%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET137-6 : 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 : 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 08:32:09 AM UTC 2026
% Result : Unsatisfiable 15.88s 17.18s
% Output : CNFRefutation 15.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 21
% Syntax : Number of clauses : 109 ( 56 unt; 25 nHn; 46 RR)
% Number of literals : 176 ( 56 equ; 48 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 168 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_of_set_builder,axiom,
union(singleton(X0),X1) = 'set$ubuilder'(X0,X1) ).
cnf(prove_member_of_triple_kludge1_1,negated_conjecture,
member(u,x) ).
cnf(prove_member_of_triple_kludge1_4,negated_conjecture,
'set$ubuilder'(u,'set$ubuilder'(v,'set$ubuilder'(w,'null$uclass'))) = 'null$uclass' ).
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(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(unordered_pair3,axiom,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(union,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ).
cnf(symmetric_difference,axiom,
intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = 'symmetric$udifference'(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$uclass' ) ).
cnf(c0,plain,
union(singleton(X0),X1) = 'set$ubuilder'(X0,X1),
inference(clausification,[status(esa)],[definition_of_set_builder]) ).
cnf(c1,plain,
member(u,x),
inference(clausification,[status(esa)],[prove_member_of_triple_kludge1_1]) ).
cnf(c4,plain,
'set$ubuilder'(u,'set$ubuilder'(v,'set$ubuilder'(w,'null$uclass'))) = 'null$uclass',
inference(clausification,[status(esa)],[prove_member_of_triple_kludge1_4]) ).
cnf(c5,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c6,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c7,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c8,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c11,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c14,plain,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair3]) ).
cnf(c16,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c25,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c26,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c27,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c28,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c29,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c30,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(clausification,[status(esa)],[union]) ).
cnf(c31,plain,
intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = 'symmetric$udifference'(X0,X1),
inference(clausification,[status(esa)],[symmetric_difference]) ).
cnf(c32,plain,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,X1,X2),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c34,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c70,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(c71,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity2]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c16,c14]) ).
cnf(d1,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c25,c6]) ).
cnf(d2,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( X0 = 'null$uclass'
| subclass('null$uclass',X0) ),
inference(superposition,[status(thm)],[c71,d2]) ).
cnf(d4,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass'
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d6,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( subclass(X0,complement(X1))
| ~ member('not$usubclass$uelement'(X0,complement(X1)),'universal$uclass')
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c29,c7]) ).
cnf(d8,plain,
( subclass(X0,complement(X1))
| subclass(X0,complement(X1))
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ member('not$usubclass$uelement'(X0,complement(complement(X1))),X1)
| subclass(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d8,c28]) ).
cnf(d10,plain,
( subclass(X0,complement(complement(X0)))
| subclass(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c26,c6]) ).
cnf(d12,plain,
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
intersection(X0,'null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d4,d12]) ).
cnf(d14,plain,
( ~ subclass(X0,intersection(X0,X1))
| X0 = intersection(X0,X1) ),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d15,plain,
( subclass(X0,intersection(X1,X2))
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c27,c7]) ).
cnf(d16,plain,
( subclass(X0,intersection(X0,X1))
| subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
( subclass(X0,intersection(X0,'universal$uclass'))
| subclass(X0,intersection(X0,'universal$uclass')) ),
inference(resolution,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
X0 = intersection(X0,'universal$uclass'),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
( ~ subclass('universal$uclass',X0)
| 'universal$uclass' = X0 ),
inference(resolution,[status(thm)],[c11,c8]) ).
cnf(d20,plain,
subclass(restrict(X0,X1,X2),X0),
inference(superposition,[status(thm)],[c32,d2]) ).
cnf(d21,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(resolution,[status(thm)],[d4,d20]) ).
cnf(d22,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d21,c34]) ).
cnf(d23,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d23,c70]) ).
cnf(d25,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d23,d24]) ).
cnf(d26,plain,
subclass(X0,complement('null$uclass')),
inference(resolution,[status(thm)],[d8,d25]) ).
cnf(d27,plain,
'universal$uclass' = complement('null$uclass'),
inference(resolution,[status(thm)],[d26,d19]) ).
cnf(d28,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c28,c6]) ).
cnf(d29,plain,
( subclass(complement('universal$uclass'),X0)
| subclass(complement('universal$uclass'),X0) ),
inference(resolution,[status(thm)],[d28,d6]) ).
cnf(d30,plain,
complement('universal$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d4,d29]) ).
cnf(d31,plain,
complement(intersection(complement(X0),'null$uclass')) = union(X0,'universal$uclass'),
inference(superposition,[status(thm)],[d30,c30]) ).
cnf(d32,plain,
complement('null$uclass') = union(X0,'universal$uclass'),
inference(demodulation,[status(thm)],[d31,d13]) ).
cnf(d33,plain,
'universal$uclass' = union(X0,'universal$uclass'),
inference(demodulation,[status(thm)],[d32,d27]) ).
cnf(d34,plain,
complement(intersection(complement(X2),union(X0,X1))) = union(X2,intersection(complement(X0),complement(X1))),
inference(superposition,[status(thm)],[c30,c30]) ).
cnf(d35,plain,
complement(intersection(complement(X0),union(X1,'universal$uclass'))) = union(X0,intersection(complement(X1),'null$uclass')),
inference(superposition,[status(thm)],[d30,d34]) ).
