%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU213+1 : TPTP v9.3.1. Released v3.3.0.
% 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 4.13s 1.52s
% Output : Refutation 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 138 ( 14 unt; 6 def)
% Number of atoms : 582 ( 48 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 764 ( 320 ~; 333 |; 74 &)
% ( 22 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 189 ( 0 sgn 159 !; 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(f15,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f20,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(f36,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(f37,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)],[f36]) ).
fof(f44,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,[],[f37]) ).
fof(f45,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,[],[f44]) ).
fof(f50,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(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 = 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(f53,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,[],[f52]) ).
fof(f58,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f59,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f58]) ).
fof(f65,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f66,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f65]) ).
fof(f68,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,[],[f45]) ).
fof(f69,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,[],[f68]) ).
fof(f70,plain,
( ( ~ in(sK0,relation_dom(sK2))
| ~ in(apply(sK2,sK0),relation_dom(sK1))
| ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) )
& ( ( in(sK0,relation_dom(sK2))
& in(apply(sK2,sK0),relation_dom(sK1)) )
| in(sK0,relation_dom(relation_composition(sK2,sK1))) )
& relation(sK2)
& function(sK2)
& relation(sK1)
& function(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f69]) ).
fof(f71,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,[],[f50]) ).
fof(f72,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,[],[f71]) ).
fof(f73,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))],[f72]) ).
fof(f74,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(f75,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,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f75]) ).
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,[],[f53]) ).
fof(f82,plain,
function(sK1),
inference(cnf_transformation,[],[f70]) ).
fof(f83,plain,
relation(sK1),
inference(cnf_transformation,[],[f70]) ).
fof(f84,plain,
function(sK2),
inference(cnf_transformation,[],[f70]) ).
fof(f85,plain,
relation(sK2),
inference(cnf_transformation,[],[f70]) ).
fof(f86,plain,
( in(apply(sK2,sK0),relation_dom(sK1))
| in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f87,plain,
( in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f88,plain,
( ~ in(sK0,relation_dom(sK2))
| ~ in(apply(sK2,sK0),relation_dom(sK1))
| ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f92,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,[],[f73]) ).
fof(f93,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,[],[f73]) ).
fof(f94,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,[],[f73]) ).
fof(f98,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f104,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(f105,plain,
! [X2,X0,X1] :
( ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f112,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f128,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f130,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,[],[f94]) ).
fof(f131,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,[],[f93]) ).
fof(f132,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,[],[f92]) ).
fof(f133,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f99]) ).
fof(f134,plain,
! [X0,X5] :
( ~ in(X5,relation_dom(X0))
| in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f98]) ).
fof(f135,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f104]) ).
fof(f138,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,[],[f132,f128]) ).
fof(f139,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,[],[f131,f128]) ).
fof(f140,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,[],[f130,f128]) ).
fof(f142,definition,
( spl14_1
<=> in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f143,plain,
( ~ in(sK0,relation_dom(relation_composition(sK2,sK1)))
| spl14_1 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f144,plain,
( in(sK0,relation_dom(relation_composition(sK2,sK1)))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f146,definition,
( spl14_2
<=> in(apply(sK2,sK0),relation_dom(sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f147,plain,
( ~ in(apply(sK2,sK0),relation_dom(sK1))
| spl14_2 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( in(apply(sK2,sK0),relation_dom(sK1))
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f86,f146,f142]) ).
fof(f151,definition,
( spl14_3
<=> in(sK0,relation_dom(sK2)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f152,plain,
( ~ in(sK0,relation_dom(sK2))
| spl14_3 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( in(sK0,relation_dom(sK2))
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl14_1
| spl14_3 ),
inference(avatar_split_clause,[],[f87,f151,f142]) ).
fof(f155,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f88,f151,f146,f142]) ).
fof(f175,plain,
( in(ordered_pair(sK0,apply(sK2,sK0)),sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl14_3 ),
inference(resolution,[],[f135,f153]) ).
fof(f176,plain,
( in(ordered_pair(apply(sK2,sK0),apply(sK1,apply(sK2,sK0))),sK1)
| ~ relation(sK1)
| ~ function(sK1)
| ~ spl14_2 ),
inference(resolution,[],[f135,f148]) ).
fof(f177,plain,
( in(ordered_pair(apply(sK2,sK0),apply(sK1,apply(sK2,sK0))),sK1)
| ~ function(sK1)
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f176,f83]) ).
