%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET641+3 : TPTP v9.3.1. Released v2.2.0.
% 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 08:32:59 AM UTC 2026
% Result : Theorem 13.46s 3.59s
% Output : CNFRefutation 13.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 8 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 151 ( 59 ~; 60 |; 3 &)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,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(p5,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(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$uset'(X0))) ) ) ) ).
fof(p10,axiom,
! [X0] :
( 'ilf$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(p11,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p12,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(p18,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_3,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( subset(X0,'cross$uproduct'(X1,X2))
=> 'ilf$utype'(X0,'relation$utype'(X1,X2)) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( subset(X0,'cross$uproduct'(X1,X2))
=> 'ilf$utype'(X0,'relation$utype'(X1,X2)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_3]) ).
cnf(c0,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$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c12,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| ~ subset(X2,X1)
| ~ member(X0,X2)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| member(X0,X1) ),
inference(clausification,[status(esa)],[p5]) ).
cnf(c18,plain,
( ~ 'ilf$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(c23,plain,
( member(sK31(X0,X1),X0)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p10]) ).
cnf(c24,plain,
( ~ member(sK31(X0,X1),X1)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p10]) ).
cnf(c25,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p11]) ).
cnf(c28,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(clausification,[status(esa)],[p12]) ).
cnf(c43,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p18]) ).
cnf(c47,plain,
subset(sK53,'cross$uproduct'(sK54,sK55)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
~ 'ilf$utype'(sK53,'relation$utype'(sK54,sK55)),
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$utype') ),
inference(resolution,[status(thm)],[c43,c0]) ).
cnf(d1,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c43,d0]) ).
cnf(d2,plain,
( member(sK31(X1,X0),X1)
| member(X1,'power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c43,c23]) ).
cnf(d3,plain,
( ~ subset(X1,X0)
| ~ member(X2,X1)
| member(X2,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c43,c12]) ).
cnf(d4,plain,
( member(X0,'cross$uproduct'(sK54,sK55))
| ~ member(X0,sK53)
| ~ 'ilf$utype'('cross$uproduct'(sK54,sK55),'set$utype')
| ~ 'ilf$utype'(sK53,'set$utype') ),
inference(resolution,[status(thm)],[d3,c47]) ).
cnf(d5,plain,
( ~ member(X0,sK53)
| member(X0,'cross$uproduct'(sK54,sK55))
| ~ 'ilf$utype'(sK53,'set$utype') ),
inference(resolution,[status(thm)],[c43,d4]) ).
cnf(d6,plain,
( ~ member(sK31(X1,X0),X0)
| member(X1,'power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c43,c24]) ).
cnf(d7,plain,
( ~ member(sK31(X0,'cross$uproduct'(sK54,sK55)),sK53)
| ~ 'ilf$utype'(sK53,'set$utype')
| member(X0,'power$uset'('cross$uproduct'(sK54,sK55)))
| ~ 'ilf$utype'('cross$uproduct'(sK54,sK55),'set$utype') ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ member(sK31(X0,'cross$uproduct'(sK54,sK55)),sK53)
| member(X0,'power$uset'('cross$uproduct'(sK54,sK55)))
| ~ 'ilf$utype'(sK53,'set$utype') ),
inference(resolution,[status(thm)],[c43,d7]) ).
cnf(d9,plain,
( member(sK53,'power$uset'('cross$uproduct'(sK54,sK55)))
| ~ 'ilf$utype'('cross$uproduct'(sK54,sK55),'set$utype')
| member(sK53,'power$uset'('cross$uproduct'(sK54,sK55)))
| ~ 'ilf$utype'(sK53,'set$utype') ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( member(sK53,'power$uset'('cross$uproduct'(sK54,sK55)))
| ~ 'ilf$utype'(sK53,'set$utype') ),
inference(resolution,[status(thm)],[c43,d9]) ).
cnf(d11,plain,
( ~ 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| ~ 'ilf$utype'(X0,'set$utype')
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c43,c18]) ).
cnf(d12,plain,
( empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c43,c28]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| 'ilf$utype'(X0,'subset$utype'(X1))
| empty('power$uset'(X1))
| ~ member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( empty('power$uset'(X1))
| ~ member(X0,'power$uset'(X1))
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c43,d13]) ).
cnf(d15,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c43,c25]) ).
cnf(d16,plain,
( ~ member(X0,'power$uset'(X1))
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( ~ 'ilf$utype'(sK53,'set$utype')
| 'ilf$utype'(sK53,'subset$utype'('cross$uproduct'(sK54,sK55))) ),
inference(resolution,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
'ilf$utype'(sK53,'subset$utype'('cross$uproduct'(sK54,sK55))),
inference(resolution,[status(thm)],[c43,d17]) ).
cnf(d19,plain,
'ilf$utype'(sK53,'relation$utype'(sK54,sK55)),
inference(resolution,[status(thm)],[d18,d1]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[c48,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET641+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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 08:02:29 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.46/3.59 % SZS status Theorem for theBenchmark.p
% 13.46/3.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------