%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA002+2 : 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 09:55:19 AM UTC 2026
% Result : Theorem 3.25s 1.21s
% Output : Refutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 26
% Syntax : Number of formulae : 179 ( 29 unt; 16 def)
% Number of atoms : 620 ( 100 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 763 ( 322 ~; 325 |; 83 &)
% ( 20 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 18 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 260 ( 0 sgn 244 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( edge(X0)
& edge(X1)
& X0 != X1
& head_of(X0) = tail_of(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
fof(f9,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& ( sequential(X3,X4)
| ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) ) )
=> precedes(X3,X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ~ ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& ~ precedes(X3,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f13,axiom,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(f15,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f16,axiom,
! [X0,X1,X2] :
( ( path(X1,X2,X0)
& ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) )
=> ? [X5] : triangle(X3,X4,X5) ) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f17,axiom,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f18,axiom,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
fof(f19,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f24,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) )
| ~ complete ),
inference(ennf_transformation,[],[f18]) ).
fof(f26,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] :
( edge(X5)
& tail_of(X5) = head_of(X3)
& head_of(X5) = tail_of(X2) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) )
| ~ complete ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f38,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(f39,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,[],[f38]) ).
fof(f40,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(f43,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(f44,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,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) )
& ( ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) )
| ~ triangle(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) )
& ( ( edge(X0)
& edge(X1)
& edge(X2)
& sequential(X0,X1)
& sequential(X1,X2)
& sequential(X2,X0) )
| ~ triangle(X0,X1,X2) ) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ( ! [X5] : ~ triangle(sK0(X0),sK1(X0),X5)
& on_path(sK0(X0),X0)
& on_path(sK1(X0),X0)
& sequential(sK0(X0),sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0)),skolemize(X4,sK1(X0))],[f24]) ).
fof(f48,plain,
( ! [X0,X1,X2,X3,X4] :
( ( edge(sK2(X2,X3))
& head_of(X3) = tail_of(sK2(X2,X3))
& tail_of(X2) = head_of(sK2(X2,X3)) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X5,sK2(X2,X3))],[f26]) ).
fof(f49,plain,
( ~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph))
& shortest_path(sK4,sK5,sK3)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f27]) ).
fof(f50,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(f51,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,[],[f50]) ).
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
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK10(X0,X1,X2)))
& path(X0,X1,sK10(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,[sK10]),skolemize(X3,sK10(X0,X1,X2))],[f65]) ).
fof(f74,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,[],[f46]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK0(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK1(X0),X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK0(X0),X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK0(X0),sK1(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f81,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f17]) ).
fof(f82,plain,
! [X2,X3,X0,X1,X4] :
( tail_of(X2) = head_of(sK2(X2,X3))
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f83,plain,
! [X2,X3,X0,X1,X4] :
( head_of(X3) = tail_of(sK2(X2,X3))
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4] :
( edge(sK2(X2,X3))
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ complete ),
inference(cnf_transformation,[],[f48]) ).
fof(f85,plain,
complete,
inference(cnf_transformation,[],[f49]) ).
fof(f86,plain,
shortest_path(sK4,sK5,sK3),
inference(cnf_transformation,[],[f49]) ).
fof(f87,plain,
~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f49]) ).
fof(f90,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f91,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f92,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f132,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| head_of(X3) != head_of(X5)
| ~ shortest_path(X0,X1,X4)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f44]) ).
fof(f169,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| tail_of(X2) = head_of(sK2(X2,X3)) ),
inference(forward_subsumption_resolution,[],[f82,f85]) ).
fof(f170,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) = tail_of(sK2(X2,X3)) ),
inference(forward_subsumption_resolution,[],[f83,f85]) ).
fof(f171,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| edge(sK2(X2,X3))
| ~ precedes(X2,X3,X4) ),
inference(forward_subsumption_resolution,[],[f84,f85]) ).
fof(f172,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(forward_subsumption_resolution,[],[f74,f90]) ).
