%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU213+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:47:46 PM UTC 2026
% Result : Theorem 2.94s 1.34s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 142 ( 16 unt; 8 def)
% Number of atoms : 564 ( 46 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 719 ( 297 ~; 309 |; 74 &)
% ( 24 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 185 ( 0 sgn 155 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f57]) ).
fof(f66,plain,
? [X0,X1] :
( ? [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<~> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f67,plain,
? [X0,X1] :
( ? [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<~> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f66]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f79]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK3(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK4(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK3(X0,X1,X2),sK5(X0,X1,X2)),X0)
& in(ordered_pair(sK5(X0,X1,X2),sK4(X0,X1,X2)),X1) )
| in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X4,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X10,sK6(X0,X1,X7,X8))],[f82]) ).
fof(f93,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1))) )
& ( ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) )
| in(X0,relation_dom(relation_composition(X2,X1))) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(nnf_transformation,[],[f67]) ).
fof(f94,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1))) )
& ( ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) )
| in(X0,relation_dom(relation_composition(X2,X1))) )
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
( ( ~ in(sK16,relation_dom(sK18))
| ~ in(apply(sK18,sK16),relation_dom(sK17))
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17))) )
& ( ( in(sK16,relation_dom(sK18))
& in(apply(sK18,sK16),relation_dom(sK17)) )
| in(sK16,relation_dom(relation_composition(sK18,sK17))) )
& relation(sK18)
& function(sK18)
& relation(sK17)
& function(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f94]) ).
fof(f102,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f103,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f104,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f105,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f109,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f110,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f111,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f115,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f150,plain,
function(sK17),
inference(cnf_transformation,[],[f95]) ).
fof(f151,plain,
relation(sK17),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
function(sK18),
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
relation(sK18),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
( in(apply(sK18,sK16),relation_dom(sK17))
| in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
( in(sK16,relation_dom(sK18))
| in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f156,plain,
( ~ in(sK16,relation_dom(sK18))
| ~ in(apply(sK18,sK16),relation_dom(sK17))
| ~ in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f164,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f102]) ).
fof(f167,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f168,plain,
! [X0,X5] :
( ~ in(X5,relation_dom(X0))
| in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f104]) ).
fof(f169,plain,
! [X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f111]) ).
fof(f170,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f110]) ).
fof(f171,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f109]) ).
fof(f173,definition,
( spl19_1
<=> in(sK16,relation_dom(relation_composition(sK18,sK17))) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f174,plain,
( ~ in(sK16,relation_dom(relation_composition(sK18,sK17)))
| spl19_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f175,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f177,definition,
( spl19_2
<=> in(apply(sK18,sK16),relation_dom(sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f179,plain,
( in(apply(sK18,sK16),relation_dom(sK17))
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f154,f177,f173]) ).
fof(f182,definition,
( spl19_3
<=> in(sK16,relation_dom(sK18)) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f184,plain,
( in(sK16,relation_dom(sK18))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f185,plain,
( spl19_1
| spl19_3 ),
inference(avatar_split_clause,[],[f155,f182,f173]) ).
fof(f186,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3 ),
inference(avatar_split_clause,[],[f156,f182,f177,f173]) ).
fof(f224,plain,
( in(ordered_pair(sK16,apply(sK18,sK16)),sK18)
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl19_3 ),
inference(resolution,[],[f164,f184]) ).
fof(f225,plain,
( in(ordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16))),sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_2 ),
inference(resolution,[],[f164,f179]) ).
fof(f226,plain,
( in(ordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16))),sK17)
| ~ function(sK17)
| ~ spl19_2 ),
inference(forward_subsumption_resolution,[],[f225,f151]) ).
fof(f227,plain,
( in(ordered_pair(sK16,apply(sK18,sK16)),sK18)
| ~ function(sK18)
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f224,f153]) ).
fof(f228,plain,
( in(ordered_pair(apply(sK18,sK16),apply(sK17,apply(sK18,sK16))),sK17)
| ~ spl19_2 ),
inference(forward_subsumption_resolution,[],[f226,f150]) ).
