%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA008+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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:55:20 AM UTC 2026
% Result : Theorem 6.66s 1.99s
% Output : Refutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 213 ( 25 unt; 13 def)
% Number of atoms : 852 ( 175 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1068 ( 429 ~; 474 |; 128 &)
% ( 17 <=>; 15 =>; 0 <=; 5 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 15 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 331 ( 0 sgn 301 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
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(f10,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) ) ) ),
file('/export/starexec/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(f18,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
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(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(f34,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f35,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(flattening,[],[f36]) ).
fof(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(f44,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
& complete ),
inference(ennf_transformation,[],[f19]) ).
fof(f45,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4)
& sequential(X2,X3) )
& complete ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X0,X1] :
( ? [X2] :
( edge(X2)
& ( head_of(X2) != X1
| tail_of(X2) != X0
| head_of(X2) != X0
| tail_of(X2) != X1 )
& ( ( X1 = head_of(X2)
& X0 = tail_of(X2) )
| ( X0 = head_of(X2)
& X1 = tail_of(X2) ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(nnf_transformation,[],[f24]) ).
fof(f47,plain,
( ! [X0,X1] :
( ? [X2] :
( edge(X2)
& ( head_of(X2) != X1
| tail_of(X2) != X0
| head_of(X2) != X0
| tail_of(X2) != X1 )
& ( ( X1 = head_of(X2)
& X0 = tail_of(X2) )
| ( X0 = head_of(X2)
& X1 = tail_of(X2) ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( ! [X0,X1] :
( ( edge(sK0(X0,X1))
& ( head_of(sK0(X0,X1)) != X1
| tail_of(sK0(X0,X1)) != X0
| head_of(sK0(X0,X1)) != X0
| tail_of(sK0(X0,X1)) != X1 )
& ( ( head_of(sK0(X0,X1)) = X1
& tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0
& tail_of(sK0(X0,X1)) = X1 ) ) )
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f47]) ).
fof(f53,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(f54,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| head_of(X0) != tail_of(X1) )
& ( ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| head_of(X0) != tail_of(X1) )
& ( ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( sequential(X3,X6)
& precedes(X6,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ( sequential(X3,sK4(X0,X3,X4))
& precedes(sK4(X0,X3,X4),X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X6,sK4(X0,X3,X4))],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2)))
& path(X0,X1,sK5(X0,X1,X2)) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f62]) ).
fof(f65,plain,
( ! [X5] : ~ triangle(sK10,sK11,X5)
& shortest_path(sK8,sK9,sK12)
& precedes(sK10,sK11,sK12)
& sequential(sK10,sK11)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12)],[f45]) ).
fof(f69,plain,
! [X0,X1] :
( tail_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f70,plain,
! [X0,X1] :
( tail_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X0,X1] :
( head_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f72,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,[],[f48]) ).
fof(f74,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| in_path(tail_of(X3),X2)
| ~ on_path(X3,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f87,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| in_path(head_of(X3),X2)
| ~ on_path(X3,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| vertex(X3)
| ~ in_path(X3,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X0,X1] :
( X0 != X1
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f95,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f96,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4,X5] :
( precedes(X3,X4,X0)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f103,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4,X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f37]) ).
fof(f111,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(f119,plain,
complete,
inference(cnf_transformation,[],[f65]) ).
fof(f120,plain,
sequential(sK10,sK11),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f65]) ).
fof(f122,plain,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f65]) ).
fof(f123,plain,
! [X5] : ~ triangle(sK10,sK11,X5),
inference(cnf_transformation,[],[f65]) ).
fof(f129,plain,
! [X1] : ~ sequential(X1,X1),
inference(equality_resolution,[],[f93]) ).
fof(f131,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X5,X4,X0)
| ~ on_path(X3,X0)
| ~ sequential(X3,X5)
| precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(forward_subsumption_resolution,[],[f97,f102]) ).
fof(f133,plain,
! [X0,X1] :
( ~ vertex(X1)
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X0
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f69,f119]) ).
fof(f134,plain,
! [X0,X1] :
( ~ vertex(X1)
| head_of(sK0(X0,X1)) = X0
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X0
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f70,f119]) ).
fof(f135,plain,
! [X0,X1] :
( ~ vertex(X1)
| tail_of(sK0(X0,X1)) = X1
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f71,f119]) ).
fof(f136,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,[],[f72,f119]) ).
fof(f138,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f74,f119]) ).
fof(f140,plain,
! [X0] :
( ~ edge(sK10)
| ~ edge(sK11)
| ~ edge(X0)
| ~ sequential(sK10,sK11)
| ~ sequential(sK11,X0)
| ~ sequential(X0,sK10) ),
inference(resolution,[],[f111,f123]) ).
