%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET136-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 116.64s 28.86s
% Output : CNFRefutation 116.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 22
% Syntax : Number of clauses : 148 ( 71 unt; 37 nHn; 73 RR)
% Number of literals : 249 ( 89 equ; 69 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 203 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_of_set_builder,axiom,
union(singleton(X0),X1) = 'set$ubuilder'(X0,X1) ).
cnf(prove_corollary_4_to_member_of_triple_1,negated_conjecture,
member(u,'universal$uclass') ).
cnf(prove_corollary_4_to_member_of_triple_2,negated_conjecture,
'set$ubuilder'(x,'set$ubuilder'(y,'set$ubuilder'(u,'null$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_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ 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$uclass' ) ).
cnf(c0,plain,
'set$ubuilder'(X0,X1) = union(singleton(X0),X1),
inference(clausification,[status(esa)],[definition_of_set_builder]) ).
cnf(c1,plain,
member(u,'universal$uclass'),
inference(clausification,[status(esa)],[prove_corollary_4_to_member_of_triple_1]) ).
cnf(c2,plain,
'set$ubuilder'(x,'set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))) = 'null$uclass',
inference(clausification,[status(esa)],[prove_corollary_4_to_member_of_triple_2]) ).
cnf(c3,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c4,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c5,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c6,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c9,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c10,plain,
( X2 = X1
| ~ member(X1,'unordered$upair'(X0,X2))
| X0 = X1 ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c11,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c14,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c23,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c24,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c25,plain,
( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c26,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c27,plain,
( member(X0,X1)
| ~ member(X0,'universal$uclass')
| member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c28,plain,
union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
inference(clausification,[status(esa)],[union]) ).
cnf(c29,plain,
'symmetric$udifference'(X0,X1) = intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))),
inference(clausification,[status(esa)],[symmetric_difference]) ).
cnf(c30,plain,
restrict(X0,X1,X2) = intersection(X0,'cross$uproduct'(X1,X2)),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c32,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c68,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(c69,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity2]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c11]) ).
cnf(d1,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c3,c6]) ).
cnf(d2,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( member(regular(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c68,d1]) ).
cnf(d4,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c26,c68]) ).
cnf(d5,plain,
( complement('universal$uclass') = 'null$uclass'
| complement('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d5,c26]) ).
cnf(d7,plain,
( subclass('null$uclass',X0)
| ~ member('not$usubclass$uelement'('null$uclass',X0),'universal$uclass') ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( subclass('null$uclass',X0)
| subclass('null$uclass',X0) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( ~ subclass(X0,'null$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c24,c4]) ).
cnf(d11,plain,
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
( ~ subclass(X1,intersection(X0,X1))
| intersection(X0,X1) = X1 ),
inference(resolution,[status(thm)],[d11,c9]) ).
cnf(d13,plain,
( subclass(X0,intersection(X1,X2))
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d14,plain,
( subclass(X0,intersection('universal$uclass',X1))
| subclass(X0,intersection('universal$uclass',X1))
| ~ member('not$usubclass$uelement'(X0,intersection('universal$uclass',X1)),X1) ),
inference(resolution,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
( subclass(X0,intersection('universal$uclass',X0))
| subclass(X0,intersection('universal$uclass',X0)) ),
inference(resolution,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
intersection('universal$uclass',X0) = X0,
inference(resolution,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
( X0 = X1
| X0 = X1
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d18,plain,
( singleton(X0) = 'null$uclass'
| X0 = regular(singleton(X0)) ),
inference(resolution,[status(thm)],[d17,c68]) ).
cnf(d19,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[d18,c68]) ).
cnf(d21,plain,
( X0 = 'null$uclass'
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| member(X1,'null$uclass') ),
inference(superposition,[status(thm)],[c69,c25]) ).
cnf(d22,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c23,c4]) ).
cnf(d23,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d22,c5]) ).
cnf(d24,plain,
'null$uclass' = intersection('null$uclass',X0),
inference(resolution,[status(thm)],[d23,d9]) ).
cnf(d25,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(superposition,[status(thm)],[d24,c30]) ).
cnf(d26,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d25,c32]) ).
cnf(d27,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d27,c68]) ).
cnf(d29,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d27,d28]) ).
cnf(d30,plain,
( ~ member(X1,regular(X0))
| ~ member(X1,X0)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X1,singleton(X0))
| singleton(X0) = 'null$uclass'
| ~ member(X1,X0) ),
inference(superposition,[status(thm)],[d18,d30]) ).
cnf(d32,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X0,X0)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d31,d20]) ).
cnf(d33,plain,
( singleton('universal$uclass') = 'null$uclass'
| singleton('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d32,d19]) ).
cnf(d34,plain,
'set$ubuilder'('universal$uclass',X0) = union('null$uclass',X0),
inference(superposition,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
( ~ subclass('universal$uclass',X0)
| X0 = 'universal$uclass' ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d36,plain,
( subclass(X0,complement(X1))
| ~ member('not$usubclass$uelement'(X0,complement(X1)),'universal$uclass')
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c27,c5]) ).
cnf(d37,plain,
( subclass(X0,complement(X1))
| subclass(X0,complement(X1))
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[d36,d2]) ).
cnf(d38,plain,
subclass(X0,complement('null$uclass')),
inference(resolution,[status(thm)],[d37,d29]) ).
cnf(d39,plain,
complement('null$uclass') = 'universal$uclass',
inference(resolution,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
union('null$uclass',X0) = complement(intersection('universal$uclass',complement(X0))),
inference(superposition,[status(thm)],[d39,c28]) ).
cnf(d41,plain,
'set$ubuilder'('universal$uclass',X0) = complement(intersection('universal$uclass',complement(X0))),
inference(demodulation,[status(thm)],[d40,d34]) ).
cnf(d42,plain,
'set$ubuilder'('universal$uclass',X0) = complement(complement(X0)),
inference(demodulation,[status(thm)],[d41,d16]) ).
cnf(d43,plain,
( ~ member('not$usubclass$uelement'(X0,complement(complement(X1))),X1)
| subclass(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d37,c26]) ).
cnf(d44,plain,
( subclass(X1,complement(complement(X0)))
| ~ member('not$usubclass$uelement'(X1,'set$ubuilder'('universal$uclass',X0)),X0) ),
inference(demodulation,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
( subclass(X1,'set$ubuilder'('universal$uclass',X0))
| ~ member('not$usubclass$uelement'(X1,'set$ubuilder'('universal$uclass',X0)),X0) ),
inference(demodulation,[status(thm)