%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA007+2 : 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 : n019.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 09:55:20 AM UTC 2026
% Result : Theorem 4.61s 1.81s
% Output : Refutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 186 ( 27 unt; 18 def)
% Number of atoms : 723 ( 160 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 893 ( 356 ~; 386 |; 110 &)
% ( 21 <=>; 15 =>; 0 <=; 5 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 20 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 248 ( 0 sgn 221 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_loops) ).
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(f3,axiom,
( complete
=> ! [X0,X1] :
( ( vertex(X0)
& vertex(X1)
& X0 != X1 )
=> ? [X2] :
( edge(X2)
& ( ( X0 = head_of(X2)
& X1 = tail_of(X2) )
<~> ( X1 = head_of(X2)
& X0 = tail_of(X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_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(f9,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [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) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_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(f19,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',back_edge) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f27,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] :
( ~ edge(X5)
| head_of(X3) != tail_of(X5)
| tail_of(X2) != head_of(X5) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] :
( ~ edge(X5)
| head_of(X3) != tail_of(X5)
| tail_of(X2) != head_of(X5) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
& complete ),
inference(flattening,[],[f27]) ).
fof(f29,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(f30,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,[],[f29]) ).
fof(f34,plain,
( ! [X0,X1] :
( ? [X2] :
( edge(X2)
& ( ( X0 = head_of(X2)
& X1 = tail_of(X2) )
<~> ( X1 = head_of(X2)
& X0 = tail_of(X2) ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(ennf_transformation,[],[f3]) ).
fof(f35,plain,
( ! [X0,X1] :
( ? [X2] :
( edge(X2)
& ( ( X0 = head_of(X2)
& X1 = tail_of(X2) )
<~> ( X1 = head_of(X2)
& X0 = tail_of(X2) ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ( vertex(head_of(X0))
& vertex(tail_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f38,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(f39,plain,
! [X0,X1,X2] :
( ! [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) ) ) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ! [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) ) ) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f39]) ).
fof(f41,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(f44,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(f45,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,[],[f44]) ).
fof(f49,plain,
( ! [X5] :
( ~ edge(X5)
| tail_of(X5) != head_of(sK5)
| head_of(X5) != tail_of(sK4) )
& shortest_path(sK2,sK3,sK6)
& precedes(sK4,sK5,sK6)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5),skolemize(X4,sK6)],[f28]) ).
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(f56,plain,
( ! [X0,X1] :
( ? [X2] :
( edge(X2)
& ( head_of(X2) != X1
| tail_of(X2) != X0
| head_of(X2) != X0
| tail_of(X2) != X1 )
& ( ( X1 = head_of(X2)
& X0 = tail_of(X2) )
| ( X0 = head_of(X2)
& X1 = tail_of(X2) ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(nnf_transformation,[],[f35]) ).
fof(f57,plain,
( ! [X0,X1] :
( ? [X2] :
( edge(X2)
& ( head_of(X2) != X1
| tail_of(X2) != X0
| head_of(X2) != X0
| tail_of(X2) != X1 )
& ( ( X1 = head_of(X2)
& X0 = tail_of(X2) )
| ( X0 = head_of(X2)
& X1 = tail_of(X2) ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
( ! [X0,X1] :
( ( edge(sK9(X0,X1))
& ( head_of(sK9(X0,X1)) != X1
| tail_of(sK9(X0,X1)) != X0
| head_of(sK9(X0,X1)) != X0
| tail_of(sK9(X0,X1)) != X1 )
& ( ( head_of(sK9(X0,X1)) = X1
& tail_of(sK9(X0,X1)) = X0 )
| ( head_of(sK9(X0,X1)) = X0
& tail_of(sK9(X0,X1)) = X1 ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f57]) ).
fof(f59,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,[],[f38]) ).
fof(f60,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,[],[f59]) ).
fof(f61,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,[],[f60]) ).
fof(f62,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,sK10(X0,X3,X4))
& precedes(sK10(X0,X3,X4),X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X6,sK10(X0,X3,X4))],[f61]) ).
fof(f63,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,[],[f41]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK11(X0,X1,X2)))
& path(X0,X1,sK11(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,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f65]) ).