fof(f141,plain,
! [X0] :
( ~ edge(sK10)
| ~ edge(X0)
| ~ sequential(sK10,sK11)
| ~ sequential(sK11,X0)
| ~ sequential(X0,sK10) ),
inference(forward_subsumption_resolution,[],[f140,f94]) ).
fof(f142,plain,
! [X0] :
( ~ edge(sK10)
| ~ sequential(sK10,sK11)
| ~ sequential(sK11,X0)
| ~ sequential(X0,sK10) ),
inference(forward_subsumption_resolution,[],[f141,f94]) ).
fof(f143,plain,
! [X0] :
( ~ sequential(sK10,sK11)
| ~ sequential(sK11,X0)
| ~ sequential(X0,sK10) ),
inference(forward_subsumption_resolution,[],[f142,f94]) ).
fof(f144,plain,
! [X0] :
( ~ sequential(sK11,X0)
| ~ sequential(X0,sK10) ),
inference(forward_subsumption_resolution,[],[f143,f120]) ).
fof(f145,plain,
edge(sK11),
inference(resolution,[],[f94,f120]) ).
fof(f146,plain,
edge(sK10),
inference(resolution,[],[f95,f120]) ).
fof(f147,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X0) != head_of(X1)
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X1,X0,X4) ),
inference(equality_resolution,[],[f110]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ precedes(X3,X3,X2) ),
inference(equality_resolution,[],[f147]) ).
fof(f149,plain,
! [X0] : ~ precedes(X0,X0,sK12),
inference(resolution,[],[f148,f122]) ).
fof(f151,plain,
path(sK8,sK9,sK12),
inference(resolution,[],[f106,f122]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ on_path(X0,sK12)
| ~ sequential(X0,sK10)
| precedes(X0,sK11,sK12)
| ~ path(X1,X2,sK12) ),
inference(resolution,[],[f131,f121]) ).
fof(f154,definition,
( spl13_1
<=> ! [X2,X1] : ~ path(X1,X2,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f155,plain,
( ! [X2,X1] : ~ path(X1,X2,sK12)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,definition,
( spl13_2
<=> ! [X0] :
( ~ on_path(X0,sK12)
| precedes(X0,sK11,sK12)
| ~ sequential(X0,sK10) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f158,plain,
( ! [X0] :
( precedes(X0,sK11,sK12)
| ~ on_path(X0,sK12)
| ~ sequential(X0,sK10) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f152,f157,f154]) ).
fof(f160,plain,
( ~ on_path(sK11,sK12)
| ~ sequential(sK11,sK10)
| ~ spl13_2 ),
inference(resolution,[],[f158,f149]) ).
fof(f167,definition,
( spl13_4
<=> sequential(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f169,plain,
( ~ sequential(sK11,sK10)
| spl13_4 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f171,definition,
( spl13_5
<=> on_path(sK11,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f172,plain,
( on_path(sK11,sK12)
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f173,plain,
( ~ on_path(sK11,sK12)
| spl13_5 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( ~ spl13_4
| ~ spl13_5
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f160,f157,f171,f167]) ).
fof(f175,plain,
( $false
| ~ spl13_1 ),
inference(resolution,[],[f155,f151]) ).
fof(f176,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f177,plain,
! [X0,X1] :
( on_path(sK11,sK12)
| ~ path(X0,X1,sK12) ),
inference(resolution,[],[f102,f121]) ).
fof(f180,plain,
( ! [X0,X1] : ~ path(X0,X1,sK12)
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f177,f173]) ).
fof(f185,plain,
( spl13_1
| spl13_5 ),
inference(avatar_split_clause,[],[f180,f171,f154]) ).
fof(f186,plain,
! [X0,X1] :
( on_path(sK10,sK12)
| ~ path(X0,X1,sK12) ),
inference(resolution,[],[f103,f121]) ).
fof(f189,definition,
( spl13_7
<=> on_path(sK10,sK12) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f191,plain,
( on_path(sK10,sK12)
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f192,plain,
( spl13_1
| spl13_7 ),
inference(avatar_split_clause,[],[f186,f189,f154]) ).
fof(f280,plain,
! [X0] :
( ~ in_path(X0,sK12)
| vertex(X0) ),
inference(resolution,[],[f91,f151]) ).
fof(f353,plain,
! [X0] :
( in_path(tail_of(X0),sK12)
| ~ on_path(X0,sK12) ),
inference(resolution,[],[f86,f151]) ).
fof(f354,plain,
! [X0] :
( ~ on_path(X0,sK12)
| vertex(tail_of(X0)) ),
inference(resolution,[],[f353,f280]) ).
