%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET676+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 : n004.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 08:33:04 AM UTC 2026
% Result : Theorem 12.06s 1.94s
% Output : CNFRefutation 12.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 11 ~; 9 |; 0 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> 'ilf$utype'('cross$uproduct'(X0,X1),'relation$utype'(X0,X1)) ) ) ).
fof(p4,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
<=> 'ilf$utype'(X1,'relation$utype'(X0,X0)) ) ) ) ).
fof(p19,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_41,conjecture,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> 'ilf$utype'('cross$uproduct'(X0,X0),'identity$urelation$uof$utype'(X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> 'ilf$utype'('cross$uproduct'(X0,X0),'identity$urelation$uof$utype'(X0)) ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_41]) ).
cnf(c0,plain,
( 'ilf$utype'('cross$uproduct'(X0,X1),'relation$utype'(X0,X1))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c11,plain,
( ~ 'ilf$utype'(X1,'relation$utype'(X0,X0))
| 'ilf$utype'(X1,'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p4]) ).
cnf(c42,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p19]) ).
cnf(c44,plain,
~ 'ilf$utype'('cross$uproduct'(sK54,sK54),'identity$urelation$uof$utype'(sK54)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'ilf$utype'(X1,'set$utype')
| 'ilf$utype'(X0,'identity$urelation$uof$utype'(X1))
| ~ 'ilf$utype'(X0,'relation$utype'(X1,X1)) ),
inference(resolution,[status(thm)],[c42,c11]) ).
cnf(d1,plain,
( 'ilf$utype'('cross$uproduct'(X1,X0),'relation$utype'(X1,X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c42,c0]) ).
cnf(d2,plain,
'ilf$utype'('cross$uproduct'(X0,X1),'relation$utype'(X0,X1)),
inference(resolution,[status(thm)],[c42,d1]) ).
cnf(d3,plain,
( 'ilf$utype'('cross$uproduct'(X0,X0),'identity$urelation$uof$utype'(X0))
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
'ilf$utype'('cross$uproduct'(X0,X0),'identity$urelation$uof$utype'(X0)),
inference(resolution,[status(thm)],[c42,d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,c44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET676+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
% 0.08/0.36 % Computer : n004.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:04:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.06/1.94 % SZS status Theorem for theBenchmark.p
% 12.06/1.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------