%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA002+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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:55:19 AM UTC 2026
% Result : Theorem 7.55s 2.06s
% Output : Refutation 9.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 31
% Syntax : Number of formulae : 265 ( 33 unt; 18 def)
% Number of atoms : 977 ( 240 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1171 ( 459 ~; 567 |; 106 &)
% ( 19 <=>; 17 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 28 ( 26 usr; 17 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 334 ( 0 sgn 313 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_loops) ).
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(f7,axiom,
! [X0,X1,X2,X3] :
( ( path(X0,X1,X2)
& in_path(X3,X2) )
=> ( vertex(X3)
& ? [X4] :
( on_path(X4,X2)
& ( X3 = head_of(X4)
| X3 = tail_of(X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_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(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(f15,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
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(f17,axiom,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f21,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
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(f30,plain,
! [X0,X1,X2,X3] :
( ( vertex(X3)
& ? [X4] :
( on_path(X4,X2)
& ( X3 = head_of(X4)
| X3 = tail_of(X4) ) ) )
| ~ path(X0,X1,X2)
| ~ in_path(X3,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ( vertex(X3)
& ? [X4] :
( on_path(X4,X2)
& ( X3 = head_of(X4)
| X3 = tail_of(X4) ) ) )
| ~ path(X0,X1,X2)
| ~ in_path(X3,X2) ),
inference(flattening,[],[f30]) ).
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(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(f38,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(flattening,[],[f38]) ).
fof(f41,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f19]) ).
fof(f45,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(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(flattening,[],[f45]) ).
fof(f47,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))],[f46]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ( vertex(X3)
& on_path(sK3(X2,X3),X2)
& ( head_of(sK3(X2,X3)) = X3
| tail_of(sK3(X2,X3)) = X3 ) )
| ~ path(X0,X1,X2)
| ~ in_path(X3,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X2,X3))],[f31]) ).
fof(f53,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(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(flattening,[],[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,[],[f35]) ).
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(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))],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
& on_path(sK6(X0),X0)
& on_path(sK7(X0),X0)
& sequential(sK6(X0),sK7(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X3,sK6(X0)),skolemize(X4,sK7(X0))],[f43]) ).
fof(f64,plain,
( ~ less_or_equal(minus(length_of(sK8),n1),number_of_in(triangles,graph))
& shortest_path(sK9,sK10,sK8)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f44]) ).
fof(f65,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f68,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,[],[f47]) ).
fof(f69,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,[],[f47]) ).
fof(f70,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,[],[f47]) ).
fof(f71,plain,
! [X0,X1] :
( head_of(sK0(X0,X1)) = X1
| head_of(sK0(X0,X1)) = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f47]) ).
fof(f73,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f47]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| in_path(tail_of(X3),X2)
| ~ on_path(X3,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| in_path(head_of(X3),X2)
| ~ on_path(X3,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X3)
| ~ in_path(X3,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f91,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f93,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f95,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X4)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f37]) ).
fof(f109,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(f110,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,[],[f39]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK6(X0),sK7(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK7(X0),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK6(X0),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f116,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK6(X0),sK7(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f117,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f17]) ).
fof(f118,plain,
complete,
inference(cnf_transformation,[],[f64]) ).
fof(f119,plain,
shortest_path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f64]) ).
fof(f120,plain,
~ less_or_equal(minus(length_of(sK8),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f64]) ).
fof(f128,definition,
sF11 = length_of(sK8),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f129,plain,
length_of(sK8) = sF11,
inference(reorient_equations,[],[f128]) ).
fof(f130,definition,
sF12 = minus(sF11,n1),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f131,plain,
minus(sF11,n1) = sF12,
inference(reorient_equations,[],[f130]) ).
fof(f132,definition,
sF13 = number_of_in(triangles,graph),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f133,plain,
number_of_in(triangles,graph) = sF13,
inference(reorient_equations,[],[f132]) ).
fof(f134,plain,
~ less_or_equal(sF12,sF13),
inference(definition_folding,[],[f120,f133,f131,f129]) ).
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,[],[f68,f118]) ).
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,[],[f69,f118]) ).
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,[],[f70,f118]) ).
fof(f140,plain,
! [X0,X1] :
( ~ vertex(X1)
| head_of(sK0(X0,X1)) = X0
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f71,f118]) ).
fof(f142,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f73,f118]) ).
fof(f147,plain,
path(sK9,sK10,sK8),
inference(resolution,[],[f105,f119]) ).
fof(f148,plain,
minus(length_of(sK8),n1) = number_of_in(sequential_pairs,sK8),
inference(resolution,[],[f147,f112]) ).
fof(f149,plain,
minus(sF11,n1) = number_of_in(sequential_pairs,sK8),
inference(forward_demodulation,[],[f148,f129]) ).
fof(f150,plain,
sF12 = number_of_in(sequential_pairs,sK8),
inference(forward_demodulation,[],[f149,f131]) ).
fof(f152,plain,
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| sequential(sK6(sK8),sK7(sK8)) ),
inference(resolution,[],[f113,f147]) ).
fof(f153,plain,
( sF12 = number_of_in(triangles,sK8)
| sequential(sK6(sK8),sK7(sK8)) ),
inference(forward_demodulation,[],[f152,f150]) ).
