%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW367+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 105.75s 27.07s
% Output : CNFRefutation 105.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 4 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 18 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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$umember'(X3),X2),X0)) ) ) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),'v$uG'),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))) ).
fof(conj_4,hypothesis,
hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),'v$upn'),'v$uU')) ).
fof(conj_6,conjecture,
hBOOL(hAPP(hAPP('c$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$upn')),'v$uG')),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$upn')),'v$uG')),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))),
inference(negate_conjecture,[status(cth)],[conj_6]) ).
cnf(c47,plain,
( hBOOL(hAPP(hAPP('c$umember'(X3),hAPP(X4,X1)),hAPP('c$uSet$uOimage'(X0,X3,X4),X2)))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_imageI]) ).
cnf(c67,plain,
( ~ hBOOL(hAPP(hAPP('c$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(c613,plain,
hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),'v$uG'),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c614,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),'v$upn'),'v$uU')),
inference(clausification,[status(esa)],[conj_4]) ).
cnf(c616,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')),'v$uG')),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ hBOOL(hAPP(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$ufun'('t$ua','tc$uHOL$uObool')),'v$uG'),hAPP('c$uSet$uOimage'('tc$uCom$uOpname','t$ua','v$umgt$u$ucall'),'v$uU')))
| ~ hBOOL(hAPP(hAPP('c$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)],[c67,c616]) ).
cnf(d1,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$uU'))),
inference(resolution,[status(thm)],[c613,d0]) ).
cnf(d2,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$uCom$uOpname'),'v$upn'),'v$uU')),
inference(resolution,[status(thm)],[d1,c47]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c614,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW367+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n009.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 15:45:29 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 105.75/27.07 % SZS status Theorem for theBenchmark.p
% 105.75/27.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------