fof(f175,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ edge(X0)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(forward_subsumption_resolution,[],[f172,f90]) ).
fof(f176,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(forward_subsumption_resolution,[],[f175,f90]) ).
fof(f179,plain,
path(sK4,sK5,sK3),
inference(resolution,[],[f125,f86]) ).
fof(f180,plain,
( number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3)
| on_path(sK0(sK3),sK3) ),
inference(resolution,[],[f179,f79]) ).
fof(f182,plain,
minus(length_of(sK3),n1) = number_of_in(sequential_pairs,sK3),
inference(resolution,[],[f179,f76]) ).
fof(f184,definition,
( spl12_8
<=> on_path(sK0(sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f185,plain,
( on_path(sK0(sK3),sK3)
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,definition,
( spl12_9
<=> number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f188,plain,
( number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3)
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( spl12_8
| spl12_9 ),
inference(avatar_split_clause,[],[f180,f187,f184]) ).
fof(f190,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK3),number_of_in(triangles,graph)),
inference(superposition,[],[f87,f182]) ).
fof(f191,plain,
( number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3)
| on_path(sK1(sK3),sK3) ),
inference(resolution,[],[f78,f179]) ).
fof(f192,plain,
( number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3)
| sequential(sK0(sK3),sK1(sK3)) ),
inference(resolution,[],[f77,f179]) ).
fof(f193,plain,
( less_or_equal(number_of_in(sequential_pairs,sK3),number_of_in(triangles,graph))
| ~ spl12_9 ),
inference(superposition,[],[f81,f188]) ).
fof(f194,plain,
( $false
| ~ spl12_9 ),
inference(forward_subsumption_resolution,[],[f193,f190]) ).
fof(f195,plain,
~ spl12_9,
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f197,definition,
( spl12_10
<=> on_path(sK1(sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f198,plain,
( on_path(sK1(sK3),sK3)
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f199,plain,
( spl12_10
| spl12_9 ),
inference(avatar_split_clause,[],[f191,f187,f197]) ).
fof(f201,definition,
( spl12_11
<=> sequential(sK0(sK3),sK1(sK3)) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f202,plain,
( sequential(sK0(sK3),sK1(sK3))
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
( spl12_11
| spl12_9 ),
inference(avatar_split_clause,[],[f192,f187,f201]) ).
fof(f204,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ sequential(sK0(X2),sK1(X2))
| ~ sequential(sK1(X2),X3)
| ~ sequential(X3,sK0(X2)) ),
inference(resolution,[],[f80,f176]) ).
fof(f205,plain,
! [X2,X3,X0,X1] :
( ~ sequential(sK1(X2),X3)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ path(X0,X1,X2)
| ~ sequential(X3,sK0(X2)) ),
inference(forward_subsumption_resolution,[],[f204,f77]) ).
fof(f206,plain,
( edge(sK1(sK3))
| ~ spl12_11 ),
inference(resolution,[],[f90,f202]) ).
fof(f207,plain,
( edge(sK0(sK3))
| ~ spl12_11 ),
inference(resolution,[],[f91,f202]) ).
fof(f210,plain,
( ! [X2,X0,X1] :
( ~ on_path(sK1(sK3),X0)
| ~ on_path(sK0(sK3),X0)
| precedes(sK0(sK3),sK1(sK3),X0)
| ~ path(X1,X2,X0) )
| ~ spl12_11 ),
inference(resolution,[],[f122,f202]) ).
fof(f211,plain,
( ! [X0,X1] :
( ~ on_path(sK0(sK3),sK3)
| precedes(sK0(sK3),sK1(sK3),sK3)
| ~ path(X0,X1,sK3) )
| ~ spl12_10
| ~ spl12_11 ),
inference(resolution,[],[f210,f198]) ).
fof(f212,plain,
( ! [X0,X1] :
( precedes(sK0(sK3),sK1(sK3),sK3)
| ~ path(X0,X1,sK3) )
| ~ spl12_8
| ~ spl12_10
| ~ spl12_11 ),
inference(forward_subsumption_resolution,[],[f211,f185]) ).