fof(f155,definition,
( spl14_1
<=> sequential(sK6(sK8),sK7(sK8)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f157,plain,
( sequential(sK6(sK8),sK7(sK8))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f159,definition,
( spl14_2
<=> sF12 = number_of_in(triangles,sK8) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f160,plain,
( sF12 != number_of_in(triangles,sK8)
| spl14_2 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f161,plain,
( sF12 = number_of_in(triangles,sK8)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f153,f159,f155]) ).
fof(f164,plain,
( less_or_equal(sF12,number_of_in(triangles,graph))
| ~ spl14_2 ),
inference(superposition,[],[f117,f161]) ).
fof(f165,plain,
( less_or_equal(sF12,sF13)
| ~ spl14_2 ),
inference(forward_demodulation,[],[f164,f133]) ).
fof(f168,plain,
( $false
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f165,f134]) ).
fof(f169,plain,
~ spl14_2,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f172,plain,
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| on_path(sK7(sK8),sK8) ),
inference(resolution,[],[f114,f147]) ).
fof(f173,plain,
( sF12 = number_of_in(triangles,sK8)
| on_path(sK7(sK8),sK8) ),
inference(forward_demodulation,[],[f172,f150]) ).
fof(f174,plain,
( on_path(sK7(sK8),sK8)
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f173,f160]) ).
fof(f175,plain,
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| on_path(sK6(sK8),sK8) ),
inference(resolution,[],[f115,f147]) ).
fof(f176,plain,
( sF12 = number_of_in(triangles,sK8)
| on_path(sK6(sK8),sK8) ),
inference(forward_demodulation,[],[f175,f150]) ).
fof(f177,plain,
( on_path(sK6(sK8),sK8)
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f176,f160]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ edge(sK6(X2))
| ~ edge(sK7(X2))
| ~ edge(X3)
| ~ sequential(sK6(X2),sK7(X2))
| ~ sequential(sK7(X2),X3)
| ~ sequential(X3,sK6(X2)) ),
inference(resolution,[],[f116,f110]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ edge(sK6(X2))
| ~ edge(sK7(X2))
| ~ edge(X3)
| ~ sequential(sK7(X2),X3)
| ~ sequential(X3,sK6(X2)) ),
inference(forward_subsumption_resolution,[],[f178,f113]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ edge(sK6(X2))
| ~ edge(sK7(X2))
| ~ sequential(sK7(X2),X3)
| ~ sequential(X3,sK6(X2)) ),
inference(forward_subsumption_resolution,[],[f179,f93]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ edge(sK7(X2))
| ~ sequential(sK7(X2),X3)
| ~ sequential(X3,sK6(X2)) ),
inference(forward_subsumption_resolution,[],[f180,f93]) ).
fof(f182,plain,
! [X2,X3,X0,X1] :
( ~ sequential(sK7(X2),X3)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ path(X0,X1,X2)
| ~ sequential(X3,sK6(X2)) ),
inference(forward_subsumption_resolution,[],[f181,f94]) ).
fof(f186,plain,
( edge(sK7(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f93,f157]) ).
fof(f187,plain,
( edge(sK6(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f94,f157]) ).
fof(f188,plain,
! [X0,X1] :
( precedes(X0,X1,sK8)
| ~ on_path(X1,sK8)
| ~ sequential(X0,X1)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f97,f147]) ).
fof(f206,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK8)
| ~ precedes(X0,X1,sK8) ),
inference(resolution,[],[f108,f119]) ).
fof(f207,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK8)
| ~ on_path(X0,sK8)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK8) ),
inference(resolution,[],[f206,f188]) ).
fof(f219,definition,
( spl14_3
<=> ! [X4,X3] : ~ path(X3,X4,sK8) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f220,plain,
( ! [X3,X4] : ~ path(X3,X4,sK8)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f225,plain,
( head_of(sK6(sK8)) = tail_of(sK7(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f91,f157]) ).
fof(f226,plain,
( head_of(sK6(sK8)) != head_of(sK7(sK8))
| ~ edge(sK7(sK8))
| ~ spl14_1 ),
inference(superposition,[],[f65,f225]) ).
fof(f231,plain,
( head_of(sK6(sK8)) != head_of(sK7(sK8))
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f226,f186]) ).
fof(f244,plain,
( $false
| ~ spl14_3 ),
inference(resolution,[],[f220,f147]) ).
fof(f245,plain,
~ spl14_3,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f246,plain,
! [X0,X1] :
( ~ on_path(X0,sK8)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK8)
| ~ on_path(X1,sK8)
| ~ sequential(X0,X1)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f207,f188]) ).
fof(f247,plain,
! [X0,X1] :
( ~ sequential(X1,X0)
| ~ on_path(X0,sK8)
| ~ on_path(X1,sK8)
| ~ sequential(X0,X1) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f248,plain,
( ~ on_path(sK7(sK8),sK8)
| ~ on_path(sK6(sK8),sK8)
| ~ sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f247,f157]) ).
fof(f249,plain,
( ~ on_path(sK6(sK8),sK8)
| ~ sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f248,f174]) ).
fof(f250,plain,
( ~ sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f249,f177]) ).
fof(f257,plain,
! [X0] :
( ~ in_path(X0,sK8)
| vertex(X0) ),
inference(resolution,[],[f90,f147]) ).