fof(f83,plain,
complete,
inference(cnf_transformation,[],[f49]) ).
fof(f84,plain,
precedes(sK4,sK5,sK6),
inference(cnf_transformation,[],[f49]) ).
fof(f85,plain,
shortest_path(sK2,sK3,sK6),
inference(cnf_transformation,[],[f49]) ).
fof(f86,plain,
! [X5] :
( tail_of(X5) != head_of(sK5)
| ~ edge(X5)
| head_of(X5) != tail_of(sK4) ),
inference(cnf_transformation,[],[f49]) ).
fof(f91,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f30]) ).
fof(f106,plain,
! [X0,X1] :
( tail_of(sK9(X0,X1)) = X0
| tail_of(sK9(X0,X1)) = X1
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f58]) ).
fof(f108,plain,
! [X0,X1] :
( head_of(sK9(X0,X1)) = X1
| tail_of(sK9(X0,X1)) = X1
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f58]) ).
fof(f109,plain,
! [X0,X1] :
( head_of(sK9(X0,X1)) = X1
| head_of(sK9(X0,X1)) = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f58]) ).
fof(f111,plain,
! [X0,X1] :
( edge(sK9(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f58]) ).
fof(f112,plain,
! [X0] :
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f113,plain,
! [X0] :
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f114,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f118,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f119,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f45]) ).
fof(f131,plain,
! [X2,X3,X0,X1,X4,X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f45]) ).
fof(f140,definition,
( spl13_1
<=> complete ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f141,plain,
( ~ complete
| spl13_1 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,definition,
( spl13_2
<=> ! [X0,X1] :
( tail_of(sK9(X0,X1)) = X0
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK9(X0,X1)) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f144,plain,
( ! [X0,X1] :
( ~ vertex(X0)
| X0 = X1
| ~ vertex(X1)
| tail_of(sK9(X0,X1)) = X0
| tail_of(sK9(X0,X1)) = X1 )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f145,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f106,f143,f140]) ).
fof(f151,definition,
( spl13_4
<=> ! [X0,X1] :
( head_of(sK9(X0,X1)) = X1
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK9(X0,X1)) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f152,plain,
( ! [X0,X1] :
( ~ vertex(X0)
| X0 = X1
| ~ vertex(X1)
| head_of(sK9(X0,X1)) = X1
| tail_of(sK9(X0,X1)) = X1 )
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( ~ spl13_1
| spl13_4 ),
inference(avatar_split_clause,[],[f108,f151,f140]) ).
fof(f155,definition,
( spl13_5
<=> ! [X0,X1] :
( head_of(sK9(X0,X1)) = X1
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK9(X0,X1)) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f156,plain,
( ! [X0,X1] :
( ~ vertex(X0)
| X0 = X1
| ~ vertex(X1)
| head_of(sK9(X0,X1)) = X1
| head_of(sK9(X0,X1)) = X0 )
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( ~ spl13_1
| spl13_5 ),
inference(avatar_split_clause,[],[f109,f155,f140]) ).
fof(f163,definition,
( spl13_7
<=> ! [X0,X1] :
( edge(sK9(X0,X1))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f164,plain,
( ! [X0,X1] :
( edge(sK9(X0,X1))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f165,plain,
( ~ spl13_1
| spl13_7 ),
inference(avatar_split_clause,[],[f111,f163,f140]) ).
fof(f173,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f141,f83]) ).
fof(f174,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f175,plain,
path(sK2,sK3,sK6),
inference(resolution,[],[f124,f85]) ).
fof(f176,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK6)
| ~ precedes(X0,X1,sK6) ),
inference(resolution,[],[f130,f85]) ).
fof(f177,plain,
! [X0,X1] :
( on_path(sK5,sK6)
| ~ path(X0,X1,sK6) ),
inference(resolution,[],[f118,f84]) ).
fof(f179,definition,
( spl13_8
<=> ! [X0,X1] : ~ path(X0,X1,sK6) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f180,plain,
( ! [X0,X1] : ~ path(X0,X1,sK6)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,definition,
( spl13_9
<=> on_path(sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f183,plain,
( on_path(sK5,sK6)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f184,plain,
( spl13_8
| spl13_9 ),
inference(avatar_split_clause,[],[f177,f182,f179]) ).
