%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n009.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 09:55:19 AM UTC 2026
% Result : Theorem 2.66s 1.28s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 116 ( 19 unt; 9 def)
% Number of atoms : 460 ( 81 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 546 ( 202 ~; 192 |; 127 &)
% ( 12 <=>; 9 =>; 0 <=; 4 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 10 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 228 ( 0 sgn 199 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(head_of(X0))
& vertex(tail_of(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
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/theBenchmark.p',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/theBenchmark.p',on_path_properties) ).
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_defn) ).
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/theBenchmark.p',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/theBenchmark.p',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/theBenchmark.p',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(f23,plain,
! [X0] :
( ( vertex(head_of(X0))
& vertex(tail_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
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(f50,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| head_of(X0) != tail_of(X1) )
& ( ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| head_of(X0) != tail_of(X1) )
& ( ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f50]) ).
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(f63,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| tail_of(sK0(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f48]) ).
fof(f73,plain,
! [X2,X0,X1] :
( edge(sK0(X0,X1,X2))
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f74,plain,
! [X2,X0,X1] :
( vertex(X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f85,plain,
! [X0,X1] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f90,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| sequential(X3,X4)
| sequential(X3,sK3(X0,X3,X4))
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f55]) ).
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(f95,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,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(f120,definition,
( spl12_1
<=> path(sK7,sK8,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f121,plain,
( path(sK7,sK8,sK11)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl12_2
<=> sK9 = sK10 ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f126,plain,
( sK9 = sK10
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f128,definition,
( spl12_3
<=> edge(sK10) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f130,plain,
( ~ edge(sK10)
| spl12_3 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f132,definition,
( spl12_4
<=> edge(sK9) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f134,plain,
( ~ edge(sK9)
| spl12_4 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f136,definition,
( spl12_5
<=> sK7 = sK8 ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f138,plain,
( sK7 = sK8
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f140,definition,
( spl12_6
<=> vertex(sK8) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f142,plain,
( ~ vertex(sK8)
| spl12_6 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f144,definition,
( spl12_7
<=> vertex(sK7) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f147,plain,
( ~ spl12_1
| spl12_2
| ~ spl12_3
| ~ spl12_4
| spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f111,f144,f140,f136,f132,f128,f124,f120]) ).
fof(f148,plain,
path(sK7,sK8,sK11),
inference(resolution,[],[f96,f110]) ).
fof(f151,plain,
spl12_1,
inference(avatar_split_clause,[],[f148,f120]) ).
fof(f155,plain,
( sK7 = tail_of(sK0(sK7,sK8,sK11))
| ~ spl12_1 ),
inference(resolution,[],[f72,f121]) ).
fof(f159,plain,
( vertex(sK7)
| ~ edge(sK0(sK7,sK8,sK11))
| ~ spl12_1 ),
inference(superposition,[],[f63,f155]) ).
fof(f161,definition,
( spl12_8
<=> edge(sK0(sK7,sK8,sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f163,plain,
( ~ edge(sK0(sK7,sK8,sK11))
| spl12_8 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( ~ spl12_8
| spl12_7
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f159,f120,f144,f161]) ).
fof(f170,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( edge(X1)
| ~ path(X3,X4,X2)
| ~ path(X5,X6,X2)
| ~ precedes(X0,X1,X2) ),
inference(resolution,[],[f92,f78]) ).
fof(f171,plain,
( ~ path(sK7,sK8,sK11)
| spl12_8 ),
inference(resolution,[],[f163,f73]) ).
fof(f174,plain,
( $false
| ~ spl12_1
| spl12_8 ),
inference(forward_subsumption_resolution,[],[f171,f121]) ).
fof(f175,plain,
( ~ spl12_1
| spl12_8 ),
inference(avatar_contradiction_clause,[],[f174]) ).
fof(f178,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK11)
| ~ precedes(X1,X0,sK11) ),
inference(resolution,[],[f99,f110]) ).
fof(f180,plain,
! [X0] : ~ precedes(X0,X0,sK11),
inference(factoring,[],[f178]) ).