fof(f178,plain,
( in(ordered_pair(sK0,apply(sK2,sK0)),sK2)
| ~ function(sK2)
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f175,f85]) ).
fof(f179,plain,
( in(ordered_pair(apply(sK2,sK0),apply(sK1,apply(sK2,sK0))),sK1)
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f177,f82]) ).
fof(f180,plain,
( in(ordered_pair(sK0,apply(sK2,sK0)),sK2)
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f178,f84]) ).
fof(f185,plain,
( ! [X0] :
( ~ in(ordered_pair(sK0,X0),sK2)
| apply(sK2,sK0) = X0
| ~ relation(sK2)
| ~ function(sK2) )
| ~ spl14_3 ),
inference(resolution,[],[f105,f153]) ).
fof(f188,plain,
( ! [X0] :
( ~ in(ordered_pair(sK0,X0),sK2)
| apply(sK2,sK0) = X0
| ~ function(sK2) )
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f185,f85]) ).
fof(f190,plain,
( ! [X0] :
( ~ in(ordered_pair(sK0,X0),sK2)
| apply(sK2,sK0) = X0 )
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f188,f84]) ).
fof(f216,plain,
( ! [X0,X1] :
( in(ordered_pair(sK0,X0),relation_composition(sK2,X1))
| ~ in(ordered_pair(apply(sK2,sK0),X0),X1)
| ~ relation(X1)
| ~ relation(sK2) )
| ~ spl14_3 ),
inference(resolution,[],[f140,f180]) ).
fof(f217,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(apply(sK2,sK0),X0),X1)
| in(ordered_pair(sK0,X0),relation_composition(sK2,X1))
| ~ relation(X1) )
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f216,f85]) ).
fof(f276,plain,
( in(ordered_pair(sK0,apply(sK1,apply(sK2,sK0))),relation_composition(sK2,sK1))
| ~ relation(sK1)
| ~ spl14_2
| ~ spl14_3 ),
inference(resolution,[],[f217,f179]) ).
fof(f278,plain,
( in(ordered_pair(sK0,apply(sK1,apply(sK2,sK0))),relation_composition(sK2,sK1))
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f276,f83]) ).
fof(f292,plain,
( in(sK0,relation_dom(relation_composition(sK2,sK1)))
| ~ relation(relation_composition(sK2,sK1))
| ~ spl14_2
| ~ spl14_3 ),
inference(resolution,[],[f278,f133]) ).
fof(f298,plain,
( ~ relation(relation_composition(sK2,sK1))
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f292,f143]) ).
fof(f300,definition,
( spl14_4
<=> relation(relation_composition(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f301,plain,
( relation(relation_composition(sK2,sK1))
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f302,plain,
( ~ relation(relation_composition(sK2,sK1))
| spl14_4 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f309,plain,
( ~ spl14_4
| spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f298,f151,f146,f142,f300]) ).
fof(f320,plain,
( ~ relation(sK2)
| ~ relation(sK1)
| spl14_4 ),
inference(resolution,[],[f302,f128]) ).
fof(f324,plain,
( ~ relation(sK1)
| spl14_4 ),
inference(forward_subsumption_resolution,[],[f320,f85]) ).
fof(f325,plain,
( $false
| spl14_4 ),
inference(forward_subsumption_resolution,[],[f324,f83]) ).
fof(f326,plain,
spl14_4,
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f327,plain,
( ! [X0] :
( ~ in(ordered_pair(sK0,X0),relation_composition(sK2,sK1))
| apply(relation_composition(sK2,sK1),sK0) = X0
| ~ relation(relation_composition(sK2,sK1))
| ~ function(relation_composition(sK2,sK1)) )
| ~ spl14_1 ),
inference(resolution,[],[f144,f105]) ).
fof(f329,plain,
( in(ordered_pair(sK0,sK9(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1))
| ~ relation(relation_composition(sK2,sK1))
| ~ spl14_1 ),
inference(resolution,[],[f144,f134]) ).
fof(f332,plain,
( in(ordered_pair(sK0,sK9(relation_composition(sK2,sK1),sK0)),relation_composition(sK2,sK1))
| ~ spl14_1
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f329,f301]) ).
fof(f334,plain,
( ! [X0] :
( ~ in(ordered_pair(sK0,X0),relation_composition(sK2,sK1))
| apply(relation_composition(sK2,sK1),sK0) = X0
| ~ function(relation_composition(sK2,sK1)) )
| ~ spl14_1
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f327,f301]) ).
