%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA007+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 : 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 09:55:20 AM UTC 2026
% Result : Theorem 6.42s 1.94s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 27
% Syntax : Number of formulae : 194 ( 28 unt; 18 def)
% Number of atoms : 738 ( 175 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 920 ( 376 ~; 396 |; 110 &)
% ( 19 <=>; 14 =>; 0 <=; 5 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 18 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 284 ( 0 sgn 257 !; 27 ?)
% 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(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(f18,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(f19,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)],[f18]) ).
fof(f22,plain,
! [X0] :
( ( vertex(head_of(X0))
& vertex(tail_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f23,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(f24,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,[],[f23]) ).
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(ennf_transformation,[],[f6]) ).
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(flattening,[],[f28]) ).
fof(f32,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(f33,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,[],[f32]) ).
fof(f34,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(f35,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(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(ennf_transformation,[],[f12]) ).
fof(f37,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,[],[f36]) ).
fof(f44,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,[],[f19]) ).
fof(f45,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,[],[f44]) ).
fof(f46,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,[],[f24]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
( ! [X0,X1] :
( ( edge(sK0(X0,X1))
& ( head_of(sK0(X0,X1)) != X1
| tail_of(sK0(X0,X1)) != X0
| head_of(sK0(X0,X1)) != X0
| tail_of(sK0(X0,X1)) != X1 )
& ( ( head_of(sK0(X0,X1)) = X1
& tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0
& tail_of(sK0(X0,X1)) = X1 ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f47]) ).
fof(f54,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(f55,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,[],[f54]) ).
fof(f56,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,[],[f34]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[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) )
& ( ( sequential(X3,sK4(X0,X3,X4))
& precedes(sK4(X0,X3,X4),X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X6,sK4(X0,X3,X4))],[f58]) ).
fof(f60,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,[],[f35]) ).
fof(f61,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,[],[f60]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2)))
& path(X0,X1,sK5(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,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f62]) ).
fof(f65,plain,
( ! [X5] :
( ~ edge(X5)
| tail_of(X5) != head_of(sK11)
| head_of(X5) != tail_of(sK10) )
& shortest_path(sK8,sK9,sK12)
& precedes(sK10,sK11,sK12)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12)],[f45]) ).
fof(f67,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f68,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f69,plain,
! [X0,X1] :
( tail_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f70,plain,
! [X0,X1] :
( tail_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X0,X1] :
( head_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f74,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| edge(X3)
| ~ on_path(X3,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f96,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4,X5] :
( precedes(X3,X4,X0)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f103,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f110,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,[],[f37]) ).
fof(f119,plain,
complete,
inference(cnf_transformation,[],[f65]) ).
fof(f120,plain,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f65]) ).
fof(f122,plain,
! [X5] :
( ~ edge(X5)
| tail_of(X5) != head_of(sK11)
| head_of(X5) != tail_of(sK10) ),
inference(cnf_transformation,[],[f65]) ).
fof(f130,definition,
sF13 = head_of(sK11),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f131,plain,
head_of(sK11) = sF13,
inference(reorient_equations,[],[f130]) ).
fof(f132,definition,
sF14 = tail_of(sK10),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f133,plain,
tail_of(sK10) = sF14,
inference(reorient_equations,[],[f132]) ).
fof(f134,plain,
! [X5] :
( tail_of(X5) != sF13
| ~ edge(X5)
| head_of(X5) != sF14 ),
inference(definition_folding,[],[f122,f133,f131]) ).
fof(f135,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X5,X4,X0)
| ~ on_path(X3,X0)
| ~ sequential(X3,X5)
| precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(forward_subsumption_resolution,[],[f97,f102]) ).
fof(f137,plain,
! [X0,X1] :
( ~ vertex(X1)
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X0
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f69,f119]) ).
fof(f138,plain,
! [X0,X1] :
( ~ vertex(X1)
| head_of(sK0(X0,X1)) = X0
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X0
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f70,f119]) ).
fof(f139,plain,
! [X0,X1] :
( ~ vertex(X1)
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f71,f119]) ).
fof(f142,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f74,f119]) ).
