%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA006+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 : n012.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 4.45s 1.28s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 39
% Syntax : Number of formulae : 283 ( 37 unt; 29 def)
% Number of atoms : 1054 ( 279 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1303 ( 532 ~; 562 |; 156 &)
% ( 28 <=>; 17 =>; 0 <=; 8 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 25 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-3 aty)
% Number of variables : 341 ( 0 sgn 285 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(head_of(X0))
& vertex(tail_of(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
fof(f3,axiom,
( complete
=> ! [X0,X1] :
( ( vertex(X0)
& vertex(X1)
& X0 != X1 )
=> ? [X2] :
( edge(X2)
& ( ( X0 = head_of(X2)
& X1 = tail_of(X2) )
<~> ( X1 = head_of(X2)
& X0 = tail_of(X2) ) ) ) ) ),
file('/export/starexec/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(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(f18,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
<~> ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_some_way) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
<~> ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
<~> ? [X6] :
( edge(X6)
& head_of(X3) = tail_of(X6)
& tail_of(X2) = head_of(X6) ) ) ) ),
inference(rectify,[],[f19]) ).
fof(f22,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0] :
( ( vertex(head_of(X0))
& vertex(tail_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
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(ennf_transformation,[],[f3]) ).
fof(f25,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,[],[f24]) ).
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(ennf_transformation,[],[f6]) ).
fof(f30,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,[],[f29]) ).
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(ennf_transformation,[],[f9]) ).
fof(f34,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,[],[f33]) ).
fof(f35,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(f36,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(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(ennf_transformation,[],[f12]) ).
fof(f38,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,[],[f37]) ).
fof(f45,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
<=> ? [X6] :
( edge(X6)
& head_of(X3) = tail_of(X6)
& tail_of(X2) = head_of(X6) ) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f46,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
<=> ? [X6] :
( edge(X6)
& head_of(X3) = tail_of(X6)
& tail_of(X2) = head_of(X6) ) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
& complete ),
inference(flattening,[],[f45]) ).
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(nnf_transformation,[],[f25]) ).
fof(f48,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,[],[f47]) ).
fof(f49,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))],[f48]) ).
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(nnf_transformation,[],[f8]) ).
fof(f56,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,[],[f55]) ).
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(nnf_transformation,[],[f35]) ).
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) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[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) )
& ( ? [X6] :
( sequential(X3,X6)
& precedes(X6,X4,X0) )
| sequential(X3,X4) ) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f58]) ).
fof(f60,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))],[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
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f36]) ).
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
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f61]) ).
fof(f63,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,[],[f62]) ).
fof(f64,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))],[f63]) ).
fof(f66,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
| ! [X6] :
( ~ edge(X6)
| head_of(X3) != tail_of(X6)
| tail_of(X2) != head_of(X6) ) )
& ( ? [X6] :
( edge(X6)
& head_of(X3) = tail_of(X6)
& tail_of(X2) = head_of(X6) )
| ! [X5] :
( ~ edge(X5)
| tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) ) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
& complete ),
inference(nnf_transformation,[],[f46]) ).
fof(f67,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
| ! [X6] :
( ~ edge(X6)
| head_of(X3) != tail_of(X6)
| tail_of(X2) != head_of(X6) ) )
& ( ? [X6] :
( edge(X6)
& head_of(X3) = tail_of(X6)
& tail_of(X2) = head_of(X6) )
| ! [X5] :
( ~ edge(X5)
| tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) ) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
& complete ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
| ! [X6] :
( ~ edge(X6)
| head_of(X3) != tail_of(X6)
| tail_of(X2) != head_of(X6) ) )
& ( ? [X7] :
( edge(X7)
& head_of(X3) = tail_of(X7)
& tail_of(X2) = head_of(X7) )
| ! [X8] :
( ~ edge(X8)
| tail_of(X2) != tail_of(X8)
| head_of(X3) != head_of(X8) ) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
& complete ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
( ( ( edge(sK13)
& tail_of(sK10) = tail_of(sK13)
& head_of(sK11) = head_of(sK13) )
| ! [X6] :
( ~ edge(X6)
| tail_of(X6) != head_of(sK11)
| head_of(X6) != tail_of(sK10) ) )
& ( ( edge(sK14)
& head_of(sK11) = tail_of(sK14)
& tail_of(sK10) = head_of(sK14) )
| ! [X8] :
( ~ edge(X8)
| tail_of(X8) != tail_of(sK10)
| head_of(X8) != head_of(sK11) ) )
& shortest_path(sK8,sK9,sK12)
& precedes(sK10,sK11,sK12)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12),skolemize(X5,sK13),skolemize(X7,sK14)],[f68]) ).
fof(f70,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f71,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f72,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f73,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,[],[f49]) ).
fof(f74,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,[],[f49]) ).
fof(f76,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,[],[f49]) ).
fof(f78,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f49]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| edge(X3)
| ~ on_path(X3,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f99,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f100,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f102,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,[],[f34]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| sequential(X3,X4)
| sequential(X3,sK4(X0,X3,X4))
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f38]) ).
fof(f114,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,[],[f38]) ).
fof(f123,plain,
complete,
inference(cnf_transformation,[],[f69]) ).
fof(f124,plain,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f69]) ).
fof(f125,plain,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f69]) ).
fof(f126,plain,
! [X8] :
( tail_of(sK10) = head_of(sK14)
| ~ edge(X8)
| tail_of(X8) != tail_of(sK10)
| head_of(X8) != head_of(sK11) ),
inference(cnf_transformation,[],[f69]) ).
fof(f127,plain,
! [X8] :
( head_of(sK11) = tail_of(sK14)
| ~ edge(X8)
| tail_of(X8) != tail_of(sK10)
| head_of(X8) != head_of(sK11) ),
inference(cnf_transformation,[],[f69]) ).