fof(f358,plain,
( vertex(tail_of(sK10))
| ~ spl13_7 ),
inference(resolution,[],[f354,f191]) ).
fof(f363,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,tail_of(sK10))) = X0
| tail_of(sK10) = head_of(sK0(X0,tail_of(sK10)))
| tail_of(sK10) = X0 )
| ~ spl13_7 ),
inference(resolution,[],[f358,f136]) ).
fof(f364,plain,
( ! [X0] :
( ~ vertex(X0)
| tail_of(sK10) = tail_of(sK0(X0,tail_of(sK10)))
| tail_of(sK0(X0,tail_of(sK10))) = X0
| tail_of(sK10) = X0 )
| ~ spl13_7 ),
inference(resolution,[],[f358,f133]) ).
fof(f365,plain,
( ! [X0] :
( ~ vertex(X0)
| tail_of(sK10) = tail_of(sK0(X0,tail_of(sK10)))
| tail_of(sK10) = head_of(sK0(X0,tail_of(sK10)))
| tail_of(sK10) = X0 )
| ~ spl13_7 ),
inference(resolution,[],[f358,f135]) ).
fof(f366,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,tail_of(sK10))) = X0
| tail_of(sK0(X0,tail_of(sK10))) = X0
| tail_of(sK10) = X0 )
| ~ spl13_7 ),
inference(resolution,[],[f358,f134]) ).
fof(f1025,plain,
! [X0] :
( in_path(head_of(X0),sK12)
| ~ on_path(X0,sK12) ),
inference(resolution,[],[f87,f151]) ).
fof(f1026,plain,
! [X0] :
( ~ on_path(X0,sK12)
| vertex(head_of(X0)) ),
inference(resolution,[],[f1025,f280]) ).
fof(f1033,plain,
( vertex(head_of(sK11))
| ~ spl13_5 ),
inference(resolution,[],[f1026,f172]) ).
fof(f1042,plain,
( head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(sK10)))
| tail_of(sK10) = head_of(sK0(head_of(sK11),tail_of(sK10)))
| head_of(sK11) = tail_of(sK10)
| ~ spl13_5
| ~ spl13_7 ),
inference(resolution,[],[f1033,f363]) ).
fof(f1043,plain,
( tail_of(sK10) = tail_of(sK0(head_of(sK11),tail_of(sK10)))
| head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(sK10)))
| head_of(sK11) = tail_of(sK10)
| ~ spl13_5
| ~ spl13_7 ),
inference(resolution,[],[f1033,f364]) ).
fof(f1044,plain,
( tail_of(sK10) = tail_of(sK0(head_of(sK11),tail_of(sK10)))
| tail_of(sK10) = head_of(sK0(head_of(sK11),tail_of(sK10)))
| head_of(sK11) = tail_of(sK10)
| ~ spl13_5
| ~ spl13_7 ),
inference(resolution,[],[f1033,f365]) ).
fof(f1045,plain,
( head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(sK10)))
| head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(sK10)))
| head_of(sK11) = tail_of(sK10)
| ~ spl13_5
| ~ spl13_7 ),
inference(resolution,[],[f1033,f366]) ).
fof(f1047,definition,
( spl13_60
<=> head_of(sK11) = tail_of(sK10) ),
introduced(definition,[new_symbols(definition,[spl13_60])],[avatar_definition]) ).
fof(f1048,plain,
( head_of(sK11) != tail_of(sK10)
| spl13_60 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f1049,plain,
( head_of(sK11) = tail_of(sK10)
| ~ spl13_60 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f1051,definition,
( spl13_61
<=> head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_61])],[avatar_definition]) ).
fof(f1053,plain,
( head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_61 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f1055,definition,
( spl13_62
<=> head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_62])],[avatar_definition]) ).
fof(f1057,plain,
( head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_62 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1058,plain,
( spl13_60
| spl13_61
| spl13_62
| ~ spl13_5
| ~ spl13_7 ),
inference(avatar_split_clause,[],[f1045,f189,f171,f1055,f1051,f1047]) ).
fof(f1060,definition,
( spl13_63
<=> tail_of(sK10) = head_of(sK0(head_of(sK11),tail_of(sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_63])],[avatar_definition]) ).
fof(f1062,plain,
( tail_of(sK10) = head_of(sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_63 ),
inference(avatar_component_clause,[],[f1060]) ).
fof(f1064,definition,
( spl13_64
<=> tail_of(sK10) = tail_of(sK0(head_of(sK11),tail_of(sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_64])],[avatar_definition]) ).
fof(f1066,plain,
( tail_of(sK10) = tail_of(sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_64 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1067,plain,
( spl13_60
| spl13_63
| spl13_64
| ~ spl13_5
| ~ spl13_7 ),
inference(avatar_split_clause,[],[f1044,f189,f171,f1064,f1060,f1047]) ).
