%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET650+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 : n004.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 08:33:00 AM UTC 2026
% Result : Theorem 14.12s 3.96s
% Output : CNFRefutation 14.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 6 unt; 0 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 280 ( 119 ~; 122 |; 7 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 124 ( 11 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'set$utype')
=> ! [X4] :
( 'ilf$utype'(X4,'relation$utype'(X0,X1))
=> ( member('ordered$upair'(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ) ).
fof(p4,axiom,
! [X0] :
( 'ilf$utype'(X0,'binary$urelation$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( member(X1,'domain$uof'(X0))
<=> ? [X2] :
( member('ordered$upair'(X1,X2),X0)
& 'ilf$utype'(X2,'set$utype') ) ) ) ) ).
fof(p6,axiom,
! [X0] :
( 'ilf$utype'(X0,'binary$urelation$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( member(X1,'range$uof'(X0))
<=> ? [X2] :
( member('ordered$upair'(X2,X1),X0)
& 'ilf$utype'(X2,'set$utype') ) ) ) ) ).
fof(p8,axiom,
! [X0] :
( 'ilf$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$utype'(X0,X1)) ) ) ) ) ).
fof(p10,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( subset(X0,X1)
<=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ) ).
fof(p13,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'(X0,'binary$urelation$utype')
<=> ( 'ilf$utype'(X0,'set$utype')
& 'relation$ulike'(X0) ) ) ) ).
fof(p23,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
=> 'relation$ulike'(X2) ) ) ) ).
fof(p26,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_12,conjecture,
! [X0] :
( 'ilf$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$uof'(X2),X0) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$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$uof'(X2),X0) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_12]) ).
cnf(c6,plain,
( ~ 'ilf$utype'(X3,'set$utype')
| ~ member('ordered$upair'(X1,X4),X2)
| ~ 'ilf$utype'(X4,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X3))
| ~ 'ilf$utype'(X1,'set$utype')
| member(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c7,plain,
( ~ 'ilf$utype'(X3,'set$utype')
| ~ member('ordered$upair'(X1,X4),X2)
| ~ 'ilf$utype'(X4,'set$utype')
| member(X4,X3)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X3))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c9,plain,
( member('ordered$upair'(X1,sK15(X0,X1)),X0)
| ~ member(X1,'domain$uof'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c13,plain,
( member('ordered$upair'(sK20(X0,X1),X1),X0)
| ~ member(X1,'range$uof'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p6]) ).
cnf(c17,plain,
( 'ilf$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)],[p8]) ).
cnf(c21,plain,
( member(sK33(X0,X1),X0)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p10]) ).
cnf(c22,plain,
( ~ member(sK33(X0,X1),X1)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p10]) ).
cnf(c27,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p13]) ).
cnf(c50,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)],[p23]) ).
cnf(c55,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p26]) ).
cnf(c58,plain,
'ilf$utype'(sK72,'relation$utype'(sK70,sK71)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
( ~ subset('range$uof'(sK72),sK71)
| ~ subset('domain$uof'(sK72),sK70) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,c27]) ).
cnf(d1,plain,
( subset(X0,X1)
| ~ member(sK33(X0,X1),X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c55,c22]) ).
cnf(d2,plain,
( subset(X1,X0)
| member(sK33(X1,X0),X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c55,c21]) ).
cnf(d3,plain,
( ~ member('ordered$upair'(X4,X3),X0)
| member(X4,X1)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X4,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c55,c6]) ).
cnf(d4,plain,
( member('ordered$upair'(X1,sK15(X0,X1)),X0)
| ~ member(X1,'domain$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,c9]) ).
cnf(d5,plain,
( member(X1,X3)
| ~ 'ilf$utype'(X0,'relation$utype'(X3,X2))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(sK15(X0,X1),'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X1,'domain$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ member(X0,'domain$uof'(X1))
| member(X0,X2)
| ~ 'ilf$utype'(sK15(X1,X0),'set$utype')
| ~ 'ilf$utype'(X1,'relation$utype'(X2,X3))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c55,d5]) ).
