%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:08:25 AM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 117 ( 20 unt; 10 def)
% Number of atoms : 450 ( 71 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 516 ( 183 ~; 195 |; 114 &)
% ( 12 <=>; 8 =>; 0 <=; 4 <~>)
% Maximal formula depth : 15 ( 6 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 : 237 ( 0 sgn 208 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> ( vertex(X0)
& vertex(X1)
& ? [X3] :
( edge(X3)
& X0 = tail_of(X3)
& ( ( X1 = head_of(X3)
& X2 = path_cons(X3,empty) )
<~> ? [X4] :
( path(head_of(X3),X1,X4)
& X2 = path_cons(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',path_properties) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( path(X0,X1,X2)
& on_path(X3,X2) )
=> ( edge(X3)
& in_path(head_of(X3),X2)
& in_path(tail_of(X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(f10,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ~ ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& ~ precedes(X3,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f18,conjecture,
! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( vertex(X0)
& vertex(X1)
& X0 != X1
& edge(X2)
& edge(X3)
& X2 != X3
& path(X0,X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vertices_and_edges) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( vertex(X0)
& vertex(X1)
& X0 != X1
& edge(X2)
& edge(X3)
& X2 != X3
& path(X0,X1,X4) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( vertex(X0)
& vertex(X1)
& ? [X3] :
( edge(X3)
& X0 = tail_of(X3)
& ( ( X1 = head_of(X3)
& X2 = path_cons(X3,empty) )
<~> ? [X4] :
( path(head_of(X3),X1,X4)
& X2 = path_cons(X3,X4) ) ) ) )
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( edge(X3)
& in_path(head_of(X3),X2)
& in_path(tail_of(X3),X2) )
| ~ path(X0,X1,X2)
| ~ on_path(X3,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( edge(X3)
& in_path(head_of(X3),X2)
& in_path(tail_of(X3),X2) )
| ~ path(X0,X1,X2)
| ~ on_path(X3,X2) ),
inference(flattening,[],[f27]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(ennf_transformation,[],[f12]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(flattening,[],[f35]) ).
fof(f43,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ edge(X2)
| ~ edge(X3)
| X2 = X3
| ~ path(X0,X1,X4) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ edge(X2)
| ~ edge(X3)
| X2 = X3
| ~ path(X0,X1,X4) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( vertex(X0)
& vertex(X1)
& ? [X3] :
( edge(X3)
& X0 = tail_of(X3)
& ( ! [X4] :
( ~ path(head_of(X3),X1,X4)
| path_cons(X3,X4) != X2 )
| head_of(X3) != X1
| path_cons(X3,empty) != X2 )
& ( ? [X4] :
( path(head_of(X3),X1,X4)
& X2 = path_cons(X3,X4) )
| ( X1 = head_of(X3)
& X2 = path_cons(X3,empty) ) ) ) )
| ~ path(X0,X1,X2) ),
inference(nnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( vertex(X0)
& vertex(X1)
& ? [X3] :
( edge(X3)
& X0 = tail_of(X3)
& ( ! [X4] :
( ~ path(head_of(X3),X1,X4)
| path_cons(X3,X4) != X2 )
| head_of(X3) != X1
| path_cons(X3,empty) != X2 )
& ( ? [X4] :
( path(head_of(X3),X1,X4)
& X2 = path_cons(X3,X4) )
| ( X1 = head_of(X3)
& X2 = path_cons(X3,empty) ) ) ) )
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( vertex(X0)
& vertex(X1)
& ? [X3] :
( edge(X3)
& X0 = tail_of(X3)
& ( ! [X4] :
( ~ path(head_of(X3),X1,X4)
| path_cons(X3,X4) != X2 )
| head_of(X3) != X1
| path_cons(X3,empty) != X2 )
& ( ? [X5] :
( path(head_of(X3),X1,X5)
& path_cons(X3,X5) = X2 )
| ( X1 = head_of(X3)
& X2 = path_cons(X3,empty) ) ) ) )
| ~ path(X0,X1,X2) ),
inference(rectify,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( vertex(X0)
& vertex(X1)
& edge(sK0(X0,X1,X2))
& tail_of(sK0(X0,X1,X2)) = X0
& ( ! [X4] :
( ~ path(head_of(sK0(X0,X1,X2)),X1,X4)
| path_cons(sK0(X0,X1,X2),X4) != X2 )
| head_of(sK0(X0,X1,X2)) != X1
| path_cons(sK0(X0,X1,X2),empty) != X2 )
& ( ( path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2))
& path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2 )
| ( head_of(sK0(X0,X1,X2)) = X1
& path_cons(sK0(X0,X1,X2),empty) = X2 ) ) )
| ~ path(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2))],[f47]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( sequential(X3,X6)
& precedes(X6,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ( sequential(X3,sK3(X0,X3,X4))
& precedes(sK3(X0,X3,X4),X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X6,sK3(X0,X3,X4))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f58]) ).
