TSTP Solution File: GRA008+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 0.24s 4.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 100 ( 20 unt; 0 def)
% Number of atoms : 443 ( 128 equ)
% Maximal formula atoms : 37 ( 4 avg)
% Number of connectives : 562 ( 219 ~; 253 |; 69 &)
% ( 3 <=>; 15 =>; 1 <=; 2 <~>)
% 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 : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 212 ( 33 sgn 94 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sequential_is_triangle,conjecture,
( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',sequential_is_triangle) ).
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(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(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(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(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(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(no_loops,axiom,
! [X1] :
( edge(X1)
=> head_of(X1) != tail_of(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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(c_0_12,negated_conjecture,
~ ( complete
=> ! [X2,X3,X7,X8,X4] :
( ( shortest_path(X2,X3,X4)
& precedes(X7,X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) ),
inference(assume_negation,[status(cth)],[sequential_is_triangle]) ).
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,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_14,negated_conjecture,
! [X15] :
( complete
& shortest_path(esk9_0,esk10_0,esk13_0)
& precedes(esk11_0,esk12_0,esk13_0)
& sequential(esk11_0,esk12_0)
& ~ triangle(esk11_0,esk12_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_12])])])])])]) ).
fof(c_0_15,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_16,plain,
( path(X1,X2,X3)
| ~ shortest_path(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
shortest_path(esk9_0,esk10_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,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_19,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,esk5_3(X10,X13,X14))
| sequential(X13,X14)
| ~ precedes(X13,X14,X10)
| ~ path(X11,X12,X10) )
& ( precedes(esk5_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_20,plain,
( vertex(X1)
| ~ in_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
path(esk9_0,esk10_0,esk13_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in_path(head_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( on_path(X5,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
precedes(esk11_0,esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_25,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_26,negated_conjecture,
( vertex(X1)
| ~ in_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( in_path(head_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( on_path(esk12_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( in_path(tail_of(X1),X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
( on_path(X4,X3)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_31,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_32,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_25]) ).
cnf(c_0_33,negated_conjecture,
complete,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( vertex(head_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
on_path(esk12_0,esk13_0),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_36,negated_conjecture,
( in_path(tail_of(X1),esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_37,negated_conjecture,
( on_path(esk11_0,esk13_0)
| ~ path(X1,X2,esk13_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_38,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_31]) ).
cnf(c_0_39,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_32,c_0_33])]) ).
cnf(c_0_40,negated_conjecture,
vertex(head_of(esk12_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( vertex(tail_of(X1))
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
on_path(esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_37,c_0_21]) ).
fof(c_0_43,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_44,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_45,negated_conjecture,
( head_of(X1) != head_of(X2)
| tail_of(X3) != tail_of(X2)
| ~ precedes(X3,X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_17]) ).
cnf(c_0_46,negated_conjecture,
( tail_of(esk1_2(X1,head_of(esk12_0))) = head_of(esk12_0)
| tail_of(esk1_2(X1,head_of(esk12_0))) = X1
| X1 = head_of(esk12_0)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
vertex(tail_of(esk11_0)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,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_43]) ).
cnf(c_0_49,plain,
( edge(X1)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ complete
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_51,plain,
( edge(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
sequential(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_53,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_25]) ).
fof(c_0_54,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])])]) ).
fof(c_0_55,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_56,negated_conjecture,
( head_of(esk12_0) != head_of(X1)
| tail_of(esk11_0) != tail_of(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_24]) ).
cnf(c_0_57,negated_conjecture,
( tail_of(esk1_2(tail_of(esk11_0),head_of(esk12_0))) = tail_of(esk11_0)
| tail_of(esk1_2(tail_of(esk11_0),head_of(esk12_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_58,negated_conjecture,
~ triangle(esk11_0,esk12_0,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_59,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_48,c_0_49]),c_0_49]),c_0_49]) ).
cnf(c_0_60,plain,
( sequential(X1,X2)
| X1 = X2
| head_of(X1) != tail_of(X2)
| ~ edge(X2)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_61,plain,
( X1 = X2
| edge(esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_33])]) ).
cnf(c_0_62,negated_conjecture,
edge(esk12_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,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_25]) ).
cnf(c_0_64,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_53,c_0_33])]) ).
cnf(c_0_65,plain,
( vertex(head_of(X1))
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
( head_of(X1) != tail_of(X1)
| ~ edge(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_67,negated_conjecture,
( tail_of(esk1_2(tail_of(esk11_0),head_of(esk12_0))) = head_of(esk12_0)
| tail_of(esk11_0) = head_of(esk12_0)
| head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0))) != head_of(esk12_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_68,negated_conjecture,
( ~ sequential(X1,esk11_0)
| ~ sequential(esk12_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_52])]) ).