cnf(d7,plain,
( ~ member(X3,'domain$uof'(X0))
| member(X3,X1)
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d6,c55]) ).
cnf(d8,plain,
( ~ member(X3,'domain$uof'(X0))
| member(X3,X1)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,d7]) ).
cnf(d9,plain,
( ~ member(X0,'domain$uof'(sK72))
| member(X0,sK70)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d8,c58]) ).
cnf(d10,plain,
( subset('domain$uof'(sK72),X0)
| ~ 'ilf$utype'(X0,'set$utype')
| member(sK33('domain$uof'(sK72),X0),sK70)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( subset('domain$uof'(sK72),X0)
| member(sK33('domain$uof'(sK72),X0),sK70)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,d10]) ).
cnf(d12,plain,
( subset('domain$uof'(sK72),sK70)
| ~ 'ilf$utype'('domain$uof'(sK72),'set$utype')
| subset('domain$uof'(sK72),sK70)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( subset('domain$uof'(sK72),sK70)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,d12]) ).
cnf(d14,plain,
( ~ member('ordered$upair'(X4,X3),X0)
| member(X3,X2)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X4,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c55,c7]) ).
cnf(d15,plain,
( member('ordered$upair'(sK20(X0,X1),X1),X0)
| ~ member(X1,'range$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,c13]) ).
cnf(d16,plain,
( member(X1,X2)
| ~ 'ilf$utype'(X0,'relation$utype'(X3,X2))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(sK20(X0,X1),'set$utype')
| ~ member(X1,'range$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( ~ member(X0,'range$uof'(X1))
| member(X0,X3)
| ~ 'ilf$utype'(sK20(X1,X0),'set$utype')
| ~ 'ilf$utype'(X1,'relation$utype'(X2,X3))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c55,d16]) ).
cnf(d18,plain,
( ~ member(X3,'range$uof'(X0))
| member(X3,X2)
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d17,c55]) ).
cnf(d19,plain,
( ~ member(X3,'range$uof'(X0))
| member(X3,X2)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,d18]) ).
cnf(d20,plain,
( ~ member(X0,'range$uof'(sK72))
| member(X0,sK71)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d19,c58]) ).
cnf(d21,plain,
( subset('range$uof'(sK72),X0)
| ~ 'ilf$utype'(X0,'set$utype')
| member(sK33('range$uof'(sK72),X0),sK71)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d20,d2]) ).
cnf(d22,plain,
( subset('range$uof'(sK72),X0)
| member(sK33('range$uof'(sK72),X0),sK71)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,d21]) ).
cnf(d23,plain,
( subset('range$uof'(sK72),sK71)
| ~ 'ilf$utype'('range$uof'(sK72),'set$utype')
| subset('range$uof'(sK72),sK71)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d22,d1]) ).
cnf(d24,plain,
( subset('range$uof'(sK72),sK71)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c55,d23]) ).
cnf(d25,plain,
( ~ subset('domain$uof'(sK72),sK70)
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d24,c59]) ).
cnf(d26,plain,
( ~ 'ilf$utype'(sK72,'binary$urelation$utype')
| ~ 'ilf$utype'(sK72,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d25,d13]) ).
cnf(d27,plain,
~ 'relation$ulike'(sK72),
inference(resolution,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2)))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c55,c17]) ).
cnf(d29,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c55,c50]) ).
cnf(d30,plain,
( ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X2,'set$utype')
| 'relation$ulike'(X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c55,d30]) ).
cnf(d32,plain,
( 'relation$ulike'(sK72)
| ~ 'ilf$utype'(sK70,'set$utype') ),
inference(resolution,[status(thm)],[d31,c58]) ).
cnf(d33,plain,
'relation$ulike'(sK72),
inference(resolution,[status(thm)],[c55,d32]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:02:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.12/3.96 % SZS status Theorem for theBenchmark.p
% 14.12/3.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------