%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA011+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 : n004.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 09:55:21 AM UTC 2026
% Result : Theorem 5.86s 1.78s
% Output : Refutation 7.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 32
% Syntax : Number of formulae : 233 ( 35 unt; 22 def)
% Number of atoms : 811 ( 200 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 983 ( 405 ~; 436 |; 99 &)
% ( 26 <=>; 14 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 34 ( 32 usr; 24 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 249 ( 0 sgn 231 !; 18 ?)
% 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(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(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(f13,axiom,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
fof(f16,axiom,
! [X0,X1,X2] :
( ( path(X1,X2,X0)
& ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) )
=> ? [X5] : triangle(X3,X4,X5) ) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f22,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& shortest_path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f19]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ( vertex(head_of(X0))
& vertex(tail_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,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(f36,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,[],[f35]) ).
fof(f37,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(f40,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(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) )
& ( ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) )
| ~ triangle(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) )
& ( ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) )
| ~ triangle(X0,X1,X2) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ( ! [X5] : ~ triangle(sK0(X0),sK1(X0),X5)
& on_path(sK0(X0),X0)
& on_path(sK1(X0),X0)
& sequential(sK0(X0),sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0)),skolemize(X4,sK1(X0))],[f23]) ).
fof(f45,plain,
( number_of_in(sequential_pairs,sK2) != number_of_in(triangles,sK2)
& shortest_path(sK3,sK4,sK2)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f24]) ).
fof(f46,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(f47,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,[],[f46]) ).
fof(f52,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,[],[f31]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
( ! [X0,X1] :
( ( edge(sK7(X0,X1))
& ( head_of(sK7(X0,X1)) != X1
| tail_of(sK7(X0,X1)) != X0
| head_of(sK7(X0,X1)) != X0
| tail_of(sK7(X0,X1)) != X1 )
& ( ( head_of(sK7(X0,X1)) = X1
& tail_of(sK7(X0,X1)) = X0 )
| ( head_of(sK7(X0,X1)) = X0
& tail_of(sK7(X0,X1)) = X1 ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f53]) ).
fof(f59,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,[],[f37]) ).
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(flattening,[],[f59]) ).
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
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK9(X0,X1,X2)))
& path(X0,X1,sK9(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,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f61]) ).
fof(f70,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK0(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK1(X0),X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK0(X0),X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f76,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK0(X0),sK1(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f78,plain,
complete,
inference(cnf_transformation,[],[f45]) ).
fof(f79,plain,
shortest_path(sK3,sK4,sK2),
inference(cnf_transformation,[],[f45]) ).
fof(f80,plain,
number_of_in(sequential_pairs,sK2) != number_of_in(triangles,sK2),
inference(cnf_transformation,[],[f45]) ).
fof(f81,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f82,plain,
! [X0,X1] :
( X0 != X1
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f83,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f84,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f85,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f100,plain,
! [X0,X1] :
( tail_of(sK7(X0,X1)) = X0
| tail_of(sK7(X0,X1)) = X1
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f54]) ).
fof(f101,plain,
! [X0,X1] :
( tail_of(sK7(X0,X1)) = X0
| head_of(sK7(X0,X1)) = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f54]) ).
fof(f103,plain,
! [X0,X1] :
( head_of(sK7(X0,X1)) = X1
| head_of(sK7(X0,X1)) = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f54]) ).
fof(f105,plain,
! [X0,X1] :
( edge(sK7(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f54]) ).
fof(f106,plain,
! [X0] :
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f107,plain,
! [X0] :
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f108,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f115,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,[],[f36]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f124,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f41]) ).
fof(f125,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| head_of(X3) != head_of(X5)
| ~ shortest_path(X0,X1,X4)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f41]) ).
fof(f126,plain,
! [X1] : ~ sequential(X1,X1),
inference(equality_resolution,[],[f82]) ).
fof(f134,definition,
( spl11_1
<=> complete ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f135,plain,
( ~ complete
| spl11_1 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl11_2
<=> ! [X0,X1] :
( tail_of(sK7(X0,X1)) = X0
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK7(X0,X1)) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f138,plain,
( ! [X0,X1] :
( ~ vertex(X0)
| X0 = X1
| ~ vertex(X1)
| tail_of(sK7(X0,X1)) = X0
| tail_of(sK7(X0,X1)) = X1 )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f100,f137,f134]) ).
fof(f141,definition,
( spl11_3
<=> ! [X0,X1] :
( tail_of(sK7(X0,X1)) = X0
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK7(X0,X1)) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f142,plain,
( ! [X0,X1] :
( ~ vertex(X0)
| X0 = X1
| ~ vertex(X1)
| tail_of(sK7(X0,X1)) = X0
| head_of(sK7(X0,X1)) = X0 )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( ~ spl11_1
| spl11_3 ),
inference(avatar_split_clause,[],[f101,f141,f134]) ).
