%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 08:31:59 AM UTC 2026
% Result : Theorem 12.23s 14.24s
% Output : CNFRefutation 12.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 35 unt; 0 def)
% Number of atoms : 99 ( 58 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 19 ~; 22 |; 9 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 4 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_singleton_universal,axiom,
! [X0] :
( member(X0,'universal$uclass')
=> member('member$uof'(singleton(X0)),'universal$uclass') ) ).
fof(member_singleton_singleton,axiom,
! [X0] :
( member(X0,'universal$uclass')
=> singleton('member$uof'(singleton(X0))) = singleton(X0) ) ).
fof(unordered_pair_defn,axiom,
! [X0,X1,X2] :
( member(X0,'unordered$upair'(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,'universal$uclass') ) ) ).
fof(unordered_pair,axiom,
! [X0,X1] : member('unordered$upair'(X0,X1),'universal$uclass') ).
fof(singleton_set_defn,axiom,
! [X0] : singleton(X0) = 'unordered$upair'(X0,X0) ).
fof(ordered_pair_defn,axiom,
! [X0,X1] : 'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) ).
fof(first_second,axiom,
! [X0,X1] :
( ( member(X1,'universal$uclass')
& member(X0,'universal$uclass') )
=> ( second('ordered$upair'(X0,X1)) = X1
& first('ordered$upair'(X0,X1)) = X0 ) ) ).
fof(infinity,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,'universal$uclass') ) ).
fof(regularity,axiom,
! [X0] :
( X0 != 'null$uclass'
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,'universal$uclass') ) ) ).
fof(member_of_singleton,conjecture,
! [X0,X1] :
( ( X0 = singleton(X1)
& member(X1,'universal$uclass') )
=> 'member$uof'(X0) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( X0 = singleton(X1)
& member(X1,'universal$uclass') )
=> 'member$uof'(X0) = X1 ),
inference(negate_conjecture,[status(cth)],[member_of_singleton]) ).
cnf(c0,plain,
( member('member$uof'(singleton(X0)),'universal$uclass')
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[member_singleton_universal]) ).
cnf(c1,plain,
( singleton('member$uof'(singleton(X0))) = singleton(X0)
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[member_singleton_singleton]) ).
cnf(c12,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_defn]) ).
cnf(c15,plain,
member('unordered$upair'(X0,X1),'universal$uclass'),
inference(clausification,[status(esa)],[unordered_pair]) ).
cnf(c16,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set_defn]) ).
cnf(c17,plain,
'ordered$upair'(X0,X1) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))),
inference(clausification,[status(esa)],[ordered_pair_defn]) ).
cnf(c22,plain,
( second('ordered$upair'(X0,X1)) = X1
| ~ member(X1,'universal$uclass')
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[first_second]) ).
cnf(c62,plain,
member(sK62,'universal$uclass'),
inference(clausification,[status(esa)],[infinity]) ).
cnf(c88,plain,
( member(sK89(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity]) ).
cnf(c93,plain,
member(sK95,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c94,plain,
sK94 = singleton(sK95),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c95,plain,
'member$uof'(sK94) != sK95,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| second('ordered$upair'(X0,sK95)) = sK95 ),
inference(resolution,[status(thm)],[c22,c93]) ).
cnf(d1,plain,
second('ordered$upair'(sK62,sK95)) = sK95,
inference(resolution,[status(thm)],[d0,c62]) ).
cnf(d2,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c16,c12]) ).
cnf(d3,plain,
singleton('member$uof'(singleton(sK95))) = singleton(sK95),
inference(resolution,[status(thm)],[c1,c93]) ).
cnf(d4,plain,
singleton('member$uof'(sK94)) = singleton(sK95),
inference(demodulation,[status(thm)],[d3,c94]) ).
cnf(d5,plain,
singleton('member$uof'(sK94)) = sK94,
inference(demodulation,[status(thm)],[d4,c94]) ).
cnf(d6,plain,
( ~ member(sK95,'universal$uclass')
| member('member$uof'(sK94),'universal$uclass') ),
inference(superposition,[status(thm)],[c94,c0]) ).
cnf(d7,plain,
member('member$uof'(sK94),'universal$uclass'),
inference(resolution,[status(thm)],[c93,d6]) ).