fof(f185,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK6)
| edge(sK5) )
| ~ spl13_9 ),
inference(resolution,[],[f183,f94]) ).
fof(f187,definition,
( spl13_10
<=> edge(sK5) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f188,plain,
( edge(sK5)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( spl13_10
| spl13_8
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f185,f182,f179,f187]) ).
fof(f190,plain,
! [X0,X1] :
( on_path(sK4,sK6)
| ~ path(X0,X1,sK6) ),
inference(resolution,[],[f119,f84]) ).
fof(f192,plain,
( $false
| ~ spl13_8 ),
inference(unit_resulting_resolution,[],[f124,f85,f180]) ).
fof(f196,plain,
~ spl13_8,
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f198,definition,
( spl13_11
<=> on_path(sK4,sK6) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f199,plain,
( on_path(sK4,sK6)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( spl13_8
| spl13_11 ),
inference(avatar_split_clause,[],[f190,f198,f179]) ).
fof(f201,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK6)
| edge(sK4) )
| ~ spl13_11 ),
inference(resolution,[],[f199,f94]) ).
fof(f203,definition,
( spl13_12
<=> edge(sK4) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f204,plain,
( edge(sK4)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( spl13_12
| spl13_8
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f201,f198,f179,f203]) ).
fof(f207,plain,
( vertex(head_of(sK5))
| ~ spl13_10 ),
inference(resolution,[],[f113,f188]) ).
fof(f213,plain,
( vertex(tail_of(sK4))
| ~ spl13_12 ),
inference(resolution,[],[f112,f204]) ).
fof(f214,plain,
~ precedes(sK5,sK4,sK6),
inference(resolution,[],[f176,f84]) ).
fof(f215,plain,
( ! [X0] :
( ~ vertex(X0)
| tail_of(sK4) = X0
| head_of(sK9(tail_of(sK4),X0)) = X0
| tail_of(sK9(tail_of(sK4),X0)) = X0 )
| ~ spl13_4
| ~ spl13_12 ),
inference(resolution,[],[f213,f152]) ).
fof(f217,plain,
( ! [X0] :
( ~ vertex(X0)
| tail_of(sK4) = X0
| head_of(sK9(tail_of(sK4),X0)) = X0
| tail_of(sK4) = head_of(sK9(tail_of(sK4),X0)) )
| ~ spl13_5
| ~ spl13_12 ),
inference(resolution,[],[f213,f156]) ).
fof(f218,plain,
( ! [X0] :
( ~ vertex(X0)
| tail_of(sK4) = X0
| tail_of(sK4) = tail_of(sK9(tail_of(sK4),X0))
| tail_of(sK9(tail_of(sK4),X0)) = X0 )
| ~ spl13_2
| ~ spl13_12 ),
inference(resolution,[],[f213,f144]) ).
fof(f712,plain,
( head_of(sK5) = tail_of(sK4)
| head_of(sK5) = head_of(sK9(tail_of(sK4),head_of(sK5)))
| head_of(sK5) = tail_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_4
| ~ spl13_10
| ~ spl13_12 ),
inference(resolution,[],[f215,f207]) ).
fof(f754,plain,
( head_of(sK5) = tail_of(sK4)
| tail_of(sK4) = tail_of(sK9(tail_of(sK4),head_of(sK5)))
| head_of(sK5) = tail_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_2
| ~ spl13_10
| ~ spl13_12 ),
inference(resolution,[],[f218,f207]) ).
fof(f1095,definition,
( spl13_105
<=> head_of(sK5) = tail_of(sK4) ),
introduced(definition,[new_symbols(definition,[spl13_105])],[avatar_definition]) ).
fof(f1096,plain,
( head_of(sK5) = tail_of(sK4)
| ~ spl13_105 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1119,definition,
( spl13_112
<=> head_of(sK5) = tail_of(sK9(tail_of(sK4),head_of(sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_112])],[avatar_definition]) ).