fof(f149,definition,
( spl11_5
<=> ! [X0,X1] :
( head_of(sK7(X0,X1)) = X1
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK7(X0,X1)) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f150,plain,
( ! [X0,X1] :
( ~ vertex(X0)
| X0 = X1
| ~ vertex(X1)
| head_of(sK7(X0,X1)) = X1
| head_of(sK7(X0,X1)) = X0 )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f151,plain,
( ~ spl11_1
| spl11_5 ),
inference(avatar_split_clause,[],[f103,f149,f134]) ).
fof(f157,definition,
( spl11_7
<=> ! [X0,X1] :
( edge(sK7(X0,X1))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
fof(f158,plain,
( ! [X0,X1] :
( edge(sK7(X0,X1))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( ~ spl11_1
| spl11_7 ),
inference(avatar_split_clause,[],[f105,f157,f134]) ).
fof(f162,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(forward_subsumption_resolution,[],[f70,f83]) ).
fof(f165,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(forward_subsumption_resolution,[],[f162,f83]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ sequential(X2,X0)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| triangle(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f165,f83]) ).
fof(f167,plain,
( $false
| spl11_1 ),
inference(forward_subsumption_resolution,[],[f135,f78]) ).
fof(f168,plain,
spl11_1,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f169,plain,
path(sK3,sK4,sK2),
inference(resolution,[],[f118,f79]) ).
fof(f170,plain,
( number_of_in(sequential_pairs,sK2) = number_of_in(triangles,sK2)
| sequential(sK0(sK2),sK1(sK2)) ),
inference(resolution,[],[f169,f73]) ).
fof(f171,plain,
( number_of_in(sequential_pairs,sK2) = number_of_in(triangles,sK2)
| on_path(sK1(sK2),sK2) ),
inference(resolution,[],[f169,f74]) ).
fof(f172,plain,
( number_of_in(sequential_pairs,sK2) = number_of_in(triangles,sK2)
| on_path(sK0(sK2),sK2) ),
inference(resolution,[],[f169,f75]) ).
fof(f173,plain,
on_path(sK0(sK2),sK2),
inference(forward_subsumption_resolution,[],[f172,f80]) ).
fof(f174,plain,
on_path(sK1(sK2),sK2),
inference(forward_subsumption_resolution,[],[f171,f80]) ).
fof(f175,plain,
sequential(sK0(sK2),sK1(sK2)),
inference(forward_subsumption_resolution,[],[f170,f80]) ).
fof(f178,plain,
edge(sK1(sK2)),
inference(resolution,[],[f83,f175]) ).
fof(f179,plain,
edge(sK0(sK2)),
inference(resolution,[],[f84,f175]) ).
fof(f180,plain,
tail_of(sK1(sK2)) = head_of(sK0(sK2)),
inference(resolution,[],[f81,f175]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ on_path(sK1(sK2),X0)
| ~ on_path(sK0(sK2),X0)
| precedes(sK0(sK2),sK1(sK2),X0)
| ~ path(X1,X2,X0) ),
inference(resolution,[],[f115,f175]) ).
fof(f197,plain,
! [X0,X1] :
( ~ on_path(sK0(sK2),sK2)
| precedes(sK0(sK2),sK1(sK2),sK2)
| ~ path(X0,X1,sK2) ),
inference(resolution,[],[f196,f174]) ).
fof(f198,plain,
! [X0,X1] :
( precedes(sK0(sK2),sK1(sK2),sK2)
| ~ path(X0,X1,sK2) ),
inference(forward_subsumption_resolution,[],[f197,f173]) ).
fof(f200,definition,
( spl11_8
<=> ! [X0,X1] : ~ path(X0,X1,sK2) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f201,plain,
( ! [X0,X1] : ~ path(X0,X1,sK2)
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,definition,
( spl11_9
<=> precedes(sK0(sK2),sK1(sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f204,plain,
( precedes(sK0(sK2),sK1(sK2),sK2)
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( spl11_8
| spl11_9 ),
inference(avatar_split_clause,[],[f198,f203,f200]) ).
fof(f206,plain,
( ! [X2,X0,X1] :
( head_of(X0) != head_of(sK1(sK2))
| ~ shortest_path(X1,X2,sK2)
| tail_of(X0) != tail_of(sK0(sK2)) )
| ~ spl11_9 ),
inference(resolution,[],[f204,f125]) ).
fof(f208,definition,
( spl11_10
<=> ! [X2,X1] : ~ shortest_path(X1,X2,sK2) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
fof(f209,plain,
( ! [X2,X1] : ~ shortest_path(X1,X2,sK2)
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f211,definition,
( spl11_11
<=> ! [X0] :
( head_of(X0) != head_of(sK1(sK2))
| tail_of(X0) != tail_of(sK0(sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
fof(f212,plain,
( ! [X0] :
( head_of(X0) != head_of(sK1(sK2))
| tail_of(X0) != tail_of(sK0(sK2)) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( spl11_10
| spl11_11
| ~ spl11_9 ),
inference(avatar_split_clause,[],[f206,f203,f211,f208]) ).
