TSTP Solution File: GRA003+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n005.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 : 300s
% DateTime : Wed May 1 02:25:11 EDT 2024
% Result : Theorem 0.79s 0.94s
% Output : Refutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 96 ( 9 unt; 0 def)
% Number of atoms : 462 ( 98 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 558 ( 192 ~; 169 |; 158 &)
% ( 13 <=>; 20 =>; 0 <=; 6 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 11 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 247 ( 203 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f301,plain,
$false,
inference(avatar_sat_refutation,[],[f171,f178,f181,f182,f210,f212,f216,f236,f240,f287,f300]) ).
fof(f300,plain,
~ spl12_3,
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f297,plain,
( $false
| ~ spl12_3 ),
inference(resolution,[],[f290,f141]) ).
fof(f141,plain,
! [X2,X1] : ~ shortest_path(X1,X1,X2),
inference(equality_resolution,[],[f118]) ).
fof(f118,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78,f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
=> ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X2,X9] :
( shortest_path(X1,X2,X9)
<=> ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2
& path(X1,X2,X9) ) ),
file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',shortest_path_defn) ).
fof(f290,plain,
( shortest_path(sK7,sK7,sK11)
| ~ spl12_3 ),
inference(superposition,[],[f132,f154]) ).
fof(f154,plain,
( sK7 = sK8
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f152,plain,
( spl12_3
<=> sK7 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f132,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
( ( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) )
& precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f60,f83]) ).
fof(f83,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) )
& precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( path(X0,X1,X4)
& X2 != X3
& edge(X3)
& edge(X2)
& X0 != X1
& vertex(X1)
& vertex(X0) ) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( path(X1,X2,X3)
& X6 != X7
& edge(X7)
& edge(X6)
& X1 != X2
& vertex(X2)
& vertex(X1) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( path(X1,X2,X3)
& X6 != X7
& edge(X7)
& edge(X6)
& X1 != X2
& vertex(X2)
& vertex(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',vertices_and_edges) ).
fof(f287,plain,
~ spl12_6,
inference(avatar_contradiction_clause,[],[f286]) ).
fof(f286,plain,
( $false
| ~ spl12_6 ),
inference(resolution,[],[f285,f253]) ).
fof(f253,plain,
( precedes(sK9,sK9,sK11)
| ~ spl12_6 ),
inference(superposition,[],[f133,f166]) ).
fof(f166,plain,
( sK9 = sK10
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f164,plain,
( spl12_6
<=> sK9 = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f133,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f84]) ).
fof(f285,plain,
( ~ precedes(sK9,sK9,sK11)
| ~ spl12_6 ),
inference(forward_demodulation,[],[f283,f166]) ).
fof(f283,plain,
~ precedes(sK10,sK9,sK11),
inference(resolution,[],[f282,f133]) ).
fof(f282,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK11)
| ~ precedes(X1,X0,sK11) ),
inference(resolution,[],[f123,f132]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( ~ precedes(X7,X6,X3)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',shortest_path_properties) ).
fof(f240,plain,
( spl12_5
| ~ spl12_7
| ~ spl12_14 ),
inference(avatar_split_clause,[],[f237,f233,f168,f160]) ).
fof(f160,plain,
( spl12_5
<=> edge(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f168,plain,
( spl12_7
<=> path(sK7,sK8,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f233,plain,
( spl12_14
<=> on_path(sK10,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f237,plain,
( edge(sK10)
| ~ spl12_7
| ~ spl12_14 ),
inference(resolution,[],[f235,f183]) ).
fof(f183,plain,
( ! [X0] :
( ~ on_path(X0,sK11)
| edge(X0) )
| ~ spl12_7 ),
inference(resolution,[],[f99,f169]) ).
fof(f169,plain,
( path(sK7,sK8,sK11)
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X3,X0] :
( ( on_path(X0,X3)
& path(X1,X2,X3) )
=> ( in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3)
& edge(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',on_path_properties) ).
fof(f235,plain,
( on_path(sK10,sK11)
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f236,plain,
( spl12_10
| spl12_14 ),
inference(avatar_split_clause,[],[f231,f233,f204]) ).
fof(f204,plain,
( spl12_10
<=> ! [X0,X1] : ~ path(X0,X1,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f231,plain,
! [X0,X1] :
( on_path(sK10,sK11)
| ~ path(X0,X1,sK11) ),
inference(resolution,[],[f113,f133]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f73,f74]) ).