fof(f150,definition,
( spl15_2
<=> edge(sK10) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f151,plain,
( edge(sK10)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f152,plain,
( ~ edge(sK10)
| spl15_2 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f154,definition,
( spl15_3
<=> sF13 = sF14 ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f156,plain,
( sF13 != sF14
| spl15_3 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f158,plain,
! [X0] :
( head_of(X0) != sF14
| ~ edge(X0)
| ~ edge(sK10)
| sK10 = X0
| sequential(X0,sK10) ),
inference(superposition,[],[f96,f133]) ).
fof(f160,definition,
( spl15_4
<=> ! [X0] :
( head_of(X0) != sF14
| sequential(X0,sK10)
| sK10 = X0
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f161,plain,
( ! [X0] :
( head_of(X0) != sF14
| sequential(X0,sK10)
| sK10 = X0
| ~ edge(X0) )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f162,plain,
( ~ spl15_2
| spl15_4 ),
inference(avatar_split_clause,[],[f158,f160,f150]) ).
fof(f165,plain,
path(sK8,sK9,sK12),
inference(resolution,[],[f106,f121]) ).
fof(f166,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X0) != head_of(X1)
| tail_of(X0) != sF14
| ~ shortest_path(X2,X3,X4)
| ~ precedes(sK10,X1,X4) ),
inference(superposition,[],[f110,f133]) ).
fof(f168,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X0) != head_of(X1)
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X1,X0,X4) ),
inference(equality_resolution,[],[f110]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ precedes(X3,X3,X2) ),
inference(equality_resolution,[],[f168]) ).
fof(f172,plain,
! [X0] : ~ precedes(X0,X0,sK12),
inference(resolution,[],[f171,f121]) ).
fof(f173,plain,
! [X0,X1] :
( on_path(sK11,sK12)
| ~ path(X0,X1,sK12) ),
inference(resolution,[],[f102,f120]) ).
fof(f175,definition,
( spl15_5
<=> ! [X0,X1] : ~ path(X0,X1,sK12) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f176,plain,
( ! [X0,X1] : ~ path(X0,X1,sK12)
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,definition,
( spl15_6
<=> on_path(sK11,sK12) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f180,plain,
( on_path(sK11,sK12)
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( spl15_5
| spl15_6 ),
inference(avatar_split_clause,[],[f173,f178,f175]) ).
fof(f182,plain,
! [X0,X1] :
( on_path(sK10,sK12)
| ~ path(X0,X1,sK12) ),
inference(resolution,[],[f103,f120]) ).
fof(f183,plain,
! [X0] :
( ~ on_path(X0,sK12)
| edge(X0) ),
inference(resolution,[],[f88,f165]) ).
fof(f185,plain,
( $false
| ~ spl15_5 ),
inference(resolution,[],[f176,f165]) ).
fof(f186,plain,
~ spl15_5,
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f188,definition,
( spl15_7
<=> on_path(sK10,sK12) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f190,plain,
( on_path(sK10,sK12)
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
( spl15_5
| spl15_7 ),
inference(avatar_split_clause,[],[f182,f188,f175]) ).
fof(f192,plain,
( edge(sK10)
| ~ spl15_7 ),
inference(resolution,[],[f190,f183]) ).
fof(f193,plain,
( $false
| spl15_2
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f192,f152]) ).
fof(f194,plain,
( spl15_2
| ~ spl15_7 ),
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f195,plain,
( edge(sK11)
| ~ spl15_6 ),
inference(resolution,[],[f180,f183]) ).
fof(f200,definition,
( spl15_8
<=> ! [X2,X1,X3] :
( ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,sK11,X3) ) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f201,plain,
( ! [X2,X3,X1] :
( ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,sK11,X3) )
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f211,definition,
( spl15_11
<=> ! [X2,X0,X1,X3] :
( head_of(X0) != sF13
| ~ precedes(sK10,X0,X3)
| ~ shortest_path(X1,X2,X3) ) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f212,plain,
( ! [X2,X3,X0,X1] :
( head_of(X0) != sF13
| ~ precedes(sK10,X0,X3)
| ~ shortest_path(X1,X2,X3) )
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f216,plain,
( ~ precedes(sK10,sK11,sK12)
| ~ spl15_8 ),
inference(resolution,[],[f201,f121]) ).
