%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET686+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 : n009.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 08:33:05 AM UTC 2026
% Result : Theorem 29.38s 7.03s
% Output : CNFRefutation 29.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 104 ( 8 unt; 0 def)
% Number of atoms : 486 ( 3 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 711 ( 329 ~; 328 |; 16 &)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 143 ( 7 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'binary$urelation$utype')
=> ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member('ordered$upair'(X1,X3),X2)
& 'ilf$utype'(X3,'set$utype') ) ) ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'set$utype')
=> ! [X4] :
( 'ilf$utype'(X4,'relation$utype'(X0,X1))
=> ( member('ordered$upair'(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ) ).
fof(p5,axiom,
! [X0] :
( 'ilf$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$utype')
& ~ empty(X1) )
=> ( 'ilf$utype'(X0,'member$utype'(X1))
<=> member(X0,X1) ) ) ) ).
fof(p15,axiom,
! [X0] :
( 'ilf$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$ulike'(X2) ) ) ) ).
fof(p25,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ! [X3] :
( 'ilf$utype'(X3,'set$utype')
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ) ).
fof(p27,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_53,conjecture,
! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ! [X2] :
( ( 'ilf$utype'(X2,'set$utype')
& ~ empty(X2) )
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X2))
=> ! [X4] :
( 'ilf$utype'(X4,'member$utype'(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member('ordered$upair'(X4,X5),X3)
& 'ilf$utype'(X5,'member$utype'(X2)) ) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> ! [X1] :
( ( 'ilf$utype'(X1,'set$utype')
& ~ empty(X1) )
=> ! [X2] :
( ( 'ilf$utype'(X2,'set$utype')
& ~ empty(X2) )
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X2))
=> ! [X4] :
( 'ilf$utype'(X4,'member$utype'(X0))
=> ( member(X4,inverse4(X0,X2,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member('ordered$upair'(X4,X5),X3)
& 'ilf$utype'(X5,'member$utype'(X2)) ) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_53]) ).
cnf(c1,plain,
( member('ordered$upair'(X1,sK3(X2,X1,X0)),X0)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ member(X1,inverse2(X0,X2))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c2,plain,
( member(sK3(X2,X1,X0),X2)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ member(X1,inverse2(X0,X2))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c3,plain,
( ~ member(X3,X2)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ member('ordered$upair'(X0,X3),X1)
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| member(X0,inverse2(X1,X2)) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c5,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ member('ordered$upair'(X4,X0),X3)
| ~ 'ilf$utype'(X4,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X3,'relation$utype'(X2,X1))
| ~ 'ilf$utype'(X2,'set$utype')
| member(X0,X1) ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c10,plain,
( 'ilf$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(c13,plain,
( 'ilf$utype'(X0,'member$utype'(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c25,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p15]) ).
cnf(c54,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(c55,plain,
( ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| inverse4(X2,X3,X1,X0) = inverse2(X1,X0)
| ~ 'ilf$utype'(X1,'relation$utype'(X2,X3))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p25]) ).
cnf(c57,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p27]) ).
cnf(c62,plain,
~ empty(sK79),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c64,plain,
'ilf$utype'(sK80,'relation$utype'(sK77,sK79)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c67,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| member(sK81,inverse4(sK77,sK79,sK80,sK78)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c68,plain,
( member('ordered$upair'(sK81,sK83),sK80)
| member(sK81,inverse4(sK77,sK79,sK80,sK78)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c69,plain,
( member(sK83,sK78)
| member(sK81,inverse4(sK77,sK79,sK80,sK78)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c70,plain,
( ~ member(sK81,inverse4(sK77,sK79,sK80,sK78))
| ~ member(X0,sK78)
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ 'ilf$utype'(X0,'member$utype'(sK79)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c71,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ member(X0,sK78)
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ 'ilf$utype'(X0,'member$utype'(sK79)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c72,plain,
( member('ordered$upair'(sK81,sK83),sK80)
| ~ member(X0,sK78)
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ 'ilf$utype'(X0,'member$utype'(sK79)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c73,plain,
( member(sK83,sK78)
| ~ member(X0,sK78)
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ 'ilf$utype'(X0,'member$utype'(sK79)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'relation$ulike'(X0)
| 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c57,c25]) ).