fof(f214,plain,
( $false
| ~ spl11_10 ),
inference(unit_resulting_resolution,[],[f209,f79]) ).
fof(f217,plain,
~ spl11_10,
inference(avatar_contradiction_clause,[],[f214]) ).
fof(f218,plain,
( tail_of(sK1(sK2)) != tail_of(sK0(sK2))
| ~ spl11_11 ),
inference(equality_resolution,[],[f212]) ).
fof(f219,plain,
( tail_of(sK0(sK2)) != head_of(sK0(sK2))
| ~ spl11_11 ),
inference(forward_demodulation,[],[f218,f180]) ).
fof(f220,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(resolution,[],[f124,f79]) ).
fof(f221,plain,
( ~ precedes(sK1(sK2),sK0(sK2),sK2)
| ~ spl11_9 ),
inference(resolution,[],[f220,f204]) ).
fof(f228,plain,
vertex(head_of(sK1(sK2))),
inference(resolution,[],[f107,f178]) ).
fof(f234,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK1(sK2)) = X0
| head_of(sK7(head_of(sK1(sK2)),X0)) = X0
| head_of(sK1(sK2)) = head_of(sK7(head_of(sK1(sK2)),X0)) )
| ~ spl11_5 ),
inference(resolution,[],[f228,f150]) ).
fof(f236,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK1(sK2)) = X0
| head_of(sK1(sK2)) = tail_of(sK7(head_of(sK1(sK2)),X0))
| head_of(sK1(sK2)) = head_of(sK7(head_of(sK1(sK2)),X0)) )
| ~ spl11_3 ),
inference(resolution,[],[f228,f142]) ).
fof(f237,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK1(sK2)) = X0
| head_of(sK1(sK2)) = tail_of(sK7(head_of(sK1(sK2)),X0))
| tail_of(sK7(head_of(sK1(sK2)),X0)) = X0 )
| ~ spl11_2 ),
inference(resolution,[],[f228,f138]) ).
fof(f240,plain,
vertex(tail_of(sK0(sK2))),
inference(resolution,[],[f106,f179]) ).
fof(f255,plain,
( $false
| ~ spl11_8 ),
inference(unit_resulting_resolution,[],[f118,f79,f201]) ).
fof(f259,plain,
~ spl11_8,
inference(avatar_contradiction_clause,[],[f255]) ).
fof(f267,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| head_of(sK1(sK2)) = tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| head_of(sK1(sK2)) = head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_3 ),
inference(resolution,[],[f236,f240]) ).
fof(f291,definition,
( spl11_19
<=> head_of(sK1(sK2)) = head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
fof(f292,plain,
( head_of(sK1(sK2)) = head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f294,definition,
( spl11_20
<=> head_of(sK1(sK2)) = tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
fof(f295,plain,
( head_of(sK1(sK2)) = tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,definition,
( spl11_21
<=> head_of(sK1(sK2)) = tail_of(sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition]) ).
fof(f298,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( spl11_19
| spl11_20
| spl11_21
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f267,f141,f297,f294,f291]) ).
fof(f728,definition,
( spl11_76
<=> sequential(sK1(sK2),sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_76])],[avatar_definition]) ).
fof(f729,plain,
( sequential(sK1(sK2),sK0(sK2))
| ~ spl11_76 ),
inference(avatar_component_clause,[],[f728]) ).
fof(f731,definition,
( spl11_77
<=> sK0(sK2) = sK1(sK2) ),
introduced(definition,[new_symbols(definition,[spl11_77])],[avatar_definition]) ).
fof(f732,plain,
( sK0(sK2) = sK1(sK2)
| ~ spl11_77 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f1111,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| tail_of(sK0(sK2)) = head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| head_of(sK1(sK2)) = head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_5 ),
inference(resolution,[],[f234,f240]) ).
fof(f1199,plain,
( $false
| ~ spl11_9
| ~ spl11_76 ),
inference(unit_resulting_resolution,[],[f115,f169,f174,f173,f221,f729]) ).
fof(f1207,plain,
( ~ spl11_9
| ~ spl11_76 ),
inference(avatar_contradiction_clause,[],[f1199]) ).
fof(f1211,plain,
( sequential(sK0(sK2),sK0(sK2))
| ~ spl11_77 ),
inference(superposition,[],[f175,f732]) ).
fof(f1248,plain,
( $false
| ~ spl11_77 ),
inference(forward_subsumption_resolution,[],[f1211,f126]) ).
fof(f1249,plain,
~ spl11_77,
inference(avatar_contradiction_clause,[],[f1248]) ).
