%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV403+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 : n015.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 24.79s 6.40s
% Output : CNFRefutation 24.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 101 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 27 ~; 39 |; 6 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 104 ( 7 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(ax23,axiom,
! [X0,X1,X2,X3,X4] :
( 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X3)),X2,X4)
<=> ( ( X3 = X4
& X1 = X2 )
| 'pair$uin$ulist'(X0,X2,X4) ) ) ).
fof(ax29,axiom,
! [X0,X1,X2,X3] :
( 'strictly$uless$uthan'(X3,X2)
=> 'update$uslb'('insert$uslb'(X0,pair(X1,X3)),X2) = 'insert$uslb'('update$uslb'(X0,X2),pair(X1,X2)) ) ).
fof(ax30,axiom,
! [X0,X1,X2,X3] :
( 'less$uthan'(X2,X3)
=> 'update$uslb'('insert$uslb'(X0,pair(X1,X3)),X2) = 'insert$uslb'('update$uslb'(X0,X2),pair(X1,X3)) ) ).
fof(l39_co,conjecture,
! [X0] :
( ! [X1,X2,X3] :
( ( 'strictly$uless$uthan'(X2,X3)
& 'pair$uin$ulist'(X0,X1,X2) )
=> 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X3) )
=> ! [X4,X5,X6,X7,X8] :
( ( 'strictly$uless$uthan'(X5,X6)
& 'pair$uin$ulist'('insert$uslb'(X0,pair(X7,X8)),X4,X5) )
=> 'pair$uin$ulist'('update$uslb'('insert$uslb'(X0,pair(X7,X8)),X6),X4,X6) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ! [X1,X2,X3] :
( ( 'strictly$uless$uthan'(X2,X3)
& 'pair$uin$ulist'(X0,X1,X2) )
=> 'pair$uin$ulist'('update$uslb'(X0,X3),X1,X3) )
=> ! [X4,X5,X6,X7,X8] :
( ( 'strictly$uless$uthan'(X5,X6)
& 'pair$uin$ulist'('insert$uslb'(X0,pair(X7,X8)),X4,X5) )
=> 'pair$uin$ulist'('update$uslb'('insert$uslb'(X0,pair(X7,X8)),X6),X4,X6) ) ),
inference(negate_conjecture,[status(cth)],[l39_co]) ).
cnf(c1,plain,
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[totality]) ).
cnf(c5,plain,
( 'less$uthan'(X1,X0)
| ~ 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[stricly_smaller_definition]) ).
cnf(c14,plain,
( X1 = X3
| 'pair$uin$ulist'(X0,X3,X4)
| ~ 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c15,plain,
( X2 = X4
| 'pair$uin$ulist'(X0,X3,X4)
| ~ 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c16,plain,
( ~ 'pair$uin$ulist'(X0,X3,X4)
| 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c17,plain,
( X2 != X4
| X1 != X3
| 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c23,plain,
( 'update$uslb'('insert$uslb'(X2,pair(X3,X0)),X1) = 'insert$uslb'('update$uslb'(X2,X1),pair(X3,X1))
| ~ 'strictly$uless$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[ax29]) ).
cnf(c24,plain,
( 'update$uslb'('insert$uslb'(X2,pair(X3,X1)),X0) = 'insert$uslb'('update$uslb'(X2,X0),pair(X3,X1))
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[ax30]) ).
cnf(c25,plain,
( 'pair$uin$ulist'('update$uslb'(sK47,X2),X0,X2)
| ~ 'strictly$uless$uthan'(X1,X2)
| ~ 'pair$uin$ulist'(sK47,X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c26,plain,
'pair$uin$ulist'('insert$uslb'(sK47,pair(sK54,sK55)),sK51,sK52),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c27,plain,
'strictly$uless$uthan'(sK52,sK53),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c28,plain,
~ 'pair$uin$ulist'('update$uslb'('insert$uslb'(sK47,pair(sK54,sK55)),sK53),sK51,sK53),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'pair$uin$ulist'(sK47,sK51,sK52)
| sK55 = sK52 ),
inference(resolution,[status(thm)],[c15,c26]) ).
cnf(d1,plain,
( 'pair$uin$ulist'('update$uslb'(sK47,X0),sK51,X0)
| ~ 'strictly$uless$uthan'(sK52,X0)
| sK55 = sK52 ),
inference(resolution,[status(thm)],[d0,c25]) ).
cnf(d2,plain,
( 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d3,plain,
( 'update$uslb'('insert$uslb'(X2,pair(X3,X1)),X0) = 'insert$uslb'('update$uslb'(X2,X0),pair(X3,X0))
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[d2,c23]) ).