fof(f184,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X5,sK10,X2)
| ~ path(X3,X4,X2)
| ~ path(X0,X1,X2) )
| spl12_3 ),
inference(resolution,[],[f170,f130]) ).
fof(f186,plain,
( ! [X2,X3,X0,X1] :
( ~ path(X0,X1,sK11)
| ~ path(X2,X3,sK11) )
| spl12_3 ),
inference(resolution,[],[f184,f109]) ).
fof(f188,definition,
( spl12_10
<=> ! [X2,X3] : ~ path(X2,X3,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f189,plain,
( ! [X2,X3] : ~ path(X2,X3,sK11)
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( spl12_10
| spl12_10
| spl12_3 ),
inference(avatar_split_clause,[],[f186,f128,f188,f188]) ).
fof(f192,plain,
( $false
| ~ spl12_1
| ~ spl12_10 ),
inference(resolution,[],[f189,f121]) ).
fof(f193,plain,
( ~ spl12_1
| ~ spl12_10 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f195,plain,
( ! [X0] : ~ sequential(sK9,X0)
| spl12_4 ),
inference(resolution,[],[f134,f85]) ).
fof(f204,plain,
! [X0,X1] :
( sequential(sK9,sK10)
| sequential(sK9,sK3(sK11,sK9,sK10))
| ~ path(X0,X1,sK11) ),
inference(resolution,[],[f90,f109]) ).
fof(f205,plain,
( ! [X0,X1] :
( sequential(sK9,sK3(sK11,sK9,sK10))
| ~ path(X0,X1,sK11) )
| spl12_4 ),
inference(forward_subsumption_resolution,[],[f204,f195]) ).
fof(f206,plain,
( ! [X0,X1] : ~ path(X0,X1,sK11)
| spl12_4 ),
inference(forward_subsumption_resolution,[],[f205,f195]) ).
fof(f207,plain,
( spl12_10
| spl12_4 ),
inference(avatar_split_clause,[],[f206,f132,f188]) ).
fof(f219,plain,
( ! [X0,X1] : ~ path(X0,sK8,X1)
| spl12_6 ),
inference(resolution,[],[f142,f74]) ).
fof(f220,plain,
( $false
| ~ spl12_1
| spl12_6 ),
inference(resolution,[],[f219,f121]) ).
fof(f221,plain,
( ~ spl12_1
| spl12_6 ),
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f224,plain,
( precedes(sK9,sK9,sK11)
| ~ spl12_2 ),
inference(superposition,[],[f109,f126]) ).
fof(f225,plain,
( $false
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f224,f180]) ).
fof(f226,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f227,plain,
( shortest_path(sK7,sK7,sK11)
| ~ spl12_5 ),
inference(superposition,[],[f110,f138]) ).
fof(f233,plain,
( $false
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f227,f118]) ).
fof(f234,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[],[f233]) ).
cnf(s1,plain,
( ~ spl12_1
| spl12_2
| ~ spl12_3
| ~ spl12_4
| spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(sat_conversion,[],[f147]) ).
cnf(s3,plain,
spl12_1,
inference(sat_conversion,[],[f151]) ).
cnf(s4,plain,
( ~ spl12_1
| spl12_7
| ~ spl12_8 ),
inference(sat_conversion,[],[f164]) ).
cnf(s6,plain,
( ~ spl12_1
| spl12_8 ),
inference(sat_conversion,[],[f175]) ).
cnf(s7,plain,
( spl12_10
| spl12_3
| spl12_10 ),
inference(sat_conversion,[],[f190]) ).
cnf(s8,plain,
( spl12_3
| spl12_10 ),
inference(rat,[],[s7]) ).
cnf(s9,plain,
( ~ spl12_1
| ~ spl12_10 ),
inference(sat_conversion,[],[f193]) ).
cnf(s10,plain,
( spl12_4
| spl12_10 ),
inference(sat_conversion,[],[f207]) ).
cnf(s12,plain,
( ~ spl12_1
| spl12_6 ),
inference(sat_conversion,[],[f221]) ).
cnf(s13,plain,
~ spl12_2,
inference(sat_conversion,[],[f226]) ).
cnf(s14,plain,
~ spl12_5,
inference(sat_conversion,[],[f234]) ).