fof(f229,plain,
( in(ordered_pair(sK16,apply(sK18,sK16)),sK18)
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f227,f152]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f103,f167]) ).
fof(f255,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f170,f115]) ).
fof(f263,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f171,f115]) ).
fof(f269,plain,
! [X0,X1,X8,X9,X7] :
( ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ in(ordered_pair(X9,X8),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f169,f115]) ).
fof(f273,plain,
( ! [X0,X1] :
( in(ordered_pair(sK16,X0),relation_composition(sK18,X1))
| ~ in(ordered_pair(apply(sK18,sK16),X0),X1)
| ~ relation(X1)
| ~ relation(sK18) )
| ~ spl19_3 ),
inference(resolution,[],[f269,f229]) ).
fof(f276,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(apply(sK18,sK16),X0),X1)
| in(ordered_pair(sK16,X0),relation_composition(sK18,X1))
| ~ relation(X1) )
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f273,f153]) ).
fof(f283,plain,
( in(ordered_pair(sK16,apply(sK17,apply(sK18,sK16))),relation_composition(sK18,sK17))
| ~ relation(sK17)
| ~ spl19_2
| ~ spl19_3 ),
inference(resolution,[],[f276,f228]) ).
fof(f285,plain,
( in(ordered_pair(sK16,apply(sK17,apply(sK18,sK16))),relation_composition(sK18,sK17))
| ~ spl19_2
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f283,f151]) ).
fof(f307,plain,
( in(sK16,relation_dom(relation_composition(sK18,sK17)))
| ~ relation(relation_composition(sK18,sK17))
| ~ spl19_2
| ~ spl19_3 ),
inference(resolution,[],[f285,f167]) ).
fof(f312,plain,
( ~ relation(relation_composition(sK18,sK17))
| spl19_1
| ~ spl19_2
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f307,f174]) ).
fof(f314,definition,
( spl19_4
<=> function(relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f315,plain,
( function(relation_composition(sK18,sK17))
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f316,plain,
( ~ function(relation_composition(sK18,sK17))
| spl19_4 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f318,definition,
( spl19_5
<=> relation(relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f320,plain,
( ~ relation(relation_composition(sK18,sK17))
| spl19_5 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f332,plain,
( ~ spl19_5
| spl19_1
| ~ spl19_2
| ~ spl19_3 ),
inference(avatar_split_clause,[],[f312,f182,f177,f173,f318]) ).
fof(f358,plain,
( ~ relation(sK18)
| ~ relation(sK17)
| spl19_5 ),
inference(resolution,[],[f320,f115]) ).
fof(f360,plain,
( ~ relation(sK17)
| spl19_5 ),
inference(forward_subsumption_resolution,[],[f358,f153]) ).
fof(f361,plain,
( $false
| spl19_5 ),
inference(forward_subsumption_resolution,[],[f360,f151]) ).
fof(f362,plain,
spl19_5,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f363,plain,
( in(ordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17))
| ~ spl19_1 ),
inference(resolution,[],[f175,f164]) ).
fof(f364,plain,
( in(ordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ spl19_1 ),
inference(resolution,[],[f175,f168]) ).
fof(f368,definition,
( spl19_8
<=> in(ordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_8])],[avatar_definition]) ).
fof(f370,plain,
( in(ordered_pair(sK16,sK2(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17))
| ~ spl19_8 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f371,plain,
( ~ spl19_5
| spl19_8
| ~ spl19_1 ),
inference(avatar_split_clause,[],[f364,f173,f368,f318]) ).
fof(f373,definition,
( spl19_9
<=> in(ordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition]) ).
fof(f375,plain,
( in(ordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17))
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f376,plain,
( ~ spl19_4
| ~ spl19_5
| spl19_9
| ~ spl19_1 ),
inference(avatar_split_clause,[],[f363,f173,f373,f318,f314]) ).
