TSTP Solution File: GRA003+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.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 : Tue Apr 30 11:42:35 EDT 2024
% Result : Theorem 0.23s 0.40s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 119 ( 13 unt; 0 def)
% Number of atoms : 443 ( 82 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 505 ( 181 ~; 160 |; 122 &)
% ( 15 <=>; 19 =>; 0 <=; 8 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 11 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 262 ( 226 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f275,plain,
$false,
inference(avatar_sat_refutation,[],[f178,f186,f188,f210,f219,f224,f229,f256,f265,f274]) ).
fof(f274,plain,
~ spl16_10,
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f273,plain,
( $false
| ~ spl16_10 ),
inference(subsumption_resolution,[],[f266,f234]) ).
fof(f234,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK8)
| ~ precedes(X0,X1,sK8) ),
inference(resolution,[],[f149,f95]) ).
fof(f95,plain,
shortest_path(sK4,sK5,sK8),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ( ~ path(sK4,sK5,sK8)
| sK6 = sK7
| ~ edge(sK7)
| ~ edge(sK6)
| sK4 = sK5
| ~ vertex(sK5)
| ~ vertex(sK4) )
& precedes(sK6,sK7,sK8)
& shortest_path(sK4,sK5,sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f39,f68]) ).
fof(f68,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(sK4,sK5,sK8)
| sK6 = sK7
| ~ edge(sK7)
| ~ edge(sK6)
| sK4 = sK5
| ~ vertex(sK5)
| ~ vertex(sK4) )
& precedes(sK6,sK7,sK8)
& shortest_path(sK4,sK5,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f39,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,[],[f38]) ).
fof(f38,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,[],[f20]) ).
fof(f20,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/benchmark/theBenchmark.p',vertices_and_edges) ).
fof(f149,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,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,[],[f59]) ).
fof(f59,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,[],[f35]) ).
fof(f35,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/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f266,plain,
( precedes(sK6,sK6,sK8)
| ~ spl16_10 ),
inference(superposition,[],[f96,f255]) ).
fof(f255,plain,
( sK6 = sK7
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl16_10
<=> sK6 = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).
fof(f96,plain,
precedes(sK6,sK7,sK8),
inference(cnf_transformation,[],[f69]) ).
fof(f265,plain,
~ spl16_9,
inference(avatar_contradiction_clause,[],[f264]) ).
fof(f264,plain,
( $false
| ~ spl16_9 ),
inference(subsumption_resolution,[],[f257,f159]) ).
fof(f159,plain,
! [X0,X1] : ~ shortest_path(X0,X0,X1),
inference(resolution,[],[f140,f158]) ).
fof(f158,plain,
! [X2,X0] : ~ sP3(X0,X2,X2),
inference(equality_resolution,[],[f136]) ).
fof(f136,plain,
! [X2,X0,X1] :
( X1 != X2
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ~ less_or_equal(length_of(X0),length_of(sK14(X0,X1,X2)))
& path(X2,X1,sK14(X0,X1,X2)) )
| X1 = X2
| ~ path(X2,X1,X0) )
& ( ( ! [X4] :
( less_or_equal(length_of(X0),length_of(X4))
| ~ path(X2,X1,X4) )
& X1 != X2
& path(X2,X1,X0) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f89,f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X0),length_of(X3))
& path(X2,X1,X3) )
=> ( ~ less_or_equal(length_of(X0),length_of(sK14(X0,X1,X2)))
& path(X2,X1,sK14(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X0),length_of(X3))
& path(X2,X1,X3) )
| X1 = X2
| ~ path(X2,X1,X0) )
& ( ( ! [X4] :
( less_or_equal(length_of(X0),length_of(X4))
| ~ path(X2,X1,X4) )
& X1 != X2
& path(X2,X1,X0) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X2,X1,X0] :
( ( sP3(X2,X1,X0)
| ? [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) )
| ~ sP3(X2,X1,X0) ) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X2,X1,X0] :
( ( sP3(X2,X1,X0)
| ? [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) )
| ~ sP3(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X2,X1,X0] :
( sP3(X2,X1,X0)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f140,plain,
! [X2,X0,X1] :
( sP3(X2,X1,X0)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ sP3(X2,X1,X0) )
& ( sP3(X2,X1,X0)
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> sP3(X2,X1,X0) ),
inference(definition_folding,[],[f54,f66]) ).
fof(f54,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,[],[f32]) ).
fof(f32,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/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f257,plain,
( shortest_path(sK4,sK4,sK8)
| ~ spl16_9 ),
inference(superposition,[],[f95,f251]) ).
fof(f251,plain,
( sK4 = sK5
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f249,plain,
( spl16_9
<=> sK4 = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).