fof(f336,definition,
( spl14_6
<=> function(relation_composition(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
fof(f338,plain,
( ~ function(relation_composition(sK2,sK1))
| spl14_6 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f345,definition,
( spl14_8
<=> ! [X0] :
( ~ in(ordered_pair(sK0,X0),relation_composition(sK2,sK1))
| apply(relation_composition(sK2,sK1),sK0) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
fof(f346,plain,
( ! [X0] :
( ~ in(ordered_pair(sK0,X0),relation_composition(sK2,sK1))
| apply(relation_composition(sK2,sK1),sK0) = X0 )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f347,plain,
( ~ spl14_6
| spl14_8
| ~ spl14_1
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f334,f300,f142,f345,f336]) ).
fof(f348,plain,
( ~ relation(sK2)
| ~ function(sK2)
| ~ relation(sK1)
| ~ function(sK1)
| spl14_6 ),
inference(resolution,[],[f338,f112]) ).
fof(f350,plain,
( ~ function(sK2)
| ~ relation(sK1)
| ~ function(sK1)
| spl14_6 ),
inference(forward_subsumption_resolution,[],[f348,f85]) ).
fof(f351,plain,
( ~ relation(sK1)
| ~ function(sK1)
| spl14_6 ),
inference(forward_subsumption_resolution,[],[f350,f84]) ).
fof(f352,plain,
( ~ function(sK1)
| spl14_6 ),
inference(forward_subsumption_resolution,[],[f351,f83]) ).
fof(f353,plain,
( $false
| spl14_6 ),
inference(forward_subsumption_resolution,[],[f352,f82]) ).
fof(f354,plain,
spl14_6,
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f359,plain,
( in(ordered_pair(sK0,sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0))),sK2)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ spl14_1
| ~ spl14_4 ),
inference(resolution,[],[f332,f139]) ).
fof(f360,plain,
( in(ordered_pair(sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0)),sK9(relation_composition(sK2,sK1),sK0)),sK1)
| ~ relation(sK1)
| ~ relation(sK2)
| ~ spl14_1
| ~ spl14_4 ),
inference(resolution,[],[f332,f138]) ).
fof(f367,plain,
( in(ordered_pair(sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0)),sK9(relation_composition(sK2,sK1),sK0)),sK1)
| ~ relation(sK2)
| ~ spl14_1
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f360,f83]) ).
fof(f368,plain,
( in(ordered_pair(sK0,sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0))),sK2)
| ~ relation(sK2)
| ~ spl14_1
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f359,f83]) ).
fof(f369,plain,
( in(ordered_pair(sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0)),sK9(relation_composition(sK2,sK1),sK0)),sK1)
| ~ spl14_1
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f367,f85]) ).
fof(f370,plain,
( in(ordered_pair(sK0,sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0))),sK2)
| ~ spl14_1
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f368,f85]) ).
fof(f386,plain,
( apply(relation_composition(sK2,sK1),sK0) = sK9(relation_composition(sK2,sK1),sK0)
| ~ spl14_1
| ~ spl14_4
| ~ spl14_8 ),
inference(resolution,[],[f346,f332]) ).
fof(f418,plain,
( apply(sK2,sK0) = sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0))
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4 ),
inference(resolution,[],[f370,f190]) ).
fof(f420,plain,
( in(sK0,relation_dom(sK2))
| ~ relation(sK2)
| ~ spl14_1
| ~ spl14_4 ),
inference(resolution,[],[f370,f133]) ).
fof(f425,plain,
( apply(sK2,sK0) = sK6(sK2,sK1,sK0,apply(relation_composition(sK2,sK1),sK0))
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_8 ),
inference(forward_demodulation,[],[f418,f386]) ).
fof(f485,plain,
( in(sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0)),relation_dom(sK1))
| ~ relation(sK1)
| ~ spl14_1
| ~ spl14_4 ),
inference(resolution,[],[f369,f133]) ).
fof(f489,plain,
( in(sK6(sK2,sK1,sK0,sK9(relation_composition(sK2,sK1),sK0)),relation_dom(sK1))
| ~ spl14_1
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f485,f83]) ).
fof(f492,plain,
( in(sK6(sK2,sK1,sK0,apply(relation_composition(sK2,sK1),sK0)),relation_dom(sK1))
| ~ spl14_1
| ~ spl14_4
| ~ spl14_8 ),
inference(forward_demodulation,[],[f489,f386]) ).