fof(f128,plain,
! [X8] :
( edge(sK14)
| ~ edge(X8)
| tail_of(X8) != tail_of(sK10)
| head_of(X8) != head_of(sK11) ),
inference(cnf_transformation,[],[f69]) ).
fof(f129,plain,
! [X6] :
( head_of(sK11) = head_of(sK13)
| ~ edge(X6)
| tail_of(X6) != head_of(sK11)
| head_of(X6) != tail_of(sK10) ),
inference(cnf_transformation,[],[f69]) ).
fof(f130,plain,
! [X6] :
( tail_of(sK10) = tail_of(sK13)
| ~ edge(X6)
| tail_of(X6) != head_of(sK11)
| head_of(X6) != tail_of(sK10) ),
inference(cnf_transformation,[],[f69]) ).
fof(f139,definition,
sF15 = head_of(sK11),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f140,plain,
head_of(sK11) = sF15,
inference(reorient_equations,[],[f139]) ).
fof(f141,definition,
sF16 = tail_of(sK10),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f142,plain,
tail_of(sK10) = sF16,
inference(reorient_equations,[],[f141]) ).
fof(f144,definition,
sF17 = tail_of(sK13),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f145,plain,
tail_of(sK13) = sF17,
inference(reorient_equations,[],[f144]) ).
fof(f146,plain,
! [X6] :
( sF16 = sF17
| ~ edge(X6)
| tail_of(X6) != sF15
| head_of(X6) != sF16 ),
inference(definition_folding,[],[f130,f142,f140,f145,f142]) ).
fof(f147,definition,
sF18 = head_of(sK13),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f148,plain,
head_of(sK13) = sF18,
inference(reorient_equations,[],[f147]) ).
fof(f149,plain,
! [X6] :
( sF15 = sF18
| ~ edge(X6)
| tail_of(X6) != sF15
| head_of(X6) != sF16 ),
inference(definition_folding,[],[f129,f142,f140,f148,f140]) ).
fof(f150,plain,
! [X8] :
( edge(sK14)
| ~ edge(X8)
| tail_of(X8) != sF16
| head_of(X8) != sF15 ),
inference(definition_folding,[],[f128,f140,f142]) ).
fof(f151,definition,
sF19 = tail_of(sK14),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f152,plain,
tail_of(sK14) = sF19,
inference(reorient_equations,[],[f151]) ).
fof(f153,plain,
! [X8] :
( sF15 = sF19
| ~ edge(X8)
| tail_of(X8) != sF16
| head_of(X8) != sF15 ),
inference(definition_folding,[],[f127,f140,f142,f152,f140]) ).
fof(f154,definition,
sF20 = head_of(sK14),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f155,plain,
head_of(sK14) = sF20,
inference(reorient_equations,[],[f154]) ).
fof(f156,plain,
! [X8] :
( sF16 = sF20
| ~ edge(X8)
| tail_of(X8) != sF16
| head_of(X8) != sF15 ),
inference(definition_folding,[],[f126,f140,f142,f155,f142]) ).
fof(f158,definition,
( spl21_1
<=> ! [X8] :
( ~ edge(X8)
| head_of(X8) != sF15
| tail_of(X8) != sF16 ) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f159,plain,
( ! [X8] :
( tail_of(X8) != sF16
| head_of(X8) != sF15
| ~ edge(X8) )
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,definition,
( spl21_2
<=> sF16 = sF20 ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f163,plain,
( sF16 = sF20
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f156,f161,f158]) ).
fof(f166,definition,
( spl21_3
<=> sF15 = sF19 ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f168,plain,
( sF15 = sF19
| ~ spl21_3 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f169,plain,
( spl21_1
| spl21_3 ),
inference(avatar_split_clause,[],[f153,f166,f158]) ).
fof(f171,definition,
( spl21_4
<=> edge(sK14) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f173,plain,
( edge(sK14)
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( spl21_1
| spl21_4 ),
inference(avatar_split_clause,[],[f150,f171,f158]) ).
fof(f176,definition,
( spl21_5
<=> ! [X6] :
( ~ edge(X6)
| head_of(X6) != sF16
| tail_of(X6) != sF15 ) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f177,plain,
( ! [X6] :
( tail_of(X6) != sF15
| head_of(X6) != sF16
| ~ edge(X6) )
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f179,definition,
( spl21_6
<=> sF15 = sF18 ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
fof(f181,plain,
( sF15 = sF18
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl21_5
| spl21_6 ),
inference(avatar_split_clause,[],[f149,f179,f176]) ).
fof(f184,definition,
( spl21_7
<=> sF16 = sF17 ),
introduced(definition,[new_symbols(definition,[spl21_7])],[avatar_definition]) ).
fof(f186,plain,
( sF16 = sF17
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,plain,
( spl21_5
| spl21_7 ),
inference(avatar_split_clause,[],[f146,f184,f176]) ).
fof(f195,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,[],[f73,f123]) ).
fof(f196,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,[],[f74,f123]) ).
fof(f198,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,[],[f76,f123]) ).
fof(f200,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f78,f123]) ).
fof(f204,plain,
( sF15 != sF19
| head_of(sK14) != sF16
| ~ edge(sK14)
| ~ spl21_5 ),
inference(superposition,[],[f177,f152]) ).
fof(f205,plain,
( head_of(sK14) != sF16
| ~ edge(sK14)
| ~ spl21_3
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f204,f168]) ).
fof(f207,definition,
( spl21_9
<=> edge(sK10) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
fof(f208,plain,
( edge(sK10)
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( ~ edge(sK10)
| spl21_9 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f215,definition,
( spl21_11
<=> sF15 = sF16 ),
introduced(definition,[new_symbols(definition,[spl21_11])],[avatar_definition]) ).
