%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW365+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 : n016.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 09:11:46 AM UTC 2026
% Result : Theorem 112.58s 19.38s
% Output : CNFRefutation 112.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 35 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 7 |; 1 &)
% ( 3 <=>; 0 =>; 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 : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 14 sgn 13 !; 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$uObool')) ) ).
fof(fact_insert__subset,axiom,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP('c$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_6,hypothesis,
hBOOL(hAPP(hAPP('c$umember'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),'v$uG')) ).
fof(conj_7,conjecture,
hBOOL(hAPP(hAPP('c$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')))),'v$uG')) ).
fof(negated_conjecture,negated_conjecture,
~ hBOOL(hAPP(hAPP('c$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')))),'v$uG')),
inference(negate_conjecture,[status(cth)],[conj_7]) ).
cnf(c5,plain,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'(X0,'tc$uHOL$uObool')),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))),X1)),
inference(clausification,[status(esa)],[fact_empty__subsetI]) ).
cnf(c13,plain,
~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')))),
inference(clausification,[status(esa)],[fact_emptyE]) ).
cnf(c24,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c25,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c44,plain,
( X1 = 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool'))
| hBOOL(hAPP(hAPP('c$umember'(X0),sK104(X1,X0)),X1)) ),
inference(clausification,[status(esa)],[fact_ex__in__conv]) ).
cnf(c101,plain,
( ~ hBOOL(hAPP(hAPP('c$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(c769,plain,
hBOOL(hAPP(hAPP('c$umember'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),'v$uG')),
inference(clausification,[status(esa)],[conj_6]) ).
cnf(c770,plain,
~ hBOOL(hAPP(hAPP('c$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')))),'v$uG')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ hBOOL(hAPP('c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X0,'tc$uHOL$uObool')),X1)),
inference(resolution,[status(thm)],[c25,c13]) ).
cnf(d1,plain,
( hBOOL(hAPP(X0,sK104(X0,X1)))
| X0 = 'c$uOrderings$uObot$u$uclass$uObot'('tc$ufun'(X1,'tc$uHOL$uObool')) ),
inference(resolution,[status(thm)],[c44,c24]) ).
cnf(d2,plain,
'c$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$uObool')))),'v$uG')),
inference(superposition,[status(thm)],[d2,c770]) ).
cnf(d4,plain,
( ~ 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$uObool'))),'v$uG'))
| ~ hBOOL(hAPP(hAPP('c$umember'('t$ua'),hAPP('v$umgt$u$ucall','v$upn')),'v$uG')) ),
inference(resolution,[status(thm)],[c101,d3]) ).
cnf(d5,plain,
~ hBOOL(hAPP(hAPP('c$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'))),'v$uG')),
inference(resolution,[status(thm)],[c769,d4]) ).
cnf(d6,plain,
hBOOL(hAPP(hAPP('c$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,c5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW365+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
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 15:49:45 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 112.58/19.38 % SZS status Theorem for theBenchmark.p
% 112.58/19.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------