%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET668+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 : n013.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 08:33:03 AM UTC 2026
% Result : Theorem 28.65s 11.81s
% Output : CNFRefutation 28.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 14 unt; 0 def)
% Number of atoms : 250 ( 23 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 299 ( 126 ~; 125 |; 6 &)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 118 ( 2 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( ( subset(X1,X0)
& subset(X0,X1) )
=> X0 = X1 ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X1))
=> ( subset('identity$urelation$uof'(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ) ).
fof(p7,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')
=> ( 'ilf$utype'(X1,'subset$utype'(X0))
<=> 'ilf$utype'(X1,'member$utype'('power$uset'(X0))) ) ) ) ).
fof(p20,axiom,
! [X0] :
( 'ilf$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(p21,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p22,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(p28,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> domain(X0,X1,X2) = 'domain$uof'(X2) ) ) ) ).
fof(p29,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> 'ilf$utype'(domain(X0,X1,X2),'subset$utype'(X0)) ) ) ) ).
fof(p30,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> range(X0,X1,X2) = 'range$uof'(X2) ) ) ) ).
fof(p32,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_31,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X1,X0))
=> ( subset('identity$urelation$uof'(X1),X2)
=> ( subset(X1,range(X1,X0,X2))
& X1 = domain(X1,X0,X2) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X1,X0))
=> ( subset('identity$urelation$uof'(X1),X2)
=> ( subset(X1,range(X1,X0,X2))
& X1 = domain(X1,X0,X2) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_31]) ).
cnf(c0,plain,
( ~ subset(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| X0 = X1 ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| subset(X3,domain(X1,X2,X0))
| ~ subset('identity$urelation$uof'(X3),X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c2,plain,
( ~ subset('identity$urelation$uof'(X0),X3)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X3,'relation$utype'(X1,X2))
| subset(X0,range(X1,X2,X3)) ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c12,plain,
( ~ member(sK20(X0,X1),X1)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c13,plain,
( member(sK20(X0,X1),X0)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c31,plain,
( 'ilf$utype'(X1,'member$utype'('power$uset'(X0)))
| ~ 'ilf$utype'(X1,'subset$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p16]) ).
cnf(c36,plain,
( ~ member(X0,X2)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X2,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype')
| member(X0,X1) ),
inference(clausification,[status(esa)],[p20]) ).
cnf(c40,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p21]) ).
cnf(c42,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| empty(X0)
| ~ 'ilf$utype'(X1,'member$utype'(X0))
| member(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p22]) ).
cnf(c57,plain,
( 'domain$uof'(X2) = domain(X0,X1,X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p28]) ).
cnf(c58,plain,
( 'ilf$utype'(domain(X0,X1,X2),'subset$utype'(X0))
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p29]) ).
cnf(c59,plain,
( 'range$uof'(X2) = range(X0,X1,X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p30]) ).
cnf(c61,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p32]) ).
cnf(c64,plain,
'ilf$utype'(sK83,'relation$utype'(sK82,sK81)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c65,plain,
( ~ subset(sK82,range(sK82,sK81,sK83))
| domain(sK82,sK81,sK83) != sK82 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
subset('identity$urelation$uof'(sK82),sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset('identity$urelation$uof'(X3),X0)
| subset(X3,range(X1,X2,X0))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c61,c2]) ).
cnf(d1,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| 'range$uof'(X0) = range(X1,X2,X0) ),
inference(resolution,[status(thm)],[c61,c59]) ).
cnf(d2,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| 'range$uof'(sK83) = range(sK82,sK81,sK83) ),
inference(resolution,[status(thm)],[d1,c64]) ).
cnf(d3,plain,
'range$uof'(sK83) = range(sK82,sK81,sK83),
inference(resolution,[status(thm)],[c61,d2]) ).
cnf(d4,plain,
( ~ subset('identity$urelation$uof'(X0),sK83)
| ~ 'ilf$utype'(sK83,'relation$utype'(sK82,sK81))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| subset(X0,'range$uof'(sK83)) ),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ subset('identity$urelation$uof'(X0),sK83)
| subset(X0,'range$uof'(sK83))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c64,d4]) ).