fof(f216,plain,
( sF15 = sF16
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f217,plain,
( sF15 != sF16
| spl21_11 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f220,plain,
( head_of(sK14) != sF16
| ~ spl21_3
| ~ spl21_4
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f205,f173]) ).
fof(f230,plain,
( sF16 != sF20
| ~ spl21_3
| ~ spl21_4
| ~ spl21_5 ),
inference(forward_demodulation,[],[f220,f155]) ).
fof(f231,plain,
( $false
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f230,f163]) ).
fof(f232,plain,
( ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_5 ),
inference(avatar_contradiction_clause,[],[f231]) ).
fof(f248,plain,
! [X0] :
( head_of(X0) != sF16
| ~ edge(X0)
| ~ edge(sK10)
| sK10 = X0
| sequential(X0,sK10) ),
inference(superposition,[],[f100,f142]) ).
fof(f263,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X0) != head_of(X1)
| tail_of(X0) != sF16
| ~ shortest_path(X2,X3,X4)
| ~ precedes(sK10,X1,X4) ),
inference(superposition,[],[f114,f142]) ).
fof(f268,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X0) != head_of(X1)
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X1,X0,X4) ),
inference(equality_resolution,[],[f114]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ precedes(X3,X3,X2) ),
inference(equality_resolution,[],[f268]) ).
fof(f306,plain,
! [X0] : ~ precedes(X0,X0,sK12),
inference(resolution,[],[f305,f125]) ).
fof(f307,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK12)
| ~ precedes(X0,X1,sK12) ),
inference(resolution,[],[f113,f125]) ).
fof(f308,plain,
path(sK8,sK9,sK12),
inference(resolution,[],[f110,f125]) ).
fof(f309,plain,
! [X0,X1] :
( on_path(sK11,sK12)
| ~ path(X0,X1,sK12) ),
inference(resolution,[],[f106,f124]) ).
fof(f311,definition,
( spl21_20
<=> ! [X0,X1] : ~ path(X0,X1,sK12) ),
introduced(definition,[new_symbols(definition,[spl21_20])],[avatar_definition]) ).
fof(f312,plain,
( ! [X0,X1] : ~ path(X0,X1,sK12)
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f314,definition,
( spl21_21
<=> on_path(sK11,sK12) ),
introduced(definition,[new_symbols(definition,[spl21_21])],[avatar_definition]) ).
fof(f316,plain,
( on_path(sK11,sK12)
| ~ spl21_21 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f317,plain,
( spl21_20
| spl21_21 ),
inference(avatar_split_clause,[],[f309,f314,f311]) ).
fof(f318,plain,
! [X0,X1] :
( on_path(sK10,sK12)
| ~ path(X0,X1,sK12) ),
inference(resolution,[],[f107,f124]) ).
fof(f320,definition,
( spl21_22
<=> on_path(sK10,sK12) ),
introduced(definition,[new_symbols(definition,[spl21_22])],[avatar_definition]) ).
fof(f322,plain,
( on_path(sK10,sK12)
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f323,plain,
( spl21_20
| spl21_22 ),
inference(avatar_split_clause,[],[f318,f320,f311]) ).
fof(f382,definition,
( spl21_32
<=> edge(sK11) ),
introduced(definition,[new_symbols(definition,[spl21_32])],[avatar_definition]) ).
fof(f383,plain,
( edge(sK11)
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f384,plain,
( ~ edge(sK11)
| spl21_32 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f390,plain,
( vertex(sF15)
| ~ edge(sK11) ),
inference(superposition,[],[f72,f140]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( head_of(X0) != sF18
| tail_of(sK13) != sF16
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,X0,X3) ),
inference(superposition,[],[f263,f148]) ).
fof(f414,definition,
( spl21_35
<=> ! [X2,X1,X3] :
( ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,sK11,X3) ) ),
introduced(definition,[new_symbols(definition,[spl21_35])],[avatar_definition]) ).
fof(f415,plain,
( ! [X2,X3,X1] :
( ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,sK11,X3) )
| ~ spl21_35 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f420,plain,
! [X2,X3,X0,X1] :
( sF16 != sF17
| head_of(X0) != sF18
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,X0,X3) ),
inference(forward_demodulation,[],[f400,f145]) ).
fof(f435,plain,
( ~ precedes(sK10,sK11,sK12)
| ~ spl21_35 ),
inference(resolution,[],[f415,f125]) ).
fof(f436,plain,
( $false
| ~ spl21_35 ),
inference(forward_subsumption_resolution,[],[f435,f124]) ).
fof(f437,plain,
~ spl21_35,
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f446,plain,
! [X0,X1] :
( sequential(sK10,sK11)
| sequential(sK10,sK4(sK12,sK10,sK11))
| ~ path(X0,X1,sK12) ),
inference(resolution,[],[f104,f124]) ).
fof(f448,definition,
( spl21_40
<=> sequential(sK10,sK4(sK12,sK10,sK11)) ),
introduced(definition,[new_symbols(definition,[spl21_40])],[avatar_definition]) ).
fof(f450,plain,
( sequential(sK10,sK4(sK12,sK10,sK11))
| ~ spl21_40 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f452,definition,
( spl21_41
<=> sequential(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl21_41])],[avatar_definition]) ).
fof(f454,plain,
( sequential(sK10,sK11)
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f455,plain,
( spl21_20
| spl21_40
| spl21_41 ),
inference(avatar_split_clause,[],[f446,f452,f448,f311]) ).
fof(f456,plain,
( $false
| ~ spl21_20 ),
inference(resolution,[],[f312,f308]) ).
fof(f457,plain,
~ spl21_20,
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f462,plain,
( edge(sK10)
| ~ spl21_40 ),
inference(resolution,[],[f99,f450]) ).
