%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 09:02:16 AM UTC 2026
% Result : Theorem 18.08s 3.04s
% Output : CNFRefutation 18.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 55 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 55 ( 23 ~; 22 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 3 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l44_l45,lemma,
! [X0,X1,X2] :
( ( 'strictly$uless$uthan'(X1,X2)
& 'contains$uslb'(X0,X1) )
=> ( ? [X3] :
( 'less$uthan'(X2,X3)
& 'pair$uin$ulist'('update$uslb'(X0,X2),X1,X3) )
| 'pair$uin$ulist'('update$uslb'(X0,X2),X1,X2) ) ) ).
fof(ax20,axiom,
! [X0] : ~ 'contains$uslb'('create$uslb',X0) ).
fof(ax51,axiom,
! [X0,X1,X2,X3] :
( X1 != 'create$uslb'
=> 'findmin$ucpq$ures'(triple(X0,X1,X2)) = 'findmin$upqp$ures'(X0) ) ).
fof(l44_co,conjecture,
! [X0,X1,X2,X3] :
( ( 'strictly$uless$uthan'(X3,'findmin$ucpq$ures'(triple(X0,X1,X2)))
& 'contains$uslb'(X1,X3) )
=> ( ? [X4] :
( 'less$uthan'('findmin$upqp$ures'(X0),X4)
& 'pair$uin$ulist'('update$uslb'(X1,'findmin$upqp$ures'(X0)),X3,X4) )
| 'pair$uin$ulist'('update$uslb'(X1,'findmin$upqp$ures'(X0)),X3,'findmin$upqp$ures'(X0)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( 'strictly$uless$uthan'(X3,'findmin$ucpq$ures'(triple(X0,X1,X2)))
& 'contains$uslb'(X1,X3) )
=> ( ? [X4] :
( 'less$uthan'('findmin$upqp$ures'(X0),X4)
& 'pair$uin$ulist'('update$uslb'(X1,'findmin$upqp$ures'(X0)),X3,X4) )
| 'pair$uin$ulist'('update$uslb'(X1,'findmin$upqp$ures'(X0)),X3,'findmin$upqp$ures'(X0)) ) ),
inference(negate_conjecture,[status(cth)],[l44_co]) ).
cnf(c0,plain,
( 'pair$uin$ulist'('update$uslb'(X0,X2),X1,sK3(X0,X1,X2))
| 'pair$uin$ulist'('update$uslb'(X0,X2),X1,X2)
| ~ 'strictly$uless$uthan'(X1,X2)
| ~ 'contains$uslb'(X0,X1) ),
inference(clausification,[status(esa)],[l44_l45]) ).
cnf(c1,plain,
( 'less$uthan'(X2,sK3(X0,X1,X2))
| 'pair$uin$ulist'('update$uslb'(X0,X2),X1,X2)
| ~ 'strictly$uless$uthan'(X1,X2)
| ~ 'contains$uslb'(X0,X1) ),
inference(clausification,[status(esa)],[l44_l45]) ).
cnf(c11,plain,
~ 'contains$uslb'('create$uslb',X0),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c49,plain,
( 'findmin$ucpq$ures'(triple(X1,X0,X2)) = 'findmin$upqp$ures'(X1)
| X0 = 'create$uslb' ),
inference(clausification,[status(esa)],[ax51]) ).
cnf(c52,plain,
'contains$uslb'(sK122,sK124),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c53,plain,
'strictly$uless$uthan'(sK124,'findmin$ucpq$ures'(triple(sK121,sK122,sK123))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c54,plain,
~ 'pair$uin$ulist'('update$uslb'(sK122,'findmin$upqp$ures'(sK121)),sK124,'findmin$upqp$ures'(sK121)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c55,plain,
( ~ 'less$uthan'('findmin$upqp$ures'(sK121),X0)
| ~ 'pair$uin$ulist'('update$uslb'(sK122,'findmin$upqp$ures'(sK121)),sK124,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sK122 = 'create$uslb'
| 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121)) ),
inference(superposition,[status(thm)],[c49,c53]) ).
cnf(d1,plain,
( 'less$uthan'('findmin$upqp$ures'(sK121),sK3(sK122,sK124,'findmin$upqp$ures'(sK121)))
| ~ 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121))
| ~ 'contains$uslb'(sK122,sK124) ),
inference(resolution,[status(thm)],[c54,c1]) ).
cnf(d2,plain,
( 'less$uthan'('findmin$upqp$ures'(sK121),sK3(sK122,sK124,'findmin$upqp$ures'(sK121)))
| ~ 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121)) ),
inference(resolution,[status(thm)],[c52,d1]) ).
cnf(d3,plain,
( 'pair$uin$ulist'('update$uslb'(sK122,'findmin$upqp$ures'(sK121)),sK124,'findmin$upqp$ures'(sK121))
| ~ 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121))
| ~ 'contains$uslb'(sK122,sK124)
| ~ 'less$uthan'('findmin$upqp$ures'(sK121),sK3(sK122,sK124,'findmin$upqp$ures'(sK121))) ),
inference(resolution,[status(thm)],[c55,c0]) ).
cnf(d4,plain,
( ~ 'less$uthan'('findmin$upqp$ures'(sK121),sK3(sK122,sK124,'findmin$upqp$ures'(sK121)))
| 'pair$uin$ulist'('update$uslb'(sK122,'findmin$upqp$ures'(sK121)),sK124,'findmin$upqp$ures'(sK121))
| ~ 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121)) ),
inference(resolution,[status(thm)],[c52,d3]) ).
cnf(d5,plain,
( ~ 'less$uthan'('findmin$upqp$ures'(sK121),sK3(sK122,sK124,'findmin$upqp$ures'(sK121)))
| ~ 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121)) ),
inference(resolution,[status(thm)],[c54,d4]) ).
cnf(d6,plain,
( ~ 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121))
| ~ 'strictly$uless$uthan'(sK124,'findmin$upqp$ures'(sK121)) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
sK122 = 'create$uslb',
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
'contains$uslb'('create$uslb',sK124),
inference(demodulation,[status(thm)],[c52,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c11,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:42:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.08/3.04 % SZS status Theorem for theBenchmark.p
% 18.08/3.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------