fof(f1561,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| head_of(sK1(sK2)) = tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| tail_of(sK0(sK2)) = tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_2 ),
inference(resolution,[],[f237,f240]) ).
fof(f1639,plain,
( head_of(sK1(sK2)) != head_of(sK1(sK2))
| tail_of(sK0(sK2)) != tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_11
| ~ spl11_19 ),
inference(superposition,[],[f212,f292]) ).
fof(f1642,plain,
( tail_of(sK0(sK2)) != tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_11
| ~ spl11_19 ),
inference(trivial_inequality_removal,[],[f1639]) ).
fof(f4681,definition,
( spl11_359
<=> tail_of(sK0(sK2)) = tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl11_359])],[avatar_definition]) ).
fof(f4682,plain,
( tail_of(sK0(sK2)) = tail_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_359 ),
inference(avatar_component_clause,[],[f4681]) ).
fof(f4683,plain,
( spl11_359
| spl11_20
| spl11_21
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f1561,f137,f297,f294,f4681]) ).
fof(f4689,definition,
( spl11_361
<=> tail_of(sK0(sK2)) = head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl11_361])],[avatar_definition]) ).
fof(f4690,plain,
( tail_of(sK0(sK2)) = head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_361 ),
inference(avatar_component_clause,[],[f4689]) ).
fof(f4691,plain,
( spl11_19
| spl11_361
| spl11_21
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f1111,f149,f297,f4689,f291]) ).
fof(f5818,definition,
( spl11_446
<=> edge(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl11_446])],[avatar_definition]) ).
fof(f5819,plain,
( ~ edge(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| spl11_446 ),
inference(avatar_component_clause,[],[f5818]) ).
fof(f5829,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| ~ vertex(tail_of(sK0(sK2)))
| ~ vertex(head_of(sK1(sK2)))
| ~ spl11_7
| spl11_446 ),
inference(resolution,[],[f5819,f158]) ).
fof(f5836,plain,
( head_of(sK1(sK2)) != tail_of(sK0(sK2))
| spl11_21 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f5856,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| ~ vertex(head_of(sK1(sK2)))
| ~ spl11_7
| spl11_446 ),
inference(forward_subsumption_resolution,[],[f5829,f240]) ).
fof(f5858,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| ~ spl11_7
| spl11_446 ),
inference(forward_subsumption_resolution,[],[f5856,f228]) ).
fof(f5860,plain,
( spl11_21
| ~ spl11_7
| spl11_446 ),
inference(avatar_split_clause,[],[f5858,f5818,f157,f297]) ).
fof(f6706,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK0(sK2))
| ~ edge(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ edge(X0)
| sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))) = X0
| sequential(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))),X0) )
| ~ spl11_361 ),
inference(superposition,[],[f85,f4690]) ).
fof(f6711,definition,
( spl11_482
<=> ! [X0] :
( tail_of(X0) != tail_of(sK0(sK2))
| sequential(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))),X0)
| sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))) = X0
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_482])],[avatar_definition]) ).
fof(f6712,plain,
( ! [X0] :
( ~ edge(X0)
| sequential(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))),X0)
| sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))) = X0
| tail_of(X0) != tail_of(sK0(sK2)) )
| ~ spl11_482 ),
inference(avatar_component_clause,[],[f6711]) ).
fof(f6713,plain,
( ~ spl11_446
| spl11_482
| ~ spl11_361 ),
inference(avatar_split_clause,[],[f6706,f4689,f6711,f5818]) ).
fof(f6718,plain,
( sequential(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))),sK0(sK2))
| sK0(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))
| tail_of(sK0(sK2)) != tail_of(sK0(sK2))
| ~ spl11_482 ),
inference(resolution,[],[f6712,f179]) ).
fof(f6725,plain,
( sequential(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))),sK0(sK2))
| sK0(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))
| ~ spl11_482 ),
inference(trivial_inequality_removal,[],[f6718]) ).
fof(f6731,definition,
( spl11_483
<=> sK0(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl11_483])],[avatar_definition]) ).
fof(f6732,plain,
( sK0(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))
| ~ spl11_483 ),
inference(avatar_component_clause,[],[f6731]) ).
fof(f6734,definition,
( spl11_484
<=> sequential(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))),sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl11_484])],[avatar_definition]) ).
fof(f6735,plain,
( sequential(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))),sK0(sK2))
| ~ spl11_484 ),
inference(avatar_component_clause,[],[f6734]) ).
fof(f6736,plain,
( spl11_483
| spl11_484
| ~ spl11_482 ),
inference(avatar_split_clause,[],[f6725,f6711,f6734,f6731]) ).
fof(f6742,plain,
( tail_of(sK0(sK2)) = head_of(sK0(sK2))
| ~ spl11_361
| ~ spl11_483 ),
inference(superposition,[],[f4690,f6732]) ).