fof(f61,plain,
( ( ~ vertex(sK7)
| ~ vertex(sK8)
| sK7 = sK8
| ~ edge(sK9)
| ~ edge(sK10)
| sK9 = sK10
| ~ path(sK7,sK8,sK11) )
& shortest_path(sK7,sK8,sK11)
& precedes(sK9,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11)],[f44]) ).
fof(f74,plain,
! [X2,X0,X1] :
( vertex(X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
! [X2,X0,X1] :
( vertex(X0)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( edge(X3)
| ~ path(X0,X1,X2)
| ~ on_path(X3,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X3,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f95,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f96,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X2,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f109,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
( ~ vertex(sK7)
| ~ vertex(sK8)
| sK7 = sK8
| ~ edge(sK9)
| ~ edge(sK10)
| sK9 = sK10
| ~ path(sK7,sK8,sK11) ),
inference(cnf_transformation,[],[f61]) ).
fof(f118,plain,
! [X2,X1] : ~ shortest_path(X1,X1,X2),
inference(equality_resolution,[],[f95]) ).
fof(f124,plain,
! [X2,X0,X1] :
( vertex(X0)
| path(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f125,plain,
! [X2,X0,X1] :
( vertex(X1)
| path(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f74]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( path(X0,X1,X2)
| ~ edge(X3)
| ~ on_path(X3,X2) ),
inference(consistent_polarity_flipping,[],[f78]) ).
fof(f144,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X3,X0)
| precedes(X3,X4,X0)
| path(X1,X2,X0) ),
inference(consistent_polarity_flipping,[],[f93]) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| precedes(X3,X4,X0)
| path(X1,X2,X0) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2) ),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f154,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| precedes(X3,X2,X4)
| precedes(X2,X3,X4) ),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f163,plain,
( ~ vertex(sK7)
| ~ vertex(sK8)
| sK7 = sK8
| edge(sK9)
| edge(sK10)
| sK9 = sK10
| path(sK7,sK8,sK11) ),
inference(consistent_polarity_flipping,[],[f111]) ).
fof(f164,plain,
~ precedes(sK9,sK10,sK11),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f166,definition,
( spl12_1
<=> path(sK7,sK8,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f167,plain,
( ~ path(sK7,sK8,sK11)
| spl12_1 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f170,definition,
( spl12_2
<=> sK9 = sK10 ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f172,plain,
( sK9 = sK10
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,definition,
( spl12_3
<=> edge(sK10) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f178,definition,
( spl12_4
<=> edge(sK9) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f182,definition,
( spl12_5
<=> sK7 = sK8 ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f184,plain,
( sK7 = sK8
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f186,definition,
( spl12_6
<=> vertex(sK8) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f188,plain,
( ~ vertex(sK8)
| spl12_6 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl12_7
<=> vertex(sK7) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f192,plain,
( ~ vertex(sK7)
| spl12_7 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4
| spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f163,f190,f186,f182,f178,f174,f170,f166]) ).