fof(f214,definition,
( spl12_12
<=> ! [X0,X1] : ~ path(X0,X1,sK3) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f215,plain,
( ! [X0,X1] : ~ path(X0,X1,sK3)
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,definition,
( spl12_13
<=> precedes(sK0(sK3),sK1(sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
fof(f218,plain,
( precedes(sK0(sK3),sK1(sK3),sK3)
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f219,plain,
( spl12_12
| spl12_13
| ~ spl12_8
| ~ spl12_10
| ~ spl12_11 ),
inference(avatar_split_clause,[],[f212,f201,f197,f184,f217,f214]) ).
fof(f220,plain,
( ! [X2,X0,X1] :
( head_of(X0) != head_of(sK1(sK3))
| ~ shortest_path(X1,X2,sK3)
| tail_of(X0) != tail_of(sK0(sK3)) )
| ~ spl12_13 ),
inference(resolution,[],[f218,f132]) ).
fof(f221,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK3)
| tail_of(sK0(sK3)) = head_of(sK2(sK0(sK3),sK1(sK3))) )
| ~ spl12_13 ),
inference(resolution,[],[f218,f169]) ).
fof(f222,plain,
( ! [X0,X1] :
( ~ shortest_path(X0,X1,sK3)
| head_of(sK1(sK3)) = tail_of(sK2(sK0(sK3),sK1(sK3))) )
| ~ spl12_13 ),
inference(resolution,[],[f218,f170]) ).
fof(f224,definition,
( spl12_14
<=> head_of(sK1(sK3)) = tail_of(sK2(sK0(sK3),sK1(sK3))) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
fof(f225,plain,
( head_of(sK1(sK3)) = tail_of(sK2(sK0(sK3),sK1(sK3)))
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f227,definition,
( spl12_15
<=> ! [X0,X1] : ~ shortest_path(X0,X1,sK3) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
fof(f228,plain,
( ! [X0,X1] : ~ shortest_path(X0,X1,sK3)
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f229,plain,
( spl12_14
| spl12_15
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f222,f217,f227,f224]) ).
fof(f231,definition,
( spl12_16
<=> tail_of(sK0(sK3)) = head_of(sK2(sK0(sK3),sK1(sK3))) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
fof(f232,plain,
( tail_of(sK0(sK3)) = head_of(sK2(sK0(sK3),sK1(sK3)))
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f233,plain,
( spl12_16
| spl12_15
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f221,f217,f227,f231]) ).
fof(f235,definition,
( spl12_17
<=> ! [X0] :
( head_of(X0) != head_of(sK1(sK3))
| tail_of(X0) != tail_of(sK0(sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
fof(f236,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK0(sK3))
| head_of(X0) != head_of(sK1(sK3)) )
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f237,plain,
( spl12_15
| spl12_17
| ~ spl12_13 ),
inference(avatar_split_clause,[],[f220,f217,f235,f227]) ).
fof(f238,plain,
( $false
| ~ spl12_15 ),
inference(unit_resulting_resolution,[],[f228,f86]) ).
fof(f241,plain,
~ spl12_15,
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f242,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK0(sK3))
| ~ edge(sK2(sK0(sK3),sK1(sK3)))
| ~ edge(X0)
| sK2(sK0(sK3),sK1(sK3)) = X0
| sequential(sK2(sK0(sK3),sK1(sK3)),X0) )
| ~ spl12_16 ),
inference(superposition,[],[f92,f232]) ).
fof(f244,definition,
( spl12_18
<=> edge(sK2(sK0(sK3),sK1(sK3))) ),
introduced(definition,[new_symbols(definition,[spl12_18])],[avatar_definition]) ).
