjecture,
( esk7_4(esk2_0,esk3_0,X1,X2) = X2
| sequential(X2,esk7_4(esk2_0,esk3_0,X1,X2))
| ~ precedes(X1,X2,esk1_0)
| ~ edge(X2) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_62,plain,
( edge(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_63,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| tail_of(esk7_4(esk2_0,esk3_0,X1,X2)) != tail_of(esk5_1(esk1_0))
| head_of(esk6_1(esk1_0)) != tail_of(X1)
| ~ precedes(X1,X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_41]) ).
fof(c_0_64,plain,
! [X2] :
( ~ edge(X2)
| head_of(X2) != tail_of(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[no_loops])]) ).
cnf(c_0_65,negated_conjecture,
( esk7_4(esk2_0,esk3_0,esk5_1(X1),esk6_1(X1)) = esk6_1(X1)
| esk7_4(esk2_0,esk3_0,esk5_1(X1),esk6_1(X1)) = esk5_1(X1)
| number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ precedes(esk5_1(X1),esk6_1(X1),esk1_0)
| ~ path(X2,X3,X1)
| ~ edge(esk6_1(X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| edge(esk6_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_62,c_0_48]) ).
cnf(c_0_67,negated_conjecture,
( number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0)
| head_of(X1) != tail_of(esk5_1(esk1_0))
| head_of(esk6_1(esk1_0)) != tail_of(X2)
| ~ precedes(X2,X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_53]) ).
fof(c_0_68,plain,
! [X5,X6,X7] :
( ~ path(X5,X6,X7)
| number_of_in(sequential_pairs,X7) = minus(length_of(X7),n1) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[path_length_sequential_pairs])]) ).
cnf(c_0_69,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( esk7_4(esk2_0,esk3_0,esk5_1(esk1_0),esk6_1(esk1_0)) = esk5_1(esk1_0)
| esk7_4(esk2_0,esk3_0,esk5_1(esk1_0),esk6_1(esk1_0)) = esk6_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(spm,[status(thm)],[c_0_65,c_0_25]),c_0_66]),c_0_55]) ).
cnf(c_0_71,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)) ),
inference(spm,[status(thm)],[c_0_67,c_0_55]) ).
cnf(c_0_72,plain,
( number_of_in(sequential_pairs,X1) = minus(length_of(X1),n1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
fof(c_0_73,plain,
! [X13,X14] : less_or_equal(number_of_in(X13,X14),number_of_in(X13,graph)),
inference(variable_rename,[status(thm)],[graph_has_them_all]) ).
cnf(c_0_74,negated_conjecture,
( tail_of(esk7_4(esk2_0,esk3_0,X1,X2)) != tail_of(X1)
| ~ precedes(X1,X2,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_41]),c_0_42]) ).
cnf(c_0_75,negated_conjecture,
( esk7_4(esk2_0,esk3_0,esk5_1(esk1_0),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(spm,[status(thm)],[c_0_41,c_0_70]),c_0_55]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
~ less_or_equal(minus(length_of(esk1_0),n1),number_of_in(triangles,graph)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_77,negated_conjecture,
minus(length_of(esk1_0),n1) = number_of_in(sequential_pairs,esk1_0),
inference(spm,[status(thm)],[c_0_72,c_0_25]) ).
cnf(c_0_78,plain,
less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph)),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,negated_conjecture,
number_of_in(triangles,esk1_0) = number_of_in(sequential_pairs,esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_55]) ).
cnf(c_0_80,negated_conjecture,
~ less_or_equal(number_of_in(sequential_pairs,esk1_0),number_of_in(triangles,graph)),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRA002+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n027.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 : Tue May 31 01:38:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.019 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 82
% 0.22/1.41 # Proof object clause steps : 57
% 0.22/1.41 # Proof object formula steps : 25
% 0.22/1.41 # Proof object conjectures : 37
% 0.22/1.41 # Proof object clause conjectures : 34
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 21
% 0.22/1.41 # Proof object initial formulas used : 12
% 0.22/1.41 # Proof object generating inferences : 31
% 0.22/1.41 # Proof object simplifying inferences : 23
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 19
% 0.22/1.41 # Removed by relevancy pruning/SinE : 5
% 0.22/1.41 # Initial clauses : 47
% 0.22/1.41 # Removed in clause preprocessing : 1
% 0.22/1.41 # Initial clauses in saturation : 46
% 0.22/1.41 # Processed clauses : 1647
% 0.22/1.41 # ...of these trivial : 4
% 0.22/1.41 # ...subsumed : 731
% 0.22/1.41 # ...remaining for further processing : 912
% 0.22/1.41 # Other redundant clauses eliminated : 10
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 116
% 0.22/1.41 # Backward-rewritten : 480
% 0.22/1.41 # Generated clauses : 14340
% 0.22/1.41 # ...of the previous two non-trivial : 13602
% 0.22/1.41 # Contextual simplify-reflections : 1912
% 0.22/1.41 # Paramodulations : 14234
% 0.22/1.41 # Factorizations : 45
% 0.22/1.41 # Equation resolutions : 61
% 0.22/1.41 # Current number of processed clauses : 314
% 0.22/1.41 # Positive orientable unit clauses : 6
% 0.22/1.41 # Positive unorientable unit clauses: 0
% 0.22/1.41 # Negative unit clauses : 3
% 0.22/1.41 # Non-unit-clauses : 305
% 0.22/1.41 # Current number of unprocessed clauses: 502
% 0.22/1.41 # ...number of literals in the above : 5412
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 596
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 307673
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 35589
% 0.22/1.41 # Non-unit clause-clause subsumptions : 2752
% 0.22/1.41 # Unit Clause-clause subsumption calls : 125
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 2
% 0.22/1.41 # BW rewrite match successes : 2
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 547324
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.699 s
% 0.22/1.41 # System time : 0.007 s
% 0.22/1.41 # Total time : 0.706 s
% 0.22/1.41 # Maximum resident set size: 10460 pages
% 0.22/23.41 eprover: CPU time limit exceeded, terminating
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------