cnf(d6,plain,
( ~ subset('identity$urelation$uof'(X0),sK83)
| subset(X0,'range$uof'(sK83))
| ~ 'ilf$utype'(sK81,'set$utype') ),
inference(resolution,[status(thm)],[c61,d5]) ).
cnf(d7,plain,
( subset(sK82,'range$uof'(sK83))
| ~ 'ilf$utype'(sK81,'set$utype') ),
inference(resolution,[status(thm)],[d6,c66]) ).
cnf(d8,plain,
subset(sK82,'range$uof'(sK83)),
inference(resolution,[status(thm)],[c61,d7]) ).
cnf(d9,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype')
| X0 = X1 ),
inference(resolution,[status(thm)],[c61,c0]) ).
cnf(d10,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c61,d9]) ).
cnf(d11,plain,
( ~ subset('identity$urelation$uof'(X3),X0)
| subset(X3,domain(X1,X2,X0))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c61,c1]) ).
cnf(d12,plain,
( ~ subset('identity$urelation$uof'(X3),X1)
| subset(X3,domain(X2,X0,X1))
| ~ 'ilf$utype'(X1,'relation$utype'(X2,X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,d11]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| 'domain$uof'(X0) = domain(X1,X2,X0) ),
inference(resolution,[status(thm)],[c61,c57]) ).
cnf(d14,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| 'domain$uof'(sK83) = domain(sK82,sK81,sK83) ),
inference(resolution,[status(thm)],[d13,c64]) ).
cnf(d15,plain,
'domain$uof'(sK83) = domain(sK82,sK81,sK83),
inference(resolution,[status(thm)],[c61,d14]) ).
cnf(d16,plain,
( ~ subset('identity$urelation$uof'(X0),sK83)
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK83,'relation$utype'(sK82,sK81))
| subset(X0,'domain$uof'(sK83)) ),
inference(superposition,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
( ~ subset('identity$urelation$uof'(X0),sK83)
| subset(X0,'domain$uof'(sK83))
| ~ 'ilf$utype'(sK81,'set$utype') ),
inference(resolution,[status(thm)],[c64,d16]) ).
cnf(d18,plain,
( ~ subset('identity$urelation$uof'(X0),sK83)
| subset(X0,'domain$uof'(sK83)) ),
inference(resolution,[status(thm)],[c61,d17]) ).
cnf(d19,plain,
subset(sK82,'domain$uof'(sK83)),
inference(resolution,[status(thm)],[d18,c66]) ).
cnf(d20,plain,
( ~ subset('domain$uof'(sK83),sK82)
| sK82 = 'domain$uof'(sK83) ),
inference(resolution,[status(thm)],[d19,d10]) ).
cnf(d21,plain,
( ~ member(sK20(X0,X1),X1)
| subset(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c12]) ).
cnf(d22,plain,
( member(sK20(X0,X1),X0)
| subset(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c13]) ).
cnf(d23,plain,
( ~ member(X1,'power$uset'(X0))
| ~ member(X2,X1)
| member(X2,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c36]) ).
cnf(d24,plain,
( 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| ~ 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c31]) ).
cnf(d25,plain,
( empty(X1)
| member(X0,X1)
| ~ 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c42]) ).
cnf(d26,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)],[d25,d24]) ).
cnf(d27,plain,
( empty('power$uset'(X1))
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c61,d26]) ).
cnf(d28,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c61,c40]) ).
cnf(d29,plain,
( member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( 'ilf$utype'(domain(X1,X2,X0),'subset$utype'(X1))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c61,c58]) ).
cnf(d31,plain,
( ~ 'ilf$utype'(sK83,'relation$utype'(sK82,sK81))
| ~ 'ilf$utype'(sK81,'set$utype')
| 'ilf$utype'('domain$uof'(sK83),'subset$utype'(sK82)) ),
inference(superposition,[status(thm)],[d15,d30]) ).