cnf(d36,plain,
complement(intersection(complement(X1),'universal$uclass')) = union(X1,intersection(complement(X0),'null$uclass')),
inference(demodulation,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
complement(complement(X0)) = union(X0,intersection(complement(X1),'null$uclass')),
inference(demodulation,[status(thm)],[d36,d18]) ).
cnf(d38,plain,
complement(complement(X1)) = union(X1,'null$uclass'),
inference(demodulation,[status(thm)],[d37,d13]) ).
cnf(d39,plain,
( ~ subclass(X0,intersection(X1,X0))
| X0 = intersection(X1,X0) ),
inference(resolution,[status(thm)],[d12,c11]) ).
cnf(d40,plain,
( subclass(X0,intersection('universal$uclass',X1))
| subclass(X0,intersection('universal$uclass',X1))
| ~ member('not$usubclass$uelement'(X0,intersection('universal$uclass',X1)),X1) ),
inference(resolution,[status(thm)],[d15,d6]) ).
cnf(d41,plain,
( subclass(X0,intersection('universal$uclass',X0))
| subclass(X0,intersection('universal$uclass',X0)) ),
inference(resolution,[status(thm)],[d40,c6]) ).
cnf(d42,plain,
X0 = intersection('universal$uclass',X0),
inference(resolution,[status(thm)],[d41,d39]) ).
cnf(d43,plain,
intersection(complement(intersection(X0,X1)),union(X0,X1)) = 'symmetric$udifference'(X0,X1),
inference(demodulation,[status(thm)],[c31,c30]) ).
cnf(d44,plain,
intersection(complement('null$uclass'),union(X0,'null$uclass')) = 'symmetric$udifference'(X0,'null$uclass'),
inference(superposition,[status(thm)],[d13,d43]) ).
cnf(d45,plain,
intersection('universal$uclass',union(X0,'null$uclass')) = 'symmetric$udifference'(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d44,d27]) ).
cnf(d46,plain,
union(X0,'null$uclass') = 'symmetric$udifference'(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d45,d42]) ).
cnf(d47,plain,
complement(complement(X0)) = 'symmetric$udifference'(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d46,d38]) ).
cnf(d48,plain,
intersection(complement(intersection(singleton(X0),X1)),'set$ubuilder'(X0,X1)) = 'symmetric$udifference'(singleton(X0),X1),
inference(superposition,[status(thm)],[c0,d43]) ).
cnf(d49,plain,
intersection(complement('null$uclass'),'set$ubuilder'(X0,'null$uclass')) = 'symmetric$udifference'(singleton(X0),'null$uclass'),
inference(superposition,[status(thm)],[d13,d48]) ).
cnf(d50,plain,
intersection('universal$uclass','set$ubuilder'(X0,'null$uclass')) = 'symmetric$udifference'(singleton(X0),'null$uclass'),
inference(demodulation,[status(thm)],[d49,d27]) ).
cnf(d51,plain,
'set$ubuilder'(X0,'null$uclass') = 'symmetric$udifference'(singleton(X0),'null$uclass'),
inference(demodulation,[status(thm)],[d50,d42]) ).
cnf(d52,plain,
'set$ubuilder'(X0,'null$uclass') = complement(complement(singleton(X0))),
inference(demodulation,[status(thm)],[d51,d47]) ).
cnf(d53,plain,
subclass(singleton(X0),'set$ubuilder'(X0,'null$uclass')),
inference(superposition,[status(thm)],[d52,d10]) ).
cnf(d54,plain,
( member('not$usubclass$uelement'(X0,complement(intersection(X1,X2))),X1)
| subclass(X0,complement(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[d8,c25]) ).
cnf(d55,plain,
( subclass(complement(X0),complement(intersection(X0,X1)))
| subclass(complement(X0),complement(intersection(X0,X1))) ),
inference(resolution,[status(thm)],[d54,d28]) ).
cnf(d56,plain,
subclass(complement(complement(X0)),union(X0,X1)),
inference(superposition,[status(thm)],[c30,d55]) ).
cnf(d57,plain,
subclass('set$ubuilder'(X0,'null$uclass'),union(singleton(X0),X1)),
inference(superposition,[status(thm)],[d52,d56]) ).
cnf(d58,plain,
subclass('set$ubuilder'(X0,'null$uclass'),'set$ubuilder'(X0,X1)),
inference(demodulation,[status(thm)],[d57,c0]) ).
cnf(d59,plain,
subclass('set$ubuilder'(u,'null$uclass'),'null$uclass'),
inference(superposition,[status(thm)],[c4,d58]) ).
cnf(d60,plain,
'set$ubuilder'(u,'null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d59,d4]) ).
cnf(d61,plain,
subclass(singleton(u),'null$uclass'),
inference(superposition,[status(thm)],[d60,d53]) ).
cnf(d62,plain,
singleton(u) = 'null$uclass',
inference(resolution,[status(thm)],[d61,d4]) ).
cnf(d63,plain,
( ~ member(u,'universal$uclass')
| member(u,'null$uclass') ),
inference(superposition,[status(thm)],[d62,d0]) ).
cnf(d64,plain,
member(u,'universal$uclass'),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d65,plain,
member(u,'null$uclass'),
inference(resolution,[status(thm)],[d64,d63]) ).
cnf(d66,plain,
$false,
inference(resolution,[status(thm)],[d25,d65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET137-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 07:12:22 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.88/17.18 % SZS status Unsatisfiable for theBenchmark.p
% 15.88/17.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------