%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET680+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 : n011.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 08:33:04 AM UTC 2026
% Result : Theorem 18.17s 8.54s
% Output : CNFRefutation 18.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 8 unt; 0 def)
% Number of atoms : 199 ( 5 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 253 ( 108 ~; 100 |; 11 &)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 106 ( 7 sgn 29 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'binary$urelation$utype')
=> ( member(X0,'domain$uof'(X1))
<=> ? [X2] :
( member('ordered$upair'(X0,X2),X1)
& 'ilf$utype'(X2,'set$utype') ) ) ) ) ).
fof(p3,axiom,
! [X0] :
( 'ilf$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(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(p8,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(p17,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'(X0,'binary$urelation$utype')
<=> ( 'ilf$utype'(X0,'set$utype')
& 'relation$ulike'(X0) ) ) ) ).
fof(p26,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(p27,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$uof'(X2) ) ) ) ).
fof(p31,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_47,conjecture,
! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ! [X3] :
( 'ilf$utype'(X3,'member$utype'(X0))
=> ( member(X3,domain(X0,X1,X2))
<=> ? [X4] :
( member('ordered$upair'(X3,X4),X2)
& 'ilf$utype'(X4,'member$utype'(X1)) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ! [X3] :
( 'ilf$utype'(X3,'member$utype'(X0))
=> ( member(X3,domain(X0,X1,X2))
<=> ? [X4] :
( member('ordered$upair'(X3,X4),X2)
& 'ilf$utype'(X4,'member$utype'(X1)) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_47]) ).
cnf(c1,plain,
( member('ordered$upair'(X0,sK2(X0,X1)),X1)
| ~ member(X0,'domain$uof'(X1))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c2,plain,
( ~ 'ilf$utype'(X2,'binary$urelation$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| member(X0,'domain$uof'(X2))
| ~ member('ordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c6,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ member('ordered$upair'(X4,X3),X0)
| ~ 'ilf$utype'(X4,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| member(X3,X2)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c11,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$utype') ),
inference(clausification,[status(esa)],[p6]) ).
cnf(c14,plain,
( empty(X1)
| ~ 'ilf$utype'(X1,'set$utype')
| 'ilf$utype'(X0,'member$utype'(X1))
| ~ member(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p8]) ).
cnf(c27,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p17]) ).
cnf(c56,plain,
( 'relation$ulike'(X2)
| ~ 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p26]) ).
cnf(c57,plain,
( domain(X0,X1,X2) = 'domain$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p27]) ).
cnf(c61,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p31]) ).
cnf(c64,plain,
~ empty(sK84),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
'ilf$utype'(sK85,'relation$utype'(sK83,sK84)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c70,plain,
( member('ordered$upair'(sK86,sK88),sK85)
| member(sK86,domain(sK83,sK84,sK85)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c71,plain,
( ~ member(sK86,domain(sK83,sK84,sK85))
| ~ member('ordered$upair'(sK86,X0),sK85)
| ~ 'ilf$utype'(X0,'member$utype'(sK84)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,c27]) ).
cnf(d1,plain,
( ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X0,'set$utype')
| domain(X0,X1,X2) = 'domain$uof'(X2) ),
inference(resolution,[status(thm)],[c61,c57]) ).
cnf(d2,plain,
( ~ 'ilf$utype'(sK83,'set$utype')
| domain(sK83,sK84,sK85) = 'domain$uof'(sK85) ),
inference(resolution,[status(thm)],[d1,c66]) ).
cnf(d3,plain,
domain(sK83,sK84,sK85) = 'domain$uof'(sK85),
inference(resolution,[status(thm)],[c61,d2]) ).
cnf(d4,plain,
( member(sK86,'domain$uof'(sK85))
| member('ordered$upair'(sK86,sK88),sK85) ),
inference(demodulation,[status(thm)],[c70,d3]) ).
cnf(d5,plain,
( ~ member('ordered$upair'(X2,X0),X1)
| member(X2,'domain$uof'(X1))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c2]) ).
cnf(d6,plain,
( ~ member('ordered$upair'(X1,X2),X0)
| member(X1,'domain$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d5]) ).
cnf(d7,plain,
( member(sK86,'domain$uof'(sK85))
| member(sK86,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK85,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c14]) ).
cnf(d9,plain,
( empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c61,d8]) ).
cnf(d10,plain,
( ~ member(sK86,'domain$uof'(sK85))
| ~ member('ordered$upair'(sK86,X0),sK85)
| ~ 'ilf$utype'(X0,'member$utype'(sK84)) ),
inference(demodulation,[status(thm)],[c71,d3]) ).
cnf(d11,plain,
( member('ordered$upair'(X1,sK2(X1,X0)),X0)
| ~ member(X1,'domain$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,c1]) ).
cnf(d12,plain,
( ~ member(sK86,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK2(sK86,sK85),'member$utype'(sK84))
| ~ member(sK86,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK85,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( empty(sK84)
| ~ member(sK2(sK86,sK85),sK84)
| ~ member(sK86,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK85,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
( ~ member(sK86,'domain$uof'(sK85))
| ~ member(sK2(sK86,sK85),sK84)
| ~ 'ilf$utype'(sK85,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c64,d13]) ).
cnf(d15,plain,
( ~ member(X3,'domain$uof'(X1))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| member(sK2(X3,X1),X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(sK2(X3,X1),'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X1,'relation$utype'(X2,X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d16,plain,
( member(sK2(X3,X1),X2)
| ~ member(X3,'domain$uof'(X1))
| ~ 'ilf$utype'(sK2(X3,X1),'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,d15]) ).
cnf(d17,plain,
( member(sK2(X3,X1),X0)
| ~ member(X3,'domain$uof'(X1))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'relation$utype'(X2,X0))
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d16,c61]) ).
cnf(d18,plain,
( member(sK2(X3,X0),X2)
| ~ member(X3,'domain$uof'(X0))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d17]) ).
cnf(d19,plain,
( member(sK2(X0,sK85),sK84)
| ~ member(X0,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK85,'binary$urelation$utype')
| ~ 'ilf$utype'(sK84,'set$utype') ),
inference(resolution,[status(thm)],[d18,c66]) ).
cnf(d20,plain,
( member(sK2(X0,sK85),sK84)
| ~ member(X0,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK85,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d19]) ).
cnf(d21,plain,
( ~ member(sK86,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK85,'binary$urelation$utype')
| ~ member(sK86,'domain$uof'(sK85))
| ~ 'ilf$utype'(sK85,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
( ~ 'ilf$utype'(sK85,'binary$urelation$utype')
| ~ 'ilf$utype'(sK85,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d21,d7]) ).
cnf(d23,plain,
~ 'relation$ulike'(sK85),
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
( 'relation$ulike'(X1)
| ~ 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c56]) ).
cnf(d25,plain,
( 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c11]) ).
cnf(d26,plain,
( 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2)))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c61,d25]) ).
cnf(d27,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c61,d27]) ).
cnf(d29,plain,
'relation$ulike'(sK85),
inference(resolution,[status(thm)],[d28,c66]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET680+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n011.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Sat Sep 26 08:05:19 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.17/8.54 % SZS status Theorem for theBenchmark.p
% 18.17/8.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------