fof(f74,plain,
! [X0,X3,X4] :
( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
=> ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( precedes(X6,X7,X3)
=> ( ( sequential(X6,X7)
<~> ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) ) )
& on_path(X7,X3)
& on_path(X6,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',precedes_properties) ).
fof(f216,plain,
( spl12_4
| ~ spl12_7
| ~ spl12_11 ),
inference(avatar_split_clause,[],[f213,f207,f168,f156]) ).
fof(f156,plain,
( spl12_4
<=> edge(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f207,plain,
( spl12_11
<=> on_path(sK9,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f213,plain,
( edge(sK9)
| ~ spl12_7
| ~ spl12_11 ),
inference(resolution,[],[f209,f183]) ).
fof(f209,plain,
( on_path(sK9,sK11)
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f212,plain,
( ~ spl12_7
| ~ spl12_10 ),
inference(avatar_contradiction_clause,[],[f211]) ).
fof(f211,plain,
( $false
| ~ spl12_7
| ~ spl12_10 ),
inference(resolution,[],[f205,f169]) ).
fof(f205,plain,
( ! [X0,X1] : ~ path(X0,X1,sK11)
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f210,plain,
( spl12_10
| spl12_11 ),
inference(avatar_split_clause,[],[f202,f207,f204]) ).
fof(f202,plain,
! [X0,X1] :
( on_path(sK9,sK11)
| ~ path(X0,X1,sK11) ),
inference(resolution,[],[f112,f133]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f182,plain,
( spl12_1
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f180,f168,f144]) ).
fof(f144,plain,
( spl12_1
<=> vertex(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f180,plain,
( vertex(sK7)
| ~ spl12_7 ),
inference(resolution,[],[f169,f90]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ( ! [X4] :
( path_cons(sK0(X0,X1,X2),X4) != X2
| ~ path(head_of(sK0(X0,X1,X2)),X1,X4) )
| path_cons(sK0(X0,X1,X2),empty) != X2
| head_of(sK0(X0,X1,X2)) != X1 )
& ( ( path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2
& path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2)) )
| ( path_cons(sK0(X0,X1,X2),empty) = X2
& head_of(sK0(X0,X1,X2)) = X1 ) )
& tail_of(sK0(X0,X1,X2)) = X0
& edge(sK0(X0,X1,X2))
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f63,f65,f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
| path_cons(X3,empty) != X2
| head_of(X3) != X1 )
& ( ? [X5] :
( path_cons(X3,X5) = X2
& path(head_of(X3),X1,X5) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
=> ( ( ! [X4] :
( path_cons(sK0(X0,X1,X2),X4) != X2
| ~ path(head_of(sK0(X0,X1,X2)),X1,X4) )
| path_cons(sK0(X0,X1,X2),empty) != X2
| head_of(sK0(X0,X1,X2)) != X1 )
& ( ? [X5] :
( path_cons(sK0(X0,X1,X2),X5) = X2
& path(head_of(sK0(X0,X1,X2)),X1,X5) )
| ( path_cons(sK0(X0,X1,X2),empty) = X2
& head_of(sK0(X0,X1,X2)) = X1 ) )
& tail_of(sK0(X0,X1,X2)) = X0
& edge(sK0(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X5] :
( path_cons(sK0(X0,X1,X2),X5) = X2
& path(head_of(sK0(X0,X1,X2)),X1,X5) )
=> ( path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2
& path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
| path_cons(X3,empty) != X2
| head_of(X3) != X1 )
& ( ? [X5] :
( path_cons(X3,X5) = X2
& path(head_of(X3),X1,X5) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
| path_cons(X3,empty) != X2
| head_of(X3) != X1 )
& ( ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
| path_cons(X3,empty) != X2
| head_of(X3) != X1 )
& ( ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> ( ? [X3] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> ( ? [X0] :
( ( ( path_cons(X0,empty) = X3
& head_of(X0) = X2 )
<~> ? [X4] :
( path_cons(X0,X4) = X3
& path(head_of(X0),X2,X4) ) )
& tail_of(X0) = X1
& edge(X0) )
& vertex(X2)
& vertex(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945',path_properties) ).
fof(f181,plain,
( spl12_2
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f179,f168,f148]) ).