fof(f6746,plain,
( $false
| ~ spl11_11
| ~ spl11_361
| ~ spl11_483 ),
inference(forward_subsumption_resolution,[],[f6742,f219]) ).
fof(f6747,plain,
( ~ spl11_11
| ~ spl11_361
| ~ spl11_483 ),
inference(avatar_contradiction_clause,[],[f6746]) ).
fof(f6753,plain,
( edge(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_484 ),
inference(resolution,[],[f6735,f84]) ).
fof(f6757,plain,
( ! [X0] :
( ~ sequential(X0,sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ sequential(sK0(sK2),X0)
| triangle(sK0(sK2),X0,sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) )
| ~ spl11_484 ),
inference(resolution,[],[f6735,f166]) ).
fof(f6779,plain,
( ! [X0] :
( head_of(X0) != head_of(sK1(sK2))
| ~ edge(X0)
| ~ edge(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))) = X0
| sequential(X0,sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) )
| ~ spl11_20 ),
inference(superposition,[],[f85,f295]) ).
fof(f6780,plain,
( head_of(sK1(sK2)) != head_of(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ edge(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_20 ),
inference(superposition,[],[f108,f295]) ).
fof(f6784,plain,
( ! [X0] :
( ~ edge(X0)
| head_of(X0) != head_of(sK1(sK2))
| sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))) = X0
| sequential(X0,sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) )
| ~ spl11_20
| ~ spl11_484 ),
inference(forward_subsumption_resolution,[],[f6779,f6753]) ).
fof(f6787,plain,
( head_of(sK1(sK2)) != head_of(sK1(sK2))
| sK1(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))
| sequential(sK1(sK2),sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_20
| ~ spl11_484 ),
inference(resolution,[],[f6784,f178]) ).
fof(f6793,plain,
( sK1(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))
| sequential(sK1(sK2),sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_20
| ~ spl11_484 ),
inference(trivial_inequality_removal,[],[f6787]) ).
fof(f6796,definition,
( spl11_487
<=> sequential(sK1(sK2),sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl11_487])],[avatar_definition]) ).
fof(f6797,plain,
( sequential(sK1(sK2),sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_487 ),
inference(avatar_component_clause,[],[f6796]) ).
fof(f6799,definition,
( spl11_488
<=> sK1(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl11_488])],[avatar_definition]) ).
fof(f6800,plain,
( sK1(sK2) = sK7(head_of(sK1(sK2)),tail_of(sK0(sK2)))
| ~ spl11_488 ),
inference(avatar_component_clause,[],[f6799]) ).
fof(f6801,plain,
( spl11_487
| spl11_488
| ~ spl11_20
| ~ spl11_484 ),
inference(avatar_split_clause,[],[f6793,f6734,f294,f6799,f6796]) ).
fof(f6809,plain,
( ~ sequential(sK0(sK2),sK1(sK2))
| triangle(sK0(sK2),sK1(sK2),sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_484
| ~ spl11_487 ),
inference(resolution,[],[f6797,f6757]) ).
fof(f6818,plain,
( triangle(sK0(sK2),sK1(sK2),sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_484
| ~ spl11_487 ),
inference(forward_subsumption_resolution,[],[f6809,f175]) ).
fof(f6820,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK2)
| number_of_in(sequential_pairs,sK2) = number_of_in(triangles,sK2) )
| ~ spl11_484
| ~ spl11_487 ),
inference(resolution,[],[f6818,f76]) ).
fof(f6822,plain,
( ! [X0,X1] : ~ path(X0,X1,sK2)
| ~ spl11_484
| ~ spl11_487 ),
inference(forward_subsumption_resolution,[],[f6820,f80]) ).
fof(f6823,plain,
( spl11_8
| ~ spl11_484
| ~ spl11_487 ),
inference(avatar_split_clause,[],[f6822,f6796,f6734,f200]) ).
fof(f6825,plain,
( head_of(sK1(sK2)) = tail_of(sK0(sK2))
| ~ spl11_361
| ~ spl11_488 ),
inference(superposition,[],[f4690,f6800]) ).
fof(f6833,plain,
( $false
| spl11_21
| ~ spl11_361
| ~ spl11_488 ),
inference(forward_subsumption_resolution,[],[f6825,f5836]) ).
fof(f6834,plain,
( spl11_21
| ~ spl11_361
| ~ spl11_488 ),
inference(avatar_contradiction_clause,[],[f6833]) ).
fof(f6843,plain,
( ~ edge(sK7(head_of(sK1(sK2)),tail_of(sK0(sK2))))
| ~ spl11_19
| ~ spl11_20 ),
inference(forward_subsumption_resolution,[],[f6780,f292]) ).
fof(f6848,plain,
( ~ spl11_446
| ~ spl11_19
| ~ spl11_20 ),
inference(avatar_split_clause,[],[f6843,f294,f291,f5818]) ).