fof(f245,plain,
( ~ edge(sK2(sK0(sK3),sK1(sK3)))
| spl12_18 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,definition,
( spl12_19
<=> ! [X0] :
( tail_of(X0) != tail_of(sK0(sK3))
| sequential(sK2(sK0(sK3),sK1(sK3)),X0)
| sK2(sK0(sK3),sK1(sK3)) = X0
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
fof(f248,plain,
( ! [X0] :
( tail_of(X0) != tail_of(sK0(sK3))
| sequential(sK2(sK0(sK3),sK1(sK3)),X0)
| sK2(sK0(sK3),sK1(sK3)) = X0
| ~ edge(X0) )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( ~ spl12_18
| spl12_19
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f242,f231,f247,f244]) ).
fof(f251,plain,
( ! [X0] :
( head_of(X0) != head_of(sK1(sK3))
| ~ edge(X0)
| ~ edge(sK2(sK0(sK3),sK1(sK3)))
| sK2(sK0(sK3),sK1(sK3)) = X0
| sequential(X0,sK2(sK0(sK3),sK1(sK3))) )
| ~ spl12_14 ),
inference(superposition,[],[f92,f225]) ).
fof(f252,plain,
( head_of(sK1(sK3)) != tail_of(sK0(sK3))
| head_of(sK1(sK3)) != head_of(sK2(sK0(sK3),sK1(sK3)))
| ~ spl12_14
| ~ spl12_17 ),
inference(superposition,[],[f236,f225]) ).
fof(f254,plain,
( head_of(sK1(sK3)) != tail_of(sK0(sK3))
| head_of(sK1(sK3)) != tail_of(sK0(sK3))
| ~ spl12_14
| ~ spl12_16
| ~ spl12_17 ),
inference(forward_demodulation,[],[f252,f232]) ).
fof(f255,plain,
( head_of(sK1(sK3)) != tail_of(sK0(sK3))
| ~ spl12_14
| ~ spl12_16
| ~ spl12_17 ),
inference(duplicate_literal_removal,[],[f254]) ).
fof(f256,plain,
( $false
| ~ spl12_13
| spl12_18 ),
inference(unit_resulting_resolution,[],[f171,f86,f218,f245]) ).
fof(f258,plain,
( ~ spl12_13
| spl12_18 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f260,plain,
( $false
| ~ spl12_12 ),
inference(unit_resulting_resolution,[],[f125,f86,f215]) ).
fof(f264,plain,
~ spl12_12,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f266,definition,
( spl12_20
<=> ! [X0] :
( head_of(X0) != head_of(sK1(sK3))
| sequential(X0,sK2(sK0(sK3),sK1(sK3)))
| sK2(sK0(sK3),sK1(sK3)) = X0
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
fof(f267,plain,
( ! [X0] :
( head_of(X0) != head_of(sK1(sK3))
| sequential(X0,sK2(sK0(sK3),sK1(sK3)))
| sK2(sK0(sK3),sK1(sK3)) = X0
| ~ edge(X0) )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( ~ spl12_18
| spl12_20
| ~ spl12_14 ),
inference(avatar_split_clause,[],[f251,f224,f266,f244]) ).
fof(f273,plain,
( sequential(sK1(sK3),sK2(sK0(sK3),sK1(sK3)))
| sK1(sK3) = sK2(sK0(sK3),sK1(sK3))
| ~ edge(sK1(sK3))
| ~ spl12_20 ),
inference(equality_resolution,[],[f267]) ).
fof(f274,plain,
( sequential(sK1(sK3),sK2(sK0(sK3),sK1(sK3)))
| sK1(sK3) = sK2(sK0(sK3),sK1(sK3))
| ~ spl12_11
| ~ spl12_20 ),
inference(forward_subsumption_resolution,[],[f273,f206]) ).
fof(f276,definition,
( spl12_21
<=> sK1(sK3) = sK2(sK0(sK3),sK1(sK3)) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
fof(f277,plain,
( sK1(sK3) = sK2(sK0(sK3),sK1(sK3))
| ~ spl12_21 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f279,definition,
( spl12_22
<=> sequential(sK1(sK3),sK2(sK0(sK3),sK1(sK3))) ),
introduced(definition,[new_symbols(definition,[spl12_22])],[avatar_definition]) ).