fof(f463,plain,
( $false
| spl21_9
| ~ spl21_40 ),
inference(forward_subsumption_resolution,[],[f462,f209]) ).
fof(f464,plain,
( spl21_9
| ~ spl21_40 ),
inference(avatar_contradiction_clause,[],[f463]) ).
fof(f477,plain,
( vertex(sF16)
| ~ edge(sK10) ),
inference(superposition,[],[f71,f142]) ).
fof(f480,plain,
( vertex(sF16)
| ~ spl21_9 ),
inference(forward_subsumption_resolution,[],[f477,f208]) ).
fof(f625,definition,
( spl21_51
<=> sF16 = tail_of(sK0(sF16,sF15)) ),
introduced(definition,[new_symbols(definition,[spl21_51])],[avatar_definition]) ).
fof(f626,plain,
( sF16 != tail_of(sK0(sF16,sF15))
| spl21_51 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f627,plain,
( sF16 = tail_of(sK0(sF16,sF15))
| ~ spl21_51 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f629,definition,
( spl21_52
<=> sF16 = head_of(sK0(sF16,sF15)) ),
introduced(definition,[new_symbols(definition,[spl21_52])],[avatar_definition]) ).
fof(f630,plain,
( sF16 != head_of(sK0(sF16,sF15))
| spl21_52 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f631,plain,
( sF16 = head_of(sK0(sF16,sF15))
| ~ spl21_52 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f634,definition,
( spl21_53
<=> sF15 = head_of(sK0(sF16,sF15)) ),
introduced(definition,[new_symbols(definition,[spl21_53])],[avatar_definition]) ).
fof(f635,plain,
( sF15 != head_of(sK0(sF16,sF15))
| spl21_53 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f639,definition,
( spl21_54
<=> sF15 = tail_of(sK0(sF16,sF15)) ),
introduced(definition,[new_symbols(definition,[spl21_54])],[avatar_definition]) ).
fof(f640,plain,
( sF15 != tail_of(sK0(sF16,sF15))
| spl21_54 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f641,plain,
( sF15 = tail_of(sK0(sF16,sF15))
| ~ spl21_54 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f665,definition,
( spl21_57
<=> edge(sK0(sF16,sF15)) ),
introduced(definition,[new_symbols(definition,[spl21_57])],[avatar_definition]) ).
fof(f666,plain,
( edge(sK0(sF16,sF15))
| ~ spl21_57 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f667,plain,
( ~ edge(sK0(sF16,sF15))
| spl21_57 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f689,plain,
( sF16 != head_of(sK0(sF16,sF15))
| ~ edge(sK0(sF16,sF15))
| ~ spl21_51 ),
inference(superposition,[],[f70,f627]) ).
fof(f694,plain,
( sF16 != sF16
| sF15 != head_of(sK0(sF16,sF15))
| ~ edge(sK0(sF16,sF15))
| ~ spl21_1
| ~ spl21_51 ),
inference(superposition,[],[f159,f627]) ).
fof(f701,plain,
( sF15 != head_of(sK0(sF16,sF15))
| ~ edge(sK0(sF16,sF15))
| ~ spl21_1
| ~ spl21_51 ),
inference(trivial_inequality_removal,[],[f694]) ).
fof(f873,plain,
( edge(sK10)
| ~ spl21_41 ),
inference(resolution,[],[f454,f99]) ).
fof(f875,plain,
( $false
| spl21_9
| ~ spl21_41 ),
inference(forward_subsumption_resolution,[],[f873,f209]) ).
fof(f876,plain,
( spl21_9
| ~ spl21_41 ),
inference(avatar_contradiction_clause,[],[f875]) ).
fof(f878,plain,
( ! [X0] :
( head_of(X0) != sF16
| ~ edge(X0)
| sK10 = X0
| sequential(X0,sK10) )
| ~ spl21_9 ),
inference(forward_subsumption_resolution,[],[f248,f208]) ).
fof(f891,plain,
( ! [X2,X3,X0,X1] :
( head_of(X0) != sF18
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK10,X0,X3) )
| ~ spl21_7 ),
inference(forward_subsumption_resolution,[],[f420,f186]) ).
fof(f920,plain,
( sF15 != head_of(sK0(sF16,sF15))
| ~ spl21_1
| ~ spl21_51
| ~ spl21_57 ),
inference(forward_subsumption_resolution,[],[f701,f666]) ).
fof(f925,plain,
( ~ edge(sK0(sF16,sF15))
| ~ spl21_51
| ~ spl21_52 ),
inference(forward_subsumption_resolution,[],[f689,f631]) ).
fof(f931,plain,
( $false
| ~ spl21_51
| ~ spl21_52
| ~ spl21_57 ),
inference(forward_subsumption_resolution,[],[f925,f666]) ).
fof(f932,plain,
( ~ spl21_51
| ~ spl21_52
| ~ spl21_57 ),
inference(avatar_contradiction_clause,[],[f931]) ).
fof(f948,plain,
( ! [X2,X0,X1] :
( sF15 != sF18
| ~ shortest_path(X0,X1,X2)
| ~ precedes(sK10,sK11,X2) )
| ~ spl21_7 ),
inference(superposition,[],[f891,f140]) ).
fof(f971,plain,
( sF15 != sF15
| sF16 != head_of(sK0(sF16,sF15))
| ~ edge(sK0(sF16,sF15))
| ~ spl21_5
| ~ spl21_54 ),
inference(superposition,[],[f177,f641]) ).
fof(f977,plain,
( sF16 != head_of(sK0(sF16,sF15))
| ~ edge(sK0(sF16,sF15))
| ~ spl21_5
| ~ spl21_54 ),
inference(trivial_inequality_removal,[],[f971]) ).
