%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:32:43 AM UTC 2026
% Result : Unsatisfiable 12.47s 5.86s
% Output : CNFRefutation 12.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of clauses : 68 ( 28 unt; 19 nHn; 42 RR)
% Number of literals : 123 ( 45 equ; 46 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 106 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_not_singleton_of_set_1,negated_conjecture,
singleton('member$uof'(x)) = x ).
cnf(prove_not_singleton_of_set_2,negated_conjecture,
'member$uof'(x) = x ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(not_subclass_members2,axiom,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ) ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(unordered_pair3,axiom,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ) ).
cnf(unordered_pairs_in_universal,axiom,
member('unordered$upair'(X0,X1),'universal$uclass') ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(ordered_pair,axiom,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(restriction1,axiom,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,X1,X2) ).
cnf(domain1,axiom,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
singleton('member$uof'(x)) = x,
inference(clausification,[status(esa)],[prove_not_singleton_of_set_1]) ).
cnf(c1,plain,
'member$uof'(x) = x,
inference(clausification,[status(esa)],[prove_not_singleton_of_set_2]) ).
cnf(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c3,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c4,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c8,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c9,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c11,plain,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair3]) ).
cnf(c12,plain,
member('unordered$upair'(X0,X1),'universal$uclass'),
inference(clausification,[status(esa)],[unordered_pairs_in_universal]) ).
cnf(c13,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c14,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(c22,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c24,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c29,plain,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,X1,X2),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c31,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c67,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(c68,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity2]) ).
cnf(d0,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c22,c3]) ).
cnf(d1,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ subclass(X0,intersection(X0,X1))
| X0 = intersection(X0,X1) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
( subclass(X0,intersection(X1,X2))
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c24,c4]) ).
cnf(d4,plain,
( subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1)
| subclass(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( subclass(X0,intersection(X0,X0))
| subclass(X0,intersection(X0,X0)) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
X0 = intersection(X0,X0),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d8,plain,
singleton(x) = x,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d9,plain,
( X0 = x
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( x = 'null$uclass'
| regular(x) = x ),
inference(resolution,[status(thm)],[d9,c67]) ).
cnf(d11,plain,
( x = 'null$uclass'
| x = 'null$uclass'
| intersection(x,x) = 'null$uclass' ),
inference(superposition,[status(thm)],[d10,c68]) ).
cnf(d12,plain,
( x = 'null$uclass'
| x = 'null$uclass' ),
inference(demodulation,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
subclass(restrict(X0,X1,X2),X0),
inference(superposition,[status(thm)],[c29,d1]) ).
cnf(d14,plain,
( X0 = 'null$uclass'
| subclass('null$uclass',X0) ),
inference(superposition,[status(thm)],[c68,d1]) ).
cnf(d15,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass'
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d14,c8]) ).
cnf(d16,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d16,c31]) ).
cnf(d18,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d18,c67]) ).
cnf(d20,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d18,d19]) ).
cnf(d21,plain,
( member(X0,X2)
| ~ subclass('unordered$upair'(X1,X0),X2)
| ~ member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d22,plain,
( ~ member('unordered$upair'(X0,singleton(X1)),'universal$uclass')
| member('unordered$upair'(X0,singleton(X1)),X2)
| ~ subclass('ordered$upair'(X0,X1),X2) ),
inference(superposition,[status(thm)],[c14,d21]) ).
cnf(d23,plain,
( member('unordered$upair'(X0,singleton(X1)),X2)
| ~ subclass('ordered$upair'(X0,X1),X2) ),
inference(resolution,[status(thm)],[c12,d22]) ).
cnf(d24,plain,
~ subclass('ordered$upair'(X0,X1),'null$uclass'),
inference(resolution,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
'unordered$upair'(singleton(singleton(X0)),singleton(singleton(X0))) = 'ordered$upair'(singleton(X0),X0),
inference(superposition,[status(thm)],[c13,c14]) ).
cnf(d26,plain,
singleton(singleton(singleton(X0))) = 'ordered$upair'(singleton(X0),X0),
inference(demodulation,[status(thm)],[d25,c13]) ).
cnf(d27,plain,
~ subclass(singleton(singleton(singleton(X0))),'null$uclass'),
inference(superposition,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
~ subclass(singleton(singleton(x)),'null$uclass'),
inference(superposition,[status(thm)],[d8,d27]) ).
cnf(d29,plain,
~ subclass(singleton(x),'null$uclass'),
inference(demodulation,[status(thm)],[d28,d8]) ).
cnf(d30,plain,
~ subclass(x,'null$uclass'),
inference(demodulation,[status(thm)],[d29,d8]) ).
cnf(d31,plain,
~ subclass('null$uclass','null$uclass'),
inference(demodulation,[status(thm)],[d30,d12]) ).
cnf(d32,plain,
( subclass(X0,X0)
| subclass(X0,X0) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.56 % Computer : n016.cluster.edu
% 0.17/0.56 % Model : x86_64 x86_64
% 0.17/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.56 % Memory : 8046.5625MB
% 0.17/0.56 % OS : Linux 6.8.0-71-generic
% 0.17/0.56 % CPULimit : 300
% 0.17/0.56 % WCLimit : 300
% 0.17/0.56 % DateTime : Sat Sep 26 07:55:45 UTC 2026
% 0.17/0.56 % CPUTime :
% 0.17/0.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.47/5.86 % SZS status Unsatisfiable for theBenchmark.p
% 12.47/5.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------