%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP020+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 11:28:36 AM UTC 2026
% Result : Theorem 2.32s 1.16s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 227 ( 107 ~; 90 |; 17 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 83 ( 72 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
fof(f25,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EUNIV) ).
fof(f26,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ne(ty_2Epair_2Eprod(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Epair_2Eprod) ).
fof(f27,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECROSS) ).
fof(f29,axiom,
ne(ty_2Enum_2Enum),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Enum_2Enum) ).
fof(f51,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ? [X4] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
<=> ? [X5] :
( mem(X5,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EBIJ__SYM) ).
fof(f62,axiom,
? [X0] :
( mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ) ).
fof(f63,conjecture,
? [X0] :
( mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
fof(f64,negated_conjecture,
~ ? [X0] :
( mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f82,plain,
! [X0] :
( ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f118,plain,
! [X0] :
( mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ne(ty_2Epair_2Eprod(X0,X1))
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool))))
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ? [X4] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
<=> ? [X5] :
( mem(X5,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f236,plain,
( mem(sK38,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK38),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(X0,sK38)],[f62]) ).
fof(f237,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( ? [X4] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
| ! [X5] :
( ~ mem(X5,arr(X1,X0))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
& ( ? [X5] :
( mem(X5,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) )
| ! [X4] :
( ~ mem(X4,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( ? [X4] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
| ! [X5] :
( ~ mem(X5,arr(X1,X0))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
& ( ? [X6] :
( mem(X6,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X6),X3),X2)) )
| ! [X7] :
( ~ mem(X7,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3)) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( ( mem(sK39(X0,X1,X2,X3),arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),sK39(X0,X1,X2,X3)),X2),X3)) )
| ! [X5] :
( ~ mem(X5,arr(X1,X0))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
& ( ( mem(sK40(X0,X1,X2,X3),arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),sK40(X0,X1,X2,X3)),X3),X2)) )
| ! [X7] :
( ~ mem(X7,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3)) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39,sK40]),skolemize(X4,sK39(X0,X1,X2,X3)),skolemize(X6,sK40(X0,X1,X2,X3))],[f238]) ).
fof(f240,plain,
! [X0] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
| ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(cnf_transformation,[],[f82]) ).
fof(f443,plain,
! [X2,X3,X0,X1] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f444,plain,
p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK38),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),
inference(cnf_transformation,[],[f236]) ).
fof(f445,plain,
mem(sK38,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)),
inference(cnf_transformation,[],[f236]) ).
fof(f446,plain,
! [X0] :
( mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f447,plain,
! [X0,X1] :
( ne(ty_2Epair_2Eprod(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f448,plain,
! [X0,X1] :
( mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool))))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f449,plain,
! [X2,X3,X0,X1,X7] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),sK40(X0,X1,X2,X3)),X3),X2))
| ~ mem(X7,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,bool))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f450,plain,
! [X2,X3,X0,X1,X7] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3))
| ~ mem(X7,arr(X0,X1))
| mem(sK40(X0,X1,X2,X3),arr(X1,X0))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,bool))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f454,plain,
ne(ty_2Enum_2Enum),
inference(cnf_transformation,[],[f29]) ).
fof(f738,plain,
! [X0] :
( ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ ne(ty_2Enum_2Enum)
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ mem(sK40(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum,ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(resolution,[],[f449,f240]) ).
fof(f745,plain,
! [X0] :
( ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ ne(ty_2Enum_2Enum)
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
inference(forward_subsumption_resolution,[],[f738,f450]) ).
fof(f746,plain,
! [X0] :
( ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ ne(ty_2Enum_2Enum)
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
inference(forward_subsumption_resolution,[],[f745,f446]) ).
fof(f747,plain,
! [X0] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
inference(forward_subsumption_resolution,[],[f746,f454]) ).
fof(f748,plain,
( ~ mem(sK38,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
inference(resolution,[],[f747,f444]) ).
fof(f752,plain,
( ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
inference(forward_subsumption_resolution,[],[f748,f445]) ).
fof(f764,plain,
! [X0] :
( ~ mem(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),X0)
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
inference(resolution,[],[f752,f443]) ).
