%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET642+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 08:32:59 AM UTC 2026
% Result : Theorem 13.14s 3.57s
% Output : CNFRefutation 13.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 81 ( 33 ~; 29 |; 0 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 15 !; 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$utype'(X3,'relation$utype'(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,'cross$uproduct'(X1,X2)) ) ) ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ! [X2] :
( 'ilf$utype'(X2,'set$utype')
=> ( subset(X0,'cross$uproduct'(X1,X2))
=> 'ilf$utype'(X0,'relation$utype'(X1,X2)) ) ) ) ) ).
fof(prove_relset_1_4,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'(X1,X2))
=> ( subset(X0,X3)
=> 'ilf$utype'(X0,'relation$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'(X1,X2))
=> ( subset(X0,X3)
=> 'ilf$utype'(X0,'relation$utype'(X1,X2)) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_4]) ).
cnf(c0,plain,
( ~ 'ilf$utype'(X3,'relation$utype'(X1,X2))
| ~ subset(X0,X3)
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| subset(X0,'cross$uproduct'(X1,X2)) ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c1,plain,
( 'ilf$utype'(X0,'relation$utype'(X1,X2))
| ~ 'ilf$utype'(X0,'set$utype')
| ~ 'ilf$utype'(X2,'set$utype')
| ~ 'ilf$utype'(X1,'set$utype')
| ~ subset(X0,'cross$uproduct'(X1,X2)) ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c38,plain,
'ilf$utype'(sK52,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c39,plain,
'ilf$utype'(sK53,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c40,plain,
'ilf$utype'(sK54,'set$utype'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c41,plain,
'ilf$utype'(sK55,'relation$utype'(sK53,sK54)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c42,plain,
subset(sK52,sK55),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c43,plain,
~ 'ilf$utype'(sK52,'relation$utype'(sK53,sK54)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(X0,'cross$uproduct'(sK53,sK54))
| ~ subset(X0,sK55)
| ~ 'ilf$utype'(sK54,'set$utype')
| ~ 'ilf$utype'(sK53,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c41,c0]) ).
cnf(d1,plain,
( ~ subset(X0,sK55)
| subset(X0,'cross$uproduct'(sK53,sK54))
| ~ 'ilf$utype'(sK54,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c39,d0]) ).
cnf(d2,plain,
( ~ subset(X0,sK55)
| subset(X0,'cross$uproduct'(sK53,sK54))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c40,d1]) ).
cnf(d3,plain,
( ~ 'ilf$utype'(sK53,'set$utype')
| ~ 'ilf$utype'(sK54,'set$utype')
| 'ilf$utype'(X0,'relation$utype'(sK53,sK54))
| ~ 'ilf$utype'(X0,'set$utype')
| ~ subset(X0,sK55)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( ~ subset(X0,sK55)
| ~ 'ilf$utype'(sK54,'set$utype')
| 'ilf$utype'(X0,'relation$utype'(sK53,sK54))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c39,d3]) ).
cnf(d5,plain,
( ~ subset(X0,sK55)
| 'ilf$utype'(X0,'relation$utype'(sK53,sK54))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c40,d4]) ).
cnf(d6,plain,
( ~ subset(sK52,sK55)
| ~ 'ilf$utype'(sK52,'set$utype') ),
inference(resolution,[status(thm)],[d5,c43]) ).
cnf(d7,plain,
~ subset(sK52,sK55),
inference(resolution,[status(thm)],[c38,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c42,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+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
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 08:02:29 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.14/3.57 % SZS status Theorem for theBenchmark.p
% 13.14/3.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------