fof(f312,plain,
! [X0] :
( in_path(head_of(X0),sK8)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f86,f147]) ).
fof(f314,plain,
! [X0] :
( ~ on_path(X0,sK8)
| vertex(head_of(X0)) ),
inference(resolution,[],[f312,f257]) ).
fof(f315,plain,
( vertex(head_of(sK7(sK8)))
| spl14_2 ),
inference(resolution,[],[f314,f174]) ).
fof(f572,plain,
! [X0] :
( in_path(tail_of(X0),sK8)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f85,f147]) ).
fof(f574,plain,
! [X0] :
( ~ on_path(X0,sK8)
| vertex(tail_of(X0)) ),
inference(resolution,[],[f572,f257]) ).
fof(f578,plain,
( vertex(tail_of(sK6(sK8)))
| spl14_2 ),
inference(resolution,[],[f574,f177]) ).
fof(f580,plain,
( ! [X0] :
( ~ vertex(X0)
| tail_of(sK6(sK8)) = tail_of(sK0(X0,tail_of(sK6(sK8))))
| tail_of(sK0(X0,tail_of(sK6(sK8)))) = X0
| tail_of(sK6(sK8)) = X0 )
| spl14_2 ),
inference(resolution,[],[f578,f137]) ).
fof(f581,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,tail_of(sK6(sK8)))) = X0
| tail_of(sK0(X0,tail_of(sK6(sK8)))) = X0
| tail_of(sK6(sK8)) = X0 )
| spl14_2 ),
inference(resolution,[],[f578,f138]) ).
fof(f582,plain,
( ! [X0] :
( ~ vertex(X0)
| tail_of(sK6(sK8)) = tail_of(sK0(X0,tail_of(sK6(sK8))))
| tail_of(sK6(sK8)) = head_of(sK0(X0,tail_of(sK6(sK8))))
| tail_of(sK6(sK8)) = X0 )
| spl14_2 ),
inference(resolution,[],[f578,f139]) ).
fof(f583,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,tail_of(sK6(sK8)))) = X0
| tail_of(sK6(sK8)) = head_of(sK0(X0,tail_of(sK6(sK8))))
| tail_of(sK6(sK8)) = X0 )
| spl14_2 ),
inference(resolution,[],[f578,f140]) ).
fof(f664,definition,
( spl14_43
<=> head_of(sK7(sK8)) = tail_of(sK6(sK8)) ),
introduced(definition,[new_symbols(definition,[spl14_43])],[avatar_definition]) ).
fof(f665,plain,
( head_of(sK7(sK8)) != tail_of(sK6(sK8))
| spl14_43 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f666,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_43 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f690,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| ~ edge(sK6(sK8))
| sK6(sK8) = X0
| sequential(X0,sK6(sK8)) )
| ~ spl14_43 ),
inference(superposition,[],[f95,f666]) ).
fof(f697,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| sK6(sK8) = X0
| sequential(X0,sK6(sK8)) )
| ~ spl14_1
| ~ spl14_43 ),
inference(forward_subsumption_resolution,[],[f690,f187]) ).
fof(f701,plain,
( ~ edge(sK7(sK8))
| sK6(sK8) = sK7(sK8)
| sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| ~ spl14_43 ),
inference(equality_resolution,[],[f697]) ).
fof(f704,plain,
( sK6(sK8) = sK7(sK8)
| sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| ~ spl14_43 ),
inference(forward_subsumption_resolution,[],[f701,f186]) ).
fof(f705,plain,
( sK6(sK8) = sK7(sK8)
| ~ spl14_1
| spl14_2
| ~ spl14_43 ),
inference(forward_subsumption_resolution,[],[f704,f250]) ).
fof(f709,plain,
( head_of(sK6(sK8)) = tail_of(sK6(sK8))
| ~ spl14_1
| spl14_2
| ~ spl14_43 ),
inference(superposition,[],[f225,f705]) ).
fof(f722,plain,
( head_of(sK6(sK8)) = head_of(sK7(sK8))
| ~ spl14_1
| spl14_2
| ~ spl14_43 ),
inference(forward_demodulation,[],[f709,f666]) ).
fof(f727,plain,
( $false
| ~ spl14_1
| spl14_2
| ~ spl14_43 ),
inference(forward_subsumption_resolution,[],[f722,f231]) ).
fof(f728,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_43 ),
inference(avatar_contradiction_clause,[],[f727]) ).
fof(f765,definition,
( spl14_55
<=> head_of(sK6(sK8)) = tail_of(sK6(sK8)) ),
introduced(definition,[new_symbols(definition,[spl14_55])],[avatar_definition]) ).
fof(f766,plain,
( head_of(sK6(sK8)) = tail_of(sK6(sK8))
| ~ spl14_55 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f767,plain,
( head_of(sK6(sK8)) != tail_of(sK6(sK8))
| spl14_55 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f783,plain,
( head_of(sK7(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| tail_of(sK6(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2 ),
inference(resolution,[],[f583,f315]) ).
fof(f811,plain,
( head_of(sK7(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| tail_of(sK6(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| spl14_2
| spl14_43 ),
inference(forward_subsumption_resolution,[],[f783,f665]) ).
fof(f822,definition,
( spl14_64
<=> tail_of(sK6(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_64])],[avatar_definition]) ).