fof(f256,plain,
( spl16_9
| spl16_10
| ~ spl16_2
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f247,f183,f175,f253,f249]) ).
fof(f175,plain,
( spl16_2
<=> on_path(sK6,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f183,plain,
( spl16_3
<=> on_path(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
fof(f247,plain,
( sK6 = sK7
| sK4 = sK5
| ~ spl16_2
| ~ spl16_3 ),
inference(subsumption_resolution,[],[f246,f164]) ).
fof(f164,plain,
vertex(sK4),
inference(resolution,[],[f162,f117]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( sP1(X1,X2,X0)
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(definition_folding,[],[f44,f62,f61]) ).
fof(f61,plain,
! [X2,X3,X1] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
| ~ sP0(X2,X3,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f62,plain,
! [X1,X2,X0] :
( ? [X3] :
( sP0(X2,X3,X1)
& tail_of(X3) = X0
& edge(X3) )
| ~ sP1(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f44,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,[],[f26]) ).
fof(f26,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/benchmark/theBenchmark.p',path_properties) ).
fof(f162,plain,
path(sK4,sK5,sK8),
inference(resolution,[],[f160,f95]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(resolution,[],[f140,f135]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| path(X2,X1,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f246,plain,
( sK6 = sK7
| sK4 = sK5
| ~ vertex(sK4)
| ~ spl16_2
| ~ spl16_3 ),
inference(subsumption_resolution,[],[f245,f163]) ).
fof(f163,plain,
vertex(sK5),
inference(resolution,[],[f162,f118]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f245,plain,
( sK6 = sK7
| sK4 = sK5
| ~ vertex(sK5)
| ~ vertex(sK4)
| ~ spl16_2
| ~ spl16_3 ),
inference(subsumption_resolution,[],[f244,f179]) ).
fof(f179,plain,
( edge(sK6)
| ~ spl16_2 ),
inference(resolution,[],[f177,f166]) ).
fof(f166,plain,
! [X0] :
( ~ on_path(X0,sK8)
| edge(X0) ),
inference(resolution,[],[f145,f162]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,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,[],[f57]) ).
fof(f57,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,[],[f34]) ).
fof(f34,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/benchmark/theBenchmark.p',on_path_properties) ).
fof(f177,plain,
( on_path(sK6,sK8)
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f244,plain,
( sK6 = sK7
| ~ edge(sK6)
| sK4 = sK5
| ~ vertex(sK5)
| ~ vertex(sK4)
| ~ spl16_3 ),
inference(subsumption_resolution,[],[f243,f189]) ).
fof(f189,plain,
( edge(sK7)
| ~ spl16_3 ),
inference(resolution,[],[f185,f166]) ).
fof(f185,plain,
( on_path(sK7,sK8)
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f243,plain,
( sK6 = sK7
| ~ edge(sK7)
| ~ edge(sK6)
| sK4 = sK5
| ~ vertex(sK5)
| ~ vertex(sK4) ),
inference(subsumption_resolution,[],[f97,f162]) ).
fof(f97,plain,
( ~ path(sK4,sK5,sK8)
| sK6 = sK7
| ~ edge(sK7)
| ~ edge(sK6)
| sK4 = sK5
| ~ vertex(sK5)
| ~ vertex(sK4) ),
inference(cnf_transformation,[],[f69]) ).
fof(f229,plain,
( spl16_1
| spl16_8 ),
inference(avatar_split_clause,[],[f221,f226,f172]) ).
fof(f172,plain,
( spl16_1
<=> ! [X0,X1] : ~ path(X0,X1,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f226,plain,
( spl16_8
<=> sP2(sK8,sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).
fof(f221,plain,
! [X0,X1] :
( sP2(sK8,sK7,sK6)
| ~ path(X0,X1,sK8) ),
inference(resolution,[],[f125,f96]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| sP2(X0,X4,X3)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( sP2(X0,X4,X3)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(definition_folding,[],[f45,f64]) ).
fof(f64,plain,
! [X0,X4,X3] :
( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
| ~ sP2(X0,X4,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f45,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/benchmark/theBenchmark.p',precedes_properties) ).
fof(f224,plain,
spl16_6,
inference(avatar_contradiction_clause,[],[f223]) ).
fof(f223,plain,
( $false
| spl16_6 ),
inference(subsumption_resolution,[],[f222,f162]) ).
fof(f222,plain,
( ~ path(sK4,sK5,sK8)
| spl16_6 ),
inference(resolution,[],[f220,f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( sP1(X1,X2,X0)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f220,plain,
( ~ sP1(sK5,sK8,sK4)
| spl16_6 ),
inference(resolution,[],[f214,f109]) ).