cnf(c_0_69,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_60,c_0_61]) ).
cnf(c_0_70,negated_conjecture,
edge(esk11_0),
inference(spm,[status(thm)],[c_0_49,c_0_52]) ).
cnf(c_0_71,negated_conjecture,
( esk12_0 = X1
| sequential(esk12_0,X1)
| tail_of(X1) != head_of(esk12_0)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_62]) ).
cnf(c_0_72,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_63,c_0_33])]) ).
cnf(c_0_73,plain,
( head_of(esk1_2(X1,head_of(X2))) = head_of(X2)
| head_of(esk1_2(X1,head_of(X2))) = X1
| X1 = head_of(X2)
| ~ vertex(X1)
| ~ edge(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0))) != head_of(esk12_0)
| ~ edge(esk1_2(tail_of(esk11_0),head_of(esk12_0))) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( esk1_2(X1,X2) = esk11_0
| X1 = X2
| head_of(esk1_2(X1,X2)) != tail_of(esk11_0)
| ~ sequential(esk12_0,esk1_2(X1,X2))
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_76,negated_conjecture,
( head_of(esk1_2(X1,X2)) = X2
| esk1_2(X1,X2) = esk12_0
| X1 = X2
| sequential(esk12_0,esk1_2(X1,X2))
| X2 != head_of(esk12_0)
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_61]) ).
cnf(c_0_77,negated_conjecture,
( head_of(esk1_2(tail_of(esk11_0),head_of(X1))) = tail_of(esk11_0)
| head_of(esk1_2(tail_of(esk11_0),head_of(X1))) = head_of(X1)
| tail_of(esk11_0) = head_of(X1)
| ~ edge(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_47]) ).
cnf(c_0_78,negated_conjecture,
( tail_of(esk11_0) = head_of(esk12_0)
| head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0))) != head_of(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_61]),c_0_40]),c_0_47])]) ).
cnf(c_0_79,plain,
( head_of(X1) = tail_of(X2)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_80,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_81,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_25]) ).
cnf(c_0_82,negated_conjecture,
( head_of(esk1_2(X1,X2)) = X2
| esk1_2(X1,X2) = esk12_0
| esk1_2(X1,X2) = esk11_0
| X1 = X2
| head_of(esk1_2(X1,X2)) != tail_of(esk11_0)
| X2 != head_of(esk12_0)
| ~ vertex(X2)
| ~ vertex(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0))) = tail_of(esk11_0)
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_62]),c_0_78]) ).
cnf(c_0_84,negated_conjecture,
tail_of(esk12_0) = head_of(esk11_0),
inference(spm,[status(thm)],[c_0_79,c_0_52]) ).
cnf(c_0_85,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_80]) ).
cnf(c_0_86,plain,
( ~ precedes(X1,X2,X3)
| ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_87,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_81,c_0_33])]) ).
cnf(c_0_88,negated_conjecture,
( esk1_2(tail_of(esk11_0),head_of(esk12_0)) = esk11_0
| esk1_2(tail_of(esk11_0),head_of(esk12_0)) = esk12_0
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_40]),c_0_47])]) ).
cnf(c_0_89,negated_conjecture,
tail_of(esk11_0) != head_of(esk11_0),
inference(spm,[status(thm)],[c_0_56,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( precedes(X1,X2,esk13_0)
| ~ sequential(X1,X2)
| ~ on_path(X2,esk13_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_85,c_0_21]) ).
cnf(c_0_91,negated_conjecture,
( ~ precedes(X1,X2,esk13_0)
| ~ precedes(X2,X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_86,c_0_17]) ).
cnf(c_0_92,negated_conjecture,
( esk1_2(tail_of(esk11_0),head_of(esk12_0)) = esk11_0
| tail_of(esk11_0) = head_of(esk12_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_84]),c_0_40]),c_0_47])]),c_0_89]) ).
cnf(c_0_93,negated_conjecture,
head_of(esk12_0) != head_of(esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_84]),c_0_62])]) ).
cnf(c_0_94,negated_conjecture,
( precedes(X1,esk11_0,esk13_0)
| ~ sequential(X1,esk11_0)
| ~ on_path(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_90,c_0_42]) ).
cnf(c_0_95,negated_conjecture,
~ precedes(esk12_0,esk11_0,esk13_0),
inference(spm,[status(thm)],[c_0_91,c_0_24]) ).
cnf(c_0_96,negated_conjecture,
tail_of(esk11_0) = head_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_72,c_0_92]),c_0_40]),c_0_47])]),c_0_93]) ).
cnf(c_0_97,negated_conjecture,
~ sequential(esk12_0,esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_35]),c_0_95]) ).
cnf(c_0_98,negated_conjecture,
esk12_0 = esk11_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_96]),c_0_70])]),c_0_97]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_98])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 03:06:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.24/4.42 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.24/4.42 # Preprocessing time : 0.019 s
% 0.24/4.42
% 0.24/4.42 # Proof found!