fof(f823,plain,
( tail_of(sK6(sK8)) != head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| spl14_64 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f824,plain,
( tail_of(sK6(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_64 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f826,definition,
( spl14_65
<=> head_of(sK7(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_65])],[avatar_definition]) ).
fof(f828,plain,
( head_of(sK7(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_65 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f829,plain,
( spl14_64
| spl14_65
| spl14_2
| spl14_43 ),
inference(avatar_split_clause,[],[f811,f664,f159,f826,f822]) ).
fof(f841,plain,
( head_of(sK6(sK8)) != head_of(sK6(sK8))
| ~ edge(sK6(sK8))
| ~ spl14_55 ),
inference(superposition,[],[f65,f766]) ).
fof(f848,plain,
( ~ edge(sK6(sK8))
| ~ spl14_55 ),
inference(trivial_inequality_removal,[],[f841]) ).
fof(f853,plain,
( $false
| ~ spl14_1
| ~ spl14_55 ),
inference(forward_subsumption_resolution,[],[f848,f187]) ).
fof(f854,plain,
( ~ spl14_1
| ~ spl14_55 ),
inference(avatar_contradiction_clause,[],[f853]) ).
fof(f868,plain,
( tail_of(sK6(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2 ),
inference(resolution,[],[f580,f315]) ).
fof(f876,plain,
( tail_of(sK6(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| spl14_2
| spl14_43 ),
inference(forward_subsumption_resolution,[],[f868,f665]) ).
fof(f907,definition,
( spl14_70
<=> head_of(sK7(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_70])],[avatar_definition]) ).
fof(f908,plain,
( head_of(sK7(sK8)) != tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| spl14_70 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f909,plain,
( head_of(sK7(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_70 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f911,definition,
( spl14_71
<=> tail_of(sK6(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_71])],[avatar_definition]) ).
fof(f913,plain,
( tail_of(sK6(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_71 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f914,plain,
( spl14_70
| spl14_71
| spl14_2
| spl14_43 ),
inference(avatar_split_clause,[],[f876,f664,f159,f911,f907]) ).
fof(f945,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK6(sK8))
| ~ edge(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ edge(X0)
| sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))) = X0
| sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),X0) )
| ~ spl14_64 ),
inference(superposition,[],[f95,f824]) ).
fof(f979,plain,
( tail_of(sK6(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| tail_of(sK6(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2 ),
inference(resolution,[],[f582,f315]) ).
fof(f1017,definition,
( spl14_81
<=> edge(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_81])],[avatar_definition]) ).
fof(f1018,plain,
( edge(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_81 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1019,plain,
( ~ edge(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| spl14_81 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1021,definition,
( spl14_82
<=> ! [X0] :
( tail_of(X0) != tail_of(sK6(sK8))
| sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),X0)
| sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))) = X0
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[spl14_82])],[avatar_definition]) ).
fof(f1022,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK6(sK8))
| sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),X0)
| sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))) = X0
| ~ edge(X0) )
| ~ spl14_82 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1023,plain,
( ~ spl14_81
| spl14_82
| ~ spl14_64 ),
inference(avatar_split_clause,[],[f945,f822,f1021,f1017]) ).
fof(f1032,plain,
( ~ vertex(head_of(sK7(sK8)))
| ~ vertex(tail_of(sK6(sK8)))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_81 ),
inference(resolution,[],[f1019,f142]) ).
fof(f1033,plain,
( ~ vertex(tail_of(sK6(sK8)))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2
| spl14_81 ),
inference(forward_subsumption_resolution,[],[f1032,f315]) ).
fof(f1034,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2
| spl14_81 ),
inference(forward_subsumption_resolution,[],[f1033,f578]) ).
fof(f1035,plain,
( $false
| spl14_2
| spl14_43
| spl14_81 ),
inference(forward_subsumption_resolution,[],[f1034,f665]) ).
fof(f1036,plain,
( spl14_2
| spl14_43
| spl14_81 ),
inference(avatar_contradiction_clause,[],[f1035]) ).
fof(f1040,plain,
( tail_of(sK6(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2
| spl14_64 ),
inference(forward_subsumption_resolution,[],[f979,f823]) ).
fof(f1045,plain,
( tail_of(sK6(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| spl14_2
| spl14_43
| spl14_64 ),
inference(forward_subsumption_resolution,[],[f1040,f665]) ).
fof(f1046,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2
| spl14_43
| spl14_64
| ~ spl14_70 ),
inference(forward_demodulation,[],[f1045,f909]) ).
fof(f1047,plain,
( $false
| spl14_2
| spl14_43
| spl14_64
| ~ spl14_70 ),
inference(forward_subsumption_resolution,[],[f1046,f665]) ).
fof(f1048,plain,
( spl14_2
| spl14_43
| spl14_64
| ~ spl14_70 ),
inference(avatar_contradiction_clause,[],[f1047]) ).
fof(f1063,plain,
( ! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK6(sK8))
| head_of(X1) != head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4) )
| ~ spl14_71 ),
inference(superposition,[],[f109,f913]) ).
fof(f1067,plain,
( ! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK6(sK8))
| head_of(X1) != head_of(sK7(sK8))
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4) )
| ~ spl14_65
| ~ spl14_71 ),
inference(forward_demodulation,[],[f1063,f828]) ).
