%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV409+1 : 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 : n026.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 11.60s 3.87s
% Output : CNFRefutation 11.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 103 ( 47 ~; 40 |; 10 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l45_li4647,lemma,
! [X0,X1] :
( 'contains$uslb'(X0,X1)
=> ? [X2] : 'pair$uin$ulist'(X0,X1,X2) ) ).
fof(l45_l48,lemma,
! [X0,X1,X2,X3] :
( ( 'strictly$uless$uthan'(X2,X3)
& 'strictly$uless$uthan'(X1,X3)
& 'pair$uin$ulist'(X0,X1,X2) )
=> 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X3) ) ).
fof(l45_l49,lemma,
! [X0,X1,X2,X3] :
( ( 'less$uthan'(X3,X2)
& 'strictly$uless$uthan'(X1,X3)
& 'pair$uin$ulist'(X0,X1,X2) )
=> ? [X4] :
( 'less$uthan'(X3,X4)
& 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X4) ) ) ).
fof(totality,axiom,
! [X0,X1] :
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ) ).
fof(stricly_smaller_definition,axiom,
! [X0,X1] :
( 'strictly$uless$uthan'(X0,X1)
<=> ( ~ 'less$uthan'(X1,X0)
& 'less$uthan'(X0,X1) ) ) ).
fof(l45_co,conjecture,
! [X0,X1,X2] :
( ( 'strictly$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$uslb'(X0,X2),X1,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'strictly$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$uslb'(X0,X2),X1,X2) ) ),
inference(negate_conjecture,[status(cth)],[l45_co]) ).
cnf(c0,plain,
( 'pair$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$uthan'(X2,X3)
| ~ 'strictly$uless$uthan'(X1,X3)
| ~ 'pair$uin$ulist'(X0,X1,X2) ),
inference(clausification,[status(esa)],[l45_l48]) ).
cnf(c2,plain,
( 'pair$uin$ulist'('update$uslb'(X0,X3),X1,sK11(X0,X1,X3))
| ~ 'less$uthan'(X3,X2)
| ~ 'strictly$uless$uthan'(X1,X3)
| ~ 'pair$uin$ulist'(X0,X1,X2) ),
inference(clausification,[status(esa)],[l45_l49]) ).
cnf(c3,plain,
( 'less$uthan'(X3,sK11(X0,X1,X3))
| ~ 'less$uthan'(X3,X2)
| ~ 'strictly$uless$uthan'(X1,X3)
| ~ 'pair$uin$ulist'(X0,X1,X2) ),
inference(clausification,[status(esa)],[l45_l49]) ).
cnf(c5,plain,
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[totality]) ).
cnf(c9,plain,
( 'less$uthan'(X1,X0)
| ~ 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[stricly_smaller_definition]) ).
cnf(c29,plain,
'contains$uslb'(sK59,sK60),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
'strictly$uless$uthan'(sK60,sK61),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
~ 'pair$uin$ulist'('update$uslb'(sK59,sK61),sK60,sK61),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c32,plain,
( ~ 'less$uthan'(sK61,X0)
| ~ 'pair$uin$ulist'('update$uslb'(sK59,sK61),sK60,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'contains$uslb'(X2,X0)
| 'less$uthan'(X1,sK11(X2,X0,X1))
| ~ 'less$uthan'(X1,sK2(X2,X0))
| ~ 'strictly$uless$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
( ~ 'contains$uslb'(X0,X2)
| ~ 'less$uthan'(X1,sK2(X0,X2))
| ~ 'strictly$uless$uthan'(X2,X1)
| 'pair$uin$ulist'('update$uslb'(X0,X1),X2,sK11(X0,X2,X1)) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d2,plain,
( ~ 'less$uthan'(sK61,sK11(sK59,sK60,sK61))
| ~ 'less$uthan'(sK61,sK2(sK59,sK60))
| ~ 'strictly$uless$uthan'(sK60,sK61)
| ~ 'contains$uslb'(sK59,sK60) ),
inference(resolution,[status(thm)],[d1,c32]) ).
cnf(d3,plain,
( ~ 'less$uthan'(sK61,sK11(sK59,sK60,sK61))
| ~ 'less$uthan'(sK61,sK2(sK59,sK60))
| ~ 'strictly$uless$uthan'(sK60,sK61) ),
inference(resolution,[status(thm)],[c29,d2]) ).
cnf(d4,plain,
( ~ 'less$uthan'(sK61,sK11(sK59,sK60,sK61))
| ~ 'less$uthan'(sK61,sK2(sK59,sK60)) ),
inference(resolution,[status(thm)],[c30,d3]) ).
cnf(d5,plain,
( 'less$uthan'(X1,X0)
| 'less$uthan'(X1,X0)
| 'strictly$uless$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[c9,c5]) ).
cnf(d6,plain,
( ~ 'contains$uslb'(X0,X2)
| ~ 'strictly$uless$uthan'(X2,X1)
| ~ 'strictly$uless$uthan'(sK2(X0,X2),X1)
| 'pair$uin$ulist'('update$uslb'(X0,X1),X2,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d7,plain,
( ~ 'strictly$uless$uthan'(sK2(sK59,sK60),sK61)
| ~ 'strictly$uless$uthan'(sK60,sK61)
| ~ 'contains$uslb'(sK59,sK60) ),
inference(resolution,[status(thm)],[d6,c31]) ).
cnf(d8,plain,
( ~ 'strictly$uless$uthan'(sK60,sK61)
| ~ 'strictly$uless$uthan'(sK2(sK59,sK60),sK61) ),
inference(resolution,[status(thm)],[c29,d7]) ).
cnf(d9,plain,
~ 'strictly$uless$uthan'(sK2(sK59,sK60),sK61),
inference(resolution,[status(thm)],[c30,d8]) ).
cnf(d10,plain,
'less$uthan'(sK61,sK2(sK59,sK60)),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
~ 'less$uthan'(sK61,sK11(sK59,sK60,sK61)),
inference(resolution,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
( ~ 'less$uthan'(sK61,sK2(sK59,sK60))
| ~ 'strictly$uless$uthan'(sK60,sK61)
| ~ 'contains$uslb'(sK59,sK60) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( ~ 'less$uthan'(sK61,sK2(sK59,sK60))
| ~ 'strictly$uless$uthan'(sK60,sK61) ),
inference(resolution,[status(thm)],[c29,d12]) ).
cnf(d14,plain,
~ 'less$uthan'(sK61,sK2(sK59,sK60)),
inference(resolution,[status(thm)],[c30,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d10,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 13:44:26 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.60/3.87 % SZS status Theorem for theBenchmark.p
% 11.60/3.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------