fof(f1120,plain,
( head_of(sK5) = tail_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_112 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f1122,definition,
( spl13_113
<=> head_of(sK5) = head_of(sK9(tail_of(sK4),head_of(sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_113])],[avatar_definition]) ).
fof(f1123,plain,
( head_of(sK5) = head_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_113 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1124,plain,
( spl13_112
| spl13_113
| spl13_105
| ~ spl13_4
| ~ spl13_10
| ~ spl13_12 ),
inference(avatar_split_clause,[],[f712,f203,f187,f151,f1095,f1122,f1119]) ).
fof(f1141,definition,
( spl13_118
<=> tail_of(sK4) = tail_of(sK9(tail_of(sK4),head_of(sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_118])],[avatar_definition]) ).
fof(f1142,plain,
( tail_of(sK4) = tail_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_118 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f1143,plain,
( spl13_112
| spl13_118
| spl13_105
| ~ spl13_2
| ~ spl13_10
| ~ spl13_12 ),
inference(avatar_split_clause,[],[f754,f203,f187,f143,f1095,f1141,f1119]) ).
fof(f1186,plain,
( head_of(sK5) != tail_of(sK4)
| spl13_105 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1261,plain,
( ! [X0] :
( head_of(X0) != head_of(sK5)
| ~ edge(X0)
| ~ edge(sK4)
| sK4 = X0
| sequential(X0,sK4) )
| ~ spl13_105 ),
inference(superposition,[],[f91,f1096]) ).
fof(f1273,plain,
( ! [X0] :
( head_of(X0) != head_of(sK5)
| ~ edge(X0)
| sK4 = X0
| sequential(X0,sK4) )
| ~ spl13_12
| ~ spl13_105 ),
inference(forward_subsumption_resolution,[],[f1261,f204]) ).
fof(f2102,plain,
( ~ edge(sK5)
| sK4 = sK5
| sequential(sK5,sK4)
| ~ spl13_12
| ~ spl13_105 ),
inference(equality_resolution,[],[f1273]) ).
fof(f2104,plain,
( sK4 = sK5
| sequential(sK5,sK4)
| ~ spl13_10
| ~ spl13_12
| ~ spl13_105 ),
inference(forward_subsumption_resolution,[],[f2102,f188]) ).
fof(f2106,definition,
( spl13_205
<=> sequential(sK5,sK4) ),
introduced(definition,[new_symbols(definition,[spl13_205])],[avatar_definition]) ).
fof(f2107,plain,
( sequential(sK5,sK4)
| ~ spl13_205 ),
inference(avatar_component_clause,[],[f2106]) ).
fof(f2109,definition,
( spl13_206
<=> sK4 = sK5 ),
introduced(definition,[new_symbols(definition,[spl13_206])],[avatar_definition]) ).
fof(f2110,plain,
( sK4 = sK5
| ~ spl13_206 ),
inference(avatar_component_clause,[],[f2109]) ).
fof(f2111,plain,
( spl13_205
| spl13_206
| ~ spl13_10
| ~ spl13_12
| ~ spl13_105 ),
inference(avatar_split_clause,[],[f2104,f1095,f203,f187,f2109,f2106]) ).
fof(f2112,plain,
( precedes(sK4,sK4,sK6)
| ~ spl13_206 ),
inference(superposition,[],[f84,f2110]) ).
fof(f2117,plain,
( ~ precedes(sK4,sK4,sK6)
| ~ spl13_206 ),
inference(superposition,[],[f214,f2110]) ).
fof(f2197,plain,
( $false
| ~ spl13_206 ),
inference(forward_subsumption_resolution,[],[f2112,f2117]) ).
fof(f2198,plain,
~ spl13_206,
inference(avatar_contradiction_clause,[],[f2197]) ).
fof(f2220,plain,
( $false
| ~ spl13_9
| ~ spl13_11
| ~ spl13_205 ),
inference(unit_resulting_resolution,[],[f121,f175,f183,f199,f214,f2107]) ).
fof(f2228,plain,
( ~ spl13_9
| ~ spl13_11
| ~ spl13_205 ),
inference(avatar_contradiction_clause,[],[f2220]) ).