fof(f217,plain,
( $false
| ~ spl15_8 ),
inference(forward_subsumption_resolution,[],[f216,f120]) ).
fof(f218,plain,
~ spl15_8,
inference(avatar_contradiction_clause,[],[f217]) ).
fof(f219,plain,
( sF13 != sF14
| sequential(sK11,sK10)
| sK10 = sK11
| ~ edge(sK11)
| ~ spl15_4 ),
inference(superposition,[],[f161,f131]) ).
fof(f220,plain,
( sF13 != sF14
| sequential(sK11,sK10)
| sK10 = sK11
| ~ spl15_4
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f219,f195]) ).
fof(f222,definition,
( spl15_12
<=> sK10 = sK11 ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
fof(f224,plain,
( sK10 = sK11
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl15_13
<=> sequential(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
fof(f229,plain,
( spl15_12
| spl15_13
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f220,f178,f160,f154,f226,f222]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ on_path(X0,sK12)
| ~ sequential(X0,sK10)
| precedes(X0,sK11,sK12)
| ~ path(X1,X2,sK12) ),
inference(resolution,[],[f135,f120]) ).
fof(f232,definition,
( spl15_14
<=> ! [X0] :
( ~ on_path(X0,sK12)
| precedes(X0,sK11,sK12)
| ~ sequential(X0,sK10) ) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
fof(f233,plain,
( ! [X0] :
( precedes(X0,sK11,sK12)
| ~ on_path(X0,sK12)
| ~ sequential(X0,sK10) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( spl15_5
| spl15_14 ),
inference(avatar_split_clause,[],[f230,f232,f175]) ).
fof(f255,plain,
( vertex(sF13)
| ~ edge(sK11) ),
inference(superposition,[],[f68,f131]) ).
fof(f256,plain,
( vertex(sF13)
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f255,f195]) ).
fof(f257,plain,
( ! [X0] :
( ~ vertex(X0)
| sF13 = tail_of(sK0(X0,sF13))
| tail_of(sK0(X0,sF13)) = X0
| sF13 = X0 )
| ~ spl15_6 ),
inference(resolution,[],[f256,f137]) ).
fof(f259,plain,
( ! [X0] :
( ~ vertex(X0)
| sF13 = tail_of(sK0(X0,sF13))
| sF13 = head_of(sK0(X0,sF13))
| sF13 = X0 )
| ~ spl15_6 ),
inference(resolution,[],[f256,f139]) ).
fof(f260,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,sF13)) = X0
| tail_of(sK0(X0,sF13)) = X0
| sF13 = X0 )
| ~ spl15_6 ),
inference(resolution,[],[f256,f138]) ).
fof(f288,plain,
( ~ on_path(sK11,sK12)
| ~ sequential(sK11,sK10)
| ~ spl15_14 ),
inference(resolution,[],[f233,f172]) ).
fof(f307,plain,
( ~ sequential(sK11,sK10)
| ~ spl15_6
| ~ spl15_14 ),
inference(forward_subsumption_resolution,[],[f288,f180]) ).
fof(f308,plain,
( ~ spl15_13
| ~ spl15_6
| ~ spl15_14 ),
inference(avatar_split_clause,[],[f307,f232,f178,f226]) ).
fof(f344,plain,
( vertex(sF14)
| ~ edge(sK10) ),
inference(superposition,[],[f67,f133]) ).
fof(f345,plain,
( vertex(sF14)
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f344,f151]) ).
fof(f350,plain,
( sF13 = tail_of(sK0(sF14,sF13))
| sF14 = tail_of(sK0(sF14,sF13))
| sF13 = sF14
| ~ spl15_2
| ~ spl15_6 ),
inference(resolution,[],[f345,f257]) ).
fof(f352,plain,
( sF13 = tail_of(sK0(sF14,sF13))
| sF13 = head_of(sK0(sF14,sF13))
| sF13 = sF14
| ~ spl15_2
| ~ spl15_6 ),
inference(resolution,[],[f345,f259]) ).