fof(f1076,plain,
( head_of(sK7(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2 ),
inference(resolution,[],[f581,f315]) ).
fof(f1117,plain,
( ! [X2,X3,X0,X1] :
( head_of(X0) != head_of(sK7(sK8))
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK6(sK8),X0,X3) )
| ~ spl14_65
| ~ spl14_71 ),
inference(equality_resolution,[],[f1067]) ).
fof(f1123,plain,
( ! [X2,X0,X1] :
( ~ precedes(sK6(sK8),sK7(sK8),X2)
| ~ shortest_path(X0,X1,X2) )
| ~ spl14_65
| ~ spl14_71 ),
inference(equality_resolution,[],[f1117]) ).
fof(f1127,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK8)
| ~ on_path(sK7(sK8),sK8)
| ~ sequential(sK6(sK8),sK7(sK8))
| ~ on_path(sK6(sK8),sK8) )
| ~ spl14_65
| ~ spl14_71 ),
inference(resolution,[],[f1123,f188]) ).
fof(f1128,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK8)
| ~ sequential(sK6(sK8),sK7(sK8))
| ~ on_path(sK6(sK8),sK8) )
| spl14_2
| ~ spl14_65
| ~ spl14_71 ),
inference(forward_subsumption_resolution,[],[f1127,f174]) ).
fof(f1129,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK8)
| ~ on_path(sK6(sK8),sK8) )
| ~ spl14_1
| spl14_2
| ~ spl14_65
| ~ spl14_71 ),
inference(forward_subsumption_resolution,[],[f1128,f157]) ).
fof(f1130,plain,
( ! [X0,X1] : ~ shortest_path(X0,X1,sK8)
| ~ spl14_1
| spl14_2
| ~ spl14_65
| ~ spl14_71 ),
inference(forward_subsumption_resolution,[],[f1129,f177]) ).
fof(f1131,plain,
( $false
| ~ spl14_1
| spl14_2
| ~ spl14_65
| ~ spl14_71 ),
inference(resolution,[],[f1130,f119]) ).
fof(f1132,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_65
| ~ spl14_71 ),
inference(avatar_contradiction_clause,[],[f1131]) ).
fof(f1137,plain,
( sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),sK6(sK8))
| sK6(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))
| ~ edge(sK6(sK8))
| ~ spl14_82 ),
inference(equality_resolution,[],[f1022]) ).
fof(f1138,plain,
( sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),sK6(sK8))
| sK6(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))
| ~ spl14_1
| ~ spl14_82 ),
inference(forward_subsumption_resolution,[],[f1137,f187]) ).
fof(f1140,definition,
( spl14_88
<=> sK6(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))) ),
introduced(definition,[new_symbols(definition,[spl14_88])],[avatar_definition]) ).
fof(f1142,plain,
( sK6(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))
| ~ spl14_88 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f1144,definition,
( spl14_89
<=> sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),sK6(sK8)) ),
introduced(definition,[new_symbols(definition,[spl14_89])],[avatar_definition]) ).
fof(f1146,plain,
( sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),sK6(sK8))
| ~ spl14_89 ),
inference(avatar_component_clause,[],[f1144]) ).
fof(f1147,plain,
( spl14_88
| spl14_89
| ~ spl14_1
| ~ spl14_82 ),
inference(avatar_split_clause,[],[f1138,f1021,f155,f1144,f1140]) ).
fof(f1160,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| ~ edge(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))) = X0
| sequential(X0,sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) )
| ~ spl14_70 ),
inference(superposition,[],[f95,f909]) ).
fof(f1167,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))) = X0
| sequential(X0,sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) )
| ~ spl14_70
| ~ spl14_81 ),
inference(forward_subsumption_resolution,[],[f1160,f1018]) ).
fof(f1174,plain,
( ~ edge(sK7(sK8))
| sK7(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))
| sequential(sK7(sK8),sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_70
| ~ spl14_81 ),
inference(equality_resolution,[],[f1167]) ).
fof(f1177,plain,
( sK7(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))
| sequential(sK7(sK8),sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_1
| ~ spl14_70
| ~ spl14_81 ),
inference(forward_subsumption_resolution,[],[f1174,f186]) ).
fof(f1179,definition,
( spl14_90
<=> sequential(sK7(sK8),sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_90])],[avatar_definition]) ).
fof(f1181,plain,
( sequential(sK7(sK8),sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| ~ spl14_90 ),
inference(avatar_component_clause,[],[f1179]) ).
fof(f1183,definition,
( spl14_91
<=> sK7(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))) ),
introduced(definition,[new_symbols(definition,[spl14_91])],[avatar_definition]) ).
fof(f1185,plain,
( sK7(sK8) = sK0(head_of(sK7(sK8)),tail_of(sK6(sK8)))
| ~ spl14_91 ),
inference(avatar_component_clause,[],[f1183]) ).
fof(f1186,plain,
( spl14_90
| spl14_91
| ~ spl14_1
| ~ spl14_70
| ~ spl14_81 ),
inference(avatar_split_clause,[],[f1177,f1017,f907,f155,f1183,f1179]) ).
fof(f1188,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_64
| ~ spl14_91 ),
inference(superposition,[],[f824,f1185]) ).
