%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET648+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 : n026.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 100.78s 18.84s
% Output : CNFRefutation 100.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 16 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 75 ~; 81 |; 5 &)
% ( 4 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 2 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')
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'binary$urelation$utype')
=> subset(X0,'cross$uproduct'('domain$uof'(X0),'range$uof'(X0))) ) ).
fof(p3,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( subset(X0,X1)
=> ( subset('cross$uproduct'(X2,X0),'cross$uproduct'(X2,X1))
& subset('cross$uproduct'(X0,X2),'cross$uproduct'(X1,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(p12,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(p15,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$uset'(X0))) ) ) ) ).
fof(p20,axiom,
! [X0] :
( 'ilf$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(p21,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( 'ilf$utype'('power$uset'(X0),'set$utype')
& ~ empty('power$uset'(X0)) ) ) ).
fof(p22,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(p26,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_10,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'binary$urelation$utype')
=> ( subset('range$uof'(X1),X0)
=> 'ilf$utype'(X1,'relation$utype'('domain$uof'(X1),X0)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'binary$urelation$utype')
=> ( subset('range$uof'(X1),X0)
=> 'ilf$utype'(X1,'relation$utype'('domain$uof'(X1),X0)) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_10]) ).
cnf(c0,plain,
( ~ subset(X0,X2)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ subset(X2,X1)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| subset(X0,X1) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( subset(X0,'cross$uproduct'('domain$uof'(X0),'range$uof'(X0)))
| ~ 'ilf$utype'(X0,'binary$urelation$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c3,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| subset('cross$uproduct'(X2,X0),'cross$uproduct'(X2,X1))
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c4,plain,
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1)))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c19,plain,
( ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ member(X0,X2)
| ~ subset(X2,X1)
| member(X0,X1) ),
inference(clausification,[status(esa)],[p12]) ).
cnf(c26,plain,
( ~ 'ilf$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)],[p15]) ).
cnf(c39,plain,
( ~ member(sK53(X0,X1),X1)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p20]) ).
cnf(c40,plain,
( member(sK53(X0,X1),X0)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p20]) ).
cnf(c41,plain,
( ~ empty('power$uset'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p21]) ).
cnf(c44,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| empty(X1)
| 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype')
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[p22]) ).
cnf(c50,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p26]) ).
cnf(c52,plain,
'ilf$utype'(sK65,'binary$urelation$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c53,plain,
~ 'ilf$utype'(sK65,'relation$utype'('domain$uof'(sK65),sK64)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c54,plain,
subset('range$uof'(sK65),sK64),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c50,c4]) ).
cnf(d1,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) ),
inference(resolution,[status(thm)],[c50,d0]) ).
cnf(d2,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[c50,c26]) ).
cnf(d3,plain,
( ~ 'ilf$utype'(X0,'member$utype'('power$uset'(X1)))
| 'ilf$utype'(X0,'subset$utype'(X1)) ),
inference(resolution,[status(thm)],[d2,c50]) ).
cnf(d4,plain,
( empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,c44]) ).
cnf(d5,plain,
( empty(X1)
| ~ member(X0,X1)
| 'ilf$utype'(X0,'member$utype'(X1)) ),
inference(resolution,[status(thm)],[d4,c50]) ).
cnf(d6,plain,
( ~ member(sK53(X0,X1),X1)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,c39]) ).
cnf(d7,plain,
( ~ member(sK53(X0,X1),X1)
| member(X0,'power$uset'(X1)) ),
inference(resolution,[status(thm)],[d6,c50]) ).
cnf(d8,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,c19]) ).
cnf(d9,plain,
( ~ member(X2,X0)
| member(X2,X1)
| ~ subset(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d8,c50]) ).
cnf(d10,plain,
( ~ member(X2,X0)
| member(X2,X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c50,d9]) ).
cnf(d11,plain,
subset(sK65,'cross$uproduct'('domain$uof'(sK65),'range$uof'(sK65))),
inference(resolution,[status(thm)],[c1,c52]) ).
cnf(d12,plain,
( subset(X1,X0)
| ~ subset(X1,X2)
| ~ subset(X2,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,c0]) ).
