%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET653+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 : n008.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 08:33:01 AM UTC 2026
% Result : Theorem 10.97s 3.85s
% Output : CNFRefutation 10.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 101 ( 41 ~; 36 |; 2 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 19 !; 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$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'relation$utype'(X0,X1))
=> ( subset('range$uof'(X2),X1)
& subset('domain$uof'(X2),X0) ) ) ) ) ).
fof(p3,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X2))
=> ( subset('domain$uof'(X3),X1)
=> 'ilf$utype'(X3,'relation$utype'(X1,X2)) ) ) ) ) ) ).
fof(p22,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_15,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X2))
=> ( subset(X0,X1)
=> 'ilf$utype'(X3,'relation$utype'(X1,X2)) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ! [X3] :
( 'ilf$utype'(X3,'relation$utype'(X0,X2))
=> ( subset(X0,X1)
=> 'ilf$utype'(X3,'relation$utype'(X1,X2)) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_15]) ).
cnf(c0,plain,
( ~ subset(X0,X2)
| ~ 'ilf$utype'(X2,'set$utype')
| ~ subset(X2,X1)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| subset(X0,X1) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( subset('domain$uof'(X2),X0)
| ~ 'ilf$utype'(X2,'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c3,plain,
( 'ilf$utype'(X1,'relation$utype'(X2,X0))
| ~ 'ilf$utype'(X1,'relation$utype'(X3,X0))
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X3,'set$utype')
| ~ subset('domain$uof'(X1),X2)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p3]) ).
cnf(c41,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p22]) ).
cnf(c42,plain,
'ilf$utype'(sK57,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c43,plain,
'ilf$utype'(sK58,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c44,plain,
'ilf$utype'(sK59,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c45,plain,
'ilf$utype'(sK60,'relation$utype'(sK57,sK59)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c46,plain,
subset(sK57,sK58),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
~ 'ilf$utype'(sK60,'relation$utype'(sK58,sK59)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset('domain$uof'(sK60),X0)
| ~ 'ilf$utype'(sK57,'set$utype')
| 'ilf$utype'(sK60,'relation$utype'(X0,sK59))
| ~ 'ilf$utype'(sK59,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c45,c3]) ).
cnf(d1,plain,
( ~ subset('domain$uof'(sK60),X0)
| 'ilf$utype'(sK60,'relation$utype'(X0,sK59))
| ~ 'ilf$utype'(sK59,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,d0]) ).
cnf(d2,plain,
( ~ subset('domain$uof'(sK60),X0)
| 'ilf$utype'(sK60,'relation$utype'(X0,sK59))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c44,d1]) ).
cnf(d3,plain,
( ~ subset('domain$uof'(sK60),sK58)
| ~ 'ilf$utype'(sK58,'set$utype') ),
inference(resolution,[status(thm)],[d2,c47]) ).
cnf(d4,plain,
~ subset('domain$uof'(sK60),sK58),
inference(resolution,[status(thm)],[c43,d3]) ).
cnf(d5,plain,
( subset('domain$uof'(sK60),sK57)
| ~ 'ilf$utype'(sK57,'set$utype')
| ~ 'ilf$utype'(sK59,'set$utype') ),
inference(resolution,[status(thm)],[c45,c1]) ).
cnf(d6,plain,
( subset('domain$uof'(sK60),sK57)
| ~ 'ilf$utype'(sK59,'set$utype') ),
inference(resolution,[status(thm)],[c42,d5]) ).
cnf(d7,plain,
subset('domain$uof'(sK60),sK57),
inference(resolution,[status(thm)],[c44,d6]) ).
cnf(d8,plain,
( subset('domain$uof'(sK60),X0)
| ~ subset(sK57,X0)
| ~ 'ilf$utype'('domain$uof'(sK60),'set$utype')
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(sK57,'set$utype') ),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
( ~ subset(sK57,X0)
| subset('domain$uof'(sK60),X0)
| ~ 'ilf$utype'('domain$uof'(sK60),'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,d8]) ).
cnf(d10,plain,
( ~ subset(sK57,X0)
| subset('domain$uof'(sK60),X0)
| ~ 'ilf$utype'('domain$uof'(sK60),'set$utype') ),
inference(resolution,[status(thm)],[c41,d9]) ).
cnf(d11,plain,
( ~ subset(sK57,X0)
| subset('domain$uof'(sK60),X0) ),
inference(resolution,[status(thm)],[c41,d10]) ).
cnf(d12,plain,
~ subset(sK57,sK58),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c46,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET653+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
% 0.10/0.36 % Computer : n008.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 08:04:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.97/3.85 % SZS status Theorem for theBenchmark.p
% 10.97/3.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------