%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 15.93s 4.01s
% Output : CNFRefutation 15.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 20 |; 7 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l45_li4647,lemma,
! [X0,X1] :
( 'contains$uslb'(X0,X1)
=> ? [X2] : 'pair$uin$ulist'(X0,X1,X2) ) ).
fof(l48_li3839,lemma,
! [X0,X1,X2,X3] :
( ( 'strictly$uless$uthan'(X2,X3)
& 'pair$uin$ulist'(X0,X1,X2) )
=> 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X3) ) ).
fof(l49_li3637,lemma,
! [X0,X1,X2,X3] :
( ( 'less$uthan'(X3,X2)
& 'pair$uin$ulist'(X0,X1,X2) )
=> 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X2) ) ).
fof(totality,axiom,
! [X0,X1] :
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ) ).
fof(stricly_smaller_definition,axiom,
! [X0,X1] :
( 'strictly$uless$uthan'(X0,X1)
<=> ( ~ 'less$uthan'(X1,X0)
& 'less$uthan'(X0,X1) ) ) ).
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'(X0,X1,sK2(X0,X1))
| ~ 'contains$uslb'(X0,X1) ),
inference(clausification,[status(esa)],[l45_li4647]) ).
cnf(c1,plain,
( 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X3)
| ~ 'strictly$uless$uthan'(X2,X3)
| ~ 'pair$uin$ulist'(X0,X1,X2) ),
inference(clausification,[status(esa)],[l48_li3839]) ).
cnf(c2,plain,
( 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X2)
| ~ 'less$uthan'(X3,X2)
| ~ 'pair$uin$ulist'(X0,X1,X2) ),
inference(clausification,[status(esa)],[l49_li3637]) ).
cnf(c4,plain,
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[totality]) ).
cnf(c8,plain,
( 'less$uthan'(X1,X0)
| ~ 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[stricly_smaller_definition]) ).
cnf(c53,plain,
'contains$uslb'(sK129,sK131),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c55,plain,
~ 'pair$uin$ulist'('update$uslb'(sK129,'findmin$upqp$ures'(sK128)),sK131,'findmin$upqp$ures'(sK128)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
( ~ 'less$uthan'('findmin$upqp$ures'(sK128),X0)
| ~ 'pair$uin$ulist'('update$uslb'(sK129,'findmin$upqp$ures'(sK128)),sK131,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'less$uthan'('findmin$upqp$ures'(sK128),X0)
| ~ 'pair$uin$ulist'(sK129,sK131,X0)
| ~ 'less$uthan'('findmin$upqp$ures'(sK128),X0) ),
inference(resolution,[status(thm)],[c56,c2]) ).
cnf(d1,plain,
( 'less$uthan'(X0,'findmin$upqp$ures'(sK128))
| ~ 'pair$uin$ulist'(sK129,sK131,X0) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ 'contains$uslb'(sK129,sK131)
| 'less$uthan'(sK2(sK129,sK131),'findmin$upqp$ures'(sK128)) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
'less$uthan'(sK2(sK129,sK131),'findmin$upqp$ures'(sK128)),
inference(resolution,[status(thm)],[c53,d2]) ).
cnf(d4,plain,
( 'less$uthan'('findmin$upqp$ures'(sK128),sK2(sK129,sK131))
| 'strictly$uless$uthan'(sK2(sK129,sK131),'findmin$upqp$ures'(sK128)) ),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
( ~ 'contains$uslb'(X0,X2)
| ~ 'strictly$uless$uthan'(sK2(X0,X2),X1)
| 'pair$uin$ulist'('update$uslb'(X0,X1),X2,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d6,plain,
( ~ 'strictly$uless$uthan'(sK2(sK129,sK131),'findmin$upqp$ures'(sK128))
| ~ 'contains$uslb'(sK129,sK131) ),
inference(resolution,[status(thm)],[d5,c55]) ).
cnf(d7,plain,
~ 'strictly$uless$uthan'(sK2(sK129,sK131),'findmin$upqp$ures'(sK128)),
inference(resolution,[status(thm)],[c53,d6]) ).
cnf(d8,plain,
'less$uthan'('findmin$upqp$ures'(sK128),sK2(sK129,sK131)),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
~ 'pair$uin$ulist'(sK129,sK131,sK2(sK129,sK131)),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
~ 'contains$uslb'(sK129,sK131),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c53,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n013.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 13:41:21 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.93/4.01 % SZS status Theorem for theBenchmark.p
% 15.93/4.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------