%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV391+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 09:02:14 AM UTC 2026
% Result : Theorem 80.97s 12.08s
% Output : CNFRefutation 80.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 12 unt; 0 def)
% Number of atoms : 132 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 131 ( 51 ~; 61 |; 6 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 117 ( 29 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l27_li4142,lemma,
! [X0,X1,X2] :
( 'check$ucpq'(triple(X0,X1,X2))
<=> ! [X3,X4] :
( 'pair$uin$ulist'(X1,X3,X4)
=> 'less$uthan'(X4,X3) ) ) ).
fof(l27_li2829,lemma,
! [X0,X1,X2] :
( 'pair$uin$ulist'(X0,X1,X2)
=> ! [X3] :
( 'contains$uslb'(X0,X3)
=> ( X1 = X3
| 'pair$uin$ulist'('remove$uslb'(X0,X3),X1,X2) ) ) ) ).
fof(l27_l30,lemma,
! [X0,X1,X2,X3] :
( ( ok('remove$ucpq'(triple(X0,X1,X2),X3))
& 'check$ucpq'('remove$ucpq'(triple(X0,X1,X2),X3)) )
=> ! [X4] :
( 'pair$uin$ulist'(X1,X3,X4)
=> 'less$uthan'(X4,X3) ) ) ).
fof(l27_l33,lemma,
! [X0,X1,X2,X3] :
( ok('remove$ucpq'(triple(X0,X1,X2),X3))
=> 'contains$uslb'(X1,X3) ) ).
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(ax40,axiom,
! [X0,X1] :
( ok(triple(X0,X1,bad))
<=> $false ) ).
fof(ax44,axiom,
! [X0,X1,X2,X3] :
( ( 'less$uthan'('lookup$uslb'(X1,X3),X3)
& 'contains$uslb'(X1,X3) )
=> 'remove$ucpq'(triple(X0,X1,X2),X3) = triple('remove$upqp'(X0,X3),'remove$uslb'(X1,X3),X2) ) ).
fof(ax45,axiom,
! [X0,X1,X2,X3] :
( ( 'strictly$uless$uthan'(X3,'lookup$uslb'(X1,X3))
& 'contains$uslb'(X1,X3) )
=> 'remove$ucpq'(triple(X0,X1,X2),X3) = triple('remove$upqp'(X0,X3),'remove$uslb'(X1,X3),bad) ) ).
fof(l27_co,conjecture,
! [X0,X1,X2,X3] :
( ( ok('remove$ucpq'(triple(X0,X1,X2),X3))
& 'check$ucpq'('remove$ucpq'(triple(X0,X1,X2),X3)) )
=> 'check$ucpq'(triple(X0,X1,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ok('remove$ucpq'(triple(X0,X1,X2),X3))
& 'check$ucpq'('remove$ucpq'(triple(X0,X1,X2),X3)) )
=> 'check$ucpq'(triple(X0,X1,X2)) ),
inference(negate_conjecture,[status(cth)],[l27_co]) ).
cnf(c0,plain,
( 'less$uthan'(X4,X3)
| ~ 'pair$uin$ulist'(X1,X3,X4)
| ~ 'check$ucpq'(triple(X0,X1,X2)) ),
inference(clausification,[status(esa)],[l27_li4142]) ).
cnf(c1,plain,
( 'pair$uin$ulist'(X1,sK5(X1),sK6(X1))
| 'check$ucpq'(triple(X0,X1,X2)) ),
inference(clausification,[status(esa)],[l27_li4142]) ).
cnf(c2,plain,
( ~ 'less$uthan'(sK6(X1),sK5(X1))
| 'check$ucpq'(triple(X0,X1,X2)) ),
inference(clausification,[status(esa)],[l27_li4142]) ).
cnf(c3,plain,
( X1 = X3
| 'pair$uin$ulist'('remove$uslb'(X0,X3),X1,X2)
| ~ 'contains$uslb'(X0,X3)
| ~ 'pair$uin$ulist'(X0,X1,X2) ),
inference(clausification,[status(esa)],[l27_li2829]) ).