fof(f280,plain,
( sequential(sK1(sK3),sK2(sK0(sK3),sK1(sK3)))
| ~ spl12_22 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f281,plain,
( spl12_21
| spl12_22
| ~ spl12_11
| ~ spl12_20 ),
inference(avatar_split_clause,[],[f274,f266,f201,f279,f276]) ).
fof(f282,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3)
| ~ path(X0,X1,sK3)
| ~ sequential(sK2(sK0(sK3),sK1(sK3)),sK0(sK3)) )
| ~ spl12_22 ),
inference(resolution,[],[f280,f205]) ).
fof(f287,definition,
( spl12_23
<=> sequential(sK2(sK0(sK3),sK1(sK3)),sK0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl12_23])],[avatar_definition]) ).
fof(f288,plain,
( ~ sequential(sK2(sK0(sK3),sK1(sK3)),sK0(sK3))
| spl12_23 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f289,plain,
( ~ spl12_23
| spl12_12
| spl12_9
| ~ spl12_22 ),
inference(avatar_split_clause,[],[f282,f279,f187,f214,f287]) ).
fof(f290,plain,
( sequential(sK2(sK0(sK3),sK1(sK3)),sK0(sK3))
| sK0(sK3) = sK2(sK0(sK3),sK1(sK3))
| ~ edge(sK0(sK3))
| ~ spl12_19 ),
inference(equality_resolution,[],[f248]) ).
fof(f291,plain,
( sK0(sK3) = sK2(sK0(sK3),sK1(sK3))
| ~ edge(sK0(sK3))
| ~ spl12_19
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f290,f288]) ).
fof(f292,plain,
( sK0(sK3) = sK2(sK0(sK3),sK1(sK3))
| ~ spl12_11
| ~ spl12_19
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f291,f207]) ).
fof(f295,plain,
( head_of(sK1(sK3)) = tail_of(sK0(sK3))
| ~ spl12_11
| ~ spl12_14
| ~ spl12_19
| spl12_23 ),
inference(superposition,[],[f225,f292]) ).
fof(f297,plain,
( $false
| ~ spl12_11
| ~ spl12_14
| ~ spl12_16
| ~ spl12_17
| ~ spl12_19
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f295,f255]) ).
fof(f298,plain,
( ~ spl12_11
| ~ spl12_14
| ~ spl12_16
| ~ spl12_17
| ~ spl12_19
| spl12_23 ),
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f334,plain,
( head_of(sK1(sK3)) = tail_of(sK0(sK3))
| ~ spl12_16
| ~ spl12_21 ),
inference(superposition,[],[f232,f277]) ).
fof(f335,plain,
( $false
| ~ spl12_14
| ~ spl12_16
| ~ spl12_17
| ~ spl12_21 ),
inference(forward_subsumption_resolution,[],[f334,f255]) ).
fof(f336,plain,
( ~ spl12_14
| ~ spl12_16
| ~ spl12_17
| ~ spl12_21 ),
inference(avatar_contradiction_clause,[],[f335]) ).
cnf(s8,plain,
( spl12_8
| spl12_9 ),
inference(sat_conversion,[],[f189]) ).
cnf(s9,plain,
~ spl12_9,
inference(sat_conversion,[],[f195]) ).
cnf(s10,plain,
( spl12_9
| spl12_10 ),
inference(sat_conversion,[],[f199]) ).
cnf(s11,plain,
( spl12_9
| spl12_11 ),
inference(sat_conversion,[],[f203]) ).
cnf(s12,plain,
( ~ spl12_8
| ~ spl12_10
| ~ spl12_11
| spl12_12
| spl12_13 ),
inference(sat_conversion,[],[f219]) ).
