%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA012+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 8.65s 2.06s
% Output : Refutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 31
% Syntax : Number of formulae : 244 ( 28 unt; 19 def)
% Number of atoms : 934 ( 218 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1202 ( 512 ~; 544 |; 106 &)
% ( 20 <=>; 17 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 29 ( 27 usr; 18 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 327 ( 0 sgn 306 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(triangles,X0) = minus(length_of(X0),n1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_on_a_path) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(triangles,X0) = minus(length_of(X0),n1) ) ),
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] :
( number_of_in(triangles,X0) != minus(length_of(X0),n1)
& 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,
( number_of_in(triangles,sK8) != minus(length_of(sK8),n1)
& 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(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(f118,plain,
complete,
inference(cnf_transformation,[],[f64]) ).
fof(f119,plain,
shortest_path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f64]) ).
fof(f120,plain,
number_of_in(triangles,sK8) != minus(length_of(sK8),n1),
inference(cnf_transformation,[],[f64]) ).
fof(f128,definition,
sF11 = number_of_in(triangles,sK8),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f129,plain,
number_of_in(triangles,sK8) = sF11,
inference(reorient_equations,[],[f128]) ).
fof(f130,definition,
sF12 = length_of(sK8),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f131,plain,
length_of(sK8) = sF12,
inference(reorient_equations,[],[f130]) ).
fof(f132,definition,
sF13 = minus(sF12,n1),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f133,plain,
minus(sF12,n1) = sF13,
inference(reorient_equations,[],[f132]) ).
fof(f134,plain,
sF11 != sF13,
inference(definition_folding,[],[f120,f133,f131,f129]) ).
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(f144,plain,
path(sK9,sK10,sK8),
inference(resolution,[],[f105,f119]) ).
fof(f145,plain,
( number_of_in(triangles,sK8) = number_of_in(sequential_pairs,sK8)
| on_path(sK6(sK8),sK8) ),
inference(resolution,[],[f144,f115]) ).
fof(f146,plain,
( number_of_in(triangles,sK8) = number_of_in(sequential_pairs,sK8)
| on_path(sK7(sK8),sK8) ),
inference(resolution,[],[f144,f114]) ).
fof(f147,plain,
( number_of_in(triangles,sK8) = number_of_in(sequential_pairs,sK8)
| sequential(sK6(sK8),sK7(sK8)) ),
inference(resolution,[],[f144,f113]) ).
fof(f148,plain,
minus(length_of(sK8),n1) = number_of_in(sequential_pairs,sK8),
inference(resolution,[],[f144,f112]) ).
fof(f149,plain,
minus(sF12,n1) = number_of_in(sequential_pairs,sK8),
inference(forward_demodulation,[],[f148,f131]) ).
fof(f150,plain,
( sF11 = number_of_in(sequential_pairs,sK8)
| sequential(sK6(sK8),sK7(sK8)) ),
inference(forward_demodulation,[],[f147,f129]) ).
fof(f151,plain,
( sF11 = number_of_in(sequential_pairs,sK8)
| on_path(sK7(sK8),sK8) ),
inference(forward_demodulation,[],[f146,f129]) ).
fof(f152,plain,
( sF11 = number_of_in(sequential_pairs,sK8)
| on_path(sK6(sK8),sK8) ),
inference(forward_demodulation,[],[f145,f129]) ).
fof(f153,plain,
sF13 = number_of_in(sequential_pairs,sK8),
inference(forward_demodulation,[],[f149,f133]) ).
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
<=> sF11 = number_of_in(sequential_pairs,sK8) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f161,plain,
( sF11 = number_of_in(sequential_pairs,sK8)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f150,f159,f155]) ).
fof(f164,definition,
( spl14_3
<=> on_path(sK7(sK8),sK8) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f166,plain,
( on_path(sK7(sK8),sK8)
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f167,plain,
( spl14_3
| spl14_2 ),
inference(avatar_split_clause,[],[f151,f159,f164]) ).
fof(f169,definition,
( spl14_4
<=> on_path(sK6(sK8),sK8) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f171,plain,
( on_path(sK6(sK8),sK8)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl14_4
| spl14_2 ),
inference(avatar_split_clause,[],[f152,f159,f169]) ).
fof(f173,plain,
( sF11 = sF13
| ~ spl14_2 ),
inference(forward_demodulation,[],[f161,f153]) ).
fof(f174,plain,
( $false
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f173,f134]) ).
fof(f175,plain,
~ spl14_2,
inference(avatar_contradiction_clause,[],[f174]) ).
