%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:33:30 AM UTC 2026
% Result : Theorem 80.43s 16.37s
% Output : CNFRefutation 80.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 114 ( 82 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 98 ( 25 ~; 68 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 7 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [X0,X1] : 'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
fof(d1_zfmisc_1,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ) ).
fof(d2_tarski,axiom,
! [X0,X1,X2] :
( X2 = 'unordered$upair'(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ) ).
fof(l4_zfmisc_1,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = 'empty$uset' ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t30_zfmisc_1,conjecture,
! [X0] : powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)),
inference(negate_conjecture,[status(cth)],[t30_zfmisc_1]) ).
cnf(c1,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_tarski]) ).
cnf(c5,plain,
( subset(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1)
| powerset(X0) = X1 ),
inference(clausification,[status(esa)],[d1_zfmisc_1]) ).
cnf(c6,plain,
( ~ in(sK7(X0,X1),X1)
| ~ subset(sK7(X0,X1),X0)
| powerset(X0) = X1 ),
inference(clausification,[status(esa)],[d1_zfmisc_1]) ).
cnf(c8,plain,
( X0 = X3
| X1 = X3
| ~ in(X3,X2)
| 'unordered$upair'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d2_tarski]) ).
cnf(c9,plain,
( X0 != X3
| in(X3,X2)
| 'unordered$upair'(X0,X1) != X2 ),
inference(clausification,[status(esa)],[d2_tarski]) ).
cnf(c17,plain,
( X0 = 'empty$uset'
| singleton(X1) = X0
| ~ subset(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[l4_zfmisc_1]) ).
cnf(c18,plain,
( X0 != 'empty$uset'
| subset(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[l4_zfmisc_1]) ).
cnf(c22,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c27,plain,
'unordered$upair'('empty$uset',singleton(sK23)) != powerset(singleton(sK23)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset('empty$uset',singleton(X0)),
inference(equality_resolution,[status(thm)],[c18]) ).
cnf(d1,plain,
( in(sK7(singleton(X0),X1),X1)
| powerset(singleton(X0)) = X1
| singleton(X0) = sK7(singleton(X0),X1)
| sK7(singleton(X0),X1) = 'empty$uset' ),
inference(resolution,[status(thm)],[c17,c5]) ).
cnf(d2,plain,
( ~ in(X1,'unordered$upair'(X2,X0))
| X2 = X1
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d3,plain,
( X2 = sK7(singleton(X0),'unordered$upair'(X1,X2))
| X1 = sK7(singleton(X0),'unordered$upair'(X1,X2))
| singleton(X0) = sK7(singleton(X0),'unordered$upair'(X1,X2))
| sK7(singleton(X0),'unordered$upair'(X1,X2)) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'(X1,X2) ),
inference(resolution,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
( singleton(X0) = sK7(singleton(X0),'unordered$upair'(X1,X2))
| sK7(singleton(X0),'unordered$upair'(X1,X2)) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'(X1,X2)
| X1 = sK7(singleton(X0),'unordered$upair'(X1,X2))
| ~ in(sK7(singleton(X0),'unordered$upair'(X1,X2)),'unordered$upair'(X1,X2))
| powerset(singleton(X0)) = 'unordered$upair'(X1,X2)
| ~ subset(X2,singleton(X0)) ),
inference(superposition,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( singleton(X1) = sK7(singleton(X1),'unordered$upair'(X0,X2))
| sK7(singleton(X1),'unordered$upair'(X0,X2)) = 'empty$uset'
| powerset(singleton(X1)) = 'unordered$upair'(X0,X2)
| ~ subset(X2,singleton(X1))
| singleton(X1) = sK7(singleton(X1),'unordered$upair'(X0,X2))
| sK7(singleton(X1),'unordered$upair'(X0,X2)) = 'empty$uset'
| powerset(singleton(X1)) = 'unordered$upair'(X0,X2)
| X0 = sK7(singleton(X1),'unordered$upair'(X0,X2)) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( singleton(X1) = sK7(singleton(X1),'unordered$upair'(X0,'empty$uset'))
| sK7(singleton(X1),'unordered$upair'(X0,'empty$uset')) = 'empty$uset'
| powerset(singleton(X1)) = 'unordered$upair'(X0,'empty$uset')
| X0 = sK7(singleton(X1),'unordered$upair'(X0,'empty$uset')) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( sK7(singleton(X0),'unordered$upair'(X1,'empty$uset')) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'(X1,'empty$uset')
| X1 = sK7(singleton(X0),'unordered$upair'(X1,'empty$uset'))
| singleton(X0) != X1 ),
inference(equality_factoring,[status(thm)],[d6]) ).
cnf(d8,plain,
( sK7(singleton(X0),'unordered$upair'(singleton(X0),'empty$uset')) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'(singleton(X0),'empty$uset')
| singleton(X0) = sK7(singleton(X0),'unordered$upair'(singleton(X0),'empty$uset')) ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( singleton(X0) = sK7(singleton(X0),'unordered$upair'(singleton(X0),'empty$uset'))
| sK7(singleton(X0),'unordered$upair'(singleton(X0),'empty$uset')) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)) ),
inference(demodulation,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
( singleton(X0) = sK7(singleton(X0),'unordered$upair'(singleton(X0),'empty$uset'))
| sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)) ),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
( singleton(X0) = sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0)))
| sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)) ),
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
( sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| ~ in(sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))),'unordered$upair'('empty$uset',singleton(X0)))
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| ~ subset(singleton(X0),singleton(X0)) ),
inference(superposition,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
( ~ in(sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))),'unordered$upair'('empty$uset',singleton(X0)))
| sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)) ),
inference(resolution,[status(thm)],[c22,d12]) ).
cnf(d14,plain,
( sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| ~ in(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) ),
inference(superposition,[status(thm)],[d11,d13]) ).
cnf(d15,plain,
( in(X1,'unordered$upair'(X0,X2))
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(d16,plain,
in(X0,'unordered$upair'(X0,X1)),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
in(X0,'unordered$upair'(X1,X0)),
inference(superposition,[status(thm)],[c1,d16]) ).
cnf(d18,plain,
( sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))) = 'empty$uset'
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)) ),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
( powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| ~ in(sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))),'unordered$upair'('empty$uset',singleton(X0)))
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| ~ subset('empty$uset',singleton(X0)) ),
inference(superposition,[status(thm)],[d18,c6]) ).
cnf(d20,plain,
( ~ in(sK7(singleton(X0),'unordered$upair'('empty$uset',singleton(X0))),'unordered$upair'('empty$uset',singleton(X0)))
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)) ),
inference(resolution,[status(thm)],[d0,d19]) ).
cnf(d21,plain,
( powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0))
| ~ in('empty$uset','unordered$upair'('empty$uset',singleton(X0))) ),
inference(superposition,[status(thm)],[d18,d20]) ).
cnf(d22,plain,
powerset(singleton(X0)) = 'unordered$upair'('empty$uset',singleton(X0)),
inference(resolution,[status(thm)],[d16,d21]) ).
cnf(d23,plain,
powerset(singleton(sK23)) != powerset(singleton(sK23)),
inference(demodulation,[status(thm)],[c27,d22]) ).
cnf(d24,plain,
$false,
inference(equality_resolution,[status(thm)],[d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:24:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.43/16.37 % SZS status Theorem for theBenchmark.p
% 80.43/16.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------