%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET679+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 08:33:04 AM UTC 2026
% Result : Theorem 12.00s 1.98s
% Output : CNFRefutation 12.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 56 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 23 ~; 17 |; 2 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 3 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( member(X1,X0)
<=> member('ordered$upair'(X1,X1),'identity$urelation$uof'(X0)) ) ) ) ).
fof(p2,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ~ member(X0,'empty$uset') ) ).
fof(p7,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ( 'not$uequal'(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(p8,axiom,
! [X0] :
( 'ilf$utype'(X0,'set$utype')
=> ( empty(X0)
<=> ! [X1] :
( 'ilf$utype'(X1,'set$utype')
=> ~ member(X1,X0) ) ) ) ).
fof(p22,axiom,
! [X0] : 'ilf$utype'(X0,'set$utype') ).
fof(prove_relset_1_46,conjecture,
! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> 'not$uequal'('identity$urelation$uof'(X0),'empty$uset') ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'ilf$utype'(X0,'set$utype')
& ~ empty(X0) )
=> 'not$uequal'('identity$urelation$uof'(X0),'empty$uset') ),
inference(negate_conjecture,[status(cth)],[prove_relset_1_46]) ).
cnf(c0,plain,
( member('ordered$upair'(X1,X1),'identity$urelation$uof'(X0))
| ~ member(X1,X0)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p1]) ).
cnf(c2,plain,
( ~ member(X0,'empty$uset')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p2]) ).
cnf(c19,plain,
( X0 = X1
| 'not$uequal'(X0,X1)
| ~ 'ilf$utype'(X1,'set$utype')
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p7]) ).
cnf(c22,plain,
( member(sK16(X0),X0)
| empty(X0)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(clausification,[status(esa)],[p8]) ).
cnf(c51,plain,
'ilf$utype'(X0,'set$utype'),
inference(clausification,[status(esa)],[p22]) ).
cnf(c52,plain,
~ empty(sK49),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c54,plain,
~ 'not$uequal'('identity$urelation$uof'(sK49),'empty$uset'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( empty(X0)
| member(sK16(X0),X0) ),
inference(resolution,[status(thm)],[c51,c22]) ).
cnf(d1,plain,
( member('ordered$upair'(X0,X0),'identity$urelation$uof'(X1))
| ~ member(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype') ),
inference(resolution,[status(thm)],[c51,c0]) ).
cnf(d2,plain,
( member('ordered$upair'(X0,X0),'identity$urelation$uof'(X1))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c51,d1]) ).
cnf(d3,plain,
( 'not$uequal'(X0,X1)
| ~ 'ilf$utype'(X0,'set$utype')
| X0 = X1 ),
inference(resolution,[status(thm)],[c51,c19]) ).
cnf(d4,plain,
( 'not$uequal'(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d3,c51]) ).
cnf(d5,plain,
'identity$urelation$uof'(sK49) = 'empty$uset',
inference(resolution,[status(thm)],[d4,c54]) ).
cnf(d6,plain,
( ~ member(X0,sK49)
| member('ordered$upair'(X0,X0),'empty$uset') ),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
~ member(X0,'empty$uset'),
inference(resolution,[status(thm)],[c51,c2]) ).
cnf(d8,plain,
~ member(X0,sK49),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
empty(sK49),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c52,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET679+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 08:07:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.00/1.98 % SZS status Theorem for theBenchmark.p
% 12.00/1.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------