fof(f177,plain,
! [X2,X3,X0,X1] :
( ~ edge(sK6(X0))
| ~ edge(sK7(X0))
| ~ edge(X1)
| ~ sequential(sK6(X0),sK7(X0))
| ~ sequential(sK7(X0),X1)
| ~ sequential(X1,sK6(X0))
| ~ path(X2,X3,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(resolution,[],[f110,f116]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( ~ edge(sK6(X0))
| ~ edge(X1)
| ~ sequential(sK6(X0),sK7(X0))
| ~ sequential(sK7(X0),X1)
| ~ sequential(X1,sK6(X0))
| ~ path(X2,X3,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(forward_subsumption_resolution,[],[f177,f93]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( ~ edge(sK6(X0))
| ~ sequential(sK6(X0),sK7(X0))
| ~ sequential(sK7(X0),X1)
| ~ sequential(X1,sK6(X0))
| ~ path(X2,X3,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(forward_subsumption_resolution,[],[f178,f93]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( ~ sequential(sK6(X0),sK7(X0))
| ~ sequential(sK7(X0),X1)
| ~ sequential(X1,sK6(X0))
| ~ path(X2,X3,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(forward_subsumption_resolution,[],[f179,f93]) ).
fof(f181,plain,
! [X2,X3,X0,X1] :
( ~ sequential(sK7(X0),X1)
| ~ sequential(X1,sK6(X0))
| ~ path(X2,X3,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(forward_subsumption_resolution,[],[f180,f113]) ).
fof(f184,plain,
( edge(sK7(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f93,f157]) ).
fof(f185,plain,
( edge(sK6(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f94,f157]) ).
fof(f190,plain,
! [X0,X1] :
( precedes(X0,X1,sK8)
| ~ on_path(X1,sK8)
| ~ sequential(X0,X1)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f97,f144]) ).
fof(f205,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK8)
| ~ precedes(X0,X1,sK8) ),
inference(resolution,[],[f108,f119]) ).
fof(f206,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK8)
| ~ on_path(X0,sK8)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK8) ),
inference(resolution,[],[f205,f190]) ).
fof(f222,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,[],[f206,f190]) ).
fof(f223,plain,
! [X0,X1] :
( ~ sequential(X1,X0)
| ~ on_path(X0,sK8)
| ~ on_path(X1,sK8)
| ~ sequential(X0,X1) ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f224,plain,
( ~ on_path(sK7(sK8),sK8)
| ~ on_path(sK6(sK8),sK8)
| ~ sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f223,f157]) ).
fof(f225,plain,
( ~ on_path(sK6(sK8),sK8)
| ~ sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f224,f166]) ).
fof(f226,plain,
( ~ sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f225,f171]) ).
fof(f231,definition,
( spl14_5
<=> ! [X4,X3] : ~ path(X3,X4,sK8) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f232,plain,
( ! [X3,X4] : ~ path(X3,X4,sK8)
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f237,plain,
( head_of(sK6(sK8)) = tail_of(sK7(sK8))
| ~ spl14_1 ),
inference(resolution,[],[f91,f157]) ).
fof(f240,plain,
( head_of(sK6(sK8)) != head_of(sK7(sK8))
| ~ edge(sK7(sK8))
| ~ spl14_1 ),
inference(superposition,[],[f65,f237]) ).
fof(f245,plain,
( head_of(sK6(sK8)) != head_of(sK7(sK8))
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f240,f184]) ).
fof(f250,plain,
! [X0] :
( ~ in_path(X0,sK8)
| vertex(X0) ),
inference(resolution,[],[f90,f144]) ).
fof(f258,plain,
( $false
| ~ spl14_5 ),
inference(resolution,[],[f232,f144]) ).
fof(f259,plain,
~ spl14_5,
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f303,plain,
! [X0] :
( in_path(head_of(X0),sK8)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f86,f144]) ).
fof(f304,plain,
! [X0] :
( ~ on_path(X0,sK8)
| vertex(head_of(X0)) ),
inference(resolution,[],[f303,f250]) ).
fof(f305,plain,
( vertex(head_of(sK7(sK8)))
| ~ spl14_3 ),
inference(resolution,[],[f304,f166]) ).
fof(f308,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,head_of(sK7(sK8)))) = X0
| tail_of(sK0(X0,head_of(sK7(sK8)))) = X0
| head_of(sK7(sK8)) = X0 )
| ~ spl14_3 ),
inference(resolution,[],[f305,f138]) ).
fof(f309,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK7(sK8)) = tail_of(sK0(X0,head_of(sK7(sK8))))
| head_of(sK7(sK8)) = head_of(sK0(X0,head_of(sK7(sK8))))
| head_of(sK7(sK8)) = X0 )
| ~ spl14_3 ),
inference(resolution,[],[f305,f139]) ).