cnf(d1,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(resolution,[status(thm)],[c57,c55]) ).
cnf(d2,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK80,'relation$utype'(sK77,sK79))
| ~ 'ilf$utype'(sK78,'set$utype')
| 'ilf$utype'(sK83,'member$utype'(sK79))
| member(sK81,inverse2(sK80,sK78)) ),
inference(superposition,[status(thm)],[d1,c67]) ).
cnf(d3,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK78,'set$utype')
| member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[c64,d2]) ).
cnf(d4,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK79,'set$utype')
| member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[c57,d3]) ).
cnf(d5,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| member(sK3(X2,X0,X1),X2)
| ~ member(X0,inverse2(X1,X2)) ),
inference(resolution,[status(thm)],[c57,c2]) ).
cnf(d6,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'member$utype'(sK79))
| ~ member(sK3(X0,sK81,sK80),sK78)
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member(sK81,inverse2(sK80,X0)) ),
inference(resolution,[status(thm)],[c1,c71]) ).
cnf(d7,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'member$utype'(sK79))
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d6]) ).
cnf(d8,plain,
( empty(X1)
| 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c57,c13]) ).
cnf(d9,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78)
| empty(sK79)
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'set$utype')
| ~ member(sK3(X0,sK81,sK80),sK79) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'set$utype')
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK79)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c62,d9]) ).
cnf(d11,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK79)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d10]) ).
cnf(d12,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X3,'relation$utype'(X4,X1))
| ~ member('ordered$upair'(X2,X0),X3)
| member(X0,X1) ),
inference(resolution,[status(thm)],[c57,c5]) ).
cnf(d13,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member('ordered$upair'(X1,X0),sK80)
| member(X0,sK79) ),
inference(resolution,[status(thm)],[d12,c64]) ).
cnf(d14,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member('ordered$upair'(X1,X0),sK80)
| member(X0,sK79) ),
inference(resolution,[status(thm)],[c57,d13]) ).
cnf(d15,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'binary$urelation$utype')
| member('ordered$upair'(X0,sK3(X2,X0,X1)),X1)
| ~ member(X0,inverse2(X1,X2)) ),
inference(resolution,[status(thm)],[c57,c1]) ).
cnf(d16,plain,
( ~ 'ilf$utype'(X1,'binary$urelation$utype')
| member('ordered$upair'(X0,sK3(X2,X0,X1)),X1)
| ~ member(X0,inverse2(X1,X2)) ),
inference(resolution,[status(thm)],[c57,d15]) ).
cnf(d17,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK3(X1,X0,sK80),'set$utype')
| member(sK3(X1,X0,sK80),sK79)
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(X0,inverse2(sK80,X1)) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK79,'set$utype')
| member(sK3(X1,X0,sK80),sK79)
| ~ member(X0,inverse2(sK80,X1)) ),
inference(resolution,[status(thm)],[c57,d17]) ).
cnf(d19,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78)
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK79,'set$utype')
| ~ member(sK81,inverse2(sK80,X0)) ),
inference(resolution,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d19]) ).
cnf(d21,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,sK78))
| 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[d20,d5]) ).
cnf(d22,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[c57,d21]) ).
cnf(d23,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK79,'set$utype')
| 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK80,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d22,d4]) ).
cnf(d24,plain,
( 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK80,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[c57,d23]) ).
cnf(d25,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK80,'relation$utype'(sK77,sK79))
| ~ 'ilf$utype'(sK78,'set$utype')
| member('ordered$upair'(sK81,sK83),sK80)
| member(sK81,inverse2(sK80,sK78)) ),
inference(superposition,[status(thm)],[d1,c68]) ).
cnf(d26,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK78,'set$utype')
| member(sK81,inverse2(sK80,sK78))
| member('ordered$upair'(sK81,sK83),sK80) ),
inference(resolution,[status(thm)],[c64,d25]) ).
cnf(d27,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| member(sK81,inverse2(sK80,sK78))
| member('ordered$upair'(sK81,sK83),sK80) ),
inference(resolution,[status(thm)],[c57,d26]) ).
cnf(d28,plain,
( ~ 'ilf$utype'(sK3(X0,sK81,sK80),'member$utype'(sK79))
| member('ordered$upair'(sK81,sK83),sK80)
| ~ member(sK3(X0,sK81,sK80),sK78)
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member(sK81,inverse2(sK80,X0)) ),
inference(resolution,[status(thm)],[c1,c72]) ).
