%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW362+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 09:11:45 AM UTC 2026
% Result : Theorem 98.06s 14.54s
% Output : CNFRefutation 98.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 40 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 8 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 51 ( 13 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_empty__subsetI,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X1,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool'))),X0)) ).
fof(fact_emptyE,axiom,
! [X0,X1] : ~ hBOOL(hAPP(hAPP('c$umember'(X1),X0),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool')))) ).
fof(fact_mem__def,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP('c$umember'(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ) ).
fof(fact_ex__in__conv,axiom,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(hAPP('c$umember'(X1),X2),X0))
<=> X0 != 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool')) ) ).
fof(fact_imageI,axiom,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP('c$umember'(X4),X3),X2))
=> hBOOL(hAPP(hAPP('c$umember'(X1),hAPP(X0,X3)),hAPP('c$uSet$uOimage'(X4,X1,X0),X2))) ) ).
fof(fact_insert__subset,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X3,'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'(X3),X2),X1)),X0))
<=> ( hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X3,'tc$uHOL$uObool')),X1),X0))
& hBOOL(hAPP(hAPP('c$umember'(X3),X2),X0)) ) ) ).
fof(conj_2,hypothesis,
hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),'v$upn'),'v$uU')) ).
fof(conj_3,conjecture,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('t$ua','tc$uHOL$uObool')))),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))) ).
fof(negated_conjecture,negated_conjecture,
~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('t$ua','tc$uHOL$uObool')))),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))),
inference(negate_conjecture,[status(cth)],[conj_3]) ).
cnf(c2,plain,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X1)),
inference(clausification,[status(esa)],[fact_empty__subsetI]) ).
cnf(c10,plain,
~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[fact_emptyE]) ).
cnf(c23,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c24,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c42,plain,
( X1 = 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))
| hBOOL(hAPP(hAPP('c$umember'(X0),sK100(X1,X0)),X1)) ),
inference(clausification,[status(esa)],[fact_ex__in__conv]) ).
cnf(c57,plain,
( hBOOL(hAPP(hAPP('c$umember'(X3),hAPP(X4,X1)),hAPP('c$uSet$uOimage'(X0,X3,X4),X2)))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_imageI]) ).
cnf(c99,plain,
( ~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),X2),X3))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X3))
| hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'(X0),X1),X2)),X3)) ),
inference(clausification,[status(esa)],[fact_insert__subset]) ).
cnf(c626,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),'v$upn'),'v$uU')),
inference(clausification,[status(esa)],[conj_2]) ).
cnf(c627,plain,
~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'('t$ua','tc$uHOL$uObool')))),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ hBOOL(hAPP('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')),X1)),
inference(resolution,[status(thm)],[c24,c10]) ).
cnf(d1,plain,
( hBOOL(hAPP(X0,sK100(X0,X1)))
| X0 = 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool')) ),
inference(resolution,[status(thm)],[c42,c23]) ).
cnf(d2,plain,
'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')) = 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool')),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),hAPP(hAPP('c$uSet$uOinsert'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')))),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))),
inference(superposition,[status(thm)],[d2,c627]) ).
cnf(d4,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU')))
| ~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))) ),
inference(resolution,[status(thm)],[c99,d3]) ).
cnf(d5,plain,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool'))),X2)),
inference(superposition,[status(thm)],[d2,c2]) ).
cnf(d6,plain,
~ hBOOL(hAPP(hAPP('c$umember'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),'v$upn'),'v$uU')),
inference(resolution,[status(thm)],[d6,c57]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c626,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW362+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 15:42:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.06/14.54 % SZS status Theorem for theBenchmark.p
% 98.06/14.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------