fof(f1068,plain,
( spl13_60
| spl13_61
| spl13_64
| ~ spl13_5
| ~ spl13_7 ),
inference(avatar_split_clause,[],[f1043,f189,f171,f1064,f1051,f1047]) ).
fof(f1069,plain,
( spl13_60
| spl13_63
| spl13_62
| ~ spl13_5
| ~ spl13_7 ),
inference(avatar_split_clause,[],[f1042,f189,f171,f1055,f1060,f1047]) ).
fof(f1093,plain,
( ! [X0] :
( head_of(X0) != head_of(sK11)
| ~ edge(X0)
| ~ edge(sK10)
| sK10 = X0
| sequential(X0,sK10) )
| ~ spl13_60 ),
inference(superposition,[],[f96,f1049]) ).
fof(f1107,plain,
( ! [X0] :
( head_of(X0) != head_of(sK11)
| ~ edge(X0)
| sK10 = X0
| sequential(X0,sK10) )
| ~ spl13_60 ),
inference(forward_subsumption_resolution,[],[f1093,f146]) ).
fof(f1127,plain,
( ~ edge(sK11)
| sK10 = sK11
| sequential(sK11,sK10)
| ~ spl13_60 ),
inference(equality_resolution,[],[f1107]) ).
fof(f1128,plain,
( sK10 = sK11
| sequential(sK11,sK10)
| ~ spl13_60 ),
inference(forward_subsumption_resolution,[],[f1127,f145]) ).
fof(f1129,plain,
( sK10 = sK11
| spl13_4
| ~ spl13_60 ),
inference(forward_subsumption_resolution,[],[f1128,f169]) ).
fof(f1130,plain,
( sequential(sK10,sK10)
| spl13_4
| ~ spl13_60 ),
inference(superposition,[],[f120,f1129]) ).
fof(f1165,plain,
( $false
| spl13_4
| ~ spl13_60 ),
inference(forward_subsumption_resolution,[],[f1130,f129]) ).
fof(f1166,plain,
( spl13_4
| ~ spl13_60 ),
inference(avatar_contradiction_clause,[],[f1165]) ).
fof(f1173,plain,
( ! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK10)
| head_of(X1) != head_of(sK0(head_of(sK11),tail_of(sK10)))
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4) )
| ~ spl13_64 ),
inference(superposition,[],[f110,f1066]) ).
fof(f1182,definition,
( spl13_68
<=> edge(sK0(head_of(sK11),tail_of(sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_68])],[avatar_definition]) ).
fof(f1183,plain,
( edge(sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_68 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f1184,plain,
( ~ edge(sK0(head_of(sK11),tail_of(sK10)))
| spl13_68 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f1199,plain,
( ! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK10)
| head_of(X1) != head_of(sK11)
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4) )
| ~ spl13_62
| ~ spl13_64 ),
inference(forward_demodulation,[],[f1173,f1057]) ).
fof(f1209,plain,
( ! [X2,X3,X0,X1] :
( head_of(X0) != head_of(sK11)
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,X0,X3) )
| ~ spl13_62
| ~ spl13_64 ),
inference(equality_resolution,[],[f1199]) ).
fof(f1217,plain,
( ! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ precedes(sK10,sK11,X2) )
| ~ spl13_62
| ~ spl13_64 ),
inference(equality_resolution,[],[f1209]) ).
fof(f1218,plain,
( ~ precedes(sK10,sK11,sK12)
| ~ spl13_62
| ~ spl13_64 ),
inference(resolution,[],[f1217,f122]) ).
fof(f1219,plain,
( $false
| ~ spl13_62
| ~ spl13_64 ),
inference(forward_subsumption_resolution,[],[f1218,f121]) ).
fof(f1220,plain,
( ~ spl13_62
| ~ spl13_64 ),
inference(avatar_contradiction_clause,[],[f1219]) ).
fof(f1221,plain,
( head_of(sK11) = tail_of(sK10)
| ~ spl13_62
| ~ spl13_63 ),
inference(forward_demodulation,[],[f1062,f1057]) ).
fof(f1223,plain,
( $false
| spl13_60
| ~ spl13_62
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f1221,f1048]) ).
fof(f1224,plain,
( spl13_60
| ~ spl13_62
| ~ spl13_63 ),
inference(avatar_contradiction_clause,[],[f1223]) ).
fof(f1226,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK10)
| ~ edge(sK0(head_of(sK11),tail_of(sK10)))
| ~ edge(X0)
| sK0(head_of(sK11),tail_of(sK10)) = X0
| sequential(sK0(head_of(sK11),tail_of(sK10)),X0) )
| ~ spl13_63 ),
inference(superposition,[],[f96,f1062]) ).