fof(f353,plain,
( sF14 = head_of(sK0(sF14,sF13))
| sF14 = tail_of(sK0(sF14,sF13))
| sF13 = sF14
| ~ spl15_2
| ~ spl15_6 ),
inference(resolution,[],[f345,f260]) ).
fof(f354,plain,
( sF14 = head_of(sK0(sF14,sF13))
| sF14 = tail_of(sK0(sF14,sF13))
| ~ spl15_2
| spl15_3
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f353,f156]) ).
fof(f357,plain,
( sF13 = tail_of(sK0(sF14,sF13))
| sF14 = tail_of(sK0(sF14,sF13))
| ~ spl15_2
| spl15_3
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f350,f156]) ).
fof(f359,definition,
( spl15_25
<=> sF14 = tail_of(sK0(sF14,sF13)) ),
introduced(definition,[new_symbols(definition,[spl15_25])],[avatar_definition]) ).
fof(f361,plain,
( sF14 = tail_of(sK0(sF14,sF13))
| ~ spl15_25 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f363,definition,
( spl15_26
<=> sF14 = head_of(sK0(sF14,sF13)) ),
introduced(definition,[new_symbols(definition,[spl15_26])],[avatar_definition]) ).
fof(f365,plain,
( sF14 = head_of(sK0(sF14,sF13))
| ~ spl15_26 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f366,plain,
( spl15_25
| spl15_26
| ~ spl15_2
| spl15_3
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f354,f178,f154,f150,f363,f359]) ).
fof(f368,definition,
( spl15_27
<=> sF13 = head_of(sK0(sF14,sF13)) ),
introduced(definition,[new_symbols(definition,[spl15_27])],[avatar_definition]) ).
fof(f370,plain,
( sF13 = head_of(sK0(sF14,sF13))
| ~ spl15_27 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f372,definition,
( spl15_28
<=> sF13 = tail_of(sK0(sF14,sF13)) ),
introduced(definition,[new_symbols(definition,[spl15_28])],[avatar_definition]) ).
fof(f374,plain,
( sF13 = tail_of(sK0(sF14,sF13))
| ~ spl15_28 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f377,plain,
( spl15_25
| spl15_28
| ~ spl15_2
| spl15_3
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f357,f178,f154,f150,f372,f359]) ).
fof(f378,plain,
( precedes(sK10,sK10,sK12)
| ~ spl15_12 ),
inference(superposition,[],[f120,f224]) ).
fof(f388,plain,
( $false
| ~ spl15_12 ),
inference(forward_subsumption_resolution,[],[f378,f172]) ).
fof(f389,plain,
~ spl15_12,
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f393,plain,
( ! [X2,X3,X0,X1] :
( head_of(X0) != sF13
| sF14 != tail_of(sK0(sF14,sF13))
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,X0,X3) )
| ~ spl15_27 ),
inference(superposition,[],[f166,f370]) ).
fof(f398,plain,
( ! [X2,X3,X0,X1] :
( head_of(X0) != sF13
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,X0,X3) )
| ~ spl15_25
| ~ spl15_27 ),
inference(forward_subsumption_resolution,[],[f393,f361]) ).
fof(f400,definition,
( spl15_29
<=> edge(sK0(sF14,sF13)) ),
introduced(definition,[new_symbols(definition,[spl15_29])],[avatar_definition]) ).
fof(f401,plain,
( edge(sK0(sF14,sF13))
| ~ spl15_29 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f402,plain,
( ~ edge(sK0(sF14,sF13))
| spl15_29 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f407,plain,
( spl15_11
| ~ spl15_25
| ~ spl15_27 ),
inference(avatar_split_clause,[],[f398,f368,f359,f211]) ).
fof(f482,plain,
( ~ vertex(sF14)
| ~ vertex(sF13)
| sF13 = sF14
| spl15_29 ),
inference(resolution,[],[f402,f142]) ).