fof(f7421,plain,
( ! [X0] :
( head_of(X0) != head_of(sK1(sK2))
| ~ edge(X0)
| ~ edge(sK0(sK2))
| sK0(sK2) = X0
| sequential(X0,sK0(sK2)) )
| ~ spl11_21 ),
inference(superposition,[],[f85,f298]) ).
fof(f7423,plain,
( ! [X0] :
( ~ edge(X0)
| head_of(X0) != head_of(sK1(sK2))
| sK0(sK2) = X0
| sequential(X0,sK0(sK2)) )
| ~ spl11_21 ),
inference(forward_subsumption_resolution,[],[f7421,f179]) ).
fof(f7467,plain,
( head_of(sK1(sK2)) != head_of(sK1(sK2))
| sK0(sK2) = sK1(sK2)
| sequential(sK1(sK2),sK0(sK2))
| ~ spl11_21 ),
inference(resolution,[],[f7423,f178]) ).
fof(f7473,plain,
( sK0(sK2) = sK1(sK2)
| sequential(sK1(sK2),sK0(sK2))
| ~ spl11_21 ),
inference(trivial_inequality_removal,[],[f7467]) ).
fof(f7474,plain,
( spl11_76
| spl11_77
| ~ spl11_21 ),
inference(avatar_split_clause,[],[f7473,f297,f731,f728]) ).
fof(f7475,plain,
( $false
| ~ spl11_11
| ~ spl11_19
| ~ spl11_359 ),
inference(forward_subsumption_resolution,[],[f4682,f1642]) ).
fof(f7476,plain,
( ~ spl11_11
| ~ spl11_19
| ~ spl11_359 ),
inference(avatar_contradiction_clause,[],[f7475]) ).
cnf(s1,plain,
( ~ spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f139]) ).
cnf(s2,plain,
( ~ spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f143]) ).
cnf(s4,plain,
( ~ spl11_1
| spl11_5 ),
inference(sat_conversion,[],[f151]) ).
cnf(s6,plain,
( ~ spl11_1
| spl11_7 ),
inference(sat_conversion,[],[f159]) ).
cnf(s7,plain,
spl11_1,
inference(sat_conversion,[],[f168]) ).
cnf(s8,plain,
( spl11_8
| spl11_9 ),
inference(sat_conversion,[],[f205]) ).
cnf(s9,plain,
( ~ spl11_9
| spl11_10
| spl11_11 ),
inference(sat_conversion,[],[f213]) ).
cnf(s11,plain,
~ spl11_10,
inference(sat_conversion,[],[f217]) ).
cnf(s15,plain,
~ spl11_8,
inference(sat_conversion,[],[f259]) ).
cnf(s18,plain,
( ~ spl11_3
| spl11_19
| spl11_20
| spl11_21 ),
inference(sat_conversion,[],[f299]) ).
cnf(s110,plain,
( ~ spl11_9
| ~ spl11_76 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s115,plain,
~ spl11_77,
inference(sat_conversion,[],[f1249]) ).
cnf(s444,plain,
( ~ spl11_2
| spl11_20
| spl11_21
| spl11_359 ),
inference(sat_conversion,[],[f4683]) ).
cnf(s446,plain,
( ~ spl11_5
| spl11_19
| spl11_21
| spl11_361 ),
inference(sat_conversion,[],[f4691]) ).
cnf(s601,plain,
( ~ spl11_7
| spl11_21
| spl11_446 ),
inference(sat_conversion,[],[f5860]) ).
cnf(s675,plain,
( ~ spl11_361
| ~ spl11_446
| spl11_482 ),
inference(sat_conversion,[],[f6713]) ).
cnf(s676,plain,
( ~ spl11_482
| spl11_483
| spl11_484 ),
inference(sat_conversion,[],[f6736]) ).
cnf(s677,plain,
( ~ spl11_11
| ~ spl11_361
| ~ spl11_483 ),
inference(sat_conversion,[],[f6747]) ).
cnf(s679,plain,
( ~ spl11_20
| ~ spl11_484
| spl11_487
| spl11_488 ),
inference(sat_conversion,[],[f6801]) ).
cnf(s682,plain,
( spl11_8
| ~ spl11_484
| ~ spl11_487 ),
inference(sat_conversion,[],[f6823]) ).
cnf(s684,plain,
( spl11_21
| ~ spl11_361
| ~ spl11_488 ),
inference(sat_conversion,[],[f6834]) ).
cnf(s687,plain,
( ~ spl11_19
| ~ spl11_20
| ~ spl11_446 ),
inference(sat_conversion,[],[f6848]) ).
cnf(s771,plain,
( ~ spl11_21
| spl11_76
| spl11_77 ),
inference(sat_conversion,[],[f7474]) ).
cnf(s772,plain,
( ~ spl11_11
| ~ spl11_19
| ~ spl11_359 ),
inference(sat_conversion,[],[f7476]) ).