fof(f1194,plain,
( $false
| spl14_43
| ~ spl14_64
| ~ spl14_91 ),
inference(forward_subsumption_resolution,[],[f1188,f665]) ).
fof(f1195,plain,
( spl14_43
| ~ spl14_64
| ~ spl14_91 ),
inference(avatar_contradiction_clause,[],[f1194]) ).
fof(f1199,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| ~ path(X0,X1,sK8)
| ~ sequential(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))),sK6(sK8)) )
| ~ spl14_90 ),
inference(resolution,[],[f1181,f182]) ).
fof(f1204,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| ~ path(X0,X1,sK8) )
| ~ spl14_89
| ~ spl14_90 ),
inference(forward_subsumption_resolution,[],[f1199,f1146]) ).
fof(f1205,plain,
( ! [X0,X1] :
( sF12 = number_of_in(triangles,sK8)
| ~ path(X0,X1,sK8) )
| ~ spl14_89
| ~ spl14_90 ),
inference(forward_demodulation,[],[f1204,f150]) ).
fof(f1206,plain,
( ! [X0,X1] : ~ path(X0,X1,sK8)
| spl14_2
| ~ spl14_89
| ~ spl14_90 ),
inference(forward_subsumption_resolution,[],[f1205,f160]) ).
fof(f1207,plain,
( spl14_3
| spl14_2
| ~ spl14_89
| ~ spl14_90 ),
inference(avatar_split_clause,[],[f1206,f1179,f1144,f159,f219]) ).
fof(f1215,plain,
( head_of(sK6(sK8)) = tail_of(sK6(sK8))
| ~ spl14_64
| ~ spl14_88 ),
inference(superposition,[],[f824,f1142]) ).
fof(f1218,plain,
( $false
| spl14_55
| ~ spl14_64
| ~ spl14_88 ),
inference(forward_subsumption_resolution,[],[f1215,f767]) ).
fof(f1219,plain,
( spl14_55
| ~ spl14_64
| ~ spl14_88 ),
inference(avatar_contradiction_clause,[],[f1218]) ).
fof(f1224,plain,
( head_of(sK7(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2
| spl14_70 ),
inference(forward_subsumption_resolution,[],[f1076,f908]) ).
fof(f1225,plain,
( head_of(sK7(sK8)) = head_of(sK0(head_of(sK7(sK8)),tail_of(sK6(sK8))))
| spl14_2
| spl14_43
| spl14_70 ),
inference(forward_subsumption_resolution,[],[f1224,f665]) ).
fof(f1226,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_2
| spl14_43
| ~ spl14_64
| spl14_70 ),
inference(forward_demodulation,[],[f1225,f824]) ).
fof(f1227,plain,
( $false
| spl14_2
| spl14_43
| ~ spl14_64
| spl14_70 ),
inference(forward_subsumption_resolution,[],[f1226,f665]) ).
fof(f1228,plain,
( spl14_2
| spl14_43
| ~ spl14_64
| spl14_70 ),
inference(avatar_contradiction_clause,[],[f1227]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f162]) ).
cnf(s3,plain,
~ spl14_2,
inference(sat_conversion,[],[f169]) ).
cnf(s6,plain,
~ spl14_3,
inference(sat_conversion,[],[f245]) ).
cnf(s38,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_43 ),
inference(sat_conversion,[],[f728]) ).
cnf(s47,plain,
( spl14_2
| spl14_43
| spl14_64
| spl14_65 ),
inference(sat_conversion,[],[f829]) ).
cnf(s49,plain,
( ~ spl14_1
| ~ spl14_55 ),
inference(sat_conversion,[],[f854]) ).
cnf(s54,plain,
( spl14_2
| spl14_43
| spl14_70
| spl14_71 ),
inference(sat_conversion,[],[f914]) ).
cnf(s65,plain,
( ~ spl14_64
| ~ spl14_81
| spl14_82 ),
inference(sat_conversion,[],[f1023]) ).
cnf(s66,plain,
( spl14_2
| spl14_43
| spl14_81 ),
inference(sat_conversion,[],[f1036]) ).
cnf(s68,plain,
( spl14_2
| spl14_43
| spl14_64
| ~ spl14_70 ),
inference(sat_conversion,[],[f1048]) ).
cnf(s72,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_65
| ~ spl14_71 ),
inference(sat_conversion,[],[f1132]) ).
cnf(s73,plain,
( ~ spl14_1
| ~ spl14_82
| spl14_88
| spl14_89 ),
inference(sat_conversion,[],[f1147]) ).
cnf(s74,plain,
( ~ spl14_1
| ~ spl14_70
| ~ spl14_81
| spl14_90
| spl14_91 ),
inference(sat_conversion,[],[f1186]) ).
cnf(s76,plain,
( spl14_43
| ~ spl14_64
| ~ spl14_91 ),
inference(sat_conversion,[],[f1195]) ).
cnf(s78,plain,
( spl14_2
| spl14_3
| ~ spl14_89
| ~ spl14_90 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s79,plain,
( spl14_55
| ~ spl14_64
| ~ spl14_88 ),
inference(sat_conversion,[],[f1219]) ).
cnf(s82,plain,
( spl14_2
| spl14_43
| ~ spl14_64
| spl14_70 ),
inference(sat_conversion,[],[f1228]) ).