cnf(d29,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'member$utype'(sK79))
| ~ member(sK81,inverse2(sK80,X0))
| member('ordered$upair'(sK81,sK83),sK80)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d28]) ).
cnf(d30,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| member('ordered$upair'(sK81,sK83),sK80)
| ~ member(sK3(X0,sK81,sK80),sK78)
| empty(sK79)
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'set$utype')
| ~ member(sK3(X0,sK81,sK80),sK79) ),
inference(resolution,[status(thm)],[d8,d29]) ).
cnf(d31,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'set$utype')
| ~ member(sK81,inverse2(sK80,X0))
| member('ordered$upair'(sK81,sK83),sK80)
| ~ member(sK3(X0,sK81,sK80),sK79)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c62,d30]) ).
cnf(d32,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| member('ordered$upair'(sK81,sK83),sK80)
| ~ member(sK3(X0,sK81,sK80),sK79)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d31]) ).
cnf(d33,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| member('ordered$upair'(sK81,sK83),sK80)
| ~ member(sK3(X0,sK81,sK80),sK78)
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK79,'set$utype')
| ~ member(sK81,inverse2(sK80,X0)) ),
inference(resolution,[status(thm)],[d18,d32]) ).
cnf(d34,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,X0))
| member('ordered$upair'(sK81,sK83),sK80)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d33]) ).
cnf(d35,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,sK78))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,sK78))
| member('ordered$upair'(sK81,sK83),sK80) ),
inference(resolution,[status(thm)],[d34,d5]) ).
cnf(d36,plain,
( ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,sK78))
| member('ordered$upair'(sK81,sK83),sK80) ),
inference(resolution,[status(thm)],[c57,d35]) ).
cnf(d37,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| member('ordered$upair'(sK81,sK83),sK80)
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member('ordered$upair'(sK81,sK83),sK80) ),
inference(resolution,[status(thm)],[d36,d27]) ).
cnf(d38,plain,
( ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member('ordered$upair'(sK81,sK83),sK80) ),
inference(resolution,[status(thm)],[c57,d37]) ).
cnf(d39,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK80,'relation$utype'(sK77,sK79))
| ~ 'ilf$utype'(sK78,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'(sK79))
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ member(X0,sK78)
| ~ member(sK81,inverse2(sK80,sK78)) ),
inference(superposition,[status(thm)],[d1,c70]) ).
cnf(d40,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK78,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'(sK79))
| ~ member(sK81,inverse2(sK80,sK78))
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ member(X0,sK78) ),
inference(resolution,[status(thm)],[c64,d39]) ).
cnf(d41,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'(sK79))
| ~ member(sK81,inverse2(sK80,sK78))
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ member(X0,sK78) ),
inference(resolution,[status(thm)],[c57,d40]) ).
cnf(d42,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X3,'binary$urelation$utype')
| ~ member('ordered$upair'(X2,X0),X3)
| member(X2,inverse2(X3,X1))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c57,c3]) ).
cnf(d43,plain,
( ~ 'ilf$utype'(sK83,'set$utype')
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK83,X0)
| member(sK81,inverse2(sK80,X0))
| ~ 'ilf$utype'(sK80,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d38,d42]) ).
cnf(d44,plain,
( ~ 'ilf$utype'(sK83,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK83,X0)
| member(sK81,inverse2(sK80,X0)) ),
inference(resolution,[status(thm)],[c57,d43]) ).
cnf(d45,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'(sK79))
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ member(X0,sK78)
| ~ 'ilf$utype'(sK83,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK83,sK78) ),
inference(resolution,[status(thm)],[d44,d41]) ).
cnf(d46,plain,
( ~ 'ilf$utype'(sK83,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'member$utype'(sK79))
| ~ member(sK83,sK78)
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ member(X0,sK78) ),
inference(resolution,[status(thm)],[c57,d45]) ).
cnf(d47,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK80,'relation$utype'(sK77,sK79))
| ~ 'ilf$utype'(sK78,'set$utype')
| member(sK83,sK78)
| member(sK81,inverse2(sK80,sK78)) ),
inference(superposition,[status(thm)],[d1,c69]) ).