cnf(s15,plain,
spl12_6,
inference(rat,[],[s12,s3]) ).
cnf(s16,plain,
~ spl12_10,
inference(rat,[],[s9,s3]) ).
cnf(s17,plain,
spl12_8,
inference(rat,[],[s6,s3]) ).
cnf(s18,plain,
spl12_7,
inference(rat,[],[s4,s17,s3]) ).
cnf(s19,plain,
spl12_4,
inference(rat,[],[s10,s16]) ).
cnf(s20,plain,
spl12_3,
inference(rat,[],[s8,s16]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s18,s15,s14,s19,s20,s13,s3]) ).
fof(f235,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 08:45:30 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.66/1.28 % (1726253)Detected formulas, will run a generic FOF schedule.
% 2.66/1.28 % (1726258)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3744365765:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.28 % (1726263)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3992530406:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.28 % (1726262)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2163848229:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.28 % (1726259)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1796316819:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.28 % (1726260)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=153212076:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.28 % (1726264)dis-21_1_sil=8000:lcm=predicate:random_seed=1952281843:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.66/1.28 % (1726261)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1797148789:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.28 % (1726262)Refutation not found, incomplete strategy
% 2.66/1.28 % (1726262)------------------------------
% 2.66/1.28 % (1726262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.28 % (1726262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.28 % (1726262)CaDiCaL version: 2.1.3
% 2.66/1.28 % (1726262)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.28 % (1726262)Time elapsed: 0.001 s
% 2.66/1.28 % (1726262)Peak memory usage: 88 MB
% 2.66/1.28 % (1726261)Refutation not found, incomplete strategy
% 2.66/1.28 % (1726261)------------------------------
% 2.66/1.28 % (1726261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.28 % (1726261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.28 % (1726261)CaDiCaL version: 2.1.3
% 2.66/1.28 % (1726261)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.28 % (1726261)Time elapsed: 0.002 s
% 2.66/1.28 % (1726261)Peak memory usage: 88 MB
% 2.66/1.28 % (1726261)Instructions burned: 1 (million)
% 2.66/1.28 % (1726263)First to succeed.
% 2.66/1.28 % (1726263)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1726253"
% 2.66/1.28 % (1726264)Instruction limit reached!
% 2.66/1.28 % (1726264)------------------------------
% 2.66/1.28 % (1726264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.28 % (1726264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.28 % (1726264)CaDiCaL version: 2.1.3
% 2.66/1.28 % (1726264)Termination reason: Instruction limit
% 2.66/1.28 % (1726264)Termination phase: Saturation
% 2.66/1.28 % (1726264)Time elapsed: 0.078 s
% 2.66/1.28 % (1726264)Peak memory usage: 90 MB
% 2.66/1.28 % (1726264)Instructions burned: 130 (million)
% 2.66/1.28 % (1726272)lrs+10_1_sil=8000:sp=occurrence:random_seed=3520913438:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.66/1.28 % (1726272)Also succeeded, but the first one will report.
% 2.66/1.28 % (1726261)------------------------------
% 2.66/1.28 % (1726261)------------------------------
% 2.66/1.28 % (1726262)------------------------------
% 2.66/1.28 % (1726262)------------------------------
% 2.66/1.28 % (1726263)Refutation found. Thanks to Tanya!
% 2.66/1.28 % SZS status Theorem for theBenchmark
% 2.66/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.48 % (1726263)------------------------------
% 3.52/1.48 % (1726263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.48 % (1726263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.48 % (1726263)CaDiCaL version: 2.1.3
% 3.52/1.48 % (1726263)Termination reason: Refutation
% 3.52/1.48 % (1726263)Time elapsed: 0.009 s
% 3.52/1.48 % (1726263)Peak memory usage: 90 MB
% 3.52/1.48 % (1726263)Instructions burned: 10 (million)
% 3.52/1.48 % (1726263)------------------------------
% 3.52/1.48 % (1726263)------------------------------
% 3.52/1.48 % (1726253)Success in time 0.415 s
% 3.52/1.48 % Vampire exiting
%------------------------------------------------------------------------------