fof(f310,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,head_of(sK7(sK8)))) = X0
| head_of(sK7(sK8)) = head_of(sK0(X0,head_of(sK7(sK8))))
| head_of(sK7(sK8)) = X0 )
| ~ spl14_3 ),
inference(resolution,[],[f305,f140]) ).
fof(f655,plain,
! [X0] :
( in_path(tail_of(X0),sK8)
| ~ on_path(X0,sK8) ),
inference(resolution,[],[f85,f144]) ).
fof(f656,plain,
! [X0] :
( ~ on_path(X0,sK8)
| vertex(tail_of(X0)) ),
inference(resolution,[],[f655,f250]) ).
fof(f670,plain,
( vertex(tail_of(sK6(sK8)))
| ~ spl14_4 ),
inference(resolution,[],[f656,f171]) ).
fof(f685,plain,
( tail_of(sK6(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| tail_of(sK6(sK8)) = tail_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_3
| ~ spl14_4 ),
inference(resolution,[],[f670,f308]) ).
fof(f686,plain,
( head_of(sK7(sK8)) = tail_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| head_of(sK7(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_3
| ~ spl14_4 ),
inference(resolution,[],[f670,f309]) ).
fof(f687,plain,
( tail_of(sK6(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| head_of(sK7(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_3
| ~ spl14_4 ),
inference(resolution,[],[f670,f310]) ).
fof(f760,definition,
( spl14_54
<=> head_of(sK7(sK8)) = tail_of(sK6(sK8)) ),
introduced(definition,[new_symbols(definition,[spl14_54])],[avatar_definition]) ).
fof(f761,plain,
( head_of(sK7(sK8)) != tail_of(sK6(sK8))
| spl14_54 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f762,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_54 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f764,definition,
( spl14_55
<=> head_of(sK7(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_55])],[avatar_definition]) ).
fof(f766,plain,
( head_of(sK7(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_55 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f768,definition,
( spl14_56
<=> tail_of(sK6(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_56])],[avatar_definition]) ).
fof(f770,plain,
( tail_of(sK6(sK8)) = head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_56 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f771,plain,
( spl14_54
| spl14_55
| spl14_56
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f687,f169,f164,f768,f764,f760]) ).
fof(f773,definition,
( spl14_57
<=> head_of(sK7(sK8)) = tail_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_57])],[avatar_definition]) ).
fof(f775,plain,
( head_of(sK7(sK8)) = tail_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_57 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f776,plain,
( spl14_54
| spl14_55
| spl14_57
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f686,f169,f164,f773,f764,f760]) ).
fof(f778,definition,
( spl14_58
<=> tail_of(sK6(sK8)) = tail_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_58])],[avatar_definition]) ).
fof(f780,plain,
( tail_of(sK6(sK8)) = tail_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_58 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f781,plain,
( spl14_54
| spl14_58
| spl14_56
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f685,f169,f164,f768,f778,f760]) ).
fof(f786,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| ~ edge(sK6(sK8))
| sK6(sK8) = X0
| sequential(X0,sK6(sK8)) )
| ~ spl14_54 ),
inference(superposition,[],[f95,f762]) ).
fof(f791,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| sK6(sK8) = X0
| sequential(X0,sK6(sK8)) )
| ~ spl14_1
| ~ spl14_54 ),
inference(forward_subsumption_resolution,[],[f786,f185]) ).
fof(f795,plain,
( ~ edge(sK7(sK8))
| sK6(sK8) = sK7(sK8)
| sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| ~ spl14_54 ),
inference(equality_resolution,[],[f791]) ).
fof(f798,plain,
( sK6(sK8) = sK7(sK8)
| sequential(sK7(sK8),sK6(sK8))
| ~ spl14_1
| ~ spl14_54 ),
inference(forward_subsumption_resolution,[],[f795,f184]) ).
fof(f799,plain,
( sK6(sK8) = sK7(sK8)
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_54 ),
inference(forward_subsumption_resolution,[],[f798,f226]) ).
fof(f804,plain,
( head_of(sK6(sK8)) = tail_of(sK6(sK8))
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_54 ),
inference(superposition,[],[f237,f799]) ).
fof(f816,plain,
( head_of(sK6(sK8)) = head_of(sK7(sK8))
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_54 ),
inference(forward_demodulation,[],[f804,f762]) ).
fof(f821,plain,
( $false
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_54 ),
inference(forward_subsumption_resolution,[],[f816,f245]) ).
fof(f822,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_54 ),
inference(avatar_contradiction_clause,[],[f821]) ).
fof(f1190,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK6(sK8))
| ~ edge(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ edge(X0)
| sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))) = X0
| sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),X0) )
| ~ spl14_56 ),
inference(superposition,[],[f95,f770]) ).