fof(f483,plain,
( ~ vertex(sF13)
| sF13 = sF14
| ~ spl15_2
| spl15_29 ),
inference(forward_subsumption_resolution,[],[f482,f345]) ).
fof(f484,plain,
( sF13 = sF14
| ~ spl15_2
| ~ spl15_6
| spl15_29 ),
inference(forward_subsumption_resolution,[],[f483,f256]) ).
fof(f485,plain,
( $false
| ~ spl15_2
| spl15_3
| ~ spl15_6
| spl15_29 ),
inference(forward_subsumption_resolution,[],[f484,f156]) ).
fof(f486,plain,
( ~ spl15_2
| spl15_3
| ~ spl15_6
| spl15_29 ),
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f492,plain,
( sF13 = tail_of(sK0(sF14,sF13))
| sF13 = head_of(sK0(sF14,sF13))
| ~ spl15_2
| spl15_3
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f352,f156]) ).
fof(f499,plain,
( sF13 = sF14
| sF13 = head_of(sK0(sF14,sF13))
| ~ spl15_2
| spl15_3
| ~ spl15_6
| ~ spl15_25 ),
inference(forward_demodulation,[],[f492,f361]) ).
fof(f500,plain,
( sF13 = head_of(sK0(sF14,sF13))
| ~ spl15_2
| spl15_3
| ~ spl15_6
| ~ spl15_25 ),
inference(forward_subsumption_resolution,[],[f499,f156]) ).
fof(f532,plain,
( spl15_27
| ~ spl15_2
| spl15_3
| ~ spl15_6
| ~ spl15_25 ),
inference(avatar_split_clause,[],[f500,f359,f178,f154,f150,f368]) ).
fof(f558,plain,
( ! [X2,X0,X1] :
( sF13 != sF13
| ~ precedes(sK10,sK11,X0)
| ~ shortest_path(X1,X2,X0) )
| ~ spl15_11 ),
inference(superposition,[],[f212,f131]) ).
fof(f563,plain,
( ! [X2,X0,X1] :
( ~ precedes(sK10,sK11,X0)
| ~ shortest_path(X1,X2,X0) )
| ~ spl15_11 ),
inference(trivial_inequality_removal,[],[f558]) ).
fof(f564,plain,
( spl15_8
| ~ spl15_11 ),
inference(avatar_split_clause,[],[f563,f211,f200]) ).
fof(f591,plain,
( sF13 != sF13
| ~ edge(sK0(sF14,sF13))
| sF14 != head_of(sK0(sF14,sF13))
| ~ spl15_28 ),
inference(superposition,[],[f134,f374]) ).
fof(f595,plain,
( ~ edge(sK0(sF14,sF13))
| sF14 != head_of(sK0(sF14,sF13))
| ~ spl15_28 ),
inference(trivial_inequality_removal,[],[f591]) ).
fof(f597,plain,
( sF14 != head_of(sK0(sF14,sF13))
| ~ spl15_28
| ~ spl15_29 ),
inference(forward_subsumption_resolution,[],[f595,f401]) ).
fof(f601,plain,
( $false
| ~ spl15_26
| ~ spl15_28
| ~ spl15_29 ),
inference(forward_subsumption_resolution,[],[f597,f365]) ).
fof(f602,plain,
( ~ spl15_26
| ~ spl15_28
| ~ spl15_29 ),
inference(avatar_contradiction_clause,[],[f601]) ).
cnf(s2,plain,
( ~ spl15_2
| spl15_4 ),
inference(sat_conversion,[],[f162]) ).
cnf(s3,plain,
( spl15_5
| spl15_6 ),
inference(sat_conversion,[],[f181]) ).
cnf(s4,plain,
~ spl15_5,
inference(sat_conversion,[],[f186]) ).
cnf(s5,plain,
( spl15_5
| spl15_7 ),
inference(sat_conversion,[],[f191]) ).
cnf(s6,plain,
( spl15_2
| ~ spl15_7 ),
inference(sat_conversion,[],[f194]) ).
cnf(s9,plain,
~ spl15_8,
inference(sat_conversion,[],[f218]) ).
