%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP023+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 : Sun Sep 27 07:38:15 AM UTC 2026
% Result : Theorem 66.69s 9.05s
% Output : CNFRefutation 66.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 118 ( 55 ~; 47 |; 1 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 45 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ne_ty_2Erealax_2Ereal,axiom,
ne('ty$u2Erealax$u2Ereal') ).
fof(mem_c_2Ereal__topology_2Eball,axiom,
mem('c$u2Ereal$u$utopology$u2Eball',arr('ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),arr('ty$u2Erealax$u2Ereal',bool))) ).
fof(mem_c_2Epair_2E_2C,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> mem('c$u2Epair$u2E$u2C'(X0,X1),arr(X0,arr(X1,'ty$u2Epair$u2Eprod'(X0,X1)))) ) ) ).
fof(mem_c_2Ereal__topology_2Ecball,axiom,
mem('c$u2Ereal$u$utopology$u2Ecball',arr('ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),arr('ty$u2Erealax$u2Ereal',bool))) ).
fof(conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
! [X0] :
( mem(X0,'ty$u2Erealax$u2Ereal')
=> ! [X1] :
( mem(X1,'ty$u2Erealax$u2Ereal')
=> p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'('ty$u2Erealax$u2Ereal'),ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))),ap('c$u2Ereal$u$utopology$u2Ecball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)))) ) ) ).
fof(conj_thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
! [X0] :
( mem(X0,arr('ty$u2Erealax$u2Ereal',bool))
=> ! [X1] :
( mem(X1,arr('ty$u2Erealax$u2Ereal',bool))
=> ( ( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'('ty$u2Erealax$u2Ereal'),X0),X1))
& p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',X1)) )
=> p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',X0)) ) ) ) ).
fof(conj_thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
! [X0] :
( mem(X0,'ty$u2Erealax$u2Ereal')
=> ! [X1] :
( mem(X1,'ty$u2Erealax$u2Ereal')
=> p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Ecball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)))) ) ) ).
fof(ap_tp,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ) ).
fof(conj_thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [X0] :
( mem(X0,'ty$u2Erealax$u2Ereal')
=> ! [X1] :
( mem(X1,'ty$u2Erealax$u2Ereal')
=> p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( mem(X0,'ty$u2Erealax$u2Ereal')
=> ! [X1] :
( mem(X1,'ty$u2Erealax$u2Ereal')
=> p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)))) ) ),
inference(negate_conjecture,[status(cth)],[conj_thm_2Ereal__topology_2EBOUNDED__BALL]) ).
cnf(c6,plain,
ne('ty$u2Erealax$u2Ereal'),
inference(clausification,[status(esa)],[ne_ty_2Erealax_2Ereal]) ).
cnf(c8,plain,
mem('c$u2Ereal$u$utopology$u2Eball',arr('ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),arr('ty$u2Erealax$u2Ereal',bool))),
inference(clausification,[status(esa)],[mem_c_2Ereal__topology_2Eball]) ).
cnf(c10,plain,
( mem('c$u2Epair$u2E$u2C'(X0,X1),arr(X0,arr(X1,'ty$u2Epair$u2Eprod'(X0,X1))))
| ~ ne(X1)
| ~ ne(X0) ),
inference(clausification,[status(esa)],[mem_c_2Epair_2E_2C]) ).
cnf(c11,plain,
mem('c$u2Ereal$u$utopology$u2Ecball',arr('ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),arr('ty$u2Erealax$u2Ereal',bool))),
inference(clausification,[status(esa)],[mem_c_2Ereal__topology_2Ecball]) ).
cnf(c89,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'('ty$u2Erealax$u2Ereal'),ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))),ap('c$u2Ereal$u$utopology$u2Ecball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))))
| ~ mem(X1,'ty$u2Erealax$u2Ereal')
| ~ mem(X0,'ty$u2Erealax$u2Ereal') ),
inference(clausification,[status(esa)],[conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL]) ).
cnf(c90,plain,
( ~ mem(X0,arr('ty$u2Erealax$u2Ereal',bool))
| p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',X1))
| ~ mem(X1,arr('ty$u2Erealax$u2Ereal',bool))
| ~ p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'('ty$u2Erealax$u2Ereal'),X1),X0))
| ~ p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',X0)) ),
inference(clausification,[status(esa)],[conj_thm_2Ereal__topology_2EBOUNDED__SUBSET]) ).
cnf(c91,plain,
( p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Ecball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))))
| ~ mem(X1,'ty$u2Erealax$u2Ereal')
| ~ mem(X0,'ty$u2Erealax$u2Ereal') ),
inference(clausification,[status(esa)],[conj_thm_2Ereal__topology_2EBOUNDED__CBALL]) ).
cnf(c227,plain,
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(clausification,[status(esa)],[ap_tp]) ).
