%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET640+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 : n012.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 08:32:59 AM UTC 2026
% Result : Theorem 11.07s 2.54s
% Output : CNFRefutation 11.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 163 ( 64 ~; 65 |; 3 &)
% ( 4 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p4,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(p6,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( subset(X0,X1)
<=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ) ).
fof(p8,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$uset'(X0))) ) ) ) ).
fof(p11,axiom,
! [X0] :
( 'ilf$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(p12,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p13,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(p19,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_2,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,'cross$uproduct'(X1,X2)) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,'cross$uproduct'(X1,X2)) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_2]) ).
cnf(c10,plain,
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c12,plain,
( ~ subset(X2,X1)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X0,X2)
| member(X0,X1) ),
inference(clausification,[status(esa)],[p6]) ).
cnf(c14,plain,
( ~ member(sK23(X0,X1),X1)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p6]) ).
cnf(c15,plain,
( member(sK23(X0,X1),X0)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p6]) ).
cnf(c17,plain,
( 'ilf$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)],[p8]) ).
cnf(c21,plain,
( ~ member(X2,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| member(X2,X1)
| ~ member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p11]) ).
cnf(c25,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p12]) ).
cnf(c27,plain,
( ~ 'ilf$utype'(X0,'member$utype'(X1))
| empty(X1)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| member(X0,X1) ),
inference(clausification,[status(esa)],[p13]) ).
cnf(c42,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p19]) ).
cnf(c46,plain,
'ilf$utype'(sK59,'relation$utype'(sK57,sK58)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
~ subset(sK56,'cross$uproduct'(sK57,sK58)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
subset(sK56,sK59),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(sK23(X0,X1),X1)
| subset(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c14]) ).
cnf(d1,plain,
( ~ member(sK23(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[d0,c42]) ).
cnf(d2,plain,
( member(X0,X1)
| ~ member(X0,X2)
| ~ member(X2,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c21]) ).
cnf(d3,plain,
( member(X0,X2)
| ~ member(X0,X1)
| ~ member(X1,'power$uset'(X2))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d2,c42]) ).
cnf(d4,plain,
( ~ member(X2,X0)
| member(X2,X1)
| ~ member(X0,'power$uset'(X1)) ),
inference(resolution,[status(thm)],[c42,d3]) ).
cnf(d5,plain,
( ~ member(X2,X1)
| member(X2,X0)
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c12]) ).
cnf(d6,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d5,c42]) ).
cnf(d7,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c42,d6]) ).
cnf(d8,plain,
( ~ member(X0,sK56)
| member(X0,sK59) ),
inference(resolution,[status(thm)],[d7,c48]) ).
cnf(d9,plain,
( member(sK23(X0,X1),X0)
| subset(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c15]) ).
cnf(d10,plain,
( member(sK23(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[d9,c42]) ).
cnf(d11,plain,
member(sK23(sK56,'cross$uproduct'(sK57,sK58)),sK56),
inference(resolution,[status(thm)],[d10,c47]) ).
cnf(d12,plain,
member(sK23(sK56,'cross$uproduct'(sK57,sK58)),sK59),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( ~ member(sK59,'power$uset'(X0))
| member(sK23(sK56,'cross$uproduct'(sK57,sK58)),X0) ),
inference(resolution,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
( ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c10]) ).
cnf(d15,plain,
( ~ 'ilf$utype'(sK57,'set$utype')
| 'ilf$utype'(sK59,'subset$utype'('cross$uproduct'(sK57,sK58))) ),
inference(resolution,[status(thm)],[d14,c46]) ).
cnf(d16,plain,
'ilf$utype'(sK59,'subset$utype'('cross$uproduct'(sK57,sK58))),
inference(resolution,[status(thm)],[c42,d15]) ).
cnf(d17,plain,
( 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| ~ 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c17]) ).
cnf(d18,plain,
( 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d17,c42]) ).
cnf(d19,plain,
'ilf$utype'(sK59,'member$utype'('power$uset'('cross$uproduct'(sK57,sK58)))),
inference(resolution,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( empty(X1)
| member(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c42,c27]) ).
cnf(d21,plain,
( empty(X1)
| member(X0,X1)
| ~ 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[d20,c42]) ).
cnf(d22,plain,
( empty('power$uset'('cross$uproduct'(sK57,sK58)))
| member(sK59,'power$uset'('cross$uproduct'(sK57,sK58))) ),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c42,c25]) ).
cnf(d24,plain,
member(sK59,'power$uset'('cross$uproduct'(sK57,sK58))),
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
member(sK23(sK56,'cross$uproduct'(sK57,sK58)),'cross$uproduct'(sK57,sK58)),
inference(resolution,[status(thm)],[d24,d13]) ).
cnf(d26,plain,
subset(sK56,'cross$uproduct'(sK57,sK58)),
inference(resolution,[status(thm)],[d25,d1]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[c47,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 08:01:51 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.07/2.54 % SZS status Theorem for theBenchmark.p
% 11.07/2.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------