fof(f1202,definition,
( spl14_103
<=> edge(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_103])],[avatar_definition]) ).
fof(f1203,plain,
( edge(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_103 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f1204,plain,
( ~ edge(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| spl14_103 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f1206,definition,
( spl14_104
<=> ! [X0] :
( tail_of(X0) != tail_of(sK6(sK8))
| sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),X0)
| sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))) = X0
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[spl14_104])],[avatar_definition]) ).
fof(f1207,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK6(sK8))
| sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),X0)
| sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))) = X0
| ~ edge(X0) )
| ~ spl14_104 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f1208,plain,
( ~ spl14_103
| spl14_104
| ~ spl14_56 ),
inference(avatar_split_clause,[],[f1190,f768,f1206,f1202]) ).
fof(f1209,plain,
( ~ vertex(tail_of(sK6(sK8)))
| ~ vertex(head_of(sK7(sK8)))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| spl14_103 ),
inference(resolution,[],[f1204,f142]) ).
fof(f1210,plain,
( ~ vertex(head_of(sK7(sK8)))
| head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_4
| spl14_103 ),
inference(forward_subsumption_resolution,[],[f1209,f670]) ).
fof(f1211,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_3
| ~ spl14_4
| spl14_103 ),
inference(forward_subsumption_resolution,[],[f1210,f305]) ).
fof(f1212,plain,
( $false
| ~ spl14_3
| ~ spl14_4
| spl14_54
| spl14_103 ),
inference(forward_subsumption_resolution,[],[f1211,f761]) ).
fof(f1213,plain,
( ~ spl14_3
| ~ spl14_4
| spl14_54
| spl14_103 ),
inference(avatar_contradiction_clause,[],[f1212]) ).
fof(f1234,plain,
( ! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK6(sK8))
| head_of(X1) != head_of(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4) )
| ~ spl14_58 ),
inference(superposition,[],[f109,f780]) ).
fof(f1236,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_55
| ~ spl14_58 ),
inference(forward_demodulation,[],[f1234,f766]) ).
fof(f1320,plain,
( ! [X2,X3,X0,X1] :
( head_of(X0) != head_of(sK7(sK8))
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK6(sK8),X0,X3) )
| ~ spl14_55
| ~ spl14_58 ),
inference(equality_resolution,[],[f1236]) ).
fof(f1327,plain,
( ! [X2,X0,X1] :
( ~ precedes(sK6(sK8),sK7(sK8),X2)
| ~ shortest_path(X0,X1,X2) )
| ~ spl14_55
| ~ spl14_58 ),
inference(equality_resolution,[],[f1320]) ).
fof(f1332,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK8)
| ~ on_path(sK7(sK8),sK8)
| ~ sequential(sK6(sK8),sK7(sK8))
| ~ on_path(sK6(sK8),sK8) )
| ~ spl14_55
| ~ spl14_58 ),
inference(resolution,[],[f1327,f190]) ).
fof(f1333,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK8)
| ~ sequential(sK6(sK8),sK7(sK8))
| ~ on_path(sK6(sK8),sK8) )
| ~ spl14_3
| ~ spl14_55
| ~ spl14_58 ),
inference(forward_subsumption_resolution,[],[f1332,f166]) ).
fof(f1334,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK8)
| ~ on_path(sK6(sK8),sK8) )
| ~ spl14_1
| ~ spl14_3
| ~ spl14_55
| ~ spl14_58 ),
inference(forward_subsumption_resolution,[],[f1333,f157]) ).
fof(f1335,plain,
( ! [X0,X1] : ~ shortest_path(X0,X1,sK8)
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_55
| ~ spl14_58 ),
inference(forward_subsumption_resolution,[],[f1334,f171]) ).
fof(f1336,plain,
( $false
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_55
| ~ spl14_58 ),
inference(resolution,[],[f1335,f119]) ).
fof(f1337,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_55
| ~ spl14_58 ),
inference(avatar_contradiction_clause,[],[f1336]) ).
fof(f1338,plain,
( head_of(sK7(sK8)) = tail_of(sK6(sK8))
| ~ spl14_55
| ~ spl14_56 ),
inference(forward_demodulation,[],[f770,f766]) ).
fof(f1340,plain,
( $false
| spl14_54
| ~ spl14_55
| ~ spl14_56 ),
inference(forward_subsumption_resolution,[],[f1338,f761]) ).
fof(f1341,plain,
( spl14_54
| ~ spl14_55
| ~ spl14_56 ),
inference(avatar_contradiction_clause,[],[f1340]) ).
fof(f1345,plain,
( sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),sK6(sK8))
| sK6(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))
| ~ edge(sK6(sK8))
| ~ spl14_104 ),
inference(equality_resolution,[],[f1207]) ).