% 0.24/4.42 # SZS status Theorem
% 0.24/4.42 # SZS output start CNFRefutation
% See solution above
% 0.24/4.42 # Proof object total steps : 100
% 0.24/4.42 # Proof object clause steps : 75
% 0.24/4.42 # Proof object formula steps : 25
% 0.24/4.42 # Proof object conjectures : 49
% 0.24/4.42 # Proof object clause conjectures : 46
% 0.24/4.42 # Proof object formula conjectures : 3
% 0.24/4.42 # Proof object initial clauses used : 26
% 0.24/4.42 # Proof object initial formulas used : 12
% 0.24/4.42 # Proof object generating inferences : 42
% 0.24/4.42 # Proof object simplifying inferences : 42
% 0.24/4.42 # Training examples: 0 positive, 0 negative
% 0.24/4.42 # Parsed axioms : 18
% 0.24/4.42 # Removed by relevancy pruning/SinE : 0
% 0.24/4.42 # Initial clauses : 64
% 0.24/4.42 # Removed in clause preprocessing : 1
% 0.24/4.42 # Initial clauses in saturation : 63
% 0.24/4.42 # Processed clauses : 12189
% 0.24/4.42 # ...of these trivial : 1011
% 0.24/4.42 # ...subsumed : 7087
% 0.24/4.42 # ...remaining for further processing : 4091
% 0.24/4.42 # Other redundant clauses eliminated : 92
% 0.24/4.42 # Clauses deleted for lack of memory : 0
% 0.24/4.42 # Backward-subsumed : 544
% 0.24/4.42 # Backward-rewritten : 2213
% 0.24/4.42 # Generated clauses : 120513
% 0.24/4.42 # ...of the previous two non-trivial : 110345
% 0.24/4.42 # Contextual simplify-reflections : 18121
% 0.24/4.42 # Paramodulations : 119931
% 0.24/4.42 # Factorizations : 285
% 0.24/4.42 # Equation resolutions : 297
% 0.24/4.42 # Current number of processed clauses : 1332
% 0.24/4.42 # Positive orientable unit clauses : 14
% 0.24/4.42 # Positive unorientable unit clauses: 0
% 0.24/4.42 # Negative unit clauses : 2
% 0.24/4.42 # Non-unit-clauses : 1316
% 0.24/4.42 # Current number of unprocessed clauses: 27507
% 0.24/4.42 # ...number of literals in the above : 267031
% 0.24/4.42 # Current number of archived formulas : 0
% 0.24/4.42 # Current number of archived clauses : 2757
% 0.24/4.42 # Clause-clause subsumption calls (NU) : 4041987
% 0.24/4.42 # Rec. Clause-clause subsumption calls : 248570
% 0.24/4.42 # Non-unit clause-clause subsumptions : 24391
% 0.24/4.42 # Unit Clause-clause subsumption calls : 1354
% 0.24/4.42 # Rewrite failures with RHS unbound : 0
% 0.24/4.42 # BW rewrite match attempts : 7
% 0.24/4.42 # BW rewrite match successes : 6
% 0.24/4.42 # Condensation attempts : 0
% 0.24/4.42 # Condensation successes : 0
% 0.24/4.42 # Termbank termtop insertions : 4077960
% 0.24/4.42
% 0.24/4.42 # -------------------------------------------------
% 0.24/4.42 # User time : 3.464 s
% 0.24/4.42 # System time : 0.057 s
% 0.24/4.42 # Total time : 3.521 s
% 0.24/4.42 # Maximum resident set size: 96016 pages
% 0.24/23.40 eprover: CPU time limit exceeded, terminating
% 0.24/23.40 eprover: CPU time limit exceeded, terminating
% 0.24/23.40 eprover: CPU time limit exceeded, terminating
% 0.24/23.41 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.41 eprover: No such file or directory
% 0.24/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.42 eprover: No such file or directory
% 0.24/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.42 eprover: No such file or directory
% 0.24/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.42 eprover: No such file or directory
% 0.24/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.42 eprover: No such file or directory
% 0.24/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.42 eprover: No such file or directory
% 0.24/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.42 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
%------------------------------------------------------------------------------