TSTP Solution File: GRA009+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRA009+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n032.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 07:16:08 EDT 2022
% Result : Theorem 0.17s 2.36s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 96 ( 17 unt; 0 def)
% Number of atoms : 432 ( 135 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 556 ( 220 ~; 253 |; 63 &)
% ( 3 <=>; 15 =>; 1 <=; 1 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 197 ( 23 sgn 83 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complete_means_path_means_stuff_means_triangles,conjecture,
( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',complete_means_path_means_stuff_means_triangles) ).
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(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(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(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(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',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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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(c_0_11,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( shortest_path(X2,X3,X4)
=> ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ) ),
inference(assume_negation,[status(cth)],[complete_means_path_means_stuff_means_triangles]) ).
fof(c_0_12,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,esk6_3(X11,X12,X13))
| ~ path(X11,X12,X13)
| X11 = X12
| shortest_path(X11,X12,X13) )
& ( ~ less_or_equal(length_of(X13),length_of(esk6_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_13,negated_conjecture,
! [X15] :
( complete
& shortest_path(esk10_0,esk11_0,esk9_0)
& on_path(esk12_0,esk9_0)
& on_path(esk13_0,esk9_0)
& sequential(esk12_0,esk13_0)
& ~ triangle(esk12_0,esk13_0,X15) ),
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)],[c_0_11])])])])])]) ).
fof(c_0_14,plain,
! [X7,X8,X9,X10] :
( ( vertex(X10)
| ~ path(X7,X8,X9)
| ~ in_path(X10,X9) )
& ( on_path(esk4_4(X7,X8,X9,X10),X9)
| ~ path(X7,X8,X9)
| ~ in_path(X10,X9) )
& ( X10 = head_of(esk4_4(X7,X8,X9,X10))
| X10 = tail_of(esk4_4(X7,X8,X9,X10))
| ~ path(X7,X8,X9)
| ~ in_path(X10,X9) ) ),
inference(distribute,[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)],[in_path_properties])])])])])]) ).
cnf(c_0_15,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
shortest_path(esk10_0,esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X5,X6,X7,X8] :
( ( edge(X8)
| ~ path(X5,X6,X7)
| ~ on_path(X8,X7) )
& ( in_path(head_of(X8),X7)
| ~ path(X5,X6,X7)
| ~ on_path(X8,X7) )
& ( in_path(tail_of(X8),X7)
| ~ path(X5,X6,X7)
| ~ on_path(X8,X7) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[on_path_properties])])]) ).
fof(c_0_18,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])])])])])])]) ).
fof(c_0_19,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])])])])])])]) ).
fof(c_0_20,plain,
! [X4,X5] :
( ( edge(esk1_2(X4,X5))
| ~ vertex(X4)
| ~ vertex(X5)
| X4 = X5
| ~ complete )
& ( X4 != head_of(esk1_2(X4,X5))
| X5 != tail_of(esk1_2(X4,X5))
| X5 != head_of(esk1_2(X4,X5))
| X4 != tail_of(esk1_2(X4,X5))
| ~ vertex(X4)
| ~ vertex(X5)
| X4 = X5
| ~ complete )
& ( X5 = head_of(esk1_2(X4,X5))
| X4 = head_of(esk1_2(X4,X5))
| ~ vertex(X4)
| ~ vertex(X5)
| X4 = X5
| ~ complete )
& ( X4 = tail_of(esk1_2(X4,X5))
| X4 = head_of(esk1_2(X4,X5))
| ~ vertex(X4)
| ~ vertex(X5)
| X4 = X5
| ~ complete )
& ( X5 = head_of(esk1_2(X4,X5))
| X5 = tail_of(esk1_2(X4,X5))
| ~ vertex(X4)
| ~ vertex(X5)
| X4 = X5
| ~ complete )
& ( X4 = tail_of(esk1_2(X4,X5))
| X5 = tail_of(esk1_2(X4,X5))
| ~ vertex(X4)
| ~ vertex(X5)
| X4 = X5
| ~ 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)],[inference(fof_simplification,[status(thm)],[complete_properties])])])])])])])]) ).
cnf(c_0_21,plain,
( vertex(X1)
| ~ in_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
path(esk10_0,esk11_0,esk9_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
( in_path(tail_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,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_18]) ).
cnf(c_0_25,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_19]) ).