fof(f978,plain,
( ~ edge(sK0(sF16,sF15))
| ~ spl21_5
| ~ spl21_52
| ~ spl21_54 ),
inference(forward_subsumption_resolution,[],[f977,f631]) ).
fof(f982,plain,
( $false
| ~ spl21_5
| ~ spl21_52
| ~ spl21_54
| ~ spl21_57 ),
inference(forward_subsumption_resolution,[],[f978,f666]) ).
fof(f983,plain,
( ~ spl21_5
| ~ spl21_52
| ~ spl21_54
| ~ spl21_57 ),
inference(avatar_contradiction_clause,[],[f982]) ).
fof(f1049,plain,
( sF15 != sF16
| ~ edge(sK11)
| sK10 = sK11
| sequential(sK11,sK10)
| ~ spl21_9 ),
inference(superposition,[],[f878,f140]) ).
fof(f1052,plain,
( ~ edge(sK11)
| sK10 = sK11
| sequential(sK11,sK10)
| ~ spl21_9
| ~ spl21_11 ),
inference(forward_subsumption_resolution,[],[f1049,f216]) ).
fof(f1053,plain,
( sK10 = sK11
| sequential(sK11,sK10)
| ~ spl21_9
| ~ spl21_11
| ~ spl21_32 ),
inference(forward_subsumption_resolution,[],[f1052,f383]) ).
fof(f1055,definition,
( spl21_79
<=> sequential(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl21_79])],[avatar_definition]) ).
fof(f1057,plain,
( sequential(sK11,sK10)
| ~ spl21_79 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1059,definition,
( spl21_80
<=> sK10 = sK11 ),
introduced(definition,[new_symbols(definition,[spl21_80])],[avatar_definition]) ).
fof(f1061,plain,
( sK10 = sK11
| ~ spl21_80 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1062,plain,
( spl21_79
| spl21_80
| ~ spl21_9
| ~ spl21_11
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f1053,f382,f215,f207,f1059,f1055]) ).
fof(f1189,plain,
! [X0] :
( ~ on_path(X0,sK12)
| edge(X0) ),
inference(resolution,[],[f92,f308]) ).
fof(f1191,plain,
( edge(sK11)
| ~ spl21_21 ),
inference(resolution,[],[f1189,f316]) ).
fof(f1296,plain,
! [X0,X1] :
( precedes(X0,X1,sK12)
| ~ on_path(X1,sK12)
| ~ sequential(X0,X1)
| ~ on_path(X0,sK12) ),
inference(resolution,[],[f102,f308]) ).
fof(f1301,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK12)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK12)
| ~ on_path(X0,sK12) ),
inference(resolution,[],[f1296,f307]) ).
fof(f1388,plain,
( ~ sequential(sK11,sK10)
| ~ on_path(sK11,sK12)
| ~ on_path(sK10,sK12) ),
inference(resolution,[],[f1301,f124]) ).
fof(f1391,plain,
( ~ on_path(sK11,sK12)
| ~ on_path(sK10,sK12)
| ~ spl21_79 ),
inference(forward_subsumption_resolution,[],[f1388,f1057]) ).
fof(f1392,plain,
( ~ on_path(sK10,sK12)
| ~ spl21_21
| ~ spl21_79 ),
inference(forward_subsumption_resolution,[],[f1391,f316]) ).
fof(f1393,plain,
( $false
| ~ spl21_21
| ~ spl21_22
| ~ spl21_79 ),
inference(forward_subsumption_resolution,[],[f1392,f322]) ).
fof(f1394,plain,
( ~ spl21_21
| ~ spl21_22
| ~ spl21_79 ),
inference(avatar_contradiction_clause,[],[f1393]) ).
fof(f1395,plain,
( precedes(sK10,sK10,sK12)
| ~ spl21_80 ),
inference(superposition,[],[f124,f1061]) ).
fof(f1406,plain,
( $false
| ~ spl21_80 ),
inference(forward_subsumption_resolution,[],[f1395,f306]) ).
fof(f1407,plain,
~ spl21_80,
inference(avatar_contradiction_clause,[],[f1406]) ).
fof(f1412,plain,
( $false
| ~ spl21_21
| spl21_32 ),
inference(forward_subsumption_resolution,[],[f1191,f384]) ).
fof(f1413,plain,
( ~ spl21_21
| spl21_32 ),
inference(avatar_contradiction_clause,[],[f1412]) ).
fof(f1428,plain,
( ! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ precedes(sK10,sK11,X2) )
| ~ spl21_6
| ~ spl21_7 ),
inference(forward_subsumption_resolution,[],[f948,f181]) ).
fof(f1449,plain,
( spl21_35
| ~ spl21_6
| ~ spl21_7 ),
inference(avatar_split_clause,[],[f1428,f184,f179,f414]) ).
fof(f1483,plain,
( ~ spl21_53
| ~ spl21_1
| ~ spl21_51
| ~ spl21_57 ),
inference(avatar_split_clause,[],[f920,f665,f625,f158,f634]) ).
fof(f1498,plain,
( vertex(sF15)
| ~ spl21_32 ),
inference(forward_subsumption_resolution,[],[f390,f383]) ).
fof(f1701,plain,
( ! [X0] :
( ~ vertex(X0)
| sF15 = tail_of(sK0(X0,sF15))
| tail_of(sK0(X0,sF15)) = X0
| sF15 = X0 )
| ~ spl21_32 ),
inference(resolution,[],[f1498,f195]) ).
fof(f1702,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,sF15)) = X0
| tail_of(sK0(X0,sF15)) = X0
| sF15 = X0 )
| ~ spl21_32 ),
inference(resolution,[],[f1498,f196]) ).
fof(f1704,plain,
( ! [X0] :
( ~ vertex(X0)
| head_of(sK0(X0,sF15)) = X0
| sF15 = head_of(sK0(X0,sF15))
| sF15 = X0 )
| ~ spl21_32 ),
inference(resolution,[],[f1498,f198]) ).