fof(f377,plain,
( ~ relation(sK18)
| ~ function(sK18)
| ~ relation(sK17)
| ~ function(sK17)
| spl19_4 ),
inference(resolution,[],[f316,f121]) ).
fof(f379,plain,
( ~ function(sK18)
| ~ relation(sK17)
| ~ function(sK17)
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f377,f153]) ).
fof(f380,plain,
( ~ relation(sK17)
| ~ function(sK17)
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f379,f152]) ).
fof(f381,plain,
( ~ function(sK17)
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f380,f151]) ).
fof(f382,plain,
( $false
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f381,f150]) ).
fof(f383,plain,
spl19_4,
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f389,plain,
( in(ordered_pair(sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)),sK2(relation_composition(sK18,sK17),sK16)),sK17)
| ~ relation(sK17)
| ~ relation(sK18)
| ~ spl19_8 ),
inference(resolution,[],[f370,f263]) ).
fof(f392,plain,
( apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16)
| ~ relation(relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17))
| ~ spl19_8 ),
inference(resolution,[],[f370,f234]) ).
fof(f396,plain,
( apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16)
| ~ relation(relation_composition(sK18,sK17))
| ~ spl19_4
| ~ spl19_8 ),
inference(forward_subsumption_resolution,[],[f392,f315]) ).
fof(f402,plain,
( in(ordered_pair(sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)),sK2(relation_composition(sK18,sK17),sK16)),sK17)
| ~ relation(sK18)
| ~ spl19_8 ),
inference(forward_subsumption_resolution,[],[f389,f151]) ).
fof(f404,definition,
( spl19_11
<=> apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
fof(f406,plain,
( apply(relation_composition(sK18,sK17),sK16) = sK2(relation_composition(sK18,sK17),sK16)
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f407,plain,
( ~ spl19_5
| spl19_11
| ~ spl19_4
| ~ spl19_8 ),
inference(avatar_split_clause,[],[f396,f368,f314,f404,f318]) ).
fof(f409,plain,
( in(ordered_pair(sK6(sK18,sK17,sK16,sK2(relation_composition(sK18,sK17),sK16)),sK2(relation_composition(sK18,sK17),sK16)),sK17)
| ~ spl19_8 ),
inference(forward_subsumption_resolution,[],[f402,f153]) ).
fof(f411,plain,
( in(ordered_pair(sK16,sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))),sK18)
| ~ relation(sK17)
| ~ relation(sK18)
| ~ spl19_9 ),
inference(resolution,[],[f375,f255]) ).
fof(f419,plain,
( in(ordered_pair(sK16,sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))),sK18)
| ~ relation(sK18)
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f411,f151]) ).
fof(f421,plain,
( in(ordered_pair(sK16,sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))),sK18)
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f419,f153]) ).
fof(f449,plain,
( apply(sK18,sK16) = sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl19_9 ),
inference(resolution,[],[f421,f234]) ).
fof(f450,plain,
( in(sK16,relation_dom(sK18))
| ~ relation(sK18)
| ~ spl19_9 ),
inference(resolution,[],[f421,f167]) ).
fof(f454,plain,
( apply(sK18,sK16) = sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ function(sK18)
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f449,f153]) ).
fof(f456,plain,
( apply(sK18,sK16) = sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f454,f152]) ).
fof(f481,plain,
( in(ordered_pair(sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)),apply(relation_composition(sK18,sK17),sK16)),sK17)
| ~ spl19_8
| ~ spl19_11 ),
inference(forward_demodulation,[],[f409,f406]) ).
fof(f482,plain,
( in(ordered_pair(apply(sK18,sK16),apply(relation_composition(sK18,sK17),sK16)),sK17)
| ~ spl19_8
| ~ spl19_9
| ~ spl19_11 ),
inference(forward_demodulation,[],[f481,f456]) ).
fof(f486,plain,
( in(apply(sK18,sK16),relation_dom(sK17))
| ~ relation(sK17)
| ~ spl19_8
| ~ spl19_9
| ~ spl19_11 ),
inference(resolution,[],[f482,f167]) ).