cnf(d4,plain,
( 'update$uslb'('insert$uslb'(X4,pair(X5,X2)),X3) = 'insert$uslb'('update$uslb'(X4,X3),pair(X5,X2))
| 'update$uslb'('insert$uslb'(X0,pair(X1,X2)),X3) = 'insert$uslb'('update$uslb'(X0,X3),pair(X1,X3)) ),
inference(resolution,[status(thm)],[d3,c24]) ).
cnf(d5,plain,
( 'update$uslb'('insert$uslb'(X0,pair(X1,sK55)),sK53) = 'insert$uslb'('update$uslb'(X0,sK53),pair(X1,sK53))
| ~ 'pair$uin$ulist'('insert$uslb'('update$uslb'(sK47,sK53),pair(sK54,sK55)),sK51,sK53) ),
inference(superposition,[status(thm)],[d4,c28]) ).
cnf(d6,plain,
( ~ 'pair$uin$ulist'('update$uslb'(sK47,sK53),sK51,sK53)
| 'update$uslb'('insert$uslb'(X0,pair(X1,sK55)),sK53) = 'insert$uslb'('update$uslb'(X0,sK53),pair(X1,sK53)) ),
inference(resolution,[status(thm)],[d5,c16]) ).
cnf(d7,plain,
( ~ 'strictly$uless$uthan'(sK52,sK53)
| sK55 = sK52
| 'update$uslb'('insert$uslb'(X0,pair(X1,sK55)),sK53) = 'insert$uslb'('update$uslb'(X0,sK53),pair(X1,sK53)) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( sK55 = sK52
| 'update$uslb'('insert$uslb'(X0,pair(X1,sK55)),sK53) = 'insert$uslb'('update$uslb'(X0,sK53),pair(X1,sK53)) ),
inference(resolution,[status(thm)],[c27,d7]) ).
cnf(d9,plain,
( sK55 = sK52
| ~ 'pair$uin$ulist'('insert$uslb'('update$uslb'(sK47,sK53),pair(sK54,sK53)),sK51,sK53) ),
inference(superposition,[status(thm)],[d8,c28]) ).
cnf(d10,plain,
( ~ 'pair$uin$ulist'('update$uslb'(sK47,sK53),sK51,sK53)
| sK55 = sK52 ),
inference(resolution,[status(thm)],[d9,c16]) ).
cnf(d11,plain,
( ~ 'strictly$uless$uthan'(sK52,sK53)
| sK55 = sK52
| sK55 = sK52 ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
sK55 = sK52,
inference(resolution,[status(thm)],[c27,d11]) ).
cnf(d13,plain,
( 'pair$uin$ulist'(sK47,sK51,sK52)
| sK54 = sK51 ),
inference(resolution,[status(thm)],[c14,c26]) ).
cnf(d14,plain,
( 'pair$uin$ulist'('update$uslb'(sK47,X0),sK51,X0)
| ~ 'strictly$uless$uthan'(sK52,X0)
| sK54 = sK51 ),
inference(resolution,[status(thm)],[d13,c25]) ).
cnf(d15,plain,
( 'pair$uin$ulist'('update$uslb'(sK47,X0),sK51,X0)
| ~ 'strictly$uless$uthan'(sK55,X0)
| sK54 = sK51 ),
inference(demodulation,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
'update$uslb'('insert$uslb'(X0,pair(X1,sK52)),sK53) = 'insert$uslb'('update$uslb'(X0,sK53),pair(X1,sK53)),
inference(resolution,[status(thm)],[c23,c27]) ).
cnf(d17,plain,
'update$uslb'('insert$uslb'(X0,pair(X1,sK55)),sK53) = 'insert$uslb'('update$uslb'(X0,sK53),pair(X1,sK53)),
inference(demodulation,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
~ 'pair$uin$ulist'('insert$uslb'('update$uslb'(sK47,sK53),pair(sK54,sK53)),sK51,sK53),
inference(demodulation,[status(thm)],[c28,d17]) ).
cnf(d19,plain,
~ 'pair$uin$ulist'('update$uslb'(sK47,sK53),sK51,sK53),
inference(resolution,[status(thm)],[d18,c16]) ).
cnf(d20,plain,
( ~ 'strictly$uless$uthan'(sK55,sK53)
| sK54 = sK51 ),
inference(resolution,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
'strictly$uless$uthan'(sK55,sK53),
inference(demodulation,[status(thm)],[c27,d12]) ).
cnf(d22,plain,
sK54 = sK51,
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
~ 'pair$uin$ulist'('insert$uslb'('update$uslb'(sK47,sK53),pair(sK54,sK53)),sK54,sK53),
inference(demodulation,[status(thm)],[d18,d22]) ).
cnf(d24,plain,
( 'pair$uin$ulist'('insert$uslb'(X2,pair(X0,X3)),X1,X3)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c17]) ).
cnf(d25,plain,
'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X1,X2),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV403+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 13:44:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.79/6.40 % SZS status Theorem for theBenchmark.p
% 24.79/6.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------