fof(f1718,plain,
( sF16 = head_of(sK0(sF16,sF15))
| sF16 = tail_of(sK0(sF16,sF15))
| sF15 = sF16
| ~ spl21_9
| ~ spl21_32 ),
inference(resolution,[],[f1702,f480]) ).
fof(f1754,plain,
( sF16 = head_of(sK0(sF16,sF15))
| sF15 = head_of(sK0(sF16,sF15))
| sF15 = sF16
| ~ spl21_9
| ~ spl21_32 ),
inference(resolution,[],[f1704,f480]) ).
fof(f1756,plain,
( sF15 = head_of(sK0(sF16,sF15))
| sF15 = sF16
| ~ spl21_9
| ~ spl21_32
| spl21_52 ),
inference(forward_subsumption_resolution,[],[f1754,f630]) ).
fof(f1757,plain,
( sF15 = sF16
| ~ spl21_9
| ~ spl21_32
| spl21_52
| spl21_53 ),
inference(forward_subsumption_resolution,[],[f1756,f635]) ).
fof(f1758,plain,
( $false
| ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_52
| spl21_53 ),
inference(forward_subsumption_resolution,[],[f1757,f217]) ).
fof(f1759,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_52
| spl21_53 ),
inference(avatar_contradiction_clause,[],[f1758]) ).
fof(f1855,plain,
( sF15 = tail_of(sK0(sF16,sF15))
| sF16 = tail_of(sK0(sF16,sF15))
| sF15 = sF16
| ~ spl21_9
| ~ spl21_32 ),
inference(resolution,[],[f1701,f480]) ).
fof(f1919,plain,
( ~ vertex(sF16)
| ~ vertex(sF15)
| sF15 = sF16
| spl21_57 ),
inference(resolution,[],[f667,f200]) ).
fof(f1920,plain,
( ~ vertex(sF15)
| sF15 = sF16
| ~ spl21_9
| spl21_57 ),
inference(forward_subsumption_resolution,[],[f1919,f480]) ).
fof(f1921,plain,
( sF15 = sF16
| ~ spl21_9
| ~ spl21_32
| spl21_57 ),
inference(forward_subsumption_resolution,[],[f1920,f1498]) ).
fof(f1922,plain,
( $false
| ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_57 ),
inference(forward_subsumption_resolution,[],[f1921,f217]) ).
fof(f1923,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_57 ),
inference(avatar_contradiction_clause,[],[f1922]) ).
fof(f1925,plain,
( sF16 = tail_of(sK0(sF16,sF15))
| sF15 = sF16
| ~ spl21_9
| ~ spl21_32
| spl21_52 ),
inference(forward_subsumption_resolution,[],[f1718,f630]) ).
fof(f1926,plain,
( sF16 = tail_of(sK0(sF16,sF15))
| sF15 = sF16
| ~ spl21_9
| ~ spl21_32
| spl21_54 ),
inference(forward_subsumption_resolution,[],[f1855,f640]) ).
fof(f1927,plain,
( sF15 = sF16
| ~ spl21_9
| ~ spl21_32
| spl21_51
| spl21_52 ),
inference(forward_subsumption_resolution,[],[f1925,f626]) ).
fof(f1928,plain,
( sF15 = sF16
| ~ spl21_9
| ~ spl21_32
| spl21_51
| spl21_54 ),
inference(forward_subsumption_resolution,[],[f1926,f626]) ).
fof(f1929,plain,
( $false
| ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_51
| spl21_52 ),
inference(forward_subsumption_resolution,[],[f1927,f217]) ).
fof(f1930,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_51
| spl21_52 ),
inference(avatar_contradiction_clause,[],[f1929]) ).
fof(f1931,plain,
( $false
| ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_51
| spl21_54 ),
inference(forward_subsumption_resolution,[],[f1928,f217]) ).
fof(f1932,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_51
| spl21_54 ),
inference(avatar_contradiction_clause,[],[f1931]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f164]) ).
cnf(s2,plain,
( spl21_1
| spl21_3 ),
inference(sat_conversion,[],[f169]) ).
cnf(s3,plain,
( spl21_1
| spl21_4 ),
inference(sat_conversion,[],[f174]) ).
cnf(s4,plain,
( spl21_5
| spl21_6 ),
inference(sat_conversion,[],[f182]) ).
cnf(s5,plain,
( spl21_5
| spl21_7 ),
inference(sat_conversion,[],[f187]) ).
cnf(s9,plain,
( ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_5 ),
inference(sat_conversion,[],[f232]) ).
cnf(s16,plain,
( spl21_20
| spl21_21 ),
inference(sat_conversion,[],[f317]) ).
cnf(s17,plain,
( spl21_20
| spl21_22 ),
inference(sat_conversion,[],[f323]) ).
cnf(s27,plain,
~ spl21_35,
inference(sat_conversion,[],[f437]) ).
cnf(s29,plain,
( spl21_20
| spl21_40
| spl21_41 ),
inference(sat_conversion,[],[f455]) ).
cnf(s30,plain,
~ spl21_20,
inference(sat_conversion,[],[f457]) ).
cnf(s32,plain,
( spl21_9
| ~ spl21_40 ),
inference(sat_conversion,[],[f464]) ).
cnf(s62,plain,
( spl21_9
| ~ spl21_41 ),
inference(sat_conversion,[],[f876]) ).
cnf(s67,plain,
( ~ spl21_51
| ~ spl21_52
| ~ spl21_57 ),
inference(sat_conversion,[],[f932]) ).
cnf(s70,plain,
( ~ spl21_5
| ~ spl21_52
| ~ spl21_54
| ~ spl21_57 ),
inference(sat_conversion,[],[f983]) ).