fof(f499,plain,
( in(sK16,relation_dom(sK18))
| ~ spl19_9 ),
inference(forward_subsumption_resolution,[],[f450,f153]) ).
fof(f501,plain,
( in(apply(sK18,sK16),relation_dom(sK17))
| ~ spl19_8
| ~ spl19_9
| ~ spl19_11 ),
inference(forward_subsumption_resolution,[],[f486,f151]) ).
fof(f502,plain,
( spl19_3
| ~ spl19_9 ),
inference(avatar_split_clause,[],[f499,f373,f182]) ).
fof(f504,plain,
( spl19_2
| ~ spl19_8
| ~ spl19_9
| ~ spl19_11 ),
inference(avatar_split_clause,[],[f501,f404,f373,f368,f177]) ).
cnf(s1,plain,
( spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f180]) ).
cnf(s2,plain,
( spl19_1
| spl19_3 ),
inference(sat_conversion,[],[f185]) ).
cnf(s3,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3 ),
inference(sat_conversion,[],[f186]) ).
cnf(s6,plain,
( spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_5 ),
inference(sat_conversion,[],[f332]) ).
cnf(s7,plain,
spl19_5,
inference(sat_conversion,[],[f362]) ).
cnf(s8,plain,
( ~ spl19_1
| ~ spl19_5
| spl19_8 ),
inference(sat_conversion,[],[f371]) ).
cnf(s9,plain,
( ~ spl19_1
| ~ spl19_4
| ~ spl19_5
| spl19_9 ),
inference(sat_conversion,[],[f376]) ).
cnf(s10,plain,
spl19_4,
inference(sat_conversion,[],[f383]) ).
cnf(s12,plain,
( ~ spl19_4
| ~ spl19_5
| ~ spl19_8
| spl19_11 ),
inference(sat_conversion,[],[f407]) ).
cnf(s15,plain,
( spl19_3
| ~ spl19_9 ),
inference(sat_conversion,[],[f502]) ).
cnf(s16,plain,
( spl19_2
| ~ spl19_8
| ~ spl19_9
| ~ spl19_11 ),
inference(sat_conversion,[],[f504]) ).
cnf(s18,plain,
( ~ spl19_1
| ~ spl19_5
| spl19_9 ),
inference(rat,[],[s9,s10]) ).
cnf(s19,plain,
( spl19_1
| ~ spl19_2
| ~ spl19_3 ),
inference(rat,[],[s6,s7]) ).
cnf(s22,plain,
spl19_1,
inference(rat,[],[s19,s1,s2]) ).
cnf(s23,plain,
spl19_9,
inference(rat,[],[s18,s7,s22]) ).
cnf(s24,plain,
spl19_8,
inference(rat,[],[s8,s7,s22]) ).
cnf(s25,plain,
spl19_3,
inference(rat,[],[s15,s23]) ).
cnf(s27,plain,
spl19_11,
inference(rat,[],[s12,s7,s10,s24]) ).
cnf(s28,plain,
spl19_2,
inference(rat,[],[s16,s27,s23,s24]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s3,s22,s25,s28]) ).
fof(f510,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU213+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 % Computer : n003.cluster.edu
% 0.12/0.43 % Model : x86_64 x86_64
% 0.12/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.43 % Memory : 8046.5625MB
% 0.12/0.43 % OS : Linux 6.8.0-71-generic
% 0.12/0.43 % CPULimit : 300
% 0.12/0.43 % WCLimit : 300
% 0.12/0.43 % DateTime : Mon Sep 28 04:06:27 UTC 2026
% 0.12/0.44 % CPUTime :
% 0.12/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.94/1.34 % (1176751)Detected formulas, will run a generic FOF schedule.
% 2.94/1.34 % (1176760)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2446658733:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.94/1.34 % (1176760)Instruction limit reached!