cnf(c4,plain,
( 'less$uthan'(X4,X3)
| ~ 'pair$uin$ulist'(X1,X3,X4)
| ~ ok('remove$ucpq'(triple(X0,X1,X2),X3))
| ~ 'check$ucpq'('remove$ucpq'(triple(X0,X1,X2),X3)) ),
inference(clausification,[status(esa)],[l27_l30]) ).
cnf(c5,plain,
( 'contains$uslb'(X1,X3)
| ~ ok('remove$ucpq'(triple(X0,X1,X2),X3)) ),
inference(clausification,[status(esa)],[l27_l33]) ).
cnf(c7,plain,
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[totality]) ).
cnf(c11,plain,
( 'less$uthan'(X1,X0)
| ~ 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[stricly_smaller_definition]) ).
cnf(c42,plain,
~ ok(triple(X0,X1,bad)),
inference(clausification,[status(esa)],[ax40]) ).
cnf(c46,plain,
( 'remove$ucpq'(triple(X2,X0,X3),X1) = triple('remove$upqp'(X2,X1),'remove$uslb'(X0,X1),X3)
| ~ 'less$uthan'('lookup$uslb'(X0,X1),X1)
| ~ 'contains$uslb'(X0,X1) ),
inference(clausification,[status(esa)],[ax44]) ).
cnf(c47,plain,
( 'remove$ucpq'(triple(X2,X0,X3),X1) = triple('remove$upqp'(X2,X1),'remove$uslb'(X0,X1),bad)
| ~ 'strictly$uless$uthan'(X1,'lookup$uslb'(X0,X1))
| ~ 'contains$uslb'(X0,X1) ),
inference(clausification,[status(esa)],[ax45]) ).
cnf(c56,plain,
'check$ucpq'('remove$ucpq'(triple(sK137,sK138,sK139),sK140)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
ok('remove$ucpq'(triple(sK137,sK138,sK139),sK140)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c58,plain,
~ 'check$ucpq'(triple(sK137,sK138,sK139)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'less$uthan'(X0,sK140)
| ~ 'check$ucpq'('remove$ucpq'(triple(sK137,sK138,sK139),sK140))
| ~ 'pair$uin$ulist'(sK138,sK140,X0) ),
inference(resolution,[status(thm)],[c4,c57]) ).
cnf(d1,plain,
( 'less$uthan'(X0,sK140)
| ~ 'pair$uin$ulist'(sK138,sK140,X0) ),
inference(resolution,[status(thm)],[c56,d0]) ).
cnf(d2,plain,
( ~ 'contains$uslb'(X2,X1)
| ~ 'less$uthan'('lookup$uslb'(X2,X1),X1)
| 'less$uthan'(X5,X4)
| ~ 'pair$uin$ulist'('remove$uslb'(X2,X1),X4,X5)
| ~ 'check$ucpq'('remove$ucpq'(triple(X0,X2,X3),X1)) ),
inference(superposition,[status(thm)],[c46,c0]) ).
cnf(d3,plain,
( ~ 'contains$uslb'(sK138,sK140)
| ~ 'less$uthan'('lookup$uslb'(sK138,sK140),sK140)
| 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'('remove$uslb'(sK138,sK140),X0,X1) ),
inference(resolution,[status(thm)],[d2,c56]) ).
cnf(d4,plain,
'contains$uslb'(sK138,sK140),
inference(resolution,[status(thm)],[c5,c57]) ).
cnf(d5,plain,
( ~ 'less$uthan'('lookup$uslb'(sK138,sK140),sK140)
| 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'('remove$uslb'(sK138,sK140),X0,X1) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'contains$uslb'(sK138,sK140)
| ~ 'pair$uin$ulist'(sK138,X1,X0)
| X1 = sK140
| ~ 'less$uthan'('lookup$uslb'(sK138,sK140),sK140)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
( ~ 'less$uthan'('lookup$uslb'(sK138,sK140),sK140)
| 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'(sK138,X0,X1)
| X0 = sK140 ),
inference(resolution,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
( 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[c11,c7]) ).