fof(f2410,plain,
( head_of(sK5) != head_of(sK5)
| ~ edge(sK9(tail_of(sK4),head_of(sK5)))
| tail_of(sK4) != head_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_112 ),
inference(superposition,[],[f86,f1120]) ).
fof(f2412,plain,
( head_of(sK5) != head_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ edge(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_112 ),
inference(superposition,[],[f114,f1120]) ).
fof(f2419,plain,
( ~ edge(sK9(tail_of(sK4),head_of(sK5)))
| tail_of(sK4) != head_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_112 ),
inference(trivial_inequality_removal,[],[f2410]) ).
fof(f2685,plain,
( head_of(sK5) = tail_of(sK4)
| head_of(sK5) = head_of(sK9(tail_of(sK4),head_of(sK5)))
| tail_of(sK4) = head_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_5
| ~ spl13_10
| ~ spl13_12 ),
inference(resolution,[],[f217,f207]) ).
fof(f2693,plain,
( head_of(sK5) = head_of(sK9(tail_of(sK4),head_of(sK5)))
| tail_of(sK4) = head_of(sK9(tail_of(sK4),head_of(sK5)))
| ~ spl13_5
| ~ spl13_10
| ~ spl13_12
| spl13_105 ),
inference(forward_subsumption_resolution,[],[f2685,f1186]) ).
fof(f2909,definition,
( spl13_266
<=> edge(sK9(tail_of(sK4),head_of(sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_266])],[avatar_definition]) ).
fof(f2910,plain,
( ~ edge(sK9(tail_of(sK4),head_of(sK5)))
| spl13_266 ),
inference(avatar_component_clause,[],[f2909]) ).
fof(f2927,plain,
( ~ spl13_266
| ~ spl13_113
| ~ spl13_112 ),
inference(avatar_split_clause,[],[f2412,f1119,f1122,f2909]) ).
fof(f2933,definition,
( spl13_272
<=> tail_of(sK4) = head_of(sK9(tail_of(sK4),head_of(sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_272])],[avatar_definition]) ).
fof(f2935,plain,
( ~ spl13_272
| ~ spl13_266
| ~ spl13_112 ),
inference(avatar_split_clause,[],[f2419,f1119,f2909,f2933]) ).
fof(f2974,plain,
( spl13_272
| spl13_113
| ~ spl13_5
| ~ spl13_10
| ~ spl13_12
| spl13_105 ),
inference(avatar_split_clause,[],[f2693,f1095,f203,f187,f155,f1122,f2933]) ).
fof(f4272,plain,
( head_of(sK5) = tail_of(sK4)
| ~ vertex(head_of(sK5))
| ~ vertex(tail_of(sK4))
| ~ spl13_7
| spl13_266 ),
inference(resolution,[],[f2910,f164]) ).
fof(f4274,plain,
( ~ vertex(head_of(sK5))
| ~ vertex(tail_of(sK4))
| ~ spl13_7
| spl13_105
| spl13_266 ),
inference(forward_subsumption_resolution,[],[f4272,f1186]) ).
fof(f4275,plain,
( ~ vertex(tail_of(sK4))
| ~ spl13_7
| ~ spl13_10
| spl13_105
| spl13_266 ),
inference(forward_subsumption_resolution,[],[f4274,f207]) ).
fof(f4276,plain,
( $false
| ~ spl13_7
| ~ spl13_10
| ~ spl13_12
| spl13_105
| spl13_266 ),
inference(forward_subsumption_resolution,[],[f4275,f213]) ).
fof(f4277,plain,
( ~ spl13_7
| ~ spl13_10
| ~ spl13_12
| spl13_105
| spl13_266 ),
inference(avatar_contradiction_clause,[],[f4276]) ).
fof(f5220,plain,
( $false
| ~ spl13_113
| ~ spl13_118 ),
inference(unit_resulting_resolution,[],[f131,f85,f84,f1123,f1142]) ).
fof(f5233,plain,
( ~ spl13_113
| ~ spl13_118 ),
inference(avatar_contradiction_clause,[],[f5220]) ).
cnf(s1,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f145]) ).