cnf(s88,plain,
spl14_1,
inference(rat,[],[s1,s3]) ).
cnf(s89,plain,
~ spl14_55,
inference(rat,[],[s49,s88]) ).
cnf(s90,plain,
~ spl14_43,
inference(rat,[],[s38,s3,s88]) ).
cnf(s91,plain,
spl14_81,
inference(rat,[],[s66,s3,s90]) ).
cnf(s92,plain,
spl14_64,
inference(rat,[],[s72,s54,s47,s68,s3,s88,s90]) ).
cnf(s93,plain,
~ spl14_88,
inference(rat,[],[s79,s89,s92]) ).
cnf(s94,plain,
~ spl14_91,
inference(rat,[],[s76,s90,s92]) ).
cnf(s95,plain,
spl14_82,
inference(rat,[],[s65,s91,s92]) ).
cnf(s96,plain,
spl14_70,
inference(rat,[],[s82,s90,s3,s92]) ).
cnf(s97,plain,
spl14_89,
inference(rat,[],[s73,s93,s88,s95]) ).
cnf(s98,plain,
spl14_90,
inference(rat,[],[s74,s94,s91,s88,s96]) ).
cnf(s100,plain,
$false,
inference(rat,[],[s78,s3,s6,s98,s97]) ).
fof(f1229,plain,
$false,
inference(avatar_sat_refutation,[],[s100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA002+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 08:51:00 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 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
% 7.55/2.06 % (3256962)Detected formulas, will run a generic FOF schedule.
% 7.55/2.06 % (3256969)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=3775213516:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.55/2.06 % (3256970)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2016117129:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.55/2.06 % (3256973)dis-21_1_sil=8000:lcm=predicate:random_seed=807200335: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)
% 7.55/2.06 % (3256968)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=3937444429:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.55/2.06 % (3256967)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=534646140:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.55/2.06 % (3256971)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1109557689:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.55/2.06 % (3256972)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1730560347:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.55/2.06 % (3256970)Refutation not found, incomplete strategy
% 7.55/2.06 % (3256970)------------------------------
% 7.55/2.06 % (3256970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256970)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256970)Termination reason: Refutation not found, incomplete strategy
% 7.55/2.06 % (3256970)Time elapsed: 0.002 s
% 7.55/2.06 % (3256970)Peak memory usage: 88 MB
% 7.55/2.06 % (3256973)Instruction limit reached!
% 7.55/2.06 % (3256973)------------------------------
% 7.55/2.06 % (3256973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256973)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256973)Termination reason: Instruction limit
% 7.55/2.06 % (3256973)Termination phase: Saturation
% 7.55/2.06 % (3256973)Time elapsed: 0.065 s
% 7.55/2.06 % (3256973)Peak memory usage: 88 MB
% 7.55/2.06 % (3256973)Instructions burned: 130 (million)
% 7.55/2.06 % (3256971)Instruction limit reached!
% 7.55/2.06 % (3256971)------------------------------
% 7.55/2.06 % (3256971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256971)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256971)Termination reason: Instruction limit
% 7.55/2.06 % (3256971)Termination phase: Saturation
% 7.55/2.06 % (3256971)Time elapsed: 0.067 s
% 7.55/2.06 % (3256971)Peak memory usage: 88 MB
% 7.55/2.06 % (3256971)Instructions burned: 119 (million)
% 7.55/2.06 % (3256972)Instruction limit reached!
% 7.55/2.06 % (3256972)------------------------------
% 7.55/2.06 % (3256972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256972)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256972)Termination reason: Instruction limit
% 7.55/2.06 % (3256972)Termination phase: Saturation
% 7.55/2.06 % (3256972)Time elapsed: 0.093 s
% 7.55/2.06 % (3256972)Peak memory usage: 90 MB
% 7.55/2.06 % (3256972)Instructions burned: 139 (million)
% 7.55/2.06 % (3256982)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1910078070:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.55/2.06 % (3256981)lrs+10_1_sil=8000:sp=occurrence:random_seed=3840371592:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.55/2.06 % (3256982)Refutation not found, incomplete strategy
% 7.55/2.06 % (3256982)------------------------------
% 7.55/2.06 % (3256982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256982)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256982)Termination reason: Refutation not found, incomplete strategy
% 7.55/2.06 % (3256982)Time elapsed: 0.002 s
% 7.55/2.06 % (3256982)Peak memory usage: 88 MB
% 7.55/2.06 % (3256982)Instructions burned: 1 (million)
% 7.55/2.06 % (3256970)------------------------------
% 7.55/2.06 % (3256970)------------------------------
% 7.55/2.06 % (3256983)lrs+1011_1_sil=32000:sp=occurrence:random_seed=468527438:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.55/2.06 % (3256983)Refutation not found, incomplete strategy
% 7.55/2.06 % (3256983)------------------------------
% 7.55/2.06 % (3256983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256983)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256983)Termination reason: Refutation not found, incomplete strategy
% 7.55/2.06 % (3256983)Time elapsed: 0.002 s
% 7.55/2.06 % (3256983)Peak memory usage: 88 MB
% 7.55/2.06 % (3256983)Instructions burned: 1 (million)
% 7.55/2.06 % (3256981)Instruction limit reached!
