%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP023+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 11:28:53 AM UTC 2026
% Result : Theorem 2.71s 1.28s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 11 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 204 ( 100 ~; 84 |; 5 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 67 ( 65 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
fof(f13,axiom,
ne(ty_2Erealax_2Ereal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ne_ty_2Erealax_2Ereal) ).
fof(f15,axiom,
mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ereal__topology_2Eball) ).
fof(f17,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epair_2E_2C) ).
fof(f18,axiom,
mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ereal__topology_2Ecball) ).
fof(f46,axiom,
! [X0] :
( mem(X0,ty_2Erealax_2Ereal)
=> ! [X1] :
( mem(X1,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
fof(f47,axiom,
! [X0] :
( mem(X0,arr(ty_2Erealax_2Ereal,bool))
=> ! [X1] :
( mem(X1,arr(ty_2Erealax_2Ereal,bool))
=> ( ( p(ap(c_2Ereal__topology_2Ebounded__def,X1))
& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1)) )
=> p(ap(c_2Ereal__topology_2Ebounded__def,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
fof(f48,axiom,
! [X0] :
( mem(X0,ty_2Erealax_2Ereal)
=> ! [X1] :
( mem(X1,ty_2Erealax_2Ereal)
=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__CBALL) ).
fof(f59,conjecture,
! [X0] :
( mem(X0,ty_2Erealax_2Ereal)
=> ! [X1] :
( mem(X1,ty_2Erealax_2Ereal)
=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__BALL) ).
fof(f60,negated_conjecture,
~ ! [X0] :
( mem(X0,ty_2Erealax_2Ereal)
=> ! [X1] :
( mem(X1,ty_2Erealax_2Ereal)
=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)))) ) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
& mem(X1,ty_2Erealax_2Ereal) )
& mem(X0,ty_2Erealax_2Ereal) ),
inference(ennf_transformation,[],[f60]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal) )
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(ennf_transformation,[],[f46]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1))))
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( p(ap(c_2Ereal__topology_2Ebounded__def,X0))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool)) )
| ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( p(ap(c_2Ereal__topology_2Ebounded__def,X0))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool)) )
| ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
inference(flattening,[],[f108]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal) )
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(ennf_transformation,[],[f48]) ).
fof(f134,plain,
( ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17))))
& mem(sK17,ty_2Erealax_2Ereal)
& mem(sK16,ty_2Erealax_2Ereal) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f78]) ).
fof(f195,plain,
mem(sK16,ty_2Erealax_2Ereal),
inference(cnf_transformation,[],[f134]) ).
fof(f196,plain,
mem(sK17,ty_2Erealax_2Ereal),
inference(cnf_transformation,[],[f134]) ).
fof(f197,plain,
~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17)))),
inference(cnf_transformation,[],[f134]) ).
fof(f346,plain,
! [X2,X3,X0,X1] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f347,plain,
ne(ty_2Erealax_2Ereal),
inference(cnf_transformation,[],[f13]) ).
fof(f348,plain,
! [X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(cnf_transformation,[],[f104]) ).
fof(f349,plain,
mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
inference(cnf_transformation,[],[f15]) ).
fof(f350,plain,
! [X0,X1] :
( mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1))))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f358,plain,
! [X0,X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
| p(ap(c_2Ereal__topology_2Ebounded__def,X0))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f360,plain,
! [X0,X1] :
( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(cnf_transformation,[],[f111]) ).
fof(f361,plain,
mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
inference(cnf_transformation,[],[f18]) ).
fof(f527,plain,
! [X0,X1] :
( ~ mem(X0,ty_2Erealax_2Ereal)
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X0))))
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X0))))
| ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X0)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X0)),arr(ty_2Erealax_2Ereal,bool)) ),
inference(resolution,[],[f348,f358]) ).