cnf(s3,plain,
( ~ spl13_1
| spl13_4 ),
inference(sat_conversion,[],[f153]) ).
cnf(s4,plain,
( ~ spl13_1
| spl13_5 ),
inference(sat_conversion,[],[f157]) ).
cnf(s6,plain,
( ~ spl13_1
| spl13_7 ),
inference(sat_conversion,[],[f165]) ).
cnf(s7,plain,
spl13_1,
inference(sat_conversion,[],[f174]) ).
cnf(s8,plain,
( spl13_8
| spl13_9 ),
inference(sat_conversion,[],[f184]) ).
cnf(s9,plain,
( spl13_8
| ~ spl13_9
| spl13_10 ),
inference(sat_conversion,[],[f189]) ).
cnf(s12,plain,
~ spl13_8,
inference(sat_conversion,[],[f196]) ).
cnf(s13,plain,
( spl13_8
| spl13_11 ),
inference(sat_conversion,[],[f200]) ).
cnf(s14,plain,
( spl13_8
| ~ spl13_11
| spl13_12 ),
inference(sat_conversion,[],[f205]) ).
cnf(s95,plain,
( ~ spl13_4
| ~ spl13_10
| ~ spl13_12
| spl13_105
| spl13_112
| spl13_113 ),
inference(sat_conversion,[],[f1124]) ).
cnf(s99,plain,
( ~ spl13_2
| ~ spl13_10
| ~ spl13_12
| spl13_105
| spl13_112
| spl13_118 ),
inference(sat_conversion,[],[f1143]) ).
cnf(s199,plain,
( ~ spl13_10
| ~ spl13_12
| ~ spl13_105
| spl13_205
| spl13_206 ),
inference(sat_conversion,[],[f2111]) ).
cnf(s203,plain,
~ spl13_206,
inference(sat_conversion,[],[f2198]) ).
cnf(s207,plain,
( ~ spl13_9
| ~ spl13_11
| ~ spl13_205 ),
inference(sat_conversion,[],[f2228]) ).
cnf(s279,plain,
( ~ spl13_112
| ~ spl13_113
| ~ spl13_266 ),
inference(sat_conversion,[],[f2927]) ).
cnf(s281,plain,
( ~ spl13_112
| ~ spl13_266
| ~ spl13_272 ),
inference(sat_conversion,[],[f2935]) ).
cnf(s290,plain,
( ~ spl13_5
| ~ spl13_10
| ~ spl13_12
| spl13_105
| spl13_113
| spl13_272 ),
inference(sat_conversion,[],[f2974]) ).
cnf(s441,plain,
( ~ spl13_7
| ~ spl13_10
| ~ spl13_12
| spl13_105
| spl13_266 ),
inference(sat_conversion,[],[f4277]) ).
cnf(s534,plain,
( ~ spl13_113
| ~ spl13_118 ),
inference(sat_conversion,[],[f5233]) ).
cnf(s536,plain,
( ~ spl13_10
| ~ spl13_12
| ~ spl13_105
| spl13_205 ),
inference(rat,[],[s199,s203]) ).
cnf(s541,plain,
spl13_11,
inference(rat,[],[s13,s12]) ).
cnf(s544,plain,
spl13_12,
inference(rat,[],[s14,s12,s541]) ).
cnf(s546,plain,
( ~ spl13_9
| spl13_10 ),
inference(rat,[],[s9,s12]) ).
cnf(s547,plain,
spl13_9,
inference(rat,[],[s8,s12]) ).
cnf(s548,plain,
~ spl13_205,
inference(rat,[],[s207,s541,s547]) ).
cnf(s552,plain,
spl13_10,
inference(rat,[],[s546,s547]) ).
cnf(s553,plain,
~ spl13_105,
inference(rat,[],[s536,s548,s544,s552]) ).
cnf(s555,plain,
spl13_7,
inference(rat,[],[s6,s7]) ).
cnf(s557,plain,
spl13_266,
inference(rat,[],[s441,s553,s552,s544,s555]) ).
cnf(s565,plain,
spl13_5,
inference(rat,[],[s4,s7]) ).
cnf(s566,plain,
spl13_4,
inference(rat,[],[s3,s7]) ).