cnf(s74,plain,
( ~ spl21_9
| ~ spl21_11
| ~ spl21_32
| spl21_79
| spl21_80 ),
inference(sat_conversion,[],[f1062]) ).
cnf(s90,plain,
( ~ spl21_21
| ~ spl21_22
| ~ spl21_79 ),
inference(sat_conversion,[],[f1394]) ).
cnf(s93,plain,
~ spl21_80,
inference(sat_conversion,[],[f1407]) ).
cnf(s96,plain,
( ~ spl21_21
| spl21_32 ),
inference(sat_conversion,[],[f1413]) ).
cnf(s101,plain,
( ~ spl21_6
| ~ spl21_7
| spl21_35 ),
inference(sat_conversion,[],[f1449]) ).
cnf(s106,plain,
( ~ spl21_1
| ~ spl21_51
| ~ spl21_53
| ~ spl21_57 ),
inference(sat_conversion,[],[f1483]) ).
cnf(s129,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_52
| spl21_53 ),
inference(sat_conversion,[],[f1759]) ).
cnf(s145,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_57 ),
inference(sat_conversion,[],[f1923]) ).
cnf(s146,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_51
| spl21_52 ),
inference(sat_conversion,[],[f1930]) ).
cnf(s147,plain,
( ~ spl21_9
| spl21_11
| ~ spl21_32
| spl21_51
| spl21_54 ),
inference(sat_conversion,[],[f1932]) ).
cnf(s148,plain,
( ~ spl21_9
| ~ spl21_11
| ~ spl21_32
| spl21_79 ),
inference(rat,[],[s74,s93]) ).
cnf(s152,plain,
( spl21_40
| spl21_41 ),
inference(rat,[],[s29,s30]) ).
cnf(s155,plain,
spl21_22,
inference(rat,[],[s17,s30]) ).
cnf(s156,plain,
spl21_21,
inference(rat,[],[s16,s30]) ).
cnf(s157,plain,
spl21_32,
inference(rat,[],[s96,s156]) ).
cnf(s158,plain,
~ spl21_79,
inference(rat,[],[s90,s155,s156]) ).
cnf(s159,plain,
spl21_5,
inference(rat,[],[s101,s4,s5,s27]) ).
cnf(s160,plain,
spl21_1,
inference(rat,[],[s9,s1,s2,s3,s159]) ).
cnf(s161,plain,
spl21_9,
inference(rat,[],[s152,s32,s62]) ).
cnf(s163,plain,
~ spl21_11,
inference(rat,[],[s148,s158,s157,s161]) ).
cnf(s165,plain,
spl21_57,
inference(rat,[],[s145,s161,s157,s163]) ).
cnf(s167,plain,
spl21_51,
inference(rat,[],[s70,s146,s147,s159,s165,s157,s161,s163]) ).
cnf(s168,plain,
~ spl21_53,
inference(rat,[],[s106,s165,s160,s167]) ).
cnf(s170,plain,
~ spl21_52,
inference(rat,[],[s67,s165,s167]) ).
cnf(s171,plain,
$false,
inference(rat,[],[s129,s163,s161,s157,s168,s170]) ).
fof(f1933,plain,
$false,
inference(avatar_sat_refutation,[],[s171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRA006+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 08:47:05 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 Running first-order theorem proving
% 0.07/0.34 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
% 4.45/1.28 % (2072733)Detected formulas, will run a generic FOF schedule.
% 4.45/1.28 % (2072743)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2353001397:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.45/1.28 % (2072740)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=53633726:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.45/1.28 % (2072744)dis-21_1_sil=8000:lcm=predicate:random_seed=1620516919: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)
% 4.45/1.28 % (2072742)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2127462448:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.45/1.28 % (2072739)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=1302144173:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.45/1.28 % (2072741)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=286431837:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.45/1.28 % (2072738)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=433567192:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.45/1.28 % (2072741)Refutation not found, incomplete strategy
% 4.45/1.28 % (2072741)------------------------------
% 4.45/1.28 % (2072741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072741)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072741)Termination reason: Refutation not found, incomplete strategy
% 4.45/1.28 % (2072741)Time elapsed: 0.002 s
% 4.45/1.28 % (2072741)Peak memory usage: 88 MB
% 4.45/1.28 % (2072741)Instructions burned: 3 (million)
% 4.45/1.28 % (2072742)Instruction limit reached!
% 4.45/1.28 % (2072742)------------------------------
% 4.45/1.28 % (2072742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072742)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072742)Termination reason: Instruction limit
% 4.45/1.28 % (2072742)Termination phase: Saturation
% 4.45/1.28 % (2072742)Time elapsed: 0.032 s
% 4.45/1.28 % (2072742)Peak memory usage: 87 MB
% 4.45/1.28 % (2072742)Instructions burned: 119 (million)
% 4.45/1.28 % (2072744)Instruction limit reached!
% 4.45/1.28 % (2072744)------------------------------
% 4.45/1.28 % (2072744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072744)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072744)Termination reason: Instruction limit
% 4.45/1.28 % (2072744)Termination phase: Saturation
% 4.45/1.28 % (2072744)Time elapsed: 0.036 s
% 4.45/1.28 % (2072744)Peak memory usage: 88 MB
% 4.45/1.28 % (2072744)Instructions burned: 132 (million)
% 4.45/1.28 % (2072743)Instruction limit reached!