fof(f109,plain,
! [X2,X0,X1] :
( edge(sK9(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( sP0(X1,sK9(X0,X1,X2),X0)
& tail_of(sK9(X0,X1,X2)) = X2
& edge(sK9(X0,X1,X2)) )
| ~ sP1(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f73,f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP0(X1,X3,X0)
& tail_of(X3) = X2
& edge(X3) )
=> ( sP0(X1,sK9(X0,X1,X2),X0)
& tail_of(sK9(X0,X1,X2)) = X2
& edge(sK9(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP0(X1,X3,X0)
& tail_of(X3) = X2
& edge(X3) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X1,X2,X0] :
( ? [X3] :
( sP0(X2,X3,X1)
& tail_of(X3) = X0
& edge(X3) )
| ~ sP1(X1,X2,X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f214,plain,
( ~ edge(sK9(sK5,sK8,sK4))
| spl16_6 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f212,plain,
( spl16_6
<=> edge(sK9(sK5,sK8,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
fof(f219,plain,
( ~ spl16_6
| ~ spl16_7 ),
inference(avatar_split_clause,[],[f200,f216,f212]) ).
fof(f216,plain,
( spl16_7
<=> sK4 = head_of(sK9(sK5,sK8,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).
fof(f200,plain,
( sK4 != head_of(sK9(sK5,sK8,sK4))
| ~ edge(sK9(sK5,sK8,sK4)) ),
inference(superposition,[],[f98,f198]) ).
fof(f198,plain,
sK4 = tail_of(sK9(sK5,sK8,sK4)),
inference(resolution,[],[f169,f162]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ path(X2,X0,X1)
| tail_of(sK9(X0,X1,X2)) = X2 ),
inference(resolution,[],[f110,f119]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| tail_of(sK9(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f98,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
fof(f210,plain,
( ~ spl16_4
| spl16_5 ),
inference(avatar_split_clause,[],[f199,f207,f203]) ).
fof(f203,plain,
( spl16_4
<=> on_path(sK9(sK5,sK8,sK4),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f207,plain,
( spl16_5
<=> in_path(sK4,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f199,plain,
( in_path(sK4,sK8)
| ~ on_path(sK9(sK5,sK8,sK4),sK8) ),
inference(superposition,[],[f193,f198]) ).
fof(f193,plain,
! [X0] :
( in_path(tail_of(X0),sK8)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f147,f162]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(tail_of(X3),X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f188,plain,
~ spl16_1,
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f187,plain,
( $false
| ~ spl16_1 ),
inference(resolution,[],[f173,f162]) ).
fof(f173,plain,
( ! [X0,X1] : ~ path(X0,X1,sK8)
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f186,plain,
( spl16_1
| spl16_3 ),
inference(avatar_split_clause,[],[f180,f183,f172]) ).
fof(f180,plain,
! [X0,X1] :
( on_path(sK7,sK8)
| ~ path(X0,X1,sK8) ),
inference(resolution,[],[f124,f96]) ).
fof(f124,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f178,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f170,f175,f172]) ).
fof(f170,plain,
! [X0,X1] :
( on_path(sK6,sK8)
| ~ path(X0,X1,sK8) ),
inference(resolution,[],[f123,f96]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Apr 30 02:10:32 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (10314)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.39 % (10317)WARNING: value z3 for option sas not known
% 0.23/0.39 % (10315)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.39 % (10316)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.39 % (10318)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.39 % (10317)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.23/0.39 % (10320)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.23/0.39 % (10319)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.23/0.39 % (10321)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.23/0.40 TRYING [1]
% 0.23/0.40 TRYING [1]
% 0.23/0.40 TRYING [2]
% 0.23/0.40 TRYING [2]
% 0.23/0.40 % (10317)First to succeed.
% 0.23/0.40 TRYING [1]
% 0.23/0.40 TRYING [2]
% 0.23/0.40 % (10317)Refutation found. Thanks to Tanya!
% 0.23/0.40 % SZS status Theorem for theBenchmark
% 0.23/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.41 % (10317)------------------------------
% 0.23/0.41 % (10317)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.23/0.41 % (10317)Termination reason: Refutation
% 0.23/0.41
% 0.23/0.41 % (10317)Memory used [KB]: 973
% 0.23/0.41 % (10317)Time elapsed: 0.013 s
% 0.23/0.41 % (10317)Instructions burned: 16 (million)
% 0.23/0.41 % (10317)------------------------------
% 0.23/0.41 % (10317)------------------------------
% 0.23/0.41 % (10314)Success in time 0.029 s
%------------------------------------------------------------------------------