cnf(s568,plain,
spl13_2,
inference(rat,[],[s1,s7]) ).
cnf(s570,plain,
spl13_112,
inference(rat,[],[s534,s95,s99,s544,s553,s552,s566,s568]) ).
cnf(s571,plain,
~ spl13_272,
inference(rat,[],[s281,s557,s570]) ).
cnf(s573,plain,
~ spl13_113,
inference(rat,[],[s279,s557,s570]) ).
cnf(s576,plain,
$false,
inference(rat,[],[s290,s565,s553,s552,s544,s571,s573]) ).
fof(f5252,plain,
$false,
inference(avatar_sat_refutation,[],[s576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA007+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n019.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 08:47:19 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 4.61/1.81 % (2795896)Detected formulas, will run a generic FOF schedule.
% 4.61/1.81 % (2795902)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=176648139:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.61/1.81 % (2795901)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=1487651387:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.61/1.81 % (2795906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2760356868:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.61/1.81 % (2795903)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=2092791123:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.61/1.81 % (2795904)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2849058735:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.61/1.81 % (2795907)dis-21_1_sil=8000:lcm=predicate:random_seed=3766291317: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)
% 4.61/1.81 % (2795905)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3994149777:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.61/1.81 % (2795904)Refutation not found, incomplete strategy
% 4.61/1.81 % (2795904)------------------------------
% 4.61/1.81 % (2795904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795904)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795904)Termination reason: Refutation not found, incomplete strategy
% 4.61/1.81 % (2795904)Time elapsed: 0.002 s
% 4.61/1.81 % (2795904)Peak memory usage: 88 MB
% 4.61/1.81 % (2795904)Instructions burned: 1 (million)
% 4.61/1.81 % (2795905)Instruction limit reached!
% 4.61/1.81 % (2795905)------------------------------
% 4.61/1.81 % (2795905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795905)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795905)Termination reason: Instruction limit
% 4.61/1.81 % (2795905)Termination phase: Saturation
% 4.61/1.81 % (2795905)Time elapsed: 0.067 s
% 4.61/1.81 % (2795905)Peak memory usage: 88 MB
% 4.61/1.81 % (2795905)Instructions burned: 120 (million)
% 4.61/1.81 % (2795907)Instruction limit reached!
% 4.61/1.81 % (2795907)------------------------------
% 4.61/1.81 % (2795907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795907)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795907)Termination reason: Instruction limit
% 4.61/1.81 % (2795907)Termination phase: Saturation
% 4.61/1.81 % (2795907)Time elapsed: 0.068 s
% 4.61/1.81 % (2795907)Peak memory usage: 89 MB
% 4.61/1.81 % (2795907)Instructions burned: 130 (million)
% 4.61/1.81 % (2795906)Instruction limit reached!
% 4.61/1.81 % (2795906)------------------------------
% 4.61/1.81 % (2795906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795906)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795906)Termination reason: Instruction limit
% 4.61/1.81 % (2795906)Termination phase: Saturation
% 4.61/1.81 % (2795906)Time elapsed: 0.085 s
% 4.61/1.81 % (2795906)Peak memory usage: 89 MB
% 4.61/1.81 % (2795906)Instructions burned: 140 (million)
% 4.61/1.81 % (2795916)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2521961844:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.61/1.81 % (2795915)lrs+10_1_sil=8000:sp=occurrence:random_seed=920886419:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.61/1.81 % (2795916)Refutation not found, incomplete strategy
% 4.61/1.81 % (2795916)------------------------------
% 4.61/1.81 % (2795916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795916)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795916)Termination reason: Refutation not found, incomplete strategy
% 4.61/1.81 % (2795916)Time elapsed: 0.003 s
% 4.61/1.81 % (2795916)Peak memory usage: 88 MB
% 4.61/1.81 % (2795916)Instructions burned: 2 (million)
% 4.61/1.81 % (2795904)------------------------------
% 4.61/1.81 % (2795904)------------------------------
% 4.61/1.81 % (2795917)lrs+1011_1_sil=32000:sp=occurrence:random_seed=973130156:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.61/1.81 % (2795915)Instruction limit reached!