fof(f1347,plain,
( sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),sK6(sK8))
| sK6(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))
| ~ spl14_1
| ~ spl14_104 ),
inference(forward_subsumption_resolution,[],[f1345,f185]) ).
fof(f1350,definition,
( spl14_107
<=> sK6(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))) ),
introduced(definition,[new_symbols(definition,[spl14_107])],[avatar_definition]) ).
fof(f1352,plain,
( sK6(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))
| ~ spl14_107 ),
inference(avatar_component_clause,[],[f1350]) ).
fof(f1354,definition,
( spl14_108
<=> sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),sK6(sK8)) ),
introduced(definition,[new_symbols(definition,[spl14_108])],[avatar_definition]) ).
fof(f1356,plain,
( sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),sK6(sK8))
| ~ spl14_108 ),
inference(avatar_component_clause,[],[f1354]) ).
fof(f1357,plain,
( spl14_107
| spl14_108
| ~ spl14_1
| ~ spl14_104 ),
inference(avatar_split_clause,[],[f1347,f1206,f155,f1354,f1350]) ).
fof(f1437,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| ~ edge(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))) = X0
| sequential(X0,sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) )
| ~ spl14_57 ),
inference(superposition,[],[f95,f775]) ).
fof(f1448,plain,
( ! [X0] :
( head_of(X0) != head_of(sK7(sK8))
| ~ edge(X0)
| sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))) = X0
| sequential(X0,sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) )
| ~ spl14_57
| ~ spl14_103 ),
inference(forward_subsumption_resolution,[],[f1437,f1203]) ).
fof(f1466,plain,
( ~ edge(sK7(sK8))
| sK7(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))
| sequential(sK7(sK8),sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_57
| ~ spl14_103 ),
inference(equality_resolution,[],[f1448]) ).
fof(f1470,plain,
( sK7(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))
| sequential(sK7(sK8),sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_1
| ~ spl14_57
| ~ spl14_103 ),
inference(forward_subsumption_resolution,[],[f1466,f184]) ).
fof(f1472,definition,
( spl14_114
<=> sequential(sK7(sK8),sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))) ),
introduced(definition,[new_symbols(definition,[spl14_114])],[avatar_definition]) ).
fof(f1474,plain,
( sequential(sK7(sK8),sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))))
| ~ spl14_114 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f1476,definition,
( spl14_115
<=> sK7(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))) ),
introduced(definition,[new_symbols(definition,[spl14_115])],[avatar_definition]) ).
fof(f1478,plain,
( sK7(sK8) = sK0(tail_of(sK6(sK8)),head_of(sK7(sK8)))
| ~ spl14_115 ),
inference(avatar_component_clause,[],[f1476]) ).
fof(f1479,plain,
( spl14_114
| spl14_115
| ~ spl14_1
| ~ spl14_57
| ~ spl14_103 ),
inference(avatar_split_clause,[],[f1470,f1202,f773,f155,f1476,f1472]) ).
fof(f1480,plain,
( ! [X0,X1] :
( ~ sequential(sK0(tail_of(sK6(sK8)),head_of(sK7(sK8))),sK6(sK8))
| ~ path(X0,X1,sK8)
| number_of_in(triangles,sK8) = number_of_in(sequential_pairs,sK8) )
| ~ spl14_114 ),
inference(resolution,[],[f1474,f181]) ).
fof(f1486,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK8)
| number_of_in(triangles,sK8) = number_of_in(sequential_pairs,sK8) )
| ~ spl14_108
| ~ spl14_114 ),
inference(forward_subsumption_resolution,[],[f1480,f1356]) ).
fof(f1488,plain,
( ! [X0,X1] :
( number_of_in(triangles,sK8) = sF13
| ~ path(X0,X1,sK8) )
| ~ spl14_108
| ~ spl14_114 ),
inference(forward_demodulation,[],[f1486,f153]) ).
fof(f1489,plain,
( ! [X0,X1] :
( sF11 = sF13
| ~ path(X0,X1,sK8) )
| ~ spl14_108
| ~ spl14_114 ),
inference(forward_demodulation,[],[f1488,f129]) ).
fof(f1490,plain,
( ! [X0,X1] : ~ path(X0,X1,sK8)
| ~ spl14_108
| ~ spl14_114 ),
inference(forward_subsumption_resolution,[],[f1489,f134]) ).
fof(f1491,plain,
( spl14_5
| ~ spl14_108
| ~ spl14_114 ),
inference(avatar_split_clause,[],[f1490,f1472,f1354,f231]) ).
fof(f1493,plain,
( tail_of(sK7(sK8)) = head_of(sK7(sK8))
| ~ spl14_57
| ~ spl14_115 ),
inference(superposition,[],[f775,f1478]) ).