fof(f1241,plain,
( ! [X0] :
( head_of(X0) != head_of(sK11)
| ~ edge(X0)
| ~ edge(sK0(head_of(sK11),tail_of(sK10)))
| sK0(head_of(sK11),tail_of(sK10)) = X0
| sequential(X0,sK0(head_of(sK11),tail_of(sK10))) )
| ~ spl13_61 ),
inference(superposition,[],[f96,f1053]) ).
fof(f1254,plain,
( ~ vertex(head_of(sK11))
| ~ vertex(tail_of(sK10))
| head_of(sK11) = tail_of(sK10)
| spl13_68 ),
inference(resolution,[],[f1184,f138]) ).
fof(f1255,plain,
( ~ vertex(tail_of(sK10))
| head_of(sK11) = tail_of(sK10)
| ~ spl13_5
| spl13_68 ),
inference(forward_subsumption_resolution,[],[f1254,f1033]) ).
fof(f1256,plain,
( head_of(sK11) = tail_of(sK10)
| ~ spl13_5
| ~ spl13_7
| spl13_68 ),
inference(forward_subsumption_resolution,[],[f1255,f358]) ).
fof(f1257,plain,
( $false
| ~ spl13_5
| ~ spl13_7
| spl13_60
| spl13_68 ),
inference(forward_subsumption_resolution,[],[f1256,f1048]) ).
fof(f1258,plain,
( ~ spl13_5
| ~ spl13_7
| spl13_60
| spl13_68 ),
inference(avatar_contradiction_clause,[],[f1257]) ).
fof(f1260,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK10)
| ~ edge(X0)
| sK0(head_of(sK11),tail_of(sK10)) = X0
| sequential(sK0(head_of(sK11),tail_of(sK10)),X0) )
| ~ spl13_63
| ~ spl13_68 ),
inference(forward_subsumption_resolution,[],[f1226,f1183]) ).
fof(f1261,plain,
( ! [X0] :
( head_of(X0) != head_of(sK11)
| ~ edge(X0)
| sK0(head_of(sK11),tail_of(sK10)) = X0
| sequential(X0,sK0(head_of(sK11),tail_of(sK10))) )
| ~ spl13_61
| ~ spl13_68 ),
inference(forward_subsumption_resolution,[],[f1241,f1183]) ).
fof(f1276,plain,
( ~ edge(sK11)
| sK11 = sK0(head_of(sK11),tail_of(sK10))
| sequential(sK11,sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_61
| ~ spl13_68 ),
inference(equality_resolution,[],[f1261]) ).
fof(f1277,plain,
( sK11 = sK0(head_of(sK11),tail_of(sK10))
| sequential(sK11,sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_61
| ~ spl13_68 ),
inference(forward_subsumption_resolution,[],[f1276,f145]) ).
fof(f1279,definition,
( spl13_75
<=> sequential(sK11,sK0(head_of(sK11),tail_of(sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_75])],[avatar_definition]) ).
fof(f1281,plain,
( sequential(sK11,sK0(head_of(sK11),tail_of(sK10)))
| ~ spl13_75 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f1283,definition,
( spl13_76
<=> sK11 = sK0(head_of(sK11),tail_of(sK10)) ),
introduced(definition,[new_symbols(definition,[spl13_76])],[avatar_definition]) ).
fof(f1285,plain,
( sK11 = sK0(head_of(sK11),tail_of(sK10))
| ~ spl13_76 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f1286,plain,
( spl13_75
| spl13_76
| ~ spl13_61
| ~ spl13_68 ),
inference(avatar_split_clause,[],[f1277,f1182,f1051,f1283,f1279]) ).
fof(f1287,plain,
( ~ sequential(sK0(head_of(sK11),tail_of(sK10)),sK10)
| ~ spl13_75 ),
inference(resolution,[],[f1281,f144]) ).
fof(f1296,plain,
( ~ edge(sK10)
| sK10 = sK0(head_of(sK11),tail_of(sK10))
| sequential(sK0(head_of(sK11),tail_of(sK10)),sK10)
| ~ spl13_63
| ~ spl13_68 ),
inference(equality_resolution,[],[f1260]) ).
fof(f1298,plain,
( sK10 = sK0(head_of(sK11),tail_of(sK10))
| sequential(sK0(head_of(sK11),tail_of(sK10)),sK10)
| ~ spl13_63
| ~ spl13_68 ),
inference(forward_subsumption_resolution,[],[f1296,f146]) ).
