%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET645+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 : n007.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 30.27s 7.25s
% Output : CNFRefutation 30.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 219 ( 92 ~; 88 |; 6 &)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 105 ( 4 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,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')
=> ( member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ) ).
fof(p4,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')
=> ( 'ilf$utype'(X1,'subset$utype'(X0))
<=> 'ilf$utype'(X1,'member$utype'('power$uset'(X0))) ) ) ) ).
fof(p13,axiom,
! [X0] :
( 'ilf$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(p14,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p15,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(p21,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_7,conjecture,
! [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$upair'(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'set$utype')
=> ! [X4] :
( 'ilf$utype'(X4,'relation$utype'(X0,X1))
=> ( member('ordered$upair'(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_7]) ).
cnf(c0,plain,
( ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| member(X0,X2)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member('ordered$upair'(X2,X0),'cross$uproduct'(X3,X1))
| member(X0,X1) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c7,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$utype') ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c13,plain,
( 'ilf$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)],[p10]) ).
cnf(c25,plain,
( ~ 'ilf$utype'(X0,'set$utype')
| ~ member(X2,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| member(X2,X1)
| ~ member(X0,'power$uset'(X1)) ),
inference(clausification,[status(esa)],[p13]) ).
cnf(c29,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p14]) ).
cnf(c31,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| member(X1,X0)
| ~ 'ilf$utype'(X1,'member$utype'(X0))
| ~ 'ilf$utype'(X0,'set$utype')
| empty(X0) ),
inference(clausification,[status(esa)],[p15]) ).
cnf(c47,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p21]) ).
cnf(c52,plain,
'ilf$utype'(sK63,'relation$utype'(sK59,sK60)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c53,plain,
member('ordered$upair'(sK61,sK62),sK63),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c54,plain,
( ~ member(sK62,sK60)
| ~ member(sK61,sK59) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member('ordered$upair'(X2,X0),'cross$uproduct'(X3,X1))
| member(X0,X1)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c1]) ).
cnf(d1,plain,
( ~ member(X1,'power$uset'(X0))
| ~ member(X2,X1)
| member(X2,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c25]) ).
cnf(d2,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c47,c7]) ).
cnf(d3,plain,
( 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| ~ 'ilf$utype'(X0,'subset$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c13]) ).
cnf(d4,plain,
( empty(X1)
| member(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[c47,c31]) ).
cnf(d5,plain,
( ~ 'ilf$utype'(X1,'subset$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| empty('power$uset'(X0))
| member(X1,'power$uset'(X0))
| ~ 'ilf$utype'('power$uset'(X0),'set$utype') ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( empty('power$uset'(X1))
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'('power$uset'(X1),'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c47,d5]) ).
cnf(d7,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c47,c29]) ).
cnf(d8,plain,
( member(X0,'power$uset'(X1))
| ~ 'ilf$utype'('power$uset'(X1),'set$utype')
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d8,c47]) ).
cnf(d10,plain,
( ~ 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X1,'set$utype')
| member(X0,'power$uset'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( member(X0,'power$uset'('cross$uproduct'(X1,X2)))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c47,d10]) ).
cnf(d12,plain,
( member(X3,'cross$uproduct'(X1,X2))
| ~ member(X3,X0)
| ~ 'ilf$utype'('cross$uproduct'(X1,X2),'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( member(X3,'cross$uproduct'(X1,X2))
| ~ member(X3,X0)
| ~ 'ilf$utype'('cross$uproduct'(X1,X2),'set$utype')
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[c47,d12]) ).
cnf(d14,plain,
( member(X3,'cross$uproduct'(X1,X2))
| ~ member(X3,X0)
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X2)) ),
inference(resolution,[status(thm)],[d13,c47]) ).
cnf(d15,plain,
( member(X0,'cross$uproduct'(sK59,sK60))
| ~ member(X0,sK63) ),
inference(resolution,[status(thm)],[d14,c52]) ).
cnf(d16,plain,
( member(X1,sK60)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(sK60,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member('ordered$upair'(X0,X1),sK63) ),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
( ~ member('ordered$upair'(X0,X1),sK63)
| member(X1,sK60)
| ~ 'ilf$utype'(sK60,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,d16]) ).
cnf(d18,plain,
( member(sK62,sK60)
| ~ 'ilf$utype'(sK60,'set$utype')
| ~ 'ilf$utype'(sK61,'set$utype') ),
inference(resolution,[status(thm)],[d17,c53]) ).
cnf(d19,plain,
( member(sK62,sK60)
| ~ 'ilf$utype'(sK61,'set$utype') ),
inference(resolution,[status(thm)],[c47,d18]) ).
cnf(d20,plain,
( ~ member('ordered$upair'(X2,X0),'cross$uproduct'(X3,X1))
| member(X2,X3)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,c0]) ).
cnf(d21,plain,
( ~ member('ordered$upair'(X2,X1),'cross$uproduct'(X3,X0))
| member(X2,X3)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c47,d20]) ).
cnf(d22,plain,
( member(X0,sK59)
| ~ 'ilf$utype'(sK60,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member('ordered$upair'(X0,X1),sK63) ),
inference(resolution,[status(thm)],[d15,d21]) ).
cnf(d23,plain,
( ~ member('ordered$upair'(X0,X1),sK63)
| member(X0,sK59)
| ~ 'ilf$utype'(sK60,'set$utype') ),
inference(resolution,[status(thm)],[c47,d22]) ).
cnf(d24,plain,
( member(sK61,sK59)
| ~ 'ilf$utype'(sK60,'set$utype') ),
inference(resolution,[status(thm)],[d23,c53]) ).
cnf(d25,plain,
member(sK61,sK59),
inference(resolution,[status(thm)],[c47,d24]) ).
cnf(d26,plain,
~ member(sK62,sK60),
inference(resolution,[status(thm)],[d25,c54]) ).
cnf(d27,plain,
~ 'ilf$utype'(sK61,'set$utype'),
inference(resolution,[status(thm)],[d26,d19]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[d27,c47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n007.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 08:00:39 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.27/7.25 % SZS status Theorem for theBenchmark.p
% 30.27/7.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------