fof(f1504,plain,
( head_of(sK6(sK8)) = head_of(sK7(sK8))
| ~ spl14_1
| ~ spl14_57
| ~ spl14_115 ),
inference(forward_demodulation,[],[f1493,f237]) ).
fof(f1507,plain,
( $false
| ~ spl14_1
| ~ spl14_57
| ~ spl14_115 ),
inference(forward_subsumption_resolution,[],[f1504,f245]) ).
fof(f1508,plain,
( ~ spl14_1
| ~ spl14_57
| ~ spl14_115 ),
inference(avatar_contradiction_clause,[],[f1507]) ).
fof(f1531,plain,
( sequential(sK7(sK8),sK6(sK8))
| ~ spl14_107
| ~ spl14_114 ),
inference(forward_demodulation,[],[f1474,f1352]) ).
fof(f1543,plain,
( $false
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_107
| ~ spl14_114 ),
inference(forward_subsumption_resolution,[],[f1531,f226]) ).
fof(f1544,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_107
| ~ spl14_114 ),
inference(avatar_contradiction_clause,[],[f1543]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f162]) ).
cnf(s2,plain,
( spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f167]) ).
cnf(s3,plain,
( spl14_2
| spl14_4 ),
inference(sat_conversion,[],[f172]) ).
cnf(s4,plain,
~ spl14_2,
inference(sat_conversion,[],[f175]) ).
cnf(s7,plain,
~ spl14_5,
inference(sat_conversion,[],[f259]) ).
cnf(s44,plain,
( ~ spl14_3
| ~ spl14_4
| spl14_54
| spl14_55
| spl14_56 ),
inference(sat_conversion,[],[f771]) ).
cnf(s45,plain,
( ~ spl14_3
| ~ spl14_4
| spl14_54
| spl14_55
| spl14_57 ),
inference(sat_conversion,[],[f776]) ).
cnf(s46,plain,
( ~ spl14_3
| ~ spl14_4
| spl14_54
| spl14_56
| spl14_58 ),
inference(sat_conversion,[],[f781]) ).
cnf(s51,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_54 ),
inference(sat_conversion,[],[f822]) ).
cnf(s91,plain,
( ~ spl14_56
| ~ spl14_103
| spl14_104 ),
inference(sat_conversion,[],[f1208]) ).
cnf(s92,plain,
( ~ spl14_3
| ~ spl14_4
| spl14_54
| spl14_103 ),
inference(sat_conversion,[],[f1213]) ).
cnf(s99,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_55
| ~ spl14_58 ),
inference(sat_conversion,[],[f1337]) ).
cnf(s100,plain,
( spl14_54
| ~ spl14_55
| ~ spl14_56 ),
inference(sat_conversion,[],[f1341]) ).
cnf(s101,plain,
( ~ spl14_1
| ~ spl14_104
| spl14_107
| spl14_108 ),
inference(sat_conversion,[],[f1357]) ).
cnf(s110,plain,
( ~ spl14_1
| ~ spl14_57
| ~ spl14_103
| spl14_114
| spl14_115 ),
inference(sat_conversion,[],[f1479]) ).
cnf(s111,plain,
( spl14_5
| ~ spl14_108
| ~ spl14_114 ),
inference(sat_conversion,[],[f1491]) ).
cnf(s115,plain,
( ~ spl14_1
| ~ spl14_57
| ~ spl14_115 ),
inference(sat_conversion,[],[f1508]) ).
cnf(s123,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_107
| ~ spl14_114 ),
inference(sat_conversion,[],[f1544]) ).
cnf(s133,plain,
spl14_4,
inference(rat,[],[s3,s4]) ).
cnf(s134,plain,
spl14_3,
inference(rat,[],[s2,s4]) ).
cnf(s135,plain,
spl14_1,
inference(rat,[],[s1,s4]) ).
cnf(s137,plain,
~ spl14_54,
inference(rat,[],[s51,s134,s133,s135]) ).
cnf(s139,plain,
spl14_103,
inference(rat,[],[s92,s134,s133,s137]) ).
cnf(s141,plain,
spl14_55,
inference(rat,[],[s101,s123,s111,s91,s110,s115,s44,s45,s135,s133,s134,s7,s139,s137]) ).
cnf(s142,plain,
~ spl14_56,
inference(rat,[],[s100,s137,s141]) ).
cnf(s143,plain,
~ spl14_58,
inference(rat,[],[s99,s135,s134,s133,s141]) ).
cnf(s144,plain,
$false,
inference(rat,[],[s46,s137,s134,s133,s143,s142]) ).
fof(f1552,plain,
$false,
inference(avatar_sat_refutation,[],[s144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA012+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n013.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 08:47:36 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.65/2.06 % (4118475)Detected formulas, will run a generic FOF schedule.