fof(f765,plain,
! [X0,X1] :
( ~ mem(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(X1,arr(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))))
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),X1)
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),X0) ),
inference(resolution,[],[f764,f443]) ).
fof(f786,plain,
( ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ ne(ty_2Enum_2Enum)
| ~ ne(ty_2Enum_2Enum) ),
inference(resolution,[],[f765,f448]) ).
fof(f787,plain,
( ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ ne(ty_2Enum_2Enum) ),
inference(duplicate_literal_removal,[],[f786]) ).
fof(f788,plain,
( ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ ne(ty_2Enum_2Enum) ),
inference(forward_subsumption_resolution,[],[f787,f446]) ).
fof(f789,plain,
~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),
inference(forward_subsumption_resolution,[],[f788,f454]) ).
fof(f810,plain,
( ~ ne(ty_2Enum_2Enum)
| ~ ne(ty_2Enum_2Enum) ),
inference(resolution,[],[f789,f447]) ).
fof(f811,plain,
~ ne(ty_2Enum_2Enum),
inference(duplicate_literal_removal,[],[f810]) ).
fof(f812,plain,
$false,
inference(forward_subsumption_resolution,[],[f811,f454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP020+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n006.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 12:05:41 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.32/1.16 % (2864027)Detected formulas, will run a generic FOF schedule.
% 2.32/1.16 % (2864036)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3407132875:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.32/1.16 % (2864036)First to succeed.
% 2.32/1.16 % (2864036)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2864027"
% 2.32/1.16 % (2864033)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=3023035423:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.32/1.16 % (2864035)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3356320398:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.32/1.16 % (2864034)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=2556871634:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.32/1.16 % (2864032)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=4224701465:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.32/1.16 % (2864038)dis-21_1_sil=8000:lcm=predicate:random_seed=3205829780: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)
% 2.32/1.16 % (2864037)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1135064291:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.32/1.16 % (2864035)Refutation not found, incomplete strategy
% 2.32/1.16 % (2864035)------------------------------
% 2.32/1.16 % (2864035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.16 % (2864035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.16 % (2864035)CaDiCaL version: 2.1.3
% 2.32/1.16 % (2864035)Termination reason: Refutation not found, incomplete strategy
% 2.32/1.16 % (2864035)Time elapsed: 0.018 s
% 2.32/1.16 % (2864035)Peak memory usage: 89 MB
% 2.32/1.16 % (2864035)Instructions burned: 32 (million)
% 2.32/1.16 % (2864037)Also succeeded, but the first one will report.
% 2.32/1.16 % (2864038)Instruction limit reached!
% 2.32/1.16 % (2864038)------------------------------
% 2.32/1.16 % (2864038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.16 % (2864038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.16 % (2864038)CaDiCaL version: 2.1.3
% 2.32/1.16 % (2864038)Termination reason: Instruction limit
% 2.32/1.16 % (2864038)Termination phase: Saturation
% 2.32/1.16 % (2864038)Time elapsed: 0.065 s
% 2.32/1.16 % (2864038)Peak memory usage: 90 MB
% 2.32/1.16 % (2864038)Instructions burned: 130 (million)
% 2.32/1.16 % (2864036)Refutation found. Thanks to Tanya!
% 2.32/1.16 % SZS status Theorem for theBenchmark
% 2.32/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.36 % (2864036)------------------------------
% 2.74/1.36 % (2864036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.36 % (2864036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.36 % (2864036)CaDiCaL version: 2.1.3
% 2.74/1.36 % (2864036)Termination reason: Refutation
% 2.74/1.36 % (2864036)Time elapsed: 0.009 s
% 2.74/1.36 % (2864036)Peak memory usage: 88 MB
% 2.74/1.36 % (2864036)Instructions burned: 27 (million)
% 2.74/1.36 % (2864036)------------------------------
% 2.74/1.36 % (2864036)------------------------------
% 2.74/1.36 % (2864027)Success in time 0.307 s
% 2.74/1.36 % Vampire exiting
%------------------------------------------------------------------------------