cnf(c_0_26,plain,
( X1 = X2
| X2 = tail_of(esk1_2(X1,X2))
| X1 = tail_of(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( in_path(tail_of(X1),esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_30,plain,
( in_path(head_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_31,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_32,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_33,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X3) != tail_of(X2)
| ~ precedes(X3,X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_34,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_25,c_0_22]) ).
cnf(c_0_35,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_26,c_0_27])]) ).
cnf(c_0_36,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( in_path(head_of(X1),esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_38,plain,
( X1 = X2
| X1 = head_of(esk1_2(X1,X2))
| X2 = head_of(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_42,plain,
( edge(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,negated_conjecture,
sequential(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_44,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X3) != tail_of(X2)
| ~ sequential(X3,X1)
| ~ on_path(X1,esk9_0)
| ~ on_path(X3,esk9_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_45,negated_conjecture,
on_path(esk13_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_46,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
| tail_of(esk1_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ on_path(X2,esk9_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_47,negated_conjecture,
on_path(esk12_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_48,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_49,plain,
( head_of(esk1_2(X1,X2)) = X1
| head_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_27])]) ).
cnf(c_0_50,negated_conjecture,
~ triangle(esk12_0,esk13_0,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_51,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_39,c_0_40]),c_0_40]),c_0_40]) ).
cnf(c_0_52,plain,
( sequential(X1,X2)
| X1 = X2
| head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_53,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_27])]) ).
cnf(c_0_54,negated_conjecture,
edge(esk13_0),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_55,plain,
( X1 = X2
| X1 = head_of(esk1_2(X1,X2))
| X1 = tail_of(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_56,negated_conjecture,
( head_of(esk13_0) != head_of(X1)
| tail_of(X2) != tail_of(X1)
| ~ sequential(X2,esk13_0)
| ~ on_path(X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_57,negated_conjecture,
( tail_of(esk1_2(X1,tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk1_2(X1,tail_of(esk12_0))) = X1
| X1 = tail_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_58,negated_conjecture,
vertex(head_of(esk13_0)),
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_59,negated_conjecture,
( head_of(esk1_2(X1,tail_of(X2))) = tail_of(X2)
| head_of(esk1_2(X1,tail_of(X2))) = X1
| X1 = tail_of(X2)
| ~ on_path(X2,esk9_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_36]) ).
cnf(c_0_60,negated_conjecture,
( ~ sequential(X1,esk12_0)
| ~ sequential(esk13_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_43])]) ).
cnf(c_0_61,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_52,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_40,c_0_43]) ).
cnf(c_0_63,negated_conjecture,
( esk13_0 = X1
| sequential(esk13_0,X1)
| tail_of(X1) != head_of(esk13_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_54]) ).
cnf(c_0_64,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_55,c_0_27])]) ).
cnf(c_0_65,plain,
( X1 = X2
| X2 = tail_of(esk1_2(X1,X2))
| X2 = head_of(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_66,negated_conjecture,
( head_of(esk13_0) != head_of(X1)
| tail_of(esk12_0) != tail_of(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_47]),c_0_43])]) ).
cnf(c_0_67,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( head_of(esk1_2(X1,tail_of(esk12_0))) = tail_of(esk12_0)
| head_of(esk1_2(X1,tail_of(esk12_0))) = X1
| X1 = tail_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_47]) ).
cnf(c_0_69,negated_conjecture,
( esk1_2(X1,X2) = esk12_0
| X1 = X2
| head_of(esk1_2(X1,X2)) != tail_of(esk12_0)
| ~ sequential(esk13_0,esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_70,negated_conjecture,
( head_of(esk1_2(X1,X2)) = X1
| esk1_2(X1,X2) = esk13_0
| X1 = X2
| sequential(esk13_0,esk1_2(X1,X2))
| X1 != head_of(esk13_0)
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_53]) ).
cnf(c_0_71,plain,
( tail_of(esk1_2(X1,X2)) = X2
| head_of(esk1_2(X1,X2)) = X2
| X1 = X2
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_27])]) ).
cnf(c_0_72,negated_conjecture,
( tail_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| tail_of(esk12_0) = head_of(esk13_0)
| head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) != head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = head_of(esk13_0)
| head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk12_0) = head_of(esk13_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_58]) ).
cnf(c_0_74,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_75,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_76,negated_conjecture,
( head_of(esk1_2(X1,X2)) = X1
| esk1_2(X1,X2) = esk13_0
| esk1_2(X1,X2) = esk12_0
| X1 = X2
| head_of(esk1_2(X1,X2)) != tail_of(esk12_0)
| X1 != head_of(esk13_0)
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( head_of(esk1_2(head_of(esk13_0),tail_of(esk12_0))) = tail_of(esk12_0)
| tail_of(esk12_0) = head_of(esk13_0)
| ~ vertex(tail_of(esk12_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_58])]),c_0_73]) ).