cnf(d48,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| ~ 'ilf$utype'(sK78,'set$utype')
| member(sK83,sK78)
| member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[c64,d47]) ).
cnf(d49,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| member(sK83,sK78)
| member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[c57,d48]) ).
cnf(d50,plain,
( ~ 'ilf$utype'(sK3(X0,sK81,sK80),'member$utype'(sK79))
| member(sK83,sK78)
| ~ member(sK3(X0,sK81,sK80),sK78)
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member(sK81,inverse2(sK80,X0)) ),
inference(resolution,[status(thm)],[c1,c73]) ).
cnf(d51,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'member$utype'(sK79))
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d50]) ).
cnf(d52,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78)
| empty(sK79)
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'set$utype')
| ~ member(sK3(X0,sK81,sK80),sK79) ),
inference(resolution,[status(thm)],[d8,d51]) ).
cnf(d53,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK3(X0,sK81,sK80),'set$utype')
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK79)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c62,d52]) ).
cnf(d54,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK79)
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d53]) ).
cnf(d55,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78)
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK79,'set$utype')
| ~ member(sK81,inverse2(sK80,X0)) ),
inference(resolution,[status(thm)],[d18,d54]) ).
cnf(d56,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,X0))
| ~ member(sK3(X0,sK81,sK80),sK78) ),
inference(resolution,[status(thm)],[c57,d55]) ).
cnf(d57,plain,
( ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK81,inverse2(sK80,sK78))
| ~ 'ilf$utype'(sK81,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[d56,d5]) ).
cnf(d58,plain,
( ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78)
| ~ member(sK81,inverse2(sK80,sK78)) ),
inference(resolution,[status(thm)],[c57,d57]) ).
cnf(d59,plain,
( ~ 'ilf$utype'(sK79,'set$utype')
| member(sK83,sK78)
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78) ),
inference(resolution,[status(thm)],[d58,d49]) ).
cnf(d60,plain,
( ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| member(sK83,sK78) ),
inference(resolution,[status(thm)],[c57,d59]) ).
cnf(d61,plain,
( ~ 'relation$ulike'(sK80)
| member(sK83,sK78) ),
inference(resolution,[status(thm)],[d60,d0]) ).
cnf(d62,plain,
( 'relation$ulike'(X1)
| ~ 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c57,c54]) ).
cnf(d63,plain,
( 'ilf$utype'(X1,'subset$utype'('cross$uproduct'(X0,X2)))
| ~ 'ilf$utype'(X1,'relation$utype'(X0,X2))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c57,c10]) ).
cnf(d64,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
( 'relation$ulike'(X0)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c57,d64]) ).
cnf(d66,plain,
'relation$ulike'(sK80),
inference(resolution,[status(thm)],[d65,c64]) ).
cnf(d67,plain,
member(sK83,sK78),
inference(resolution,[status(thm)],[d66,d61]) ).
cnf(d68,plain,
( ~ 'ilf$utype'(sK83,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(X0,'member$utype'(sK79))
| ~ member('ordered$upair'(sK81,X0),sK80)
| ~ member(X0,sK78) ),
inference(resolution,[status(thm)],[d67,d46]) ).
cnf(d69,plain,
( ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK83,'set$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ member(sK83,sK78) ),
inference(resolution,[status(thm)],[d68,d38]) ).
cnf(d70,plain,
( ~ 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ member(sK83,sK78) ),
inference(resolution,[status(thm)],[c57,d69]) ).
cnf(d71,plain,
( ~ 'ilf$utype'(sK83,'member$utype'(sK79))
| ~ 'ilf$utype'(sK80,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d67,d70]) ).
cnf(d72,plain,
( ~ 'ilf$utype'(sK80,'binary$urelation$utype')
| ~ 'ilf$utype'(sK80,'binary$urelation$utype') ),
inference(resolution,[status(thm)],[d71,d24]) ).
cnf(d73,plain,
~ 'relation$ulike'(sK80),
inference(resolution,[status(thm)],[d72,d0]) ).
cnf(d74,plain,
$false,
inference(resolution,[status(thm)],[d66,d73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET686+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
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:05:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.38/7.03 % SZS status Theorem for theBenchmark.p
% 29.38/7.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------