%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET667+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 : n005.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 15.73s 12.44s
% Output : CNFRefutation 15.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 9 unt; 0 def)
% Number of atoms : 236 ( 12 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 291 ( 125 ~; 122 |; 6 &)
% ( 3 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 116 ( 6 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'binary$urelation$utype')
=> ( member('ordered$upair'(X0,X1),X2)
=> ( member(X1,'range$uof'(X2))
& member(X0,'domain$uof'(X2)) ) ) ) ) ) ).
fof(p3,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member('ordered$upair'(X1,X2),'identity$urelation$uof'(X0))
<=> ( X1 = X2
& member(X1,X0) ) ) ) ) ) ).
fof(p5,axiom,
! [X0] :
( 'ilf$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$utype'(X0,X1)) ) ) ) ) ).
fof(p7,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( subset(X0,X1)
<=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ) ).
fof(p13,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'(X0,'binary$urelation$utype')
<=> ( 'ilf$utype'(X0,'set$utype')
& 'relation$ulike'(X0) ) ) ) ).
fof(p24,axiom,
! [X0] :
( 'ilf$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(p29,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$uof'(X2) ) ) ) ).
fof(p31,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_30,conjecture,
! [X0] :
( 'ilf$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$uof'(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$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$uof'(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_30]) ).
cnf(c0,plain,
( member(X2,'domain$uof'(X0))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ member('ordered$upair'(X2,X1),X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( ~ member('ordered$upair'(X2,X1),X0)
| member(X1,'range$uof'(X0))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c6,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| member('ordered$upair'(X0,X2),'identity$urelation$uof'(X1))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| X0 != X2
| ~ member(X0,X1) ),
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$utype') ),
inference(clausification,[status(esa)],[p5]) ).
cnf(c11,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X2,X0)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| member(X2,X1)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c13,plain,
( member(sK19(X0,X1),X0)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c14,plain,
( ~ member(sK19(X0,X1),X1)
| subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c28,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p13]) ).
cnf(c52,plain,
( 'relation$ulike'(X2)
| ~ 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p24]) ).
cnf(c57,plain,
( domain(X0,X1,X2) = 'domain$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(c59,plain,
( range(X0,X1,X2) = 'range$uof'(X2)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p29]) ).
cnf(c61,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p31]) ).
cnf(c65,plain,
'ilf$utype'(sK81,'relation$utype'(sK78,sK79)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
subset('identity$urelation$uof'(sK80),sK81),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c67,plain,
( ~ subset(sK80,range(sK78,sK79,sK81))
| ~ subset(sK80,domain(sK78,sK79,sK81)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,c28]) ).
cnf(d1,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| range(X0,X1,X2) = 'range$uof'(X2) ),
inference(resolution,[status(thm)],[c61,c59]) ).
cnf(d2,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| range(sK78,sK79,sK81) = 'range$uof'(sK81) ),
inference(resolution,[status(thm)],[d1,c65]) ).
cnf(d3,plain,
range(sK78,sK79,sK81) = 'range$uof'(sK81),
inference(resolution,[status(thm)],[c61,d2]) ).
cnf(d4,plain,
( ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X0,'set$utype')
| domain(X0,X1,X2) = 'domain$uof'(X2) ),
inference(resolution,[status(thm)],[c61,c57]) ).
cnf(d5,plain,
( ~ 'ilf$utype'(sK78,'set$utype')
| domain(sK78,sK79,sK81) = 'domain$uof'(sK81) ),
inference(resolution,[status(thm)],[d4,c65]) ).
cnf(d6,plain,
domain(sK78,sK79,sK81) = 'domain$uof'(sK81),
inference(resolution,[status(thm)],[c61,d5]) ).
cnf(d7,plain,
( ~ subset(sK80,range(sK78,sK79,sK81))
| ~ subset(sK80,'domain$uof'(sK81)) ),
inference(demodulation,[status(thm)],[c67,d6]) ).
cnf(d8,plain,
( ~ subset(sK80,'range$uof'(sK81))
| ~ subset(sK80,'domain$uof'(sK81)) ),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( subset(X1,X0)
| member(sK19(X1,X0),X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c13]) ).
cnf(d10,plain,
( subset(X1,X0)
| ~ member(sK19(X1,X0),X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c14]) ).
cnf(d11,plain,
( ~ member('ordered$upair'(X2,X1),X0)
| member(X1,'range$uof'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,c1]) ).
cnf(d12,plain,
( ~ member('ordered$upair'(X2,X1),X0)
| member(X1,'range$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d11]) ).
cnf(d13,plain,
( ~ subset(X1,X0)
| ~ member(X2,X1)
| member(X2,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,c11]) ).