% 7.55/2.06 % (3256981)------------------------------
% 7.55/2.06 % (3256981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256981)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256981)Termination reason: Instruction limit
% 7.55/2.06 % (3256981)Termination phase: Saturation
% 7.55/2.06 % (3256981)Time elapsed: 0.166 s
% 7.55/2.06 % (3256981)Peak memory usage: 91 MB
% 7.55/2.06 % (3256981)Instructions burned: 286 (million)
% 7.55/2.06 % (3256987)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=4030520198:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.55/2.06 % (3256982)------------------------------
% 7.55/2.06 % (3256982)------------------------------
% 7.55/2.06 % (3256983)------------------------------
% 7.55/2.06 % (3256983)------------------------------
% 7.55/2.06 % (3256988)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3007451851:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 7.55/2.06 % (3256987)Instruction limit reached!
% 7.55/2.06 % (3256987)------------------------------
% 7.55/2.06 % (3256987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256987)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256987)Termination reason: Instruction limit
% 7.55/2.06 % (3256987)Termination phase: Saturation
% 7.55/2.06 % (3256987)Time elapsed: 0.148 s
% 7.55/2.06 % (3256987)Peak memory usage: 90 MB
% 7.55/2.06 % (3256987)Instructions burned: 248 (million)
% 7.55/2.06 % (3256990)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1240740879:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 7.55/2.06 % (3256991)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3246841467:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 7.55/2.06 % (3256988)Instruction limit reached!
% 7.55/2.06 % (3256988)------------------------------
% 7.55/2.06 % (3256988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256988)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256988)Termination reason: Instruction limit
% 7.55/2.06 % (3256988)Termination phase: Saturation
% 7.55/2.06 % (3256988)Time elapsed: 0.153 s
% 7.55/2.06 % (3256988)Peak memory usage: 88 MB
% 7.55/2.06 % (3256988)Instructions burned: 295 (million)
% 7.55/2.06 % (3256993)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4012832804:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 7.55/2.06 % (3256991)Instruction limit reached!
% 7.55/2.06 % (3256991)------------------------------
% 7.55/2.06 % (3256991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256991)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256991)Termination reason: Instruction limit
% 7.55/2.06 % (3256991)Termination phase: Saturation
% 7.55/2.06 % (3256991)Time elapsed: 0.076 s
% 7.55/2.06 % (3256991)Peak memory usage: 89 MB
% 7.55/2.06 % (3256991)Instructions burned: 114 (million)
% 7.55/2.06 % (3256967)First to succeed.
% 7.55/2.06 % (3256967)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3256962"
% 7.55/2.06 % (3256993)Instruction limit reached!
% 7.55/2.06 % (3256993)------------------------------
% 7.55/2.06 % (3256993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256993)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256993)Termination reason: Instruction limit
% 7.55/2.06 % (3256993)Termination phase: Saturation
% 7.55/2.06 % (3256993)Time elapsed: 0.064 s
% 7.55/2.06 % (3256993)Peak memory usage: 88 MB
% 7.55/2.06 % (3256993)Instructions burned: 128 (million)
% 7.55/2.06 % (3256996)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1747400415:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 7.55/2.06 % (3256996)Refutation not found, incomplete strategy
% 7.55/2.06 % (3256996)------------------------------
% 7.55/2.06 % (3256996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256996)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256996)Termination reason: Refutation not found, incomplete strategy
% 7.55/2.06 % (3256996)Time elapsed: 0.002 s
% 7.55/2.06 % (3256996)Peak memory usage: 88 MB
% 7.55/2.06 % (3256996)Instructions burned: 1 (million)
% 7.55/2.06 % (3256998)lrs+10_1_sil=8000:sp=occurrence:random_seed=2131273505:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 7.55/2.06 % (3256999)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1320311948:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 7.55/2.06 % (3256999)Refutation not found, incomplete strategy
% 7.55/2.06 % (3256999)------------------------------
% 7.55/2.06 % (3256999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.55/2.06 % (3256999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.55/2.06 % (3256999)CaDiCaL version: 2.1.3
% 7.55/2.06 % (3256999)Termination reason: Refutation not found, incomplete strategy
% 7.55/2.06 % (3256999)Time elapsed: 0.002 s
% 7.55/2.06 % (3256999)Peak memory usage: 88 MB
% 7.55/2.06 % (3256999)Instructions burned: 2 (million)
% 7.55/2.06 % (3256968)Also succeeded, but the first one will report.
% 7.55/2.06 % (3256967)Refutation found. Thanks to Tanya!
% 7.55/2.06 % SZS status Theorem for theBenchmark
% 7.55/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 9.03/2.25 % (3256967)------------------------------
% 9.03/2.25 % (3256967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.03/2.25 % (3256967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.03/2.25 % (3256967)CaDiCaL version: 2.1.3
% 9.03/2.25 % (3256967)Termination reason: Refutation
% 9.03/2.25 % (3256967)Time elapsed: 0.751 s
% 9.03/2.25 % (3256967)Peak memory usage: 129 MB
% 9.03/2.25 % (3256967)Instructions burned: 1107 (million)
% 9.03/2.25 % (3256967)------------------------------
% 9.03/2.25 % (3256967)------------------------------
% 9.03/2.25 % (3256962)Success in time 1.195 s
% 9.03/2.25 % Vampire exiting
%------------------------------------------------------------------------------