cnf(c_0_78,negated_conjecture,
tail_of(esk13_0) = head_of(esk12_0),
inference(spm,[status(thm)],[c_0_74,c_0_43]) ).
fof(c_0_79,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_80,negated_conjecture,
( ~ precedes(X1,X2,esk9_0)
| ~ precedes(X2,X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_16]) ).
cnf(c_0_81,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
| esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk13_0
| tail_of(esk12_0) = head_of(esk13_0)
| ~ vertex(tail_of(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_58])]) ).
cnf(c_0_82,negated_conjecture,
tail_of(esk12_0) != head_of(esk12_0),
inference(spm,[status(thm)],[c_0_66,c_0_78]) ).
cnf(c_0_83,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( ~ precedes(X1,X2,esk9_0)
| ~ sequential(X2,X1)
| ~ on_path(X1,esk9_0)
| ~ on_path(X2,esk9_0) ),
inference(spm,[status(thm)],[c_0_80,c_0_34]) ).
cnf(c_0_85,negated_conjecture,
( esk1_2(head_of(esk13_0),tail_of(esk12_0)) = esk12_0
| tail_of(esk12_0) = head_of(esk13_0)
| ~ vertex(tail_of(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_81]),c_0_78]),c_0_58])]),c_0_82]) ).
cnf(c_0_86,negated_conjecture,
head_of(esk13_0) != head_of(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_78]),c_0_54])]) ).
fof(c_0_87,plain,
! [X2] :
( ( vertex(head_of(X2))
| ~ edge(X2) )
& ( vertex(tail_of(X2))
| ~ edge(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[edge_ends_are_vertices])])]) ).
cnf(c_0_88,negated_conjecture,
( ~ sequential(X1,X2)
| ~ sequential(X2,X1)
| ~ on_path(X2,esk9_0)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_34]) ).
cnf(c_0_89,negated_conjecture,
( tail_of(esk12_0) = head_of(esk13_0)
| ~ vertex(tail_of(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_85]),c_0_58])]),c_0_86]) ).
cnf(c_0_90,plain,
( vertex(tail_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( ~ sequential(X1,esk13_0)
| ~ sequential(esk13_0,X1)
| ~ on_path(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_45]) ).
cnf(c_0_92,negated_conjecture,
tail_of(esk12_0) = head_of(esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_62])]) ).
cnf(c_0_93,negated_conjecture,
~ sequential(esk13_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_47]),c_0_43])]) ).
cnf(c_0_94,negated_conjecture,
esk13_0 = esk12_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_92]),c_0_62])]),c_0_93]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRA009+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.05/0.10 % Command : run_ET %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon May 30 22:30:58 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.17/2.36 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.17/2.36 # Preprocessing time : 0.013 s
% 0.17/2.36
% 0.17/2.36 # Proof found!
% 0.17/2.36 # SZS status Theorem
% 0.17/2.36 # SZS output start CNFRefutation
% See solution above
% 0.17/2.36 # Proof object total steps : 96
% 0.17/2.36 # Proof object clause steps : 73
% 0.17/2.36 # Proof object formula steps : 23
% 0.17/2.36 # Proof object conjectures : 50
% 0.17/2.36 # Proof object clause conjectures : 47
% 0.17/2.36 # Proof object formula conjectures : 3
% 0.17/2.36 # Proof object initial clauses used : 25
% 0.17/2.36 # Proof object initial formulas used : 11
% 0.17/2.36 # Proof object generating inferences : 41
% 0.17/2.36 # Proof object simplifying inferences : 43
% 0.17/2.36 # Training examples: 0 positive, 0 negative
% 0.17/2.36 # Parsed axioms : 18
% 0.17/2.36 # Removed by relevancy pruning/SinE : 0
% 0.17/2.36 # Initial clauses : 65
% 0.17/2.36 # Removed in clause preprocessing : 1
% 0.17/2.36 # Initial clauses in saturation : 64
% 0.17/2.36 # Processed clauses : 6095
% 0.17/2.36 # ...of these trivial : 414
% 0.17/2.36 # ...subsumed : 3020
% 0.17/2.36 # ...remaining for further processing : 2661
% 0.17/2.36 # Other redundant clauses eliminated : 102
% 0.17/2.36 # Clauses deleted for lack of memory : 0
% 0.17/2.36 # Backward-subsumed : 249
% 0.17/2.36 # Backward-rewritten : 1448
% 0.17/2.36 # Generated clauses : 38546
% 0.17/2.36 # ...of the previous two non-trivial : 35768
% 0.17/2.36 # Contextual simplify-reflections : 6455
% 0.17/2.36 # Paramodulations : 38133
% 0.17/2.36 # Factorizations : 145
% 0.17/2.36 # Equation resolutions : 268
% 0.17/2.36 # Current number of processed clauses : 962
% 0.17/2.36 # Positive orientable unit clauses : 14
% 0.17/2.36 # Positive unorientable unit clauses: 0
% 0.17/2.36 # Negative unit clauses : 2
% 0.17/2.36 # Non-unit-clauses : 946
% 0.17/2.36 # Current number of unprocessed clauses: 9212
% 0.17/2.36 # ...number of literals in the above : 76440