cnf(s13,plain,
( ~ spl12_13
| spl12_14
| spl12_15 ),
inference(sat_conversion,[],[f229]) ).
cnf(s14,plain,
( ~ spl12_13
| spl12_15
| spl12_16 ),
inference(sat_conversion,[],[f233]) ).
cnf(s15,plain,
( ~ spl12_13
| spl12_15
| spl12_17 ),
inference(sat_conversion,[],[f237]) ).
cnf(s17,plain,
~ spl12_15,
inference(sat_conversion,[],[f241]) ).
cnf(s18,plain,
( ~ spl12_16
| ~ spl12_18
| spl12_19 ),
inference(sat_conversion,[],[f249]) ).
cnf(s19,plain,
( ~ spl12_13
| spl12_18 ),
inference(sat_conversion,[],[f258]) ).
cnf(s22,plain,
~ spl12_12,
inference(sat_conversion,[],[f264]) ).
cnf(s23,plain,
( ~ spl12_14
| ~ spl12_18
| spl12_20 ),
inference(sat_conversion,[],[f268]) ).
cnf(s24,plain,
( ~ spl12_11
| ~ spl12_20
| spl12_21
| spl12_22 ),
inference(sat_conversion,[],[f281]) ).
cnf(s25,plain,
( spl12_9
| spl12_12
| ~ spl12_22
| ~ spl12_23 ),
inference(sat_conversion,[],[f289]) ).
cnf(s26,plain,
( ~ spl12_11
| ~ spl12_14
| ~ spl12_16
| ~ spl12_17
| ~ spl12_19
| spl12_23 ),
inference(sat_conversion,[],[f298]) ).
cnf(s31,plain,
( ~ spl12_14
| ~ spl12_16
| ~ spl12_17
| ~ spl12_21 ),
inference(sat_conversion,[],[f336]) ).
cnf(s32,plain,
( ~ spl12_13
| spl12_17 ),
inference(rat,[],[s15,s17]) ).
cnf(s33,plain,
( ~ spl12_13
| spl12_16 ),
inference(rat,[],[s14,s17]) ).
cnf(s34,plain,
( ~ spl12_13
| spl12_14 ),
inference(rat,[],[s13,s17]) ).
cnf(s35,plain,
( ~ spl12_8
| ~ spl12_10
| ~ spl12_11
| spl12_13 ),
inference(rat,[],[s12,s22]) ).
cnf(s36,plain,
spl12_11,
inference(rat,[],[s11,s9]) ).
cnf(s37,plain,
spl12_10,
inference(rat,[],[s10,s9]) ).
cnf(s39,plain,
spl12_8,
inference(rat,[],[s8,s9]) ).
cnf(s40,plain,
spl12_13,
inference(rat,[],[s35,s37,s36,s39]) ).
cnf(s41,plain,
spl12_18,
inference(rat,[],[s19,s40]) ).
cnf(s42,plain,
spl12_17,
inference(rat,[],[s32,s40]) ).
cnf(s43,plain,
spl12_16,
inference(rat,[],[s33,s40]) ).
cnf(s44,plain,
spl12_14,
inference(rat,[],[s34,s40]) ).
cnf(s45,plain,
spl12_19,
inference(rat,[],[s18,s41,s43]) ).
cnf(s46,plain,
~ spl12_21,
inference(rat,[],[s31,s43,s42,s44]) ).
cnf(s47,plain,
spl12_23,
inference(rat,[],[s26,s43,s45,s42,s36,s44]) ).
cnf(s48,plain,
spl12_20,
inference(rat,[],[s23,s41,s44]) ).
cnf(s49,plain,
~ spl12_22,
inference(rat,[],[s25,s9,s22,s47]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s24,s46,s36,s49,s48]) ).
fof(f337,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRA002+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sun Sep 27 08:45:05 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 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
% 3.25/1.21 % (2070987)Detected formulas, will run a generic FOF schedule.