cnf(s10,plain,
( ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| spl15_12
| spl15_13 ),
inference(sat_conversion,[],[f229]) ).
cnf(s11,plain,
( spl15_5
| spl15_14 ),
inference(sat_conversion,[],[f234]) ).
cnf(s18,plain,
( ~ spl15_6
| ~ spl15_13
| ~ spl15_14 ),
inference(sat_conversion,[],[f308]) ).
cnf(s21,plain,
( ~ spl15_2
| spl15_3
| ~ spl15_6
| spl15_25
| spl15_26 ),
inference(sat_conversion,[],[f366]) ).
cnf(s24,plain,
( ~ spl15_2
| spl15_3
| ~ spl15_6
| spl15_25
| spl15_28 ),
inference(sat_conversion,[],[f377]) ).
cnf(s26,plain,
~ spl15_12,
inference(sat_conversion,[],[f389]) ).
cnf(s28,plain,
( spl15_11
| ~ spl15_25
| ~ spl15_27 ),
inference(sat_conversion,[],[f407]) ).
cnf(s35,plain,
( ~ spl15_2
| spl15_3
| ~ spl15_6
| spl15_29 ),
inference(sat_conversion,[],[f486]) ).
cnf(s41,plain,
( ~ spl15_2
| spl15_3
| ~ spl15_6
| ~ spl15_25
| spl15_27 ),
inference(sat_conversion,[],[f532]) ).
cnf(s43,plain,
( spl15_8
| ~ spl15_11 ),
inference(sat_conversion,[],[f564]) ).
cnf(s47,plain,
( ~ spl15_26
| ~ spl15_28
| ~ spl15_29 ),
inference(sat_conversion,[],[f602]) ).
cnf(s48,plain,
( ~ spl15_3
| ~ spl15_4
| ~ spl15_6
| spl15_13 ),
inference(rat,[],[s10,s26]) ).
cnf(s49,plain,
~ spl15_11,
inference(rat,[],[s43,s9]) ).
cnf(s55,plain,
spl15_14,
inference(rat,[],[s11,s4]) ).
cnf(s56,plain,
spl15_7,
inference(rat,[],[s5,s4]) ).
cnf(s60,plain,
spl15_2,
inference(rat,[],[s6,s56]) ).
cnf(s61,plain,
spl15_6,
inference(rat,[],[s3,s4]) ).
cnf(s62,plain,
~ spl15_13,
inference(rat,[],[s18,s55,s61]) ).
cnf(s63,plain,
spl15_4,
inference(rat,[],[s2,s60]) ).
cnf(s64,plain,
~ spl15_3,
inference(rat,[],[s48,s62,s61,s63]) ).
cnf(s65,plain,
spl15_29,
inference(rat,[],[s35,s61,s60,s64]) ).
cnf(s66,plain,
spl15_25,
inference(rat,[],[s47,s21,s24,s65,s60,s61,s64]) ).
cnf(s70,plain,
~ spl15_27,
inference(rat,[],[s28,s49,s66]) ).
cnf(s71,plain,
$false,
inference(rat,[],[s41,s64,s61,s60,s70,s66]) ).
fof(f603,plain,
$false,
inference(avatar_sat_refutation,[],[s71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA007+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 08:50:11 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 6.42/1.94 % (2537515)Detected formulas, will run a generic FOF schedule.
% 6.42/1.94 % (2537523)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3228000444:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.42/1.94 % (2537523)Refutation not found, incomplete strategy
% 6.42/1.94 % (2537523)------------------------------
% 6.42/1.94 % (2537523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537523)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537523)Termination reason: Refutation not found, incomplete strategy
% 6.42/1.94 % (2537523)Time elapsed: 0.001 s
% 6.42/1.94 % (2537523)Peak memory usage: 88 MB
% 6.42/1.94 % (2537523)Instructions burned: 1 (million)
% 6.42/1.94 % (2537522)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=283267090:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.42/1.94 % (2537521)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=3697542076:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.42/1.94 % (2537520)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=1280560511:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.42/1.94 % (2537525)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3735776946:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.42/1.94 % (2537524)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3081296873:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.42/1.94 % (2537526)dis-21_1_sil=8000:lcm=predicate:random_seed=210466849: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)
% 6.42/1.94 % (2537524)Instruction limit reached!