cnf(s794,plain,
( ~ spl11_9
| spl11_11 ),
inference(rat,[],[s9,s11]) ).
cnf(s795,plain,
spl11_9,
inference(rat,[],[s8,s15]) ).
cnf(s796,plain,
~ spl11_76,
inference(rat,[],[s110,s795]) ).
cnf(s798,plain,
spl11_11,
inference(rat,[],[s794,s795]) ).
cnf(s799,plain,
~ spl11_21,
inference(rat,[],[s771,s115,s796]) ).
cnf(s800,plain,
spl11_7,
inference(rat,[],[s6,s7]) ).
cnf(s801,plain,
spl11_446,
inference(rat,[],[s601,s799,s800]) ).
cnf(s807,plain,
spl11_5,
inference(rat,[],[s4,s7]) ).
cnf(s809,plain,
spl11_3,
inference(rat,[],[s2,s7]) ).
cnf(s810,plain,
spl11_2,
inference(rat,[],[s1,s7]) ).
cnf(s811,plain,
spl11_19,
inference(rat,[],[s679,s682,s676,s675,s677,s684,s18,s446,s15,s801,s798,s799,s809,s807]) ).
cnf(s812,plain,
~ spl11_359,
inference(rat,[],[s772,s798,s811]) ).
cnf(s813,plain,
~ spl11_20,
inference(rat,[],[s687,s801,s811]) ).
cnf(s815,plain,
$false,
inference(rat,[],[s444,s810,s799,s812,s813]) ).
fof(f7522,plain,
$false,
inference(avatar_sat_refutation,[],[s815]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA011+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 08:47:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 5.86/1.77 % (3210173)Detected formulas, will run a generic FOF schedule.
% 5.86/1.77 % (3210179)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=988201835:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.86/1.77 % (3210184)dis-21_1_sil=8000:lcm=predicate:random_seed=4258148378: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)
% 5.86/1.77 % (3210183)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4227748812:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.86/1.77 % (3210182)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=113172972:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.86/1.77 % (3210178)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=2283102973:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.86/1.77 % (3210181)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3081572806:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.86/1.77 % (3210180)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=1270195636:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.86/1.77 % (3210181)Refutation not found, incomplete strategy
% 5.86/1.77 % (3210181)------------------------------
% 5.86/1.77 % (3210181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210181)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210181)Termination reason: Refutation not found, incomplete strategy
% 5.86/1.77 % (3210181)Time elapsed: 0.001 s
% 5.86/1.77 % (3210181)Peak memory usage: 88 MB
% 5.86/1.77 % (3210182)Refutation not found, incomplete strategy
% 5.86/1.77 % (3210182)------------------------------
% 5.86/1.77 % (3210182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210182)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210182)Termination reason: Refutation not found, incomplete strategy
% 5.86/1.77 % (3210182)Time elapsed: 0.002 s
% 5.86/1.77 % (3210182)Peak memory usage: 88 MB
% 5.86/1.77 % (3210182)Instructions burned: 2 (million)
% 5.86/1.77 % (3210184)Instruction limit reached!
% 5.86/1.77 % (3210184)------------------------------
% 5.86/1.77 % (3210184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210184)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210184)Termination reason: Instruction limit
% 5.86/1.77 % (3210184)Termination phase: Saturation
% 5.86/1.77 % (3210184)Time elapsed: 0.065 s
% 5.86/1.77 % (3210184)Peak memory usage: 89 MB
% 5.86/1.77 % (3210184)Instructions burned: 129 (million)
% 5.86/1.77 % (3210183)Instruction limit reached!
% 5.86/1.77 % (3210183)------------------------------
% 5.86/1.77 % (3210183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210183)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210183)Termination reason: Instruction limit
% 5.86/1.77 % (3210183)Termination phase: Saturation
% 5.86/1.77 % (3210183)Time elapsed: 0.094 s
% 5.86/1.77 % (3210183)Peak memory usage: 89 MB
% 5.86/1.77 % (3210183)Instructions burned: 140 (million)
% 5.86/1.77 % (3210192)lrs+10_1_sil=8000:sp=occurrence:random_seed=554152656:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.86/1.77 % (3210193)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4119464055:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.86/1.77 % (3210193)Refutation not found, incomplete strategy
% 5.86/1.77 % (3210193)------------------------------
% 5.86/1.77 % (3210193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210193)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210193)Termination reason: Refutation not found, incomplete strategy
% 5.86/1.77 % (3210193)Time elapsed: 0.002 s
% 5.86/1.77 % (3210193)Peak memory usage: 88 MB
% 5.86/1.77 % (3210193)Instructions burned: 1 (million)
% 5.86/1.77 % (3210181)------------------------------
% 5.86/1.77 % (3210181)------------------------------
% 5.86/1.77 % (3210182)------------------------------
% 5.86/1.77 % (3210182)------------------------------
% 5.86/1.77 % (3210192)Instruction limit reached!