% 3.25/1.21 % (2070996)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=3255563140:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.25/1.21 % (2070999)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=626126195:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.25/1.21 % (2070995)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=453978394:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.25/1.21 % (2071000)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2503172292:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.25/1.21 % (2070997)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=1945700524:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.25/1.21 % (2071001)dis-21_1_sil=8000:lcm=predicate:random_seed=3341099232: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)
% 3.25/1.21 % (2070998)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3955202618:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.25/1.21 % (2070998)Instruction limit reached!
% 3.25/1.21 % (2070998)------------------------------
% 3.25/1.21 % (2070998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2070998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2070998)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2070998)Termination reason: Instruction limit
% 3.25/1.21 % (2070998)Termination phase: Saturation
% 3.25/1.21 % (2070998)Time elapsed: 0.036 s
% 3.25/1.21 % (2070998)Peak memory usage: 89 MB
% 3.25/1.21 % (2070998)Instructions burned: 111 (million)
% 3.25/1.21 % (2071001)Instruction limit reached!
% 3.25/1.21 % (2071001)------------------------------
% 3.25/1.21 % (2071001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071001)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071001)Termination reason: Instruction limit
% 3.25/1.21 % (2071001)Termination phase: Saturation
% 3.25/1.21 % (2071001)Time elapsed: 0.037 s
% 3.25/1.21 % (2071001)Peak memory usage: 89 MB
% 3.25/1.21 % (2071001)Instructions burned: 132 (million)
% 3.25/1.21 % (2070999)Instruction limit reached!
% 3.25/1.21 % (2070999)------------------------------
% 3.25/1.21 % (2070999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2070999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2070999)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2070999)Termination reason: Instruction limit
% 3.25/1.21 % (2070999)Termination phase: Saturation
% 3.25/1.21 % (2070999)Time elapsed: 0.046 s
% 3.25/1.21 % (2070999)Peak memory usage: 88 MB
% 3.25/1.21 % (2070999)Instructions burned: 120 (million)
% 3.25/1.21 % (2071000)Instruction limit reached!
% 3.25/1.21 % (2071000)------------------------------
% 3.25/1.21 % (2071000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071000)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071000)Termination reason: Instruction limit
% 3.25/1.21 % (2071000)Termination phase: Saturation
% 3.25/1.21 % (2071000)Time elapsed: 0.049 s
% 3.25/1.21 % (2071000)Peak memory usage: 89 MB
% 3.25/1.21 % (2071000)Instructions burned: 139 (million)
% 3.25/1.21 % (2071009)lrs+10_1_sil=8000:sp=occurrence:random_seed=356679531:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.25/1.21 % (2071010)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1962668804:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 3.25/1.21 % (2071010)Refutation not found, incomplete strategy
% 3.25/1.21 % (2071010)------------------------------
% 3.25/1.21 % (2071010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071010)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071010)Termination reason: Refutation not found, incomplete strategy
% 3.25/1.21 % (2071010)Time elapsed: 0.001 s
% 3.25/1.21 % (2071010)Peak memory usage: 88 MB
% 3.25/1.21 % (2071010)Instructions burned: 1 (million)
% 3.25/1.21 % (2071011)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1726818776:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 3.25/1.21 % (2071012)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=1402947362:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 3.25/1.21 % (2071009)Instruction limit reached!
% 3.25/1.21 % (2071009)------------------------------
% 3.25/1.21 % (2071009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071009)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071009)Termination reason: Instruction limit
% 3.25/1.21 % (2071009)Termination phase: Saturation
% 3.25/1.21 % (2071009)Time elapsed: 0.091 s
% 3.25/1.21 % (2071009)Peak memory usage: 91 MB
% 3.25/1.21 % (2071009)Instructions burned: 286 (million)
% 3.25/1.21 % (2071012)Instruction limit reached!