cnf(c236,plain,
mem(sK114,'ty$u2Erealax$u2Ereal'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c237,plain,
mem(sK115,'ty$u2Erealax$u2Ereal'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c238,plain,
~ p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),sK114),sK115)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ mem(X0,'ty$u2Erealax$u2Ereal')
| ~ mem(X1,'ty$u2Erealax$u2Ereal')
| p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))))
| ~ p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Ecball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))))
| ~ mem(ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)),arr('ty$u2Erealax$u2Ereal',bool))
| ~ mem(ap('c$u2Ereal$u$utopology$u2Ecball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)),arr('ty$u2Erealax$u2Ereal',bool)) ),
inference(resolution,[status(thm)],[c90,c89]) ).
cnf(d1,plain,
( p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))))
| ~ mem(ap('c$u2Ereal$u$utopology$u2Ecball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)),arr('ty$u2Erealax$u2Ereal',bool))
| ~ mem(ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)),arr('ty$u2Erealax$u2Ereal',bool))
| ~ mem(X0,'ty$u2Erealax$u2Ereal')
| ~ mem(X1,'ty$u2Erealax$u2Ereal')
| ~ mem(X1,'ty$u2Erealax$u2Ereal')
| ~ mem(X0,'ty$u2Erealax$u2Ereal') ),
inference(resolution,[status(thm)],[c91,d0]) ).
cnf(d2,plain,
( mem(ap('c$u2Ereal$u$utopology$u2Ecball',X0),arr('ty$u2Erealax$u2Ereal',bool))
| ~ mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(resolution,[status(thm)],[c227,c11]) ).
cnf(d3,plain,
( p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))))
| ~ mem(ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1)),arr('ty$u2Erealax$u2Ereal',bool))
| ~ mem(X0,'ty$u2Erealax$u2Ereal')
| ~ mem(X1,'ty$u2Erealax$u2Ereal')
| ~ mem(ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1),'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( mem(ap('c$u2Ereal$u$utopology$u2Eball',X0),arr('ty$u2Erealax$u2Ereal',bool))
| ~ mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(resolution,[status(thm)],[c227,c8]) ).
cnf(d5,plain,
( p(ap('c$u2Ereal$u$utopology$u2Ebounded$u$udef',ap('c$u2Ereal$u$utopology$u2Eball',ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1))))
| ~ mem(ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1),'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'))
| ~ mem(X0,'ty$u2Erealax$u2Ereal')
| ~ mem(X1,'ty$u2Erealax$u2Ereal')
| ~ mem(ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),X0),X1),'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ mem(ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),sK114),sK115),'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'))
| ~ mem(sK114,'ty$u2Erealax$u2Ereal')
| ~ mem(sK115,'ty$u2Erealax$u2Ereal') ),
inference(resolution,[status(thm)],[d5,c238]) ).
cnf(d7,plain,
( ~ mem(sK115,'ty$u2Erealax$u2Ereal')
| ~ mem(ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),sK114),sK115),'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(resolution,[status(thm)],[c236,d6]) ).
cnf(d8,plain,
~ mem(ap(ap('c$u2Epair$u2E$u2C'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'),sK114),sK115),'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')),
inference(resolution,[status(thm)],[c237,d7]) ).
cnf(d9,plain,
( ~ ne(X2)
| ~ ne(X1)
| mem(ap('c$u2Epair$u2E$u2C'(X1,X2),X0),arr(X2,'ty$u2Epair$u2Eprod'(X1,X2)))
| ~ mem(X0,X1) ),
inference(resolution,[status(thm)],[c227,c10]) ).
cnf(d10,plain,
( mem(ap(ap('c$u2Epair$u2E$u2C'(X1,X2),X0),X3),'ty$u2Epair$u2Eprod'(X1,X2))
| ~ mem(X3,X2)
| ~ ne(X1)
| ~ ne(X2)
| ~ mem(X0,X1) ),
inference(resolution,[status(thm)],[d9,c227]) ).
cnf(d11,plain,
( ~ ne('ty$u2Erealax$u2Ereal')
| ~ ne('ty$u2Erealax$u2Ereal')
| ~ mem(sK114,'ty$u2Erealax$u2Ereal')
| ~ mem(sK115,'ty$u2Erealax$u2Ereal') ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ~ ne('ty$u2Erealax$u2Ereal')
| ~ mem(sK115,'ty$u2Erealax$u2Ereal') ),
inference(resolution,[status(thm)],[c236,d11]) ).
cnf(d13,plain,
~ ne('ty$u2Erealax$u2Ereal'),
inference(resolution,[status(thm)],[c237,d12]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c6,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP023+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n019.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 17:35:03 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.69/9.05 % SZS status Theorem for theBenchmark.p
% 66.69/9.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------