fof(f1299,plain,
( sK10 = sK0(head_of(sK11),tail_of(sK10))
| ~ spl13_63
| ~ spl13_68
| ~ spl13_75 ),
inference(forward_subsumption_resolution,[],[f1298,f1287]) ).
fof(f1301,plain,
( sequential(sK11,sK10)
| ~ spl13_63
| ~ spl13_68
| ~ spl13_75 ),
inference(superposition,[],[f1281,f1299]) ).
fof(f1309,plain,
( $false
| spl13_4
| ~ spl13_63
| ~ spl13_68
| ~ spl13_75 ),
inference(forward_subsumption_resolution,[],[f1301,f169]) ).
fof(f1310,plain,
( spl13_4
| ~ spl13_63
| ~ spl13_68
| ~ spl13_75 ),
inference(avatar_contradiction_clause,[],[f1309]) ).
fof(f1315,plain,
( head_of(sK11) = tail_of(sK10)
| ~ spl13_63
| ~ spl13_76 ),
inference(superposition,[],[f1062,f1285]) ).
fof(f1317,plain,
( $false
| spl13_60
| ~ spl13_63
| ~ spl13_76 ),
inference(forward_subsumption_resolution,[],[f1315,f1048]) ).
fof(f1318,plain,
( spl13_60
| ~ spl13_63
| ~ spl13_76 ),
inference(avatar_contradiction_clause,[],[f1317]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f159]) ).
cnf(s3,plain,
( ~ spl13_2
| ~ spl13_4
| ~ spl13_5 ),
inference(sat_conversion,[],[f174]) ).
cnf(s4,plain,
~ spl13_1,
inference(sat_conversion,[],[f176]) ).
cnf(s6,plain,
( spl13_1
| spl13_5 ),
inference(sat_conversion,[],[f185]) ).
cnf(s7,plain,
( spl13_1
| spl13_7 ),
inference(sat_conversion,[],[f192]) ).
cnf(s61,plain,
( ~ spl13_5
| ~ spl13_7
| spl13_60
| spl13_61
| spl13_62 ),
inference(sat_conversion,[],[f1058]) ).
cnf(s62,plain,
( ~ spl13_5
| ~ spl13_7
| spl13_60
| spl13_63
| spl13_64 ),
inference(sat_conversion,[],[f1067]) ).
cnf(s63,plain,
( ~ spl13_5
| ~ spl13_7
| spl13_60
| spl13_61
| spl13_64 ),
inference(sat_conversion,[],[f1068]) ).
cnf(s64,plain,
( ~ spl13_5
| ~ spl13_7
| spl13_60
| spl13_62
| spl13_63 ),
inference(sat_conversion,[],[f1069]) ).
cnf(s70,plain,
( spl13_4
| ~ spl13_60 ),
inference(sat_conversion,[],[f1166]) ).
cnf(s75,plain,
( ~ spl13_62
| ~ spl13_64 ),
inference(sat_conversion,[],[f1220]) ).
cnf(s76,plain,
( spl13_60
| ~ spl13_62
| ~ spl13_63 ),
inference(sat_conversion,[],[f1224]) ).
cnf(s77,plain,
( ~ spl13_5
| ~ spl13_7
| spl13_60
| spl13_68 ),
inference(sat_conversion,[],[f1258]) ).
cnf(s79,plain,
( ~ spl13_61
| ~ spl13_68
| spl13_75
| spl13_76 ),
inference(sat_conversion,[],[f1286]) ).
cnf(s82,plain,
( spl13_4
| ~ spl13_63
| ~ spl13_68
| ~ spl13_75 ),
inference(sat_conversion,[],[f1310]) ).
cnf(s83,plain,
( spl13_60
| ~ spl13_63
| ~ spl13_76 ),
inference(sat_conversion,[],[f1318]) ).
cnf(s93,plain,
spl13_7,
inference(rat,[],[s7,s4]) ).
cnf(s94,plain,
spl13_5,
inference(rat,[],[s6,s4]) ).
cnf(s96,plain,
( ~ spl13_2
| ~ spl13_4 ),
inference(rat,[],[s3,s94]) ).
cnf(s98,plain,
spl13_2,
inference(rat,[],[s1,s4]) ).
cnf(s102,plain,
~ spl13_4,
inference(rat,[],[s96,s98]) ).
cnf(s109,plain,
~ spl13_60,
inference(rat,[],[s70,s102]) ).
cnf(s110,plain,
spl13_68,
inference(rat,[],[s77,s94,s93,s109]) ).
cnf(s111,plain,
spl13_61,
inference(rat,[],[s75,s61,s63,s93,s94,s109]) ).
cnf(s112,plain,
~ spl13_62,
inference(rat,[],[s62,s75,s76,s93,s94,s109]) ).
cnf(s113,plain,
spl13_63,
inference(rat,[],[s64,s109,s94,s93,s112]) ).
cnf(s114,plain,
~ spl13_76,
inference(rat,[],[s83,s109,s113]) ).
cnf(s115,plain,
~ spl13_75,
inference(rat,[],[s82,s110,s102,s113]) ).
cnf(s116,plain,
$false,
inference(rat,[],[s79,s111,s110,s114,s115]) ).
fof(f1322,plain,
$false,
inference(avatar_sat_refutation,[],[s116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA008+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n015.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 08:50:30 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 6.66/1.99 % (1355331)Detected formulas, will run a generic FOF schedule.