fof(f195,plain,
( ! [X0,X1] : path(sK7,X0,X1)
| spl12_7 ),
inference(resolution,[],[f124,f192]) ).
fof(f196,plain,
( $false
| spl12_1
| spl12_7 ),
inference(resolution,[],[f195,f167]) ).
fof(f197,plain,
( spl12_1
| spl12_7 ),
inference(avatar_contradiction_clause,[],[f196]) ).
fof(f198,plain,
( ! [X0,X1] : path(X0,sK8,X1)
| spl12_6 ),
inference(resolution,[],[f125,f188]) ).
fof(f199,plain,
( $false
| spl12_1
| spl12_6 ),
inference(resolution,[],[f198,f167]) ).
fof(f200,plain,
( spl12_1
| spl12_6 ),
inference(avatar_contradiction_clause,[],[f199]) ).
fof(f201,plain,
~ path(sK7,sK8,sK11),
inference(resolution,[],[f151,f110]) ).
fof(f203,plain,
( ! [X0] :
( ~ on_path(X0,sK11)
| ~ edge(X0) )
| spl12_1 ),
inference(resolution,[],[f133,f167]) ).
fof(f219,plain,
( ! [X2,X3,X0,X1] :
( precedes(X0,X1,sK11)
| path(X2,X3,sK11)
| ~ edge(X0) )
| spl12_1 ),
inference(resolution,[],[f144,f203]) ).
fof(f221,definition,
( spl12_10
<=> ! [X2,X3] : path(X2,X3,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f222,plain,
( ! [X2,X3] : path(X2,X3,sK11)
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,definition,
( spl12_11
<=> ! [X0,X1] :
( precedes(X0,X1,sK11)
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f225,plain,
( ! [X0,X1] :
( precedes(X0,X1,sK11)
| ~ edge(X0) )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( spl12_10
| spl12_11
| spl12_1 ),
inference(avatar_split_clause,[],[f219,f166,f224,f221]) ).
fof(f227,plain,
~ spl12_1,
inference(avatar_split_clause,[],[f201,f166]) ).
fof(f230,plain,
( ! [X0] :
( ~ on_path(X0,sK11)
| ~ edge(X0) )
| spl12_1 ),
inference(resolution,[],[f167,f133]) ).
fof(f232,plain,
( $false
| spl12_1
| ~ spl12_10 ),
inference(resolution,[],[f222,f167]) ).
fof(f233,plain,
( spl12_1
| ~ spl12_10 ),
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f236,plain,
( ~ edge(sK9)
| ~ spl12_11 ),
inference(resolution,[],[f225,f164]) ).
fof(f237,plain,
( ~ spl12_4
| ~ spl12_11 ),
inference(avatar_split_clause,[],[f236,f224,f178]) ).
fof(f241,plain,
( ! [X2,X3,X0,X1] :
( precedes(X0,X1,sK11)
| path(X2,X3,sK11)
| ~ edge(X1) )
| spl12_1 ),
inference(resolution,[],[f145,f230]) ).
fof(f243,definition,
( spl12_12
<=> ! [X0,X1] :
( precedes(X0,X1,sK11)
| ~ edge(X1) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f244,plain,
( ! [X0,X1] :
( precedes(X0,X1,sK11)
| ~ edge(X1) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( spl12_10
| spl12_12
| spl12_1 ),
inference(avatar_split_clause,[],[f241,f166,f243,f221]) ).
fof(f246,plain,
( ~ edge(sK10)
| ~ spl12_12 ),
inference(resolution,[],[f244,f164]) ).
fof(f247,plain,
( ~ spl12_3
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f246,f243,f174]) ).
fof(f248,plain,
( shortest_path(sK7,sK7,sK11)
| ~ spl12_5 ),
inference(superposition,[],[f110,f184]) ).
fof(f254,plain,
( $false
| ~ spl12_5 ),
inference(resolution,[],[f248,f118]) ).
fof(f256,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[],[f254]) ).