% 6.42/1.94 % (2537524)------------------------------
% 6.42/1.94 % (2537524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537524)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537524)Termination reason: Instruction limit
% 6.42/1.94 % (2537524)Termination phase: Saturation
% 6.42/1.94 % (2537524)Time elapsed: 0.066 s
% 6.42/1.94 % (2537524)Peak memory usage: 88 MB
% 6.42/1.94 % (2537524)Instructions burned: 120 (million)
% 6.42/1.94 % (2537526)Instruction limit reached!
% 6.42/1.94 % (2537526)------------------------------
% 6.42/1.94 % (2537526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537526)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537526)Termination reason: Instruction limit
% 6.42/1.94 % (2537526)Termination phase: Saturation
% 6.42/1.94 % (2537526)Time elapsed: 0.069 s
% 6.42/1.94 % (2537526)Peak memory usage: 89 MB
% 6.42/1.94 % (2537526)Instructions burned: 129 (million)
% 6.42/1.94 % (2537525)Instruction limit reached!
% 6.42/1.94 % (2537525)------------------------------
% 6.42/1.94 % (2537525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537525)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537525)Termination reason: Instruction limit
% 6.42/1.94 % (2537525)Termination phase: Saturation
% 6.42/1.94 % (2537525)Time elapsed: 0.087 s
% 6.42/1.94 % (2537525)Peak memory usage: 89 MB
% 6.42/1.94 % (2537525)Instructions burned: 140 (million)
% 6.42/1.94 % (2537523)------------------------------
% 6.42/1.94 % (2537523)------------------------------
% 6.42/1.94 % (2537537)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=2405397659:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.42/1.94 % (2537534)lrs+10_1_sil=8000:sp=occurrence:random_seed=3449991327:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.42/1.94 % (2537535)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3990963470:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.42/1.94 % (2537535)Refutation not found, incomplete strategy
% 6.42/1.94 % (2537535)------------------------------
% 6.42/1.94 % (2537535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537535)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537535)Termination reason: Refutation not found, incomplete strategy
% 6.42/1.94 % (2537535)Time elapsed: 0.003 s
% 6.42/1.94 % (2537535)Peak memory usage: 88 MB
% 6.42/1.94 % (2537535)Instructions burned: 2 (million)
% 6.42/1.94 % (2537536)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2224831789:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.42/1.94 % (2537537)Instruction limit reached!
% 6.42/1.94 % (2537537)------------------------------
% 6.42/1.94 % (2537537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537537)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537537)Termination reason: Instruction limit
% 6.42/1.94 % (2537537)Termination phase: Saturation
% 6.42/1.94 % (2537537)Time elapsed: 0.076 s
% 6.42/1.94 % (2537537)Peak memory usage: 90 MB
% 6.42/1.94 % (2537537)Instructions burned: 248 (million)
% 6.42/1.94 % (2537542)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=803996791:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.42/1.94 % (2537534)Instruction limit reached!
% 6.42/1.94 % (2537534)------------------------------
% 6.42/1.94 % (2537534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537534)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537534)Termination reason: Instruction limit
% 6.42/1.94 % (2537534)Termination phase: Saturation
% 6.42/1.94 % (2537534)Time elapsed: 0.169 s
% 6.42/1.94 % (2537534)Peak memory usage: 91 MB
% 6.42/1.94 % (2537534)Instructions burned: 286 (million)
% 6.42/1.94 % (2537536)Instruction limit reached!
% 6.42/1.94 % (2537536)------------------------------
% 6.42/1.94 % (2537536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537536)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537536)Termination reason: Instruction limit
% 6.42/1.94 % (2537536)Termination phase: Saturation
% 6.42/1.94 % (2537536)Time elapsed: 0.200 s
% 6.42/1.94 % (2537536)Peak memory usage: 91 MB
% 6.42/1.94 % (2537536)Instructions burned: 325 (million)
% 6.42/1.94 % (2537542)Instruction limit reached!