% 6.66/1.99 % (1355340)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=907099075:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.66/1.99 % (1355336)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=1571982405:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.66/1.99 % (1355337)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=2909022225:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.66/1.99 % (1355341)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2212759403:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.66/1.99 % (1355338)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=1313081061:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.66/1.99 % (1355339)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1382010879:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.66/1.99 % (1355342)dis-21_1_sil=8000:lcm=predicate:random_seed=1880628319:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.66/1.99 % (1355340)Instruction limit reached!
% 6.66/1.99 % (1355340)------------------------------
% 6.66/1.99 % (1355340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355340)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355340)Termination reason: Instruction limit
% 6.66/1.99 % (1355340)Termination phase: Saturation
% 6.66/1.99 % (1355340)Time elapsed: 0.036 s
% 6.66/1.99 % (1355340)Peak memory usage: 88 MB
% 6.66/1.99 % (1355340)Instructions burned: 122 (million)
% 6.66/1.99 % (1355339)Refutation not found, incomplete strategy
% 6.66/1.99 % (1355339)------------------------------
% 6.66/1.99 % (1355339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355339)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355339)Termination reason: Refutation not found, incomplete strategy
% 6.66/1.99 % (1355339)Time elapsed: 0.002 s
% 6.66/1.99 % (1355339)Peak memory usage: 88 MB
% 6.66/1.99 % (1355339)Instructions burned: 1 (million)
% 6.66/1.99 % (1355342)Instruction limit reached!
% 6.66/1.99 % (1355342)------------------------------
% 6.66/1.99 % (1355342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355342)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355342)Termination reason: Instruction limit
% 6.66/1.99 % (1355342)Termination phase: Saturation
% 6.66/1.99 % (1355342)Time elapsed: 0.066 s
% 6.66/1.99 % (1355342)Peak memory usage: 89 MB
% 6.66/1.99 % (1355342)Instructions burned: 131 (million)
% 6.66/1.99 % (1355341)Instruction limit reached!
% 6.66/1.99 % (1355341)------------------------------
% 6.66/1.99 % (1355341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355341)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355341)Termination reason: Instruction limit
% 6.66/1.99 % (1355341)Termination phase: Saturation
% 6.66/1.99 % (1355341)Time elapsed: 0.097 s
% 6.66/1.99 % (1355341)Peak memory usage: 90 MB
% 6.66/1.99 % (1355341)Instructions burned: 140 (million)
% 6.66/1.99 % (1355350)lrs+10_1_sil=8000:sp=occurrence:random_seed=418396453:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.66/1.99 % (1355350)Instruction limit reached!
% 6.66/1.99 % (1355350)------------------------------
% 6.66/1.99 % (1355350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355350)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355350)Termination reason: Instruction limit
% 6.66/1.99 % (1355350)Termination phase: Saturation
% 6.66/1.99 % (1355350)Time elapsed: 0.092 s
% 6.66/1.99 % (1355350)Peak memory usage: 91 MB
% 6.66/1.99 % (1355350)Instructions burned: 286 (million)
% 6.66/1.99 % (1355351)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1420835337:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.66/1.99 % (1355351)Refutation not found, incomplete strategy
% 6.66/1.99 % (1355351)------------------------------
% 6.66/1.99 % (1355351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355351)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355351)Termination reason: Refutation not found, incomplete strategy
% 6.66/1.99 % (1355351)Time elapsed: 0.004 s
% 6.66/1.99 % (1355351)Peak memory usage: 88 MB
% 6.66/1.99 % (1355351)Instructions burned: 4 (million)
% 6.66/1.99 % (1355353)lrs+1011_1_sil=32000:sp=occurrence:random_seed=703713324:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.66/1.99 % (1355353)Refutation not found, incomplete strategy
% 6.66/1.99 % (1355353)------------------------------
% 6.66/1.99 % (1355353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355353)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355353)Termination reason: Refutation not found, incomplete strategy
% 6.66/1.99 % (1355353)Time elapsed: 0.005 s
% 6.66/1.99 % (1355353)Peak memory usage: 88 MB
% 6.66/1.99 % (1355353)Instructions burned: 5 (million)
% 6.66/1.99 % (1355339)------------------------------
% 6.66/1.99 % (1355339)------------------------------
% 6.66/1.99 % (1355354)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=4288493705:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.66/1.99 % (1355354)Instruction limit reached!
