%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP023+1 : 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 : n017.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 07:38:14 AM UTC 2026
% Result : Theorem 41.19s 13.94s
% Output : CNFRefutation 41.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 29 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 6 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
! [X0,X1] :
( ( p(s('tyop$u2Emin$u2Ebool',X0))
<=> p(s('tyop$u2Emin$u2Ebool',X1)) )
=> s('tyop$u2Emin$u2Ebool',X0) = s('tyop$u2Emin$u2Ebool',X1) ) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')) ).
fof(thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
! [X0,X1] : p(s('tyop$u2Emin$u2Ebool','c$u2Epred$u$uset$u2ESUBSET$u2E2'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1))))),s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Ecball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))) ).
fof(thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
! [X0,X1] :
( ( p(s('tyop$u2Emin$u2Ebool','c$u2Epred$u$uset$u2ESUBSET$u2E2'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X0),s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X1))))
& p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X1)))) )
=> p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X0)))) ) ).
fof(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
! [X0,X1] : p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Ecball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))) ).
fof(thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [X0,X1] : p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))),
inference(negate_conjecture,[status(cth)],[thm_2Ereal__topology_2EBOUNDED__BALL]) ).
cnf(c2,plain,
( s('tyop$u2Emin$u2Ebool',X0) = s('tyop$u2Emin$u2Ebool',X1)
| p(s('tyop$u2Emin$u2Ebool',X1))
| p(s('tyop$u2Emin$u2Ebool',X0)) ),
inference(clausification,[status(esa)],[reserved_2Eho_2Eboolext]) ).
cnf(c6,plain,
~ p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')),
inference(clausification,[status(esa)],[reserved_2Eho_2Enotfalse]) ).
cnf(c109,plain,
p(s('tyop$u2Emin$u2Ebool','c$u2Epred$u$uset$u2ESUBSET$u2E2'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1))))),s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Ecball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))),
inference(clausification,[status(esa)],[thm_2Ereal__topology_2EBALL__SUBSET__CBALL]) ).
cnf(c110,plain,
( p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X1))))
| ~ p(s('tyop$u2Emin$u2Ebool','c$u2Epred$u$uset$u2ESUBSET$u2E2'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X1),s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X0))))
| ~ p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),X0)))) ),
inference(clausification,[status(esa)],[thm_2Ereal__topology_2EBOUNDED__SUBSET]) ).
cnf(c111,plain,
p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Ecball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))),
inference(clausification,[status(esa)],[thm_2Ereal__topology_2EBOUNDED__CBALL]) ).
cnf(c239,plain,
~ p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',sK126),s('tyop$u2Erealax$u2Ereal',sK127)))))))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1))))))))
| ~ p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Ecball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))) ),
inference(resolution,[status(thm)],[c110,c109]) ).
cnf(d1,plain,
p(s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',X0),s('tyop$u2Erealax$u2Ereal',X1)))))))),
inference(resolution,[status(thm)],[c111,d0]) ).
cnf(d2,plain,
( p(s('tyop$u2Emin$u2Ebool',X0))
| s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',sK126),s('tyop$u2Erealax$u2Ereal',sK127))))))) = s('tyop$u2Emin$u2Ebool',X0) ),
inference(resolution,[status(thm)],[c2,c239]) ).
cnf(d3,plain,
s('tyop$u2Emin$u2Ebool','c$u2Ereal$u$utopology$u2Ebounded$u$udef$u2E1'(s('tyop$u2Emin$u2Efun'('tyop$u2Erealax$u2Ereal','tyop$u2Emin$u2Ebool'),'c$u2Ereal$u$utopology$u2Eball$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Epair$u2E$u2C$u2E2'(s('tyop$u2Erealax$u2Ereal',sK126),s('tyop$u2Erealax$u2Ereal',sK127))))))) = s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0'),
inference(resolution,[status(thm)],[c6,d2]) ).
cnf(d4,plain,
p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c6,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP023+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 17:29:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.19/13.94 % SZS status Theorem for theBenchmark.p
% 41.19/13.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------