%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 08:33:02 AM UTC 2026
% Result : Theorem 12.56s 1.96s
% Output : CNFRefutation 12.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 36 ~; 33 |; 3 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 8 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X1))
=> 'ilf$utype'(X3,'subset$utype'('cross$uproduct'(X0,X1))) )
& ! [X2] :
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
=> 'ilf$utype'(X2,'relation$utype'(X0,X1)) ) ) ) ) ).
fof(p4,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ~ member(X0,'empty$uset') ) ).
fof(p7,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( 'ilf$utype'(X1,'subset$utype'(X0))
<=> 'ilf$utype'(X1,'member$utype'('power$uset'(X0))) ) ) ) ).
fof(p12,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( member(X0,'power$uset'(X1))
<=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ) ).
fof(p13,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p14,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ( 'ilf$utype'(X0,'member$utype'(X1))
<=> member(X0,X1) ) ) ) ).
fof(p20,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_25,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> 'ilf$utype'('empty$uset','relation$utype'(X0,X1)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> 'ilf$utype'('empty$uset','relation$utype'(X0,X1)) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_25]) ).
cnf(c1,plain,
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c4,plain,
( ~ member(X0,'empty$uset')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c9,plain,
( ~ 'ilf$utype'(X1,'member$utype'('power$uset'(X0)))
| 'ilf$utype'(X1,'subset$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c21,plain,
( member(sK27(X0,X1),X0)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p12]) ).
cnf(c23,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p13]) ).
cnf(c26,plain,
( 'ilf$utype'(X1,'member$utype'(X0))
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X1,X0)
| empty(X0) ),
inference(clausification,[status(esa)],[p14]) ).
cnf(c39,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p20]) ).
cnf(c42,plain,
~ 'ilf$utype'('empty$uset','relation$utype'(sK48,sK49)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c39,c1]) ).
cnf(d1,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c39,d0]) ).
cnf(d2,plain,
~ member(X0,'empty$uset'),
inference(resolution,[status(thm)],[c39,c4]) ).
cnf(d3,plain,
( member(sK27(X0,X1),X0)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c39,c21]) ).
cnf(d4,plain,
( member('empty$uset','power$uset'(X0))
| ~ 'ilf$utype'('empty$uset','set$utype') ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
member('empty$uset','power$uset'(X0)),
inference(resolution,[status(thm)],[c39,d4]) ).
cnf(d6,plain,
( ~ 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c39,c9]) ).
cnf(d7,plain,
( empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c39,c26]) ).
cnf(d8,plain,
( 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype')
| empty('power$uset'(X1))
| ~ member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( empty('power$uset'(X1))
| ~ member(X0,'power$uset'(X1))
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c39,d8]) ).
cnf(d10,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c39,c23]) ).
cnf(d11,plain,
( ~ member(X0,'power$uset'(X1))
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
'ilf$utype'('empty$uset','subset$utype'(X0)),
inference(resolution,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
'ilf$utype'('empty$uset','relation$utype'(X0,X1)),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,c42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:08:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.56/1.96 % SZS status Theorem for theBenchmark.p
% 12.56/1.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------