fof(f258,plain,
( ~ precedes(sK9,sK9,sK11)
| ~ spl12_2 ),
inference(superposition,[],[f164,f172]) ).
fof(f326,plain,
! [X0,X1] :
( precedes(X1,X0,sK11)
| precedes(X0,X1,sK11) ),
inference(resolution,[],[f154,f110]) ).
fof(f328,plain,
( precedes(sK9,sK9,sK11)
| ~ spl12_2 ),
inference(resolution,[],[f326,f258]) ).
fof(f330,plain,
( $false
| ~ spl12_2 ),
inference(resolution,[],[f328,f258]) ).
fof(f331,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[],[f330]) ).
cnf(s1,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4
| spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(sat_conversion,[],[f193]) ).
cnf(s2,plain,
( spl12_1
| spl12_7 ),
inference(sat_conversion,[],[f197]) ).
cnf(s3,plain,
( spl12_1
| spl12_6 ),
inference(sat_conversion,[],[f200]) ).
cnf(s5,plain,
( spl12_1
| spl12_10
| spl12_11 ),
inference(sat_conversion,[],[f226]) ).
cnf(s6,plain,
~ spl12_1,
inference(sat_conversion,[],[f227]) ).
cnf(s7,plain,
( spl12_1
| ~ spl12_10 ),
inference(sat_conversion,[],[f233]) ).
cnf(s8,plain,
( ~ spl12_4
| ~ spl12_11 ),
inference(sat_conversion,[],[f237]) ).
cnf(s9,plain,
( spl12_1
| spl12_10
| spl12_12 ),
inference(sat_conversion,[],[f245]) ).
cnf(s10,plain,
( ~ spl12_3
| ~ spl12_12 ),
inference(sat_conversion,[],[f247]) ).
cnf(s11,plain,
~ spl12_5,
inference(sat_conversion,[],[f256]) ).
cnf(s24,plain,
~ spl12_2,
inference(sat_conversion,[],[f331]) ).
cnf(s25,plain,
~ spl12_10,
inference(rat,[],[s7,s6]) ).
cnf(s27,plain,
spl12_12,
inference(rat,[],[s9,s6,s25]) ).
cnf(s30,plain,
~ spl12_3,
inference(rat,[],[s10,s27]) ).
cnf(s37,plain,
spl12_11,
inference(rat,[],[s5,s25,s6]) ).
cnf(s38,plain,
~ spl12_4,
inference(rat,[],[s8,s37]) ).
cnf(s40,plain,
spl12_6,
inference(rat,[],[s3,s6]) ).
cnf(s41,plain,
spl12_7,
inference(rat,[],[s2,s6]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s1,s41,s40,s11,s38,s30,s24,s6]) ).
fof(f332,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n026.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 08:50:01 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.44 Running first-order model finding
% 0.12/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.50 % (2537095)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (2537100)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3869323137_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % (2537101)% WARNING: option uhcvi not known.
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % TRYING [3]
% 0.16/0.50 % (2537105)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3325340656:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (2537101)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=862725643:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (2537102)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2200614047:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (2537103)dis+10_1_sil=32000:sp=arity:random_seed=872242047:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (2537104)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=523908948:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (2537106)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1341811389:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % TRYING [4]
% 0.16/0.50 % (2537106) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2537095-2537106"...
% 0.16/0.50 % (2537106)...printing done.
% 0.16/0.50 % (2537105) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2537095-2537105"...
% 0.16/0.50 % (2537102) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2537095-2537102"...
% 0.16/0.50 % (2537106)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (2537106)------------------------------
% 0.16/0.50 % (2537106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (2537106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (2537106)CaDiCaL version: 2.1.3
% 0.16/0.50 % (2537106)Termination reason: Refutation
% 0.16/0.50 % (2537106)Time elapsed: 0.008 s
% 0.16/0.50 % (2537106)Peak memory usage: 12 MB
% 0.16/0.50 % (2537106)Instructions burned: 10 (million)
% 0.16/0.50 % (2537095)Success in time 0.049 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------