cnf(d9,plain,
( ~ 'strictly$uless$uthan'(X1,'lookup$uslb'(X2,X1))
| ~ 'contains$uslb'(X2,X1)
| ~ 'strictly$uless$uthan'(X1,'lookup$uslb'(X2,X1))
| ~ 'contains$uslb'(X2,X1)
| 'remove$ucpq'(triple(X0,X2,X4),X1) = 'remove$ucpq'(triple(X0,X2,X3),X1) ),
inference(superposition,[status(thm)],[c47,c47]) ).
cnf(d10,plain,
( ~ 'strictly$uless$uthan'(sK140,'lookup$uslb'(sK138,sK140))
| ~ 'contains$uslb'(sK138,sK140)
| ok('remove$ucpq'(triple(sK137,sK138,X0),sK140)) ),
inference(superposition,[status(thm)],[d9,c57]) ).
cnf(d11,plain,
( ~ 'strictly$uless$uthan'(sK140,'lookup$uslb'(sK138,sK140))
| ok('remove$ucpq'(triple(sK137,sK138,X0),sK140)) ),
inference(resolution,[status(thm)],[d4,d10]) ).
cnf(d12,plain,
( ~ 'strictly$uless$uthan'(sK140,'lookup$uslb'(sK138,sK140))
| ~ 'contains$uslb'(sK138,sK140)
| ~ 'strictly$uless$uthan'(sK140,'lookup$uslb'(sK138,sK140))
| ok(triple('remove$upqp'(sK137,sK140),'remove$uslb'(sK138,sK140),bad)) ),
inference(superposition,[status(thm)],[c47,d11]) ).
cnf(d13,plain,
( ~ 'strictly$uless$uthan'(sK140,'lookup$uslb'(sK138,sK140))
| ~ 'contains$uslb'(sK138,sK140) ),
inference(resolution,[status(thm)],[c42,d12]) ).
cnf(d14,plain,
~ 'strictly$uless$uthan'(sK140,'lookup$uslb'(sK138,sK140)),
inference(resolution,[status(thm)],[d4,d13]) ).
cnf(d15,plain,
'less$uthan'('lookup$uslb'(sK138,sK140),sK140),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'(sK138,X0,X1)
| X0 = sK140 ),
inference(resolution,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
( 'check$ucpq'(triple(X0,sK138,X1))
| 'less$uthan'(sK6(sK138),sK5(sK138))
| sK5(sK138) = sK140 ),
inference(resolution,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
( 'check$ucpq'(triple(X2,sK138,X3))
| 'check$ucpq'(triple(X0,sK138,X1))
| sK5(sK138) = sK140 ),
inference(resolution,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
( 'check$ucpq'(triple(X0,sK138,X1))
| sK5(sK138) = sK140 ),
inference(resolution,[status(thm)],[d18,c58]) ).
cnf(d20,plain,
sK5(sK138) = sK140,
inference(resolution,[status(thm)],[d19,c58]) ).
cnf(d21,plain,
( 'check$ucpq'(triple(X0,sK138,X1))
| 'pair$uin$ulist'(sK138,sK140,sK6(sK138)) ),
inference(superposition,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
'pair$uin$ulist'(sK138,sK140,sK6(sK138)),
inference(resolution,[status(thm)],[d21,c58]) ).
cnf(d23,plain,
'less$uthan'(sK6(sK138),sK140),
inference(resolution,[status(thm)],[d22,d1]) ).
cnf(d24,plain,
( 'check$ucpq'(triple(X0,sK138,X1))
| ~ 'less$uthan'(sK6(sK138),sK140) ),
inference(superposition,[status(thm)],[d20,c2]) ).
cnf(d25,plain,
~ 'less$uthan'(sK6(sK138),sK140),
inference(resolution,[status(thm)],[d24,c58]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV391+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 13:40:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.97/12.08 % SZS status Theorem for theBenchmark.p
% 80.97/12.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------