% 0.17/2.36 # Current number of archived formulas : 0
% 0.17/2.36 # Current number of archived clauses : 1697
% 0.17/2.36 # Clause-clause subsumption calls (NU) : 1290944
% 0.17/2.36 # Rec. Clause-clause subsumption calls : 90175
% 0.17/2.36 # Non-unit clause-clause subsumptions : 9087
% 0.17/2.36 # Unit Clause-clause subsumption calls : 989
% 0.17/2.36 # Rewrite failures with RHS unbound : 0
% 0.17/2.36 # BW rewrite match attempts : 5
% 0.17/2.36 # BW rewrite match successes : 4
% 0.17/2.36 # Condensation attempts : 0
% 0.17/2.36 # Condensation successes : 0
% 0.17/2.36 # Termbank termtop insertions : 1185705
% 0.17/2.36
% 0.17/2.36 # -------------------------------------------------
% 0.17/2.36 # User time : 1.217 s
% 0.17/2.36 # System time : 0.026 s
% 0.17/2.36 # Total time : 1.243 s
% 0.17/2.36 # Maximum resident set size: 32580 pages
% 0.17/23.34 eprover: CPU time limit exceeded, terminating
% 0.17/23.35 eprover: CPU time limit exceeded, terminating
% 0.17/23.35 eprover: CPU time limit exceeded, terminating
% 0.17/23.36 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.36 eprover: No such file or directory
% 0.17/23.36 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.36 eprover: No such file or directory
% 0.17/23.36 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.36 eprover: No such file or directory
% 0.17/23.37 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37 eprover: No such file or directory
% 0.17/23.37 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.37 eprover: No such file or directory
% 0.17/23.37 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37 eprover: No such file or directory
% 0.17/23.37 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37 eprover: No such file or directory
% 0.17/23.37 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.37 eprover: No such file or directory
% 0.17/23.37 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37 eprover: No such file or directory
% 0.17/23.37 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.37 eprover: No such file or directory
% 0.17/23.38 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38 eprover: No such file or directory
% 0.17/23.38 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.38 eprover: No such file or directory
% 0.17/23.38 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38 eprover: No such file or directory
% 0.17/23.38 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.38 eprover: No such file or directory
% 0.17/23.38 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38 eprover: No such file or directory
% 0.17/23.38 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.38 eprover: No such file or directory
% 0.17/23.38 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.38 eprover: No such file or directory
% 0.17/23.39 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39 eprover: No such file or directory
% 0.17/23.39 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39 eprover: No such file or directory
% 0.17/23.39 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.39 eprover: No such file or directory
% 0.17/23.39 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39 eprover: No such file or directory
% 0.17/23.39 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.peprover:
% 0.17/23.39 Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39 eprover: No such file or directory
% 0.17/23.39 eprover: No such file or directory
% 0.17/23.39 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.39 eprover: No such file or directory
% 0.17/23.40 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.40 eprover: No such file or directory
% 0.17/23.40 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40 eprover: No such file or directory
% 0.17/23.40 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40 eprover: No such file or directory
% 0.17/23.40 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.40 eprover: No such file or directory
% 0.17/23.40 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40 eprover: No such file or directory
% 0.17/23.40 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.40 eprover: No such file or directory
% 0.17/23.40 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.40 eprover: No such file or directory
% 0.17/23.41 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.17/23.41 eprover: No such file or directory
% 0.17/23.41 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.17/23.41 eprover: No such file or directory
%------------------------------------------------------------------------------