% 5.86/1.77 % (3210192)------------------------------
% 5.86/1.77 % (3210192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210192)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210192)Termination reason: Instruction limit
% 5.86/1.77 % (3210192)Termination phase: Saturation
% 5.86/1.77 % (3210192)Time elapsed: 0.166 s
% 5.86/1.77 % (3210192)Peak memory usage: 91 MB
% 5.86/1.77 % (3210192)Instructions burned: 287 (million)
% 5.86/1.77 % (3210197)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=3883152590:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.86/1.77 % (3210196)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3498174433:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 5.86/1.77 % (3210193)------------------------------
% 5.86/1.77 % (3210193)------------------------------
% 5.86/1.77 % (3210198)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=852930938:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.86/1.77 % (3210197)Instruction limit reached!
% 5.86/1.77 % (3210197)------------------------------
% 5.86/1.77 % (3210197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210197)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210197)Termination reason: Instruction limit
% 5.86/1.77 % (3210197)Termination phase: Saturation
% 5.86/1.77 % (3210197)Time elapsed: 0.143 s
% 5.86/1.77 % (3210197)Peak memory usage: 90 MB
% 5.86/1.77 % (3210197)Instructions burned: 249 (million)
% 5.86/1.77 % (3210196)Instruction limit reached!
% 5.86/1.77 % (3210196)------------------------------
% 5.86/1.77 % (3210196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210196)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210196)Termination reason: Instruction limit
% 5.86/1.77 % (3210196)Termination phase: Saturation
% 5.86/1.77 % (3210196)Time elapsed: 0.181 s
% 5.86/1.77 % (3210196)Peak memory usage: 91 MB
% 5.86/1.77 % (3210196)Instructions burned: 326 (million)
% 5.86/1.77 % (3210179)First to succeed.
% 5.86/1.77 % (3210201)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=892384278:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 5.86/1.77 % (3210179)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3210173"
% 5.86/1.77 % (3210198)Instruction limit reached!
% 5.86/1.77 % (3210198)------------------------------
% 5.86/1.77 % (3210198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210198)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210198)Termination reason: Instruction limit
% 5.86/1.77 % (3210198)Termination phase: Saturation
% 5.86/1.77 % (3210198)Time elapsed: 0.152 s
% 5.86/1.77 % (3210198)Peak memory usage: 88 MB
% 5.86/1.77 % (3210198)Instructions burned: 295 (million)
% 5.86/1.77 % (3210203)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1313227102:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.86/1.77 % (3210204)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3356592976:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 5.86/1.77 % (3210203)Instruction limit reached!
% 5.86/1.77 % (3210203)------------------------------
% 5.86/1.77 % (3210203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.77 % (3210203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.77 % (3210203)CaDiCaL version: 2.1.3
% 5.86/1.77 % (3210203)Termination reason: Instruction limit
% 5.86/1.77 % (3210203)Termination phase: Saturation
% 5.86/1.77 % (3210203)Time elapsed: 0.077 s
% 5.86/1.77 % (3210203)Peak memory usage: 89 MB
% 5.86/1.77 % (3210203)Instructions burned: 113 (million)
% 5.86/1.77 % (3210204)Instruction limit reached!
% 5.86/1.77 % (3210204)------------------------------
% 5.86/1.78 % (3210204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.78 % (3210204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.78 % (3210204)CaDiCaL version: 2.1.3
% 5.86/1.78 % (3210204)Termination reason: Instruction limit
% 5.86/1.78 % (3210204)Termination phase: Saturation
% 5.86/1.78 % (3210204)Time elapsed: 0.064 s
% 5.86/1.78 % (3210204)Peak memory usage: 88 MB
% 5.86/1.78 % (3210204)Instructions burned: 128 (million)
% 5.86/1.78 % (3210178)Also succeeded, but the first one will report.
% 5.86/1.78 % (3210179)Refutation found. Thanks to Tanya!
% 5.86/1.78 % SZS status Theorem for theBenchmark
% 5.86/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 7.12/1.97 % (3210179)------------------------------
% 7.12/1.97 % (3210179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.12/1.97 % (3210179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.12/1.97 % (3210179)CaDiCaL version: 2.1.3
% 7.12/1.97 % (3210179)Termination reason: Refutation
% 7.12/1.97 % (3210179)Time elapsed: 0.662 s
% 7.12/1.97 % (3210179)Peak memory usage: 136 MB
% 7.12/1.97 % (3210179)Instructions burned: 1673 (million)
% 7.12/1.97 % (3210179)------------------------------
% 7.12/1.97 % (3210179)------------------------------
% 7.12/1.97 % (3210173)Success in time 0.923 s
% 7.12/1.97 % Vampire exiting
%------------------------------------------------------------------------------