fof(f494,plain,
( in(apply(sK2,sK0),relation_dom(sK1))
| ~ spl14_1
| ~ spl14_3
| ~ spl14_4
| ~ spl14_8 ),
inference(forward_demodulation,[],[f492,f425]) ).
fof(f496,plain,
( $false
| ~ spl14_1
| spl14_2
| ~ spl14_3
| ~ spl14_4
| ~ spl14_8 ),
inference(forward_subsumption_resolution,[],[f494,f147]) ).
fof(f497,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_3
| ~ spl14_4
| ~ spl14_8 ),
inference(avatar_contradiction_clause,[],[f496]) ).
fof(f503,plain,
( ~ relation(sK2)
| ~ spl14_1
| spl14_3
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f420,f152]) ).
fof(f507,plain,
( $false
| ~ spl14_1
| spl14_3
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f503,f85]) ).
fof(f508,plain,
( ~ spl14_1
| spl14_3
| ~ spl14_4 ),
inference(avatar_contradiction_clause,[],[f507]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f149]) ).
cnf(s2,plain,
( spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f154]) ).
cnf(s3,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(sat_conversion,[],[f155]) ).
cnf(s5,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f309]) ).
cnf(s6,plain,
spl14_4,
inference(sat_conversion,[],[f326]) ).
cnf(s8,plain,
( ~ spl14_1
| ~ spl14_4
| ~ spl14_6
| spl14_8 ),
inference(sat_conversion,[],[f347]) ).
cnf(s9,plain,
spl14_6,
inference(sat_conversion,[],[f354]) ).
cnf(s10,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_3
| ~ spl14_4
| ~ spl14_8 ),
inference(sat_conversion,[],[f497]) ).
cnf(s11,plain,
( ~ spl14_1
| spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f508]) ).
cnf(s13,plain,
( ~ spl14_1
| ~ spl14_4
| spl14_8 ),
inference(rat,[],[s8,s9]) ).
cnf(s15,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(rat,[],[s5,s6]) ).
cnf(s17,plain,
spl14_1,
inference(rat,[],[s15,s1,s2]) ).
cnf(s18,plain,
spl14_3,
inference(rat,[],[s11,s6,s17]) ).
cnf(s19,plain,
spl14_8,
inference(rat,[],[s13,s6,s17]) ).
cnf(s21,plain,
~ spl14_2,
inference(rat,[],[s3,s18,s17]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s10,s19,s6,s18,s17,s21]) ).
fof(f512,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU213+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:06:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 4.13/1.52 % (1177173)Detected formulas, will run a generic FOF schedule.
% 4.13/1.52 % (1177182)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1233069736:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.13/1.52 % (1177180)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=2897262602:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.13/1.52 % (1177182)Instruction limit reached!
% 4.13/1.52 % (1177182)------------------------------
% 4.13/1.52 % (1177182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177182)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177182)Termination reason: Instruction limit
% 4.13/1.52 % (1177182)Termination phase: Saturation
% 4.13/1.52 % (1177182)Time elapsed: 0.035 s
% 4.13/1.52 % (1177182)Peak memory usage: 88 MB
% 4.13/1.52 % (1177182)Instructions burned: 121 (million)
% 4.13/1.52 % (1177178)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=2228470692:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.13/1.52 % (1177179)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=3647548666:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.13/1.52 % (1177181)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4150296263:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.13/1.52 % (1177181)Refutation not found, incomplete strategy
% 4.13/1.52 % (1177181)------------------------------
% 4.13/1.52 % (1177181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177181)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177181)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.52 % (1177181)Time elapsed: 0.003 s
% 4.13/1.52 % (1177181)Peak memory usage: 88 MB
% 4.13/1.52 % (1177181)Instructions burned: 2 (million)
% 4.13/1.52 % (1177184)dis-21_1_sil=8000:lcm=predicate:random_seed=1272093193: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)
% 4.13/1.52 % (1177183)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1834083902:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.13/1.52 % (1177183)Instruction limit reached!
% 4.13/1.52 % (1177183)------------------------------
% 4.13/1.52 % (1177183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177183)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177183)Termination reason: Instruction limit
% 4.13/1.52 % (1177183)Termination phase: Saturation
% 4.13/1.52 % (1177183)Time elapsed: 0.048 s
% 4.13/1.52 % (1177183)Peak memory usage: 90 MB
% 4.13/1.52 % (1177183)Instructions burned: 142 (million)
% 4.13/1.52 % (1177184)Instruction limit reached!