cnf(d13,plain,
( subset(X2,X0)
| ~ subset(X2,X1)
| ~ subset(X1,X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,d12]) ).
cnf(d14,plain,
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[d13,c50]) ).
cnf(d15,plain,
( subset('cross$uproduct'(X0,X2),'cross$uproduct'(X0,X1))
| ~ subset(X2,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,c3]) ).
cnf(d16,plain,
( subset('cross$uproduct'(X0,X1),'cross$uproduct'(X0,X2))
| ~ subset(X1,X2)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,d15]) ).
cnf(d17,plain,
( subset('cross$uproduct'(X2,X0),'cross$uproduct'(X2,X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[d16,c50]) ).
cnf(d18,plain,
subset('cross$uproduct'(X0,'range$uof'(sK65)),'cross$uproduct'(X0,sK64)),
inference(resolution,[status(thm)],[d17,c54]) ).
cnf(d19,plain,
( ~ subset(X0,'cross$uproduct'(X1,'range$uof'(sK65)))
| subset(X0,'cross$uproduct'(X1,sK64)) ),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
subset(sK65,'cross$uproduct'('domain$uof'(sK65),sK64)),
inference(resolution,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
( ~ member(X0,sK65)
| member(X0,'cross$uproduct'('domain$uof'(sK65),sK64)) ),
inference(resolution,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
( member(sK53(X0,X1),X0)
| member(X0,'power$uset'(X1))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c50,c40]) ).
cnf(d23,plain,
( member(sK53(X0,X1),X0)
| member(X0,'power$uset'(X1)) ),
inference(resolution,[status(thm)],[d22,c50]) ).
cnf(d24,plain,
( member(sK53(X0,X1),X0)
| empty('power$uset'(X1))
| 'ilf$utype'(X0,'member$utype'('power$uset'(X1))) ),
inference(resolution,[status(thm)],[d5,d23]) ).
cnf(d25,plain,
~ empty('power$uset'(X0)),
inference(resolution,[status(thm)],[c50,c41]) ).
cnf(d26,plain,
( member(sK53(X0,X1),X0)
| 'ilf$utype'(X0,'member$utype'('power$uset'(X1))) ),
inference(resolution,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
( 'ilf$utype'(X0,'subset$utype'(X1))
| member(sK53(X0,X1),X0) ),
inference(resolution,[status(thm)],[d26,d3]) ).
cnf(d28,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X2))
| member(sK53(X0,'cross$uproduct'(X1,X2)),X0) ),
inference(resolution,[status(thm)],[d27,d1]) ).
cnf(d29,plain,
member(sK53(sK65,'cross$uproduct'('domain$uof'(sK65),sK64)),sK65),
inference(resolution,[status(thm)],[d28,c53]) ).
cnf(d30,plain,
member(sK53(sK65,'cross$uproduct'('domain$uof'(sK65),sK64)),'cross$uproduct'('domain$uof'(sK65),sK64)),
inference(resolution,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
member(sK65,'power$uset'('cross$uproduct'('domain$uof'(sK65),sK64))),
inference(resolution,[status(thm)],[d30,d7]) ).
cnf(d32,plain,
( empty('power$uset'('cross$uproduct'('domain$uof'(sK65),sK64)))
| 'ilf$utype'(sK65,'member$utype'('power$uset'('cross$uproduct'('domain$uof'(sK65),sK64)))) ),
inference(resolution,[status(thm)],[d31,d5]) ).
cnf(d33,plain,
'ilf$utype'(sK65,'member$utype'('power$uset'('cross$uproduct'('domain$uof'(sK65),sK64)))),
inference(resolution,[status(thm)],[d25,d32]) ).
cnf(d34,plain,
'ilf$utype'(sK65,'subset$utype'('cross$uproduct'('domain$uof'(sK65),sK64))),
inference(resolution,[status(thm)],[d33,d3]) ).
cnf(d35,plain,
'ilf$utype'(sK65,'relation$utype'('domain$uof'(sK65),sK64)),
inference(resolution,[status(thm)],[d34,d1]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[c53,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET648+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
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:05:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 100.78/18.84 % SZS status Theorem for theBenchmark.p
% 100.78/18.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------