% 6.66/1.99 % (1355354)------------------------------
% 6.66/1.99 % (1355354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355354)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355354)Termination reason: Instruction limit
% 6.66/1.99 % (1355354)Termination phase: Saturation
% 6.66/1.99 % (1355354)Time elapsed: 0.077 s
% 6.66/1.99 % (1355354)Peak memory usage: 90 MB
% 6.66/1.99 % (1355354)Instructions burned: 248 (million)
% 6.66/1.99 % (1355357)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=639783033:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.66/1.99 % (1355351)------------------------------
% 6.66/1.99 % (1355351)------------------------------
% 6.66/1.99 % (1355359)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3986864550:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.66/1.99 % (1355353)------------------------------
% 6.66/1.99 % (1355353)------------------------------
% 6.66/1.99 % (1355357)Instruction limit reached!
% 6.66/1.99 % (1355357)------------------------------
% 6.66/1.99 % (1355357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355357)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355357)Termination reason: Instruction limit
% 6.66/1.99 % (1355357)Termination phase: Saturation
% 6.66/1.99 % (1355357)Time elapsed: 0.158 s
% 6.66/1.99 % (1355357)Peak memory usage: 89 MB
% 6.66/1.99 % (1355357)Instructions burned: 295 (million)
% 6.66/1.99 % (1355362)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3350170258:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.66/1.99 % (1355363)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2472555919:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.66/1.99 % (1355362)Instruction limit reached!
% 6.66/1.99 % (1355362)------------------------------
% 6.66/1.99 % (1355362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355362)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355362)Termination reason: Instruction limit
% 6.66/1.99 % (1355362)Termination phase: Saturation
% 6.66/1.99 % (1355362)Time elapsed: 0.079 s
% 6.66/1.99 % (1355362)Peak memory usage: 90 MB
% 6.66/1.99 % (1355362)Instructions burned: 114 (million)
% 6.66/1.99 % (1355363)Instruction limit reached!
% 6.66/1.99 % (1355363)------------------------------
% 6.66/1.99 % (1355363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355363)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355363)Termination reason: Instruction limit
% 6.66/1.99 % (1355363)Termination phase: Saturation
% 6.66/1.99 % (1355363)Time elapsed: 0.066 s
% 6.66/1.99 % (1355363)Peak memory usage: 88 MB
% 6.66/1.99 % (1355363)Instructions burned: 129 (million)
% 6.66/1.99 % (1355364)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2787017130:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.66/1.99 % (1355336)First to succeed.
% 6.66/1.99 % (1355336)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1355331"
% 6.66/1.99 % (1355364)Instruction limit reached!
% 6.66/1.99 % (1355364)------------------------------
% 6.66/1.99 % (1355364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.66/1.99 % (1355364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.66/1.99 % (1355364)CaDiCaL version: 2.1.3
% 6.66/1.99 % (1355364)Termination reason: Instruction limit
% 6.66/1.99 % (1355364)Termination phase: Saturation
% 6.66/1.99 % (1355364)Time elapsed: 0.072 s
% 6.66/1.99 % (1355364)Peak memory usage: 89 MB
% 6.66/1.99 % (1355364)Instructions burned: 115 (million)
% 6.66/1.99 % (1355367)lrs+10_1_sil=8000:sp=occurrence:random_seed=3607186170:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.66/1.99 % (1355368)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4086485123:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.66/1.99 % (1355370)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1069182868:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.66/1.99 % (1355336)Refutation found. Thanks to Tanya!
% 6.66/1.99 % SZS status Theorem for theBenchmark
% 6.66/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 8.61/2.18 % (1355336)------------------------------
% 8.61/2.18 % (1355336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/2.18 % (1355336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/2.18 % (1355336)CaDiCaL version: 2.1.3
% 8.61/2.18 % (1355336)Termination reason: Refutation
% 8.61/2.18 % (1355336)Time elapsed: 0.743 s
% 8.61/2.18 % (1355336)Peak memory usage: 131 MB
% 8.61/2.18 % (1355336)Instructions burned: 1094 (million)
% 8.61/2.18 % (1355336)------------------------------
% 8.61/2.18 % (1355336)------------------------------
% 8.61/2.18 % (1355331)Success in time 1.136 s
% 8.61/2.18 % Vampire exiting
%------------------------------------------------------------------------------