% 6.42/1.94 % (2537542)------------------------------
% 6.42/1.94 % (2537542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537542)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537542)Termination reason: Instruction limit
% 6.42/1.94 % (2537542)Termination phase: Saturation
% 6.42/1.94 % (2537542)Time elapsed: 0.081 s
% 6.42/1.94 % (2537542)Peak memory usage: 88 MB
% 6.42/1.94 % (2537542)Instructions burned: 296 (million)
% 6.42/1.94 % (2537535)------------------------------
% 6.42/1.94 % (2537535)------------------------------
% 6.42/1.94 % (2537544)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1204924057:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.42/1.94 % (2537546)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3351103431:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.42/1.94 % (2537545)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1385275587:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.42/1.94 % (2537546)Instruction limit reached!
% 6.42/1.94 % (2537546)------------------------------
% 6.42/1.94 % (2537546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537546)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537546)Termination reason: Instruction limit
% 6.42/1.94 % (2537546)Termination phase: Saturation
% 6.42/1.94 % (2537546)Time elapsed: 0.035 s
% 6.42/1.94 % (2537546)Peak memory usage: 88 MB
% 6.42/1.94 % (2537546)Instructions burned: 128 (million)
% 6.42/1.94 % (2537547)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3104320673:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 6.42/1.94 % (2537545)Instruction limit reached!
% 6.42/1.94 % (2537545)------------------------------
% 6.42/1.94 % (2537545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537545)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537545)Termination reason: Instruction limit
% 6.42/1.94 % (2537545)Termination phase: Saturation
% 6.42/1.94 % (2537545)Time elapsed: 0.080 s
% 6.42/1.94 % (2537545)Peak memory usage: 89 MB
% 6.42/1.94 % (2537545)Instructions burned: 113 (million)
% 6.42/1.94 % (2537551)lrs+10_1_sil=8000:sp=occurrence:random_seed=3521838349:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.42/1.94 % (2537547)Instruction limit reached!
% 6.42/1.94 % (2537547)------------------------------
% 6.42/1.94 % (2537547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537547)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537547)Termination reason: Instruction limit
% 6.42/1.94 % (2537547)Termination phase: Saturation
% 6.42/1.94 % (2537547)Time elapsed: 0.075 s
% 6.42/1.94 % (2537547)Peak memory usage: 89 MB
% 6.42/1.94 % (2537547)Instructions burned: 116 (million)
% 6.42/1.94 % (2537520)First to succeed.
% 6.42/1.94 % (2537520)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2537515"
% 6.42/1.94 % (2537553)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3716316646:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.42/1.94 % (2537555)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=128920796:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.42/1.94 % (2537551)Instruction limit reached!
% 6.42/1.94 % (2537551)------------------------------
% 6.42/1.94 % (2537551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/1.94 % (2537551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/1.94 % (2537551)CaDiCaL version: 2.1.3
% 6.42/1.94 % (2537551)Termination reason: Instruction limit
% 6.42/1.94 % (2537551)Termination phase: Saturation
% 6.42/1.94 % (2537551)Time elapsed: 0.275 s
% 6.42/1.94 % (2537551)Peak memory usage: 97 MB
% 6.42/1.94 % (2537551)Instructions burned: 908 (million)
% 6.42/1.94 % (2537520)Refutation found. Thanks to Tanya!
% 6.42/1.94 % SZS status Theorem for theBenchmark
% 6.42/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/2.14 % (2537520)------------------------------
% 0.16/2.14 % (2537520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2537520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2537520)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2537520)Termination reason: Refutation
% 0.16/2.14 % (2537520)Time elapsed: 0.673 s
% 0.16/2.14 % (2537520)Peak memory usage: 130 MB
% 0.16/2.14 % (2537520)Instructions burned: 995 (million)
% 0.16/2.14 % (2537520)------------------------------
% 0.16/2.14 % (2537520)------------------------------
% 0.16/2.14 % (2537515)Success in time 1.08 s
% 0.16/2.14 % Vampire exiting
%------------------------------------------------------------------------------