% 4.13/1.52 % (1177184)------------------------------
% 4.13/1.52 % (1177184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177184)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177184)Termination reason: Instruction limit
% 4.13/1.52 % (1177184)Termination phase: Saturation
% 4.13/1.52 % (1177184)Time elapsed: 0.082 s
% 4.13/1.52 % (1177184)Peak memory usage: 90 MB
% 4.13/1.52 % (1177184)Instructions burned: 130 (million)
% 4.13/1.52 % (1177190)lrs+10_1_sil=8000:sp=occurrence:random_seed=95235430:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.13/1.52 % (1177193)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2806806003:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.13/1.52 % (1177193)Instruction limit reached!
% 4.13/1.52 % (1177193)------------------------------
% 4.13/1.52 % (1177193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177193)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177193)Termination reason: Instruction limit
% 4.13/1.52 % (1177193)Termination phase: Saturation
% 4.13/1.52 % (1177193)Time elapsed: 0.040 s
% 4.13/1.52 % (1177193)Peak memory usage: 90 MB
% 4.13/1.52 % (1177193)Instructions burned: 157 (million)
% 4.13/1.52 % (1177194)lrs+1011_1_sil=32000:sp=occurrence:random_seed=887310064:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.13/1.52 % (1177181)------------------------------
% 4.13/1.52 % (1177181)------------------------------
% 4.13/1.52 % (1177194)First to succeed.
% 4.13/1.52 % (1177194)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1177173"
% 4.13/1.52 % (1177197)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=1545365796:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.13/1.52 % (1177190)Instruction limit reached!
% 4.13/1.52 % (1177190)------------------------------
% 4.13/1.52 % (1177190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177190)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177190)Termination reason: Instruction limit
% 4.13/1.52 % (1177190)Termination phase: Saturation
% 4.13/1.52 % (1177190)Time elapsed: 0.166 s
% 4.13/1.52 % (1177190)Peak memory usage: 91 MB
% 4.13/1.52 % (1177190)Instructions burned: 286 (million)
% 4.13/1.52 % (1177197)Instruction limit reached!
% 4.13/1.52 % (1177197)------------------------------
% 4.13/1.52 % (1177197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177197)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177197)Termination reason: Instruction limit
% 4.13/1.52 % (1177197)Termination phase: Saturation
% 4.13/1.52 % (1177197)Time elapsed: 0.068 s
% 4.13/1.52 % (1177197)Peak memory usage: 93 MB
% 4.13/1.52 % (1177197)Instructions burned: 249 (million)
% 4.13/1.52 % (1177199)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3487844364:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.13/1.52 % (1177199)Refutation not found, incomplete strategy
% 4.13/1.52 % (1177199)------------------------------
% 4.13/1.52 % (1177199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177199)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177199)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.52 % (1177199)Time elapsed: 0.003 s
% 4.13/1.52 % (1177199)Peak memory usage: 89 MB
% 4.13/1.52 % (1177199)Instructions burned: 3 (million)
% 4.13/1.52 % (1177201)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1179875255:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.13/1.52 % (1177202)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4001868736:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.13/1.52 % (1177202)Instruction limit reached!
% 4.13/1.52 % (1177202)------------------------------
% 4.13/1.52 % (1177202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.52 % (1177202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.52 % (1177202)CaDiCaL version: 2.1.3
% 4.13/1.52 % (1177202)Termination reason: Instruction limit
% 4.13/1.52 % (1177202)Termination phase: Saturation
% 4.13/1.52 % (1177202)Time elapsed: 0.042 s
% 4.13/1.52 % (1177202)Peak memory usage: 90 MB
% 4.13/1.52 % (1177202)Instructions burned: 116 (million)
% 4.13/1.52 % (1177194)Refutation found. Thanks to Tanya!
% 4.13/1.52 % SZS status Theorem for theBenchmark
% 4.13/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.31/1.71 % (1177194)------------------------------
% 5.31/1.71 % (1177194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.71 % (1177194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.71 % (1177194)CaDiCaL version: 2.1.3
% 5.31/1.71 % (1177194)Termination reason: Refutation
% 5.31/1.71 % (1177194)Time elapsed: 0.018 s
% 5.31/1.71 % (1177194)Peak memory usage: 90 MB
% 5.31/1.71 % (1177194)Instructions burned: 25 (million)
% 5.31/1.71 % (1177194)------------------------------
% 5.31/1.71 % (1177194)------------------------------
% 5.31/1.71 % (1177173)Success in time 0.66 s
% 5.31/1.71 % Vampire exiting
%------------------------------------------------------------------------------