% 3.25/1.21 % (2071012)------------------------------
% 3.25/1.21 % (2071012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071012)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071012)Termination reason: Instruction limit
% 3.25/1.21 % (2071012)Termination phase: Saturation
% 3.25/1.21 % (2071012)Time elapsed: 0.079 s
% 3.25/1.21 % (2071012)Peak memory usage: 90 MB
% 3.25/1.21 % (2071012)Instructions burned: 249 (million)
% 3.25/1.21 % (2071011)Instruction limit reached!
% 3.25/1.21 % (2071011)------------------------------
% 3.25/1.21 % (2071011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071011)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071011)Termination reason: Instruction limit
% 3.25/1.21 % (2071011)Termination phase: Saturation
% 3.25/1.21 % (2071011)Time elapsed: 0.110 s
% 3.25/1.21 % (2071011)Peak memory usage: 91 MB
% 3.25/1.21 % (2071011)Instructions burned: 328 (million)
% 3.25/1.21 % (2071010)------------------------------
% 3.25/1.21 % (2071010)------------------------------
% 3.25/1.21 % (2071017)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2242478228:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 3.25/1.21 % (2070996)First to succeed.
% 3.25/1.21 % (2070996)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2070987"
% 3.25/1.21 % (2070995)Also succeeded, but the first one will report.
% 3.25/1.21 % (2071018)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3407395158:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 3.25/1.21 % (2071019)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1274648451:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 3.25/1.21 % (2071020)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=888264895:i=127:av=off:fsr=off:sup=off_2995 on theBenchmark for (2995ds/127Mi)
% 3.25/1.21 % (2071017)Instruction limit reached!
% 3.25/1.21 % (2071017)------------------------------
% 3.25/1.21 % (2071017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071017)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071017)Termination reason: Instruction limit
% 3.25/1.21 % (2071017)Termination phase: Saturation
% 3.25/1.21 % (2071017)Time elapsed: 0.089 s
% 3.25/1.21 % (2071017)Peak memory usage: 89 MB
% 3.25/1.21 % (2071017)Instructions burned: 296 (million)
% 3.25/1.21 % (2071019)Instruction limit reached!
% 3.25/1.21 % (2071019)------------------------------
% 3.25/1.21 % (2071019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071019)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071019)Termination reason: Instruction limit
% 3.25/1.21 % (2071019)Termination phase: Saturation
% 3.25/1.21 % (2071019)Time elapsed: 0.042 s
% 3.25/1.21 % (2071019)Peak memory usage: 89 MB
% 3.25/1.21 % (2071019)Instructions burned: 115 (million)
% 3.25/1.21 % (2071020)Instruction limit reached!
% 3.25/1.21 % (2071020)------------------------------
% 3.25/1.21 % (2071020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.21 % (2071020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.21 % (2071020)CaDiCaL version: 2.1.3
% 3.25/1.21 % (2071020)Termination reason: Instruction limit
% 3.25/1.21 % (2071020)Termination phase: Saturation
% 3.25/1.21 % (2071020)Time elapsed: 0.034 s
% 3.25/1.21 % (2071020)Peak memory usage: 89 MB
% 3.25/1.21 % (2071020)Instructions burned: 128 (million)
% 3.25/1.21 % (2070996)Refutation found. Thanks to Tanya!
% 3.25/1.21 % SZS status Theorem for theBenchmark
% 3.25/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 4.89/1.31 % (2070996)------------------------------
% 4.89/1.31 % (2070996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.89/1.31 % (2070996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.31 % (2070996)CaDiCaL version: 2.1.3
% 4.89/1.31 % (2070996)Termination reason: Refutation
% 4.89/1.31 % (2070996)Time elapsed: 0.361 s
% 4.89/1.31 % (2070996)Peak memory usage: 127 MB
% 4.89/1.31 % (2070996)Instructions burned: 954 (million)
% 4.89/1.31 % (2070996)------------------------------
% 4.89/1.31 % (2070996)------------------------------
% 4.89/1.31 % (2070987)Success in time 0.666 s
% 4.89/1.31 % Vampire exiting
%------------------------------------------------------------------------------