% 8.65/2.06 % (4118485)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=833293333:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.65/2.06 % (4118483)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3612683075:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.65/2.06 % (4118480)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=3243446093:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.65/2.06 % (4118484)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2477909908:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.65/2.06 % (4118482)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=2077024305:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.65/2.06 % (4118481)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=2393701944:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.65/2.06 % (4118483)Refutation not found, incomplete strategy
% 8.65/2.06 % (4118483)------------------------------
% 8.65/2.06 % (4118483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118483)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118483)Termination reason: Refutation not found, incomplete strategy
% 8.65/2.06 % (4118483)Time elapsed: 0.001 s
% 8.65/2.06 % (4118483)Peak memory usage: 87 MB
% 8.65/2.06 % (4118484)Refutation not found, incomplete strategy
% 8.65/2.06 % (4118484)------------------------------
% 8.65/2.06 % (4118484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118484)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118484)Termination reason: Refutation not found, incomplete strategy
% 8.65/2.06 % (4118484)Time elapsed: 0.002 s
% 8.65/2.06 % (4118484)Peak memory usage: 88 MB
% 8.65/2.06 % (4118484)Instructions burned: 2 (million)
% 8.65/2.06 % (4118485)Instruction limit reached!
% 8.65/2.06 % (4118485)------------------------------
% 8.65/2.06 % (4118485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118485)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118485)Termination reason: Instruction limit
% 8.65/2.06 % (4118485)Termination phase: Saturation
% 8.65/2.06 % (4118485)Time elapsed: 0.051 s
% 8.65/2.06 % (4118485)Peak memory usage: 90 MB
% 8.65/2.06 % (4118485)Instructions burned: 139 (million)
% 8.65/2.06 % (4118486)dis-21_1_sil=8000:lcm=predicate:random_seed=1774852096: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)
% 8.65/2.06 % (4118486)Instruction limit reached!
% 8.65/2.06 % (4118486)------------------------------
% 8.65/2.06 % (4118486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118486)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118486)Termination reason: Instruction limit
% 8.65/2.06 % (4118486)Termination phase: Saturation
% 8.65/2.06 % (4118486)Time elapsed: 0.066 s
% 8.65/2.06 % (4118486)Peak memory usage: 89 MB
% 8.65/2.06 % (4118486)Instructions burned: 130 (million)
% 8.65/2.06 % (4118493)lrs+10_1_sil=8000:sp=occurrence:random_seed=1328590415:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.65/2.06 % (4118493)Instruction limit reached!
% 8.65/2.06 % (4118493)------------------------------
% 8.65/2.06 % (4118493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118493)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118493)Termination reason: Instruction limit
% 8.65/2.06 % (4118493)Termination phase: Saturation
% 8.65/2.06 % (4118493)Time elapsed: 0.089 s
% 8.65/2.06 % (4118493)Peak memory usage: 91 MB
% 8.65/2.06 % (4118493)Instructions burned: 287 (million)
% 8.65/2.06 % (4118483)------------------------------
% 8.65/2.06 % (4118483)------------------------------
% 8.65/2.06 % (4118484)------------------------------
% 8.65/2.06 % (4118484)------------------------------
% 8.65/2.06 % (4118495)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1200527298:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.65/2.06 % (4118495)Refutation not found, incomplete strategy
% 8.65/2.06 % (4118495)------------------------------
% 8.65/2.06 % (4118495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118495)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118495)Termination reason: Refutation not found, incomplete strategy
% 8.65/2.06 % (4118495)Time elapsed: 0.002 s
% 8.65/2.06 % (4118495)Peak memory usage: 88 MB
% 8.65/2.06 % (4118495)Instructions burned: 1 (million)
% 8.65/2.06 % (4118497)lrs+1011_1_sil=32000:sp=occurrence:random_seed=981747906:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 8.65/2.06 % (4118499)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=1117525919:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.65/2.06 % (4118500)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=581932151:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.65/2.06 % (4118497)Instruction limit reached!
% 8.65/2.06 % (4118497)------------------------------
% 8.65/2.06 % (4118497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118497)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118497)Termination reason: Instruction limit
% 8.65/2.06 % (4118497)Termination phase: Saturation
% 8.65/2.06 % (4118497)Time elapsed: 0.101 s
% 8.65/2.06 % (4118497)Peak memory usage: 91 MB
% 8.65/2.06 % (4118497)Instructions burned: 326 (million)
% 8.65/2.06 % (4118495)------------------------------
% 8.65/2.06 % (4118495)------------------------------
% 8.65/2.06 % (4118504)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2469447331:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 8.65/2.06 % (4118499)Instruction limit reached!
