%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET666+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 : n014.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 22.98s 16.31s
% Output : CNFRefutation 22.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 181 ( 74 ~; 77 |; 3 &)
% ( 5 <=>; 22 =>; 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; 2 con; 0-2 aty)
% Number of variables : 89 ( 2 sgn 21 !; 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(p3,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> subset('identity$urelation$uof'(X0),'cross$uproduct'(X0,X0)) ) ).
fof(p6,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
<=> 'ilf$utype'(X1,'relation$utype'(X0,X0)) ) ) ) ).
fof(p12,axiom,
! [X0] :
( 'ilf$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(p14,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(p16,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( member(X0,'power$uset'(X1))
<=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ) ).
fof(p17,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p18,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ( 'ilf$utype'(X0,'member$utype'(X1))
<=> member(X0,X1) ) ) ) ).
fof(p24,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_29,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> 'ilf$utype'('identity$urelation$uof'(X0),'identity$urelation$uof$utype'(X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> 'ilf$utype'('identity$urelation$uof'(X0),'identity$urelation$uof$utype'(X0)) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_29]) ).
cnf(c0,plain,
( 'ilf$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(c3,plain,
( subset('identity$urelation$uof'(X0),'cross$uproduct'(X0,X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c9,plain,
( ~ 'ilf$utype'(X1,'relation$utype'(X0,X0))
| 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p6]) ).
cnf(c18,plain,
( ~ 'ilf$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)],[p12]) ).
cnf(c20,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X0,X2)
| ~ subset(X2,X1)
| member(X0,X1) ),
inference(clausification,[status(esa)],[p14]) ).
cnf(c27,plain,
( member(sK34(X0,X1),X0)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p16]) ).
cnf(c28,plain,
( ~ member(sK34(X0,X1),X1)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p16]) ).
cnf(c29,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p17]) ).
cnf(c32,plain,
( ~ member(X1,X0)
| empty(X0)
| 'ilf$utype'(X1,'member$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p18]) ).
cnf(c47,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p24]) ).
cnf(c49,plain,
~ 'ilf$utype'('identity$urelation$uof'(sK56),'identity$urelation$uof$utype'(sK56)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| 'ilf$utype'(X0,'identity$urelation$uof$utype'(X1))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X1)) ),
inference(resolution,[status(thm)],[c47,c9]) ).
cnf(d1,plain,
subset('identity$urelation$uof'(X0),'cross$uproduct'(X0,X0)),
inference(resolution,[status(thm)],[c47,c3]) ).
cnf(d2,plain,
( 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c0]) ).
cnf(d3,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c47,d2]) ).
cnf(d4,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c47,c18]) ).
cnf(d5,plain,
( empty(X1)
| ~ member(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c47,c32]) ).
cnf(d6,plain,
( 'ilf$utype'(X1,'subset$utype'(X0))
| ~ 'ilf$utype'(X0,'set$utype')
| empty('power$uset'(X0))
| ~ member(X1,'power$uset'(X0))
| ~ 'ilf$utype'('power$uset'(X0),'set$utype') ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( empty('power$uset'(X1))
| ~ member(X0,'power$uset'(X1))
| ~ 'ilf$utype'('power$uset'(X1),'set$utype')
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c47,d6]) ).
cnf(d8,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c47,c29]) ).
cnf(d9,plain,
( ~ member(X0,'power$uset'(X1))
| ~ 'ilf$utype'('power$uset'(X1),'set$utype')
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ member(sK34(X0,X1),X1)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c28]) ).
cnf(d11,plain,
( member(sK34(X1,X0),X1)
| member(X1,'power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c27]) ).
cnf(d12,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c20]) ).
cnf(d13,plain,
( member(X1,'power$uset'(X2))
| ~ 'ilf$utype'(X2,'set$utype')
| member(sK34(X1,X2),X0)
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( member(sK34(X0,X2),X1)
| member(X0,'power$uset'(X2))
| ~ subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,d13]) ).
cnf(d15,plain,
( member(X1,'power$uset'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| member(X1,'power$uset'(X0))
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
( member(X1,'power$uset'(X0))
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,d15]) ).
cnf(d17,plain,
( ~ 'ilf$utype'('power$uset'(X0),'set$utype')
| 'ilf$utype'(X1,'subset$utype'(X0))
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d16,d9]) ).
cnf(d18,plain,
( ~ subset(X0,X1)
| ~ 'ilf$utype'('power$uset'(X1),'set$utype')
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c47,d17]) ).
cnf(d19,plain,
( ~ subset(X0,X1)
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d18,c47]) ).
cnf(d20,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ subset(X0,'cross$uproduct'(X1,X2)) ),
inference(resolution,[status(thm)],[d19,d3]) ).
cnf(d21,plain,
'ilf$utype'('identity$urelation$uof'(X0),'relation$utype'(X0,X0)),
inference(resolution,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
( 'ilf$utype'('identity$urelation$uof'(X0),'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
'ilf$utype'('identity$urelation$uof'(X0),'identity$urelation$uof$utype'(X0)),
inference(resolution,[status(thm)],[c47,d22]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,c49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET666+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
% 0.13/10.39 % Computer : n014.cluster.edu
% 0.13/10.39 % Model : x86_64 x86_64
% 0.13/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.39 % Memory : 8046.5625MB
% 0.13/10.39 % OS : Linux 6.8.0-71-generic
% 0.13/10.40 % CPULimit : 300
% 0.13/10.40 % WCLimit : 300
% 0.13/10.40 % DateTime : Sat Sep 26 08:04:13 UTC 2026
% 0.16/10.40 % CPUTime :
% 0.16/10.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.98/16.31 % SZS status Theorem for theBenchmark.p
% 22.98/16.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------