cnf(d32,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| 'ilf$utype'('domain$uof'(sK83),'subset$utype'(sK82)) ),
inference(resolution,[status(thm)],[c64,d31]) ).
cnf(d33,plain,
'ilf$utype'('domain$uof'(sK83),'subset$utype'(sK82)),
inference(resolution,[status(thm)],[c61,d32]) ).
cnf(d34,plain,
member('domain$uof'(sK83),'power$uset'(sK82)),
inference(resolution,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
( member(X0,sK82)
| ~ member(X0,'domain$uof'(sK83))
| ~ 'ilf$utype'(sK82,'set$utype')
| ~ 'ilf$utype'('domain$uof'(sK83),'set$utype') ),
inference(resolution,[status(thm)],[d34,d23]) ).
cnf(d36,plain,
( member(X0,sK82)
| ~ member(X0,'domain$uof'(sK83))
| ~ 'ilf$utype'(sK82,'set$utype') ),
inference(resolution,[status(thm)],[c61,d35]) ).
cnf(d37,plain,
( subset('domain$uof'(sK83),X0)
| ~ 'ilf$utype'('domain$uof'(sK83),'set$utype')
| member(sK20('domain$uof'(sK83),X0),sK82)
| ~ 'ilf$utype'(sK82,'set$utype') ),
inference(resolution,[status(thm)],[d36,d22]) ).
cnf(d38,plain,
( member(sK20('domain$uof'(sK83),X0),sK82)
| subset('domain$uof'(sK83),X0)
| ~ 'ilf$utype'(sK82,'set$utype') ),
inference(resolution,[status(thm)],[c61,d37]) ).
cnf(d39,plain,
( subset('domain$uof'(sK83),sK82)
| ~ 'ilf$utype'('domain$uof'(sK83),'set$utype')
| subset('domain$uof'(sK83),sK82)
| ~ 'ilf$utype'(sK82,'set$utype') ),
inference(resolution,[status(thm)],[d38,d21]) ).
cnf(d40,plain,
( subset('domain$uof'(sK83),sK82)
| ~ 'ilf$utype'(sK82,'set$utype') ),
inference(resolution,[status(thm)],[c61,d39]) ).
cnf(d41,plain,
( sK82 = 'domain$uof'(sK83)
| ~ 'ilf$utype'(sK82,'set$utype') ),
inference(resolution,[status(thm)],[d40,d20]) ).
cnf(d42,plain,
sK82 = 'domain$uof'(sK83),
inference(resolution,[status(thm)],[c61,d41]) ).
cnf(d43,plain,
( ~ subset(sK82,range(sK82,sK81,sK83))
| 'domain$uof'(sK83) != sK82 ),
inference(demodulation,[status(thm)],[c65,d15]) ).
cnf(d44,plain,
( ~ subset(sK82,'range$uof'(sK83))
| 'domain$uof'(sK83) != sK82 ),
inference(demodulation,[status(thm)],[d43,d3]) ).
cnf(d45,plain,
( ~ subset(sK82,'range$uof'(sK83))
| sK82 != sK82 ),
inference(demodulation,[status(thm)],[d44,d42]) ).
cnf(d46,plain,
~ subset(sK82,'range$uof'(sK83)),
inference(equality_resolution,[status(thm)],[d45]) ).
cnf(d47,plain,
$false,
inference(resolution,[status(thm)],[d46,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET668+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
% 0.10/5.61 % Computer : n013.cluster.edu
% 0.10/5.61 % Model : x86_64 x86_64
% 0.10/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.61 % Memory : 8046.5625MB
% 0.10/5.61 % OS : Linux 6.8.0-71-generic
% 0.10/5.61 % CPULimit : 300
% 0.10/5.61 % WCLimit : 300
% 0.10/5.61 % DateTime : Sat Sep 26 08:03:49 UTC 2026
% 0.10/5.62 % CPUTime :
% 0.10/5.62 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.65/11.81 % SZS status Theorem for theBenchmark.p
% 28.65/11.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------