cnf(d8,plain,
singleton('member$uof'(singleton('member$uof'(sK94)))) = singleton('member$uof'(sK94)),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
singleton('member$uof'(sK94)) = singleton('member$uof'(sK94)),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
sK94 = singleton('member$uof'(sK94)),
inference(demodulation,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( X0 = 'member$uof'(sK94)
| ~ member(X0,sK94) ),
inference(superposition,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
( X0 = sK95
| ~ member(X0,sK94) ),
inference(superposition,[status(thm)],[c94,d2]) ).
cnf(d13,plain,
( sK94 = 'null$uclass'
| sK89(sK94) = sK95 ),
inference(resolution,[status(thm)],[d12,c88]) ).
cnf(d14,plain,
( sK94 = 'null$uclass'
| sK94 = 'null$uclass'
| member(sK95,sK94) ),
inference(superposition,[status(thm)],[d13,c88]) ).
cnf(d15,plain,
( sK95 = 'member$uof'(sK94)
| sK94 = 'null$uclass' ),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( sK94 = 'null$uclass'
| sK95 != sK95 ),
inference(superposition,[status(thm)],[d15,c95]) ).
cnf(d17,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c16,c15]) ).
cnf(d18,plain,
second('ordered$upair'(singleton(X0),sK95)) = sK95,
inference(resolution,[status(thm)],[d0,d17]) ).
cnf(d19,plain,
member(sK94,'universal$uclass'),
inference(superposition,[status(thm)],[d10,d17]) ).
cnf(d20,plain,
singleton('member$uof'(singleton(sK94))) = singleton(sK94),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
second('ordered$upair'(singleton(sK94),sK95)) = sK95,
inference(superposition,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
sK95 = sK95,
inference(demodulation,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
sK94 = 'null$uclass',
inference(resolution,[status(thm)],[d22,d16]) ).
cnf(d24,plain,
'ordered$upair'(X0,sK95) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,sK94)),
inference(superposition,[status(thm)],[c94,c17]) ).
cnf(d25,plain,
'ordered$upair'(X0,'member$uof'(sK94)) = 'unordered$upair'(singleton(X0),'unordered$upair'(X0,sK94)),
inference(superposition,[status(thm)],[d10,c17]) ).
cnf(d26,plain,
'ordered$upair'(X0,'member$uof'(sK94)) = 'ordered$upair'(X0,sK95),
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
'ordered$upair'(X0,'member$uof'('null$uclass')) = 'ordered$upair'(X0,sK95),
inference(demodulation,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
( ~ member(X0,'universal$uclass')
| second('ordered$upair'(X0,'member$uof'(sK94))) = 'member$uof'(sK94) ),
inference(resolution,[status(thm)],[c22,d7]) ).
cnf(d29,plain,
( ~ member(X0,'universal$uclass')
| second('ordered$upair'(X0,'member$uof'('null$uclass'))) = 'member$uof'(sK94) ),
inference(demodulation,[status(thm)],[d28,d23]) ).
cnf(d30,plain,
( ~ member(X0,'universal$uclass')
| second('ordered$upair'(X0,'member$uof'('null$uclass'))) = 'member$uof'('null$uclass') ),
inference(demodulation,[status(thm)],[d29,d23]) ).
cnf(d31,plain,
second('ordered$upair'(sK62,'member$uof'('null$uclass'))) = 'member$uof'('null$uclass'),
inference(resolution,[status(thm)],[d30,c62]) ).
cnf(d32,plain,
second('ordered$upair'(sK62,sK95)) = 'member$uof'('null$uclass'),
inference(demodulation,[status(thm)],[d31,d27]) ).
cnf(d33,plain,
sK95 = 'member$uof'('null$uclass'),
inference(demodulation,[status(thm)],[d32,d1]) ).
cnf(d34,plain,
'member$uof'('null$uclass') != sK95,
inference(demodulation,[status(thm)],[c95,d23]) ).
cnf(d35,plain,
sK95 != sK95,
inference(demodulation,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d22,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n010.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sat Sep 26 07:05:11 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.23/14.24 % SZS status Theorem for theBenchmark.p
% 12.23/14.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------