%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET663+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 : 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 08:33:02 AM UTC 2026
% Result : Theorem 15.67s 4.29s
% Output : CNFRefutation 15.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 95 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 36 ~; 32 |; 3 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 5 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( subset(X0,'empty$uset')
=> X0 = 'empty$uset' ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'binary$urelation$utype')
=> ( ( 'range$uof'(X0) = 'empty$uset'
| 'domain$uof'(X0) = 'empty$uset' )
=> X0 = 'empty$uset' ) ) ).
fof(p3,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ( subset('range$uof'(X2),X1)
& subset('domain$uof'(X2),X0) ) ) ) ) ).
fof(p6,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(p13,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'(X0,'binary$urelation$utype')
<=> ( 'ilf$utype'(X0,'set$utype')
& 'relation$ulike'(X0) ) ) ) ).
fof(p28,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
=> 'relation$ulike'(X2) ) ) ) ).
fof(p33,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_26,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ( 'ilf$utype'(X2,'relation$utype'('empty$uset',X1))
=> X2 = 'empty$uset' ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ( 'ilf$utype'(X2,'relation$utype'('empty$uset',X1))
=> X2 = 'empty$uset' ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_26]) ).
cnf(c0,plain,
( X0 = 'empty$uset'
| ~ subset(X0,'empty$uset')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( X0 = 'empty$uset'
| 'domain$uof'(X0) != 'empty$uset'
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c3,plain,
( subset('domain$uof'(X2),X0)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c9,plain,
( 'ilf$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)],[p6]) ).
cnf(c27,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p13]) ).
cnf(c60,plain,
( 'relation$ulike'(X2)
| ~ 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p28]) ).
cnf(c65,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p33]) ).
cnf(c67,plain,
'ilf$utype'(sK78,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c69,plain,
'ilf$utype'(sK79,'relation$utype'('empty$uset',sK78)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c70,plain,
sK79 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c65,c60]) ).
cnf(d1,plain,
( 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c65,c9]) ).
cnf(d2,plain,
( 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2)))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c65,d1]) ).
cnf(d3,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c65,d3]) ).
cnf(d5,plain,
'relation$ulike'(sK79),
inference(resolution,[status(thm)],[d4,c69]) ).
cnf(d6,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c65,c27]) ).
cnf(d7,plain,
( ~ 'ilf$utype'(sK78,'set$utype')
| ~ 'ilf$utype'('empty$uset','set$utype')
| subset('domain$uof'(sK79),'empty$uset') ),
inference(resolution,[status(thm)],[c69,c3]) ).
cnf(d8,plain,
( ~ 'ilf$utype'('empty$uset','set$utype')
| subset('domain$uof'(sK79),'empty$uset') ),
inference(resolution,[status(thm)],[c67,d7]) ).
cnf(d9,plain,
subset('domain$uof'(sK79),'empty$uset'),
inference(resolution,[status(thm)],[c65,d8]) ).
cnf(d10,plain,
( ~ subset(X0,'empty$uset')
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[c65,c0]) ).
cnf(d11,plain,
'domain$uof'(sK79) = 'empty$uset',
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ 'ilf$utype'(sK79,'binary$urelation$utype')
| sK79 = 'empty$uset'
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(sK79,'binary$urelation$utype')
| 'empty$uset' != 'empty$uset' ),
inference(resolution,[status(thm)],[c70,d12]) ).
cnf(d14,plain,
~ 'ilf$utype'(sK79,'binary$urelation$utype'),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
~ 'relation$ulike'(sK79),
inference(resolution,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % Computer : n015.cluster.edu
% 0.11/0.44 % Model : x86_64 x86_64
% 0.11/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44 % Memory : 8046.5625MB
% 0.11/0.44 % OS : Linux 6.8.0-71-generic
% 0.11/0.44 % CPULimit : 300
% 0.11/0.44 % WCLimit : 300
% 0.11/0.44 % DateTime : Sat Sep 26 08:06:31 UTC 2026
% 0.11/0.45 % CPUTime :
% 0.11/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.67/4.29 % SZS status Theorem for theBenchmark.p
% 15.67/4.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------