fof(f148,plain,
( spl12_2
<=> vertex(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f179,plain,
( vertex(sK8)
| ~ spl12_7 ),
inference(resolution,[],[f169,f91]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f178,plain,
spl12_7,
inference(avatar_split_clause,[],[f177,f168]) ).
fof(f177,plain,
path(sK7,sK8,sK11),
inference(resolution,[],[f117,f132]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f171,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_3
| ~ spl12_4
| ~ spl12_5
| spl12_6
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f134,f168,f164,f160,f156,f152,f148,f144]) ).
fof(f134,plain,
( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) ),
inference(cnf_transformation,[],[f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37 % Computer : n005.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue Apr 30 17:31:41 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.tCxUp0tGsv/Vampire---4.8_7945
% 0.77/0.93 % (8261)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2994ds/78Mi)
% 0.77/0.93 % (8259)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2994ds/34Mi)
% 0.77/0.93 % (8265)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2994ds/83Mi)
% 0.77/0.93 % (8262)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2994ds/33Mi)
% 0.77/0.93 % (8260)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2994ds/51Mi)
% 0.77/0.93 % (8264)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2994ds/45Mi)
% 0.77/0.93 % (8263)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2994ds/34Mi)
% 0.77/0.93 % (8266)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2994ds/56Mi)
% 0.77/0.93 % (8266)Refutation not found, incomplete strategy% (8266)------------------------------
% 0.77/0.93 % (8266)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.93 % (8264)Refutation not found, incomplete strategy% (8264)------------------------------
% 0.77/0.93 % (8264)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.93 % (8264)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.93
% 0.77/0.93 % (8264)Memory used [KB]: 979
% 0.77/0.93 % (8264)Time elapsed: 0.003 s
% 0.77/0.93 % (8264)Instructions burned: 2 (million)
% 0.77/0.93 % (8264)------------------------------
% 0.77/0.93 % (8264)------------------------------
% 0.77/0.93 % (8266)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.93
% 0.77/0.93 % (8266)Memory used [KB]: 1044
% 0.77/0.93 % (8266)Time elapsed: 0.003 s
% 0.77/0.93 % (8266)Instructions burned: 2 (million)
% 0.77/0.93 % (8266)------------------------------
% 0.77/0.93 % (8266)------------------------------
% 0.77/0.93 % (8262)Refutation not found, incomplete strategy% (8262)------------------------------
% 0.77/0.93 % (8262)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.93 % (8262)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.93
% 0.77/0.93 % (8262)Memory used [KB]: 981
% 0.77/0.93 % (8262)Time elapsed: 0.003 s
% 0.77/0.93 % (8262)Instructions burned: 3 (million)
% 0.77/0.93 % (8262)------------------------------
% 0.77/0.93 % (8262)------------------------------
% 0.77/0.94 % (8267)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2994ds/55Mi)
% 0.77/0.94 % (8260)First to succeed.
% 0.77/0.94 % (8268)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2994ds/50Mi)
% 0.77/0.94 % (8269)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2994ds/208Mi)
% 0.77/0.94 % (8267)Refutation not found, incomplete strategy% (8267)------------------------------
% 0.77/0.94 % (8267)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.77/0.94 % (8267)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.94
% 0.77/0.94 % (8267)Memory used [KB]: 1134
% 0.77/0.94 % (8267)Time elapsed: 0.005 s
% 0.79/0.94 % (8267)Instructions burned: 6 (million)
% 0.79/0.94 % (8267)------------------------------
% 0.79/0.94 % (8267)------------------------------
% 0.79/0.94 % (8260)Refutation found. Thanks to Tanya!
% 0.79/0.94 % SZS status Theorem for Vampire---4
% 0.79/0.94 % SZS output start Proof for Vampire---4
% See solution above
% 0.79/0.94 % (8260)------------------------------
% 0.79/0.94 % (8260)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.79/0.94 % (8260)Termination reason: Refutation
% 0.79/0.94
% 0.79/0.94 % (8260)Memory used [KB]: 1180
% 0.79/0.94 % (8260)Time elapsed: 0.010 s
% 0.79/0.94 % (8260)Instructions burned: 13 (million)
% 0.79/0.94 % (8260)------------------------------
% 0.79/0.94 % (8260)------------------------------
% 0.79/0.94 % (8186)Success in time 0.565 s
% 0.79/0.94 % Vampire---4.8 exiting
%------------------------------------------------------------------------------