% 8.65/2.06 % (4118499)------------------------------
% 8.65/2.06 % (4118499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118499)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118499)Termination reason: Instruction limit
% 8.65/2.06 % (4118499)Termination phase: Saturation
% 8.65/2.06 % (4118499)Time elapsed: 0.148 s
% 8.65/2.06 % (4118499)Peak memory usage: 90 MB
% 8.65/2.06 % (4118499)Instructions burned: 248 (million)
% 8.65/2.06 % (4118500)Instruction limit reached!
% 8.65/2.06 % (4118500)------------------------------
% 8.65/2.06 % (4118500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118500)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118500)Termination reason: Instruction limit
% 8.65/2.06 % (4118500)Termination phase: Saturation
% 8.65/2.06 % (4118500)Time elapsed: 0.156 s
% 8.65/2.06 % (4118500)Peak memory usage: 88 MB
% 8.65/2.06 % (4118500)Instructions burned: 299 (million)
% 8.65/2.06 % (4118505)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4238478434:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.65/2.06 % (4118505)Instruction limit reached!
% 8.65/2.06 % (4118505)------------------------------
% 8.65/2.06 % (4118505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118505)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118505)Termination reason: Instruction limit
% 8.65/2.06 % (4118505)Termination phase: Saturation
% 8.65/2.06 % (4118505)Time elapsed: 0.077 s
% 8.65/2.06 % (4118505)Peak memory usage: 89 MB
% 8.65/2.06 % (4118505)Instructions burned: 113 (million)
% 8.65/2.06 % (4118508)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=828433780:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 8.65/2.06 % (4118507)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3581635069:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 8.65/2.06 % (4118508)Refutation not found, incomplete strategy
% 8.65/2.06 % (4118508)------------------------------
% 8.65/2.06 % (4118508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118508)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118508)Termination reason: Refutation not found, incomplete strategy
% 8.65/2.06 % (4118508)Time elapsed: 0.002 s
% 8.65/2.06 % (4118508)Peak memory usage: 88 MB
% 8.65/2.06 % (4118508)Instructions burned: 1 (million)
% 8.65/2.06 % (4118480)First to succeed.
% 8.65/2.06 % (4118480)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4118475"
% 8.65/2.06 % (4118507)Instruction limit reached!
% 8.65/2.06 % (4118507)------------------------------
% 8.65/2.06 % (4118507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118507)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118507)Termination reason: Instruction limit
% 8.65/2.06 % (4118507)Termination phase: Saturation
% 8.65/2.06 % (4118507)Time elapsed: 0.064 s
% 8.65/2.06 % (4118507)Peak memory usage: 88 MB
% 8.65/2.06 % (4118507)Instructions burned: 129 (million)
% 8.65/2.06 % (4118512)lrs+10_1_sil=8000:sp=occurrence:random_seed=2486058103:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.65/2.06 % (4118504)Also succeeded, but the first one will report.
% 8.65/2.06 % (4118513)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3320828591:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.65/2.06 % (4118513)Refutation not found, incomplete strategy
% 8.65/2.06 % (4118513)------------------------------
% 8.65/2.06 % (4118513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.65/2.06 % (4118513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.65/2.06 % (4118513)CaDiCaL version: 2.1.3
% 8.65/2.06 % (4118513)Termination reason: Refutation not found, incomplete strategy
% 8.65/2.06 % (4118513)Time elapsed: 0.002 s
% 8.65/2.06 % (4118513)Peak memory usage: 89 MB
% 8.65/2.06 % (4118513)Instructions burned: 1 (million)
% 8.65/2.06 % (4118508)------------------------------
% 8.65/2.06 % (4118508)------------------------------
% 8.65/2.06 % (4118480)Refutation found. Thanks to Tanya!
% 8.65/2.06 % SZS status Theorem for theBenchmark
% 8.65/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 9.06/2.25 % (4118480)------------------------------
% 9.06/2.25 % (4118480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.06/2.25 % (4118480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.06/2.25 % (4118480)CaDiCaL version: 2.1.3
% 9.06/2.25 % (4118480)Termination reason: Refutation
% 9.06/2.25 % (4118480)Time elapsed: 0.766 s
% 9.06/2.25 % (4118480)Peak memory usage: 130 MB
% 9.06/2.25 % (4118480)Instructions burned: 1124 (million)
% 9.06/2.25 % (4118480)------------------------------
% 9.06/2.25 % (4118480)------------------------------
% 9.06/2.25 % (4118475)Success in time 1.2 s
% 9.06/2.25 % Vampire exiting
%------------------------------------------------------------------------------