cnf(d14,plain,
( member(X0,sK81)
| ~ member(X0,'identity$urelation$uof'(sK80))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'('identity$urelation$uof'(sK80),'set$utype') ),
inference(resolution,[status(thm)],[d13,c66]) ).
cnf(d15,plain,
( member(X0,sK81)
| ~ member(X0,'identity$urelation$uof'(sK80))
| ~ 'ilf$utype'(sK81,'set$utype') ),
inference(resolution,[status(thm)],[c61,d14]) ).
cnf(d16,plain,
( member('ordered$upair'(X1,X1),'identity$urelation$uof'(X0))
| ~ member(X1,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d17,plain,
( member('ordered$upair'(X1,X1),'identity$urelation$uof'(X0))
| ~ member(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c61,d16]) ).
cnf(d18,plain,
( member('ordered$upair'(X0,X0),sK81)
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ member(X0,sK80)
| ~ 'ilf$utype'(sK80,'set$utype') ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
( member('ordered$upair'(X0,X0),sK81)
| ~ member(X0,sK80)
| ~ 'ilf$utype'(sK81,'set$utype') ),
inference(resolution,[status(thm)],[c61,d18]) ).
cnf(d20,plain,
( member(X0,'range$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype')
| ~ member(X0,sK80)
| ~ 'ilf$utype'(sK81,'set$utype') ),
inference(resolution,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
( ~ member(X0,sK80)
| member(X0,'range$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d20]) ).
cnf(d22,plain,
( subset(X0,'range$uof'(sK81))
| ~ 'ilf$utype'('range$uof'(sK81),'set$utype')
| ~ member(sK19(X0,'range$uof'(sK81)),sK80)
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d21,d10]) ).
cnf(d23,plain,
( subset(X0,'range$uof'(sK81))
| ~ member(sK19(X0,'range$uof'(sK81)),sK80)
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d22]) ).
cnf(d24,plain,
( subset(sK80,'range$uof'(sK81))
| ~ 'ilf$utype'('range$uof'(sK81),'set$utype')
| subset(sK80,'range$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d23,d9]) ).
cnf(d25,plain,
( subset(sK80,'range$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d24]) ).
cnf(d26,plain,
( ~ subset(sK80,'domain$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d25,d8]) ).
cnf(d27,plain,
( ~ member('ordered$upair'(X2,X1),X0)
| member(X2,'domain$uof'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,c0]) ).
cnf(d28,plain,
( ~ member('ordered$upair'(X1,X2),X0)
| member(X1,'domain$uof'(X0))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d27]) ).
cnf(d29,plain,
( member(X0,'domain$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype')
| ~ member(X0,sK80)
| ~ 'ilf$utype'(sK81,'set$utype') ),
inference(resolution,[status(thm)],[d19,d28]) ).
cnf(d30,plain,
( ~ member(X0,sK80)
| member(X0,'domain$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d29]) ).
cnf(d31,plain,
( subset(X0,'domain$uof'(sK81))
| ~ 'ilf$utype'('domain$uof'(sK81),'set$utype')
| ~ member(sK19(X0,'domain$uof'(sK81)),sK80)
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d30,d10]) ).
cnf(d32,plain,
( subset(X0,'domain$uof'(sK81))
| ~ member(sK19(X0,'domain$uof'(sK81)),sK80)
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d31]) ).
cnf(d33,plain,
( subset(sK80,'domain$uof'(sK81))
| ~ 'ilf$utype'('domain$uof'(sK81),'set$utype')
| subset(sK80,'domain$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d32,d9]) ).
cnf(d34,plain,
( subset(sK80,'domain$uof'(sK81))
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c61,d33]) ).
cnf(d35,plain,
( ~ 'ilf$utype'(sK81,'binary$urelation$utype')
| ~ 'ilf$utype'(sK81,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d34,d26]) ).
cnf(d36,plain,
~ 'relation$ulike'(sK81),
inference(resolution,[status(thm)],[d35,d0]) ).
cnf(d37,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c61,c9]) ).
cnf(d38,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c61,c52]) ).
cnf(d39,plain,
( ~ 'ilf$utype'(X1,'relation$utype'(X2,X0))
| ~ 'ilf$utype'(X2,'set$utype')
| 'relation$ulike'(X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c61,d39]) ).
cnf(d41,plain,
( 'relation$ulike'(sK81)
| ~ 'ilf$utype'(sK79,'set$utype') ),
inference(resolution,[status(thm)],[d40,c65]) ).
cnf(d42,plain,
'relation$ulike'(sK81),
inference(resolution,[status(thm)],[c61,d41]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET667+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
% 0.12/10.40 % Computer : n005.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.12/10.40 % DateTime : Sat Sep 26 08:04:12 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.12/10.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.73/12.44 % SZS status Theorem for theBenchmark.p
% 15.73/12.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------