% 4.61/1.81 % (2795915)------------------------------
% 4.61/1.81 % (2795915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795915)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795915)Termination reason: Instruction limit
% 4.61/1.81 % (2795915)Termination phase: Saturation
% 4.61/1.81 % (2795915)Time elapsed: 0.166 s
% 4.61/1.81 % (2795915)Peak memory usage: 91 MB
% 4.61/1.81 % (2795915)Instructions burned: 286 (million)
% 4.61/1.81 % (2795921)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2418432749:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.61/1.81 % (2795917)Instruction limit reached!
% 4.61/1.81 % (2795917)------------------------------
% 4.61/1.81 % (2795917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795917)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795917)Termination reason: Instruction limit
% 4.61/1.81 % (2795917)Termination phase: Saturation
% 4.61/1.81 % (2795917)Time elapsed: 0.198 s
% 4.61/1.81 % (2795917)Peak memory usage: 91 MB
% 4.61/1.81 % (2795917)Instructions burned: 326 (million)
% 4.61/1.81 % (2795916)------------------------------
% 4.61/1.81 % (2795916)------------------------------
% 4.61/1.81 % (2795922)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2311683887:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.61/1.81 % (2795921)Instruction limit reached!
% 4.61/1.81 % (2795921)------------------------------
% 4.61/1.81 % (2795921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795921)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795921)Termination reason: Instruction limit
% 4.61/1.81 % (2795921)Termination phase: Saturation
% 4.61/1.81 % (2795921)Time elapsed: 0.142 s
% 4.61/1.81 % (2795921)Peak memory usage: 90 MB
% 4.61/1.81 % (2795921)Instructions burned: 248 (million)
% 4.61/1.81 % (2795902)First to succeed.
% 4.61/1.81 % (2795902)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2795896"
% 4.61/1.81 % (2795924)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3215387607:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 4.61/1.81 % (2795925)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1761601152:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 4.61/1.81 % (2795901)Also succeeded, but the first one will report.
% 4.61/1.81 % (2795922)Instruction limit reached!
% 4.61/1.81 % (2795922)------------------------------
% 4.61/1.81 % (2795922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795922)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795922)Termination reason: Instruction limit
% 4.61/1.81 % (2795922)Termination phase: Saturation
% 4.61/1.81 % (2795922)Time elapsed: 0.153 s
% 4.61/1.81 % (2795922)Peak memory usage: 88 MB
% 4.61/1.81 % (2795922)Instructions burned: 295 (million)
% 4.61/1.81 % (2795925)Instruction limit reached!
% 4.61/1.81 % (2795925)------------------------------
% 4.61/1.81 % (2795925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.81 % (2795925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.81 % (2795925)CaDiCaL version: 2.1.3
% 4.61/1.81 % (2795925)Termination reason: Instruction limit
% 4.61/1.81 % (2795925)Termination phase: Saturation
% 4.61/1.81 % (2795925)Time elapsed: 0.079 s
% 4.61/1.81 % (2795925)Peak memory usage: 90 MB
% 4.61/1.81 % (2795925)Instructions burned: 113 (million)
% 4.61/1.81 % (2795927)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=322741646:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 4.61/1.81 % (2795902)Refutation found. Thanks to Tanya!
% 4.61/1.81 % SZS status Theorem for theBenchmark
% 4.61/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 7.17/2.00 % (2795902)------------------------------
% 7.17/2.00 % (2795902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.17/2.00 % (2795902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.17/2.00 % (2795902)CaDiCaL version: 2.1.3
% 7.17/2.00 % (2795902)Termination reason: Refutation
% 7.17/2.00 % (2795902)Time elapsed: 0.652 s
% 7.17/2.00 % (2795902)Peak memory usage: 134 MB
% 7.17/2.00 % (2795902)Instructions burned: 1445 (million)
% 7.17/2.00 % (2795902)------------------------------
% 7.17/2.00 % (2795902)------------------------------
% 7.17/2.00 % (2795896)Success in time 0.941 s
% 7.17/2.00 % Vampire exiting
%------------------------------------------------------------------------------