fof(f528,plain,
! [X0,X1] :
( ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X0)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X1,ty_2Erealax_2Ereal)
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X0))))
| ~ mem(X0,ty_2Erealax_2Ereal)
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X1),X0)),arr(ty_2Erealax_2Ereal,bool)) ),
inference(forward_subsumption_resolution,[],[f527,f360]) ).
fof(f529,plain,
! [X2,X0,X1] :
( ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal)
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1),X2)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X2,arr(ty_2Erealax_2Ereal,bool))) ),
inference(resolution,[],[f528,f346]) ).
fof(f530,plain,
! [X2,X3,X0,X1] :
( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal)
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1),X2)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X2,arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1),X3)
| ~ mem(c_2Ereal__topology_2Eball,arr(X3,arr(ty_2Erealax_2Ereal,bool))) ),
inference(resolution,[],[f529,f346]) ).
fof(f531,plain,
! [X0,X1] :
( ~ mem(sK17,ty_2Erealax_2Ereal)
| ~ mem(sK16,ty_2Erealax_2Ereal)
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17),X0)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X0,arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17),X1)
| ~ mem(c_2Ereal__topology_2Eball,arr(X1,arr(ty_2Erealax_2Ereal,bool))) ),
inference(resolution,[],[f530,f197]) ).
fof(f532,plain,
! [X0,X1] :
( ~ mem(sK16,ty_2Erealax_2Ereal)
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17),X0)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X0,arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17),X1)
| ~ mem(c_2Ereal__topology_2Eball,arr(X1,arr(ty_2Erealax_2Ereal,bool))) ),
inference(forward_subsumption_resolution,[],[f531,f196]) ).
fof(f533,plain,
! [X0,X1] :
( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17),X1)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X0,arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17),X0)
| ~ mem(c_2Ereal__topology_2Eball,arr(X1,arr(ty_2Erealax_2Ereal,bool))) ),
inference(forward_subsumption_resolution,[],[f532,f195]) ).
fof(f535,plain,
! [X0] :
( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),sK17),X0)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X0,arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(c_2Ereal__topology_2Eball,arr(X0,arr(ty_2Erealax_2Ereal,bool))) ),
inference(factoring,[],[f533]) ).
fof(f536,plain,
! [X0,X1] :
( ~ mem(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK16),arr(X1,X0))
| ~ mem(c_2Ereal__topology_2Eball,arr(X0,arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(sK17,X1)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X0,arr(ty_2Erealax_2Ereal,bool))) ),
inference(resolution,[],[f535,f346]) ).
fof(f537,plain,
! [X2,X0,X1] :
( ~ mem(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(X2,arr(X1,X0)))
| ~ mem(sK17,X1)
| ~ mem(c_2Ereal__topology_2Ecball,arr(X0,arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(sK16,X2)
| ~ mem(c_2Ereal__topology_2Eball,arr(X0,arr(ty_2Erealax_2Ereal,bool))) ),
inference(resolution,[],[f536,f346]) ).
fof(f539,plain,
( ~ mem(sK17,ty_2Erealax_2Ereal)
| ~ mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(sK16,ty_2Erealax_2Ereal)
| ~ mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ ne(ty_2Erealax_2Ereal)
| ~ ne(ty_2Erealax_2Ereal) ),
inference(resolution,[],[f537,f350]) ).
fof(f540,plain,
( ~ mem(sK17,ty_2Erealax_2Ereal)
| ~ mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(sK16,ty_2Erealax_2Ereal)
| ~ mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ ne(ty_2Erealax_2Ereal) ),
inference(duplicate_literal_removal,[],[f539]) ).
fof(f541,plain,
( ~ mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ mem(sK16,ty_2Erealax_2Ereal)
| ~ mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ ne(ty_2Erealax_2Ereal) ),
inference(forward_subsumption_resolution,[],[f540,f196]) ).
fof(f542,plain,
( ~ mem(sK16,ty_2Erealax_2Ereal)
| ~ mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ ne(ty_2Erealax_2Ereal) ),
inference(forward_subsumption_resolution,[],[f541,f361]) ).
fof(f543,plain,
( ~ mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))
| ~ ne(ty_2Erealax_2Ereal) ),
inference(forward_subsumption_resolution,[],[f542,f195]) ).
fof(f544,plain,
~ ne(ty_2Erealax_2Ereal),
inference(forward_subsumption_resolution,[],[f543,f349]) ).
fof(f545,plain,
$false,
inference(forward_subsumption_resolution,[],[f544,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 12:09:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.71/1.28 % (3407363)Detected formulas, will run a generic FOF schedule.