% 2.94/1.34 % (1176760)------------------------------
% 2.94/1.34 % (1176760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.34 % (1176760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.34 % (1176760)CaDiCaL version: 2.1.3
% 2.94/1.34 % (1176760)Termination reason: Instruction limit
% 2.94/1.34 % (1176760)Termination phase: Saturation
% 2.94/1.34 % (1176760)Time elapsed: 0.035 s
% 2.94/1.34 % (1176760)Peak memory usage: 88 MB
% 2.94/1.34 % (1176760)Instructions burned: 121 (million)
% 2.94/1.34 % (1176762)dis-21_1_sil=8000:lcm=predicate:random_seed=322351254: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)
% 2.94/1.34 % (1176757)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=3929744493:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.94/1.34 % (1176759)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2014360770:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.94/1.34 % (1176756)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=495068365:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.94/1.34 % (1176758)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=4081961967:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.94/1.34 % (1176759)Refutation not found, incomplete strategy
% 2.94/1.34 % (1176759)------------------------------
% 2.94/1.34 % (1176759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.34 % (1176759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.34 % (1176759)CaDiCaL version: 2.1.3
% 2.94/1.34 % (1176759)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.34 % (1176759)Time elapsed: 0.003 s
% 2.94/1.34 % (1176759)Peak memory usage: 88 MB
% 2.94/1.34 % (1176759)Instructions burned: 2 (million)
% 2.94/1.34 % (1176761)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=429367246:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.94/1.34 % (1176761)First to succeed.
% 2.94/1.34 % (1176761)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1176751"
% 2.94/1.34 % (1176764)lrs+10_1_sil=8000:sp=occurrence:random_seed=1952789369:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.94/1.34 % (1176762)Instruction limit reached!
% 2.94/1.34 % (1176762)------------------------------
% 2.94/1.34 % (1176762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.34 % (1176762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.34 % (1176762)CaDiCaL version: 2.1.3
% 2.94/1.34 % (1176762)Termination reason: Instruction limit
% 2.94/1.34 % (1176762)Termination phase: Saturation
% 2.94/1.34 % (1176762)Time elapsed: 0.083 s
% 2.94/1.34 % (1176762)Peak memory usage: 90 MB
% 2.94/1.34 % (1176762)Instructions burned: 129 (million)
% 2.94/1.34 % (1176764)Instruction limit reached!
% 2.94/1.34 % (1176764)------------------------------
% 2.94/1.34 % (1176764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.34 % (1176764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.34 % (1176764)CaDiCaL version: 2.1.3
% 2.94/1.34 % (1176764)Termination reason: Instruction limit
% 2.94/1.34 % (1176764)Termination phase: Saturation
% 2.94/1.34 % (1176764)Time elapsed: 0.089 s
% 2.94/1.34 % (1176764)Peak memory usage: 91 MB
% 2.94/1.34 % (1176764)Instructions burned: 286 (million)
% 2.94/1.34 % (1176772)lrs+10_1_sil=32000:urr=on:br=off:random_seed=755742109:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.94/1.34 % (1176759)------------------------------
% 2.94/1.34 % (1176759)------------------------------
% 2.94/1.34 % (1176773)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2697948218:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 2.94/1.34 % (1176773)Also succeeded, but the first one will report.
% 2.94/1.34 % (1176761)Refutation found. Thanks to Tanya!
% 2.94/1.34 % SZS status Theorem for theBenchmark
% 2.94/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.54 % (1176761)------------------------------
% 3.66/1.54 % (1176761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.54 % (1176761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.54 % (1176761)CaDiCaL version: 2.1.3
% 3.66/1.54 % (1176761)Termination reason: Refutation
% 3.66/1.54 % (1176761)Time elapsed: 0.016 s
% 3.66/1.54 % (1176761)Peak memory usage: 90 MB
% 3.66/1.54 % (1176761)Instructions burned: 21 (million)
% 3.66/1.54 % (1176761)------------------------------
% 3.66/1.54 % (1176761)------------------------------
% 3.66/1.54 % (1176751)Success in time 0.429 s
% 3.66/1.54 % Vampire exiting
%------------------------------------------------------------------------------