% 4.45/1.28 % (2072743)------------------------------
% 4.45/1.28 % (2072743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072743)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072743)Termination reason: Instruction limit
% 4.45/1.28 % (2072743)Termination phase: Saturation
% 4.45/1.28 % (2072743)Time elapsed: 0.050 s
% 4.45/1.28 % (2072743)Peak memory usage: 89 MB
% 4.45/1.28 % (2072743)Instructions burned: 140 (million)
% 4.45/1.28 % (2072753)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1857596745:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 4.45/1.28 % (2072752)lrs+10_1_sil=8000:sp=occurrence:random_seed=3593491803:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.45/1.28 % (2072753)Refutation not found, incomplete strategy
% 4.45/1.28 % (2072753)------------------------------
% 4.45/1.28 % (2072753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072753)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072753)Termination reason: Refutation not found, incomplete strategy
% 4.45/1.28 % (2072753)Time elapsed: 0.003 s
% 4.45/1.28 % (2072753)Peak memory usage: 88 MB
% 4.45/1.28 % (2072753)Instructions burned: 5 (million)
% 4.45/1.28 % (2072741)------------------------------
% 4.45/1.28 % (2072741)------------------------------
% 4.45/1.28 % (2072754)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3477562248:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 4.45/1.28 % (2072752)Instruction limit reached!
% 4.45/1.28 % (2072752)------------------------------
% 4.45/1.28 % (2072752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072752)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072752)Termination reason: Instruction limit
% 4.45/1.28 % (2072752)Termination phase: Saturation
% 4.45/1.28 % (2072752)Time elapsed: 0.096 s
% 4.45/1.28 % (2072752)Peak memory usage: 91 MB
% 4.45/1.28 % (2072752)Instructions burned: 287 (million)
% 4.45/1.28 % (2072754)Instruction limit reached!
% 4.45/1.28 % (2072754)------------------------------
% 4.45/1.28 % (2072754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072754)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072754)Termination reason: Instruction limit
% 4.45/1.28 % (2072754)Termination phase: Saturation
% 4.45/1.28 % (2072754)Time elapsed: 0.107 s
% 4.45/1.28 % (2072754)Peak memory usage: 91 MB
% 4.45/1.28 % (2072754)Instructions burned: 325 (million)
% 4.45/1.28 % (2072757)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=2941021138:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.45/1.28 % (2072753)------------------------------
% 4.45/1.28 % (2072753)------------------------------
% 4.45/1.28 % (2072757)Instruction limit reached!
% 4.45/1.28 % (2072757)------------------------------
% 4.45/1.28 % (2072757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072757)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072757)Termination reason: Instruction limit
% 4.45/1.28 % (2072757)Termination phase: Saturation
% 4.45/1.28 % (2072757)Time elapsed: 0.077 s
% 4.45/1.28 % (2072757)Peak memory usage: 90 MB
% 4.45/1.28 % (2072757)Instructions burned: 249 (million)
% 4.45/1.28 % (2072759)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=237357029:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.45/1.28 % (2072761)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1785475092:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.45/1.28 % (2072762)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3411426790:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 4.45/1.28 % (2072738)First to succeed.
% 4.45/1.28 % (2072738)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2072733"
% 4.45/1.28 % (2072759)Instruction limit reached!
% 4.45/1.28 % (2072759)------------------------------
% 4.45/1.28 % (2072759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072759)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072759)Termination reason: Instruction limit
% 4.45/1.28 % (2072759)Termination phase: Saturation
% 4.45/1.28 % (2072759)Time elapsed: 0.081 s
% 4.45/1.28 % (2072759)Peak memory usage: 89 MB
% 4.45/1.28 % (2072759)Instructions burned: 296 (million)
% 4.45/1.28 % (2072762)Instruction limit reached!
% 4.45/1.28 % (2072762)------------------------------
% 4.45/1.28 % (2072762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072762)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072762)Termination reason: Instruction limit
% 4.45/1.28 % (2072762)Termination phase: Saturation
% 4.45/1.28 % (2072762)Time elapsed: 0.043 s
% 4.45/1.28 % (2072762)Peak memory usage: 90 MB
% 4.45/1.28 % (2072762)Instructions burned: 116 (million)
% 4.45/1.28 % (2072764)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1697282172:i=127:av=off:fsr=off:sup=off_2995 on theBenchmark for (2995ds/127Mi)
% 4.45/1.28 % (2072764)Instruction limit reached!
% 4.45/1.28 % (2072764)------------------------------
% 4.45/1.28 % (2072764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.28 % (2072764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.28 % (2072764)CaDiCaL version: 2.1.3
% 4.45/1.28 % (2072764)Termination reason: Instruction limit
% 4.45/1.28 % (2072764)Termination phase: Saturation
% 4.45/1.28 % (2072764)Time elapsed: 0.035 s
% 4.45/1.28 % (2072764)Peak memory usage: 89 MB
% 4.45/1.28 % (2072764)Instructions burned: 131 (million)
% 4.45/1.28 % (2072767)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2757585808:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 4.45/1.28 % (2072768)lrs+10_1_sil=8000:sp=occurrence:random_seed=1408562507:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2994 on theBenchmark for (2994ds/907Mi)
% 4.45/1.28 % (2072738)Refutation found. Thanks to Tanya!
% 4.45/1.28 % SZS status Theorem for theBenchmark
% 4.45/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 5.38/1.38 % (2072738)------------------------------
% 5.38/1.38 % (2072738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.38 % (2072738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.38 % (2072738)CaDiCaL version: 2.1.3
% 5.38/1.38 % (2072738)Termination reason: Refutation
% 5.38/1.38 % (2072738)Time elapsed: 0.444 s
% 5.38/1.38 % (2072738)Peak memory usage: 129 MB
% 5.38/1.38 % (2072738)Instructions burned: 1127 (million)
% 5.38/1.38 % (2072738)------------------------------
% 5.38/1.38 % (2072738)------------------------------
% 5.38/1.38 % (2072733)Success in time 0.741 s
% 5.38/1.38 % Vampire exiting
%------------------------------------------------------------------------------