% 2.71/1.28 % (3407371)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=17760413:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.28 % (3407371)Refutation not found, incomplete strategy
% 2.71/1.28 % (3407371)------------------------------
% 2.71/1.28 % (3407371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.28 % (3407371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.28 % (3407371)CaDiCaL version: 2.1.3
% 2.71/1.28 % (3407371)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.28 % (3407371)Time elapsed: 0.004 s
% 2.71/1.28 % (3407371)Peak memory usage: 88 MB
% 2.71/1.28 % (3407371)Instructions burned: 12 (million)
% 2.71/1.28 % (3407369)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=3430844666:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.28 % (3407372)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3089726542:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.28 % (3407370)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=2888948235:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.28 % (3407368)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=3183682309:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.28 % (3407374)dis-21_1_sil=8000:lcm=predicate:random_seed=95322837: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)
% 2.71/1.28 % (3407373)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2577988648:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.28 % (3407372)First to succeed.
% 2.71/1.28 % (3407372)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3407363"
% 2.71/1.28 % (3407374)Instruction limit reached!
% 2.71/1.28 % (3407374)------------------------------
% 2.71/1.28 % (3407374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.28 % (3407374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.28 % (3407374)CaDiCaL version: 2.1.3
% 2.71/1.28 % (3407374)Termination reason: Instruction limit
% 2.71/1.28 % (3407374)Termination phase: Saturation
% 2.71/1.28 % (3407374)Time elapsed: 0.076 s
% 2.71/1.28 % (3407374)Peak memory usage: 90 MB
% 2.71/1.28 % (3407374)Instructions burned: 130 (million)
% 2.71/1.28 % (3407371)------------------------------
% 2.71/1.28 % (3407371)------------------------------
% 2.71/1.28 % (3407373)Instruction limit reached!
% 2.71/1.28 % (3407373)------------------------------
% 2.71/1.28 % (3407373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.28 % (3407373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.28 % (3407373)CaDiCaL version: 2.1.3
% 2.71/1.28 % (3407373)Termination reason: Instruction limit
% 2.71/1.28 % (3407373)Termination phase: Saturation
% 2.71/1.28 % (3407373)Time elapsed: 0.098 s
% 2.71/1.28 % (3407373)Peak memory usage: 90 MB
% 2.71/1.28 % (3407373)Instructions burned: 140 (million)
% 2.71/1.28 % (3407384)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4043499458:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.71/1.28 % (3407382)lrs+10_1_sil=8000:sp=occurrence:random_seed=3415538129:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.71/1.28 % (3407382)Also succeeded, but the first one will report.
% 2.71/1.28 % (3407372)Refutation found. Thanks to Tanya!
% 2.71/1.28 % SZS status Theorem for theBenchmark
% 2.71/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.48 % (3407372)------------------------------
% 3.69/1.48 % (3407372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3407372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3407372)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3407372)Termination reason: Refutation
% 3.69/1.48 % (3407372)Time elapsed: 0.007 s
% 3.69/1.48 % (3407372)Peak memory usage: 88 MB
% 3.69/1.48 % (3407372)Instructions burned: 10 (million)
% 3.69/1.48 % (3407372)------------------------------
% 3.69/1.48 % (3407372)------------------------------
% 3.69/1.48 % (3407363)Success in time 0.443 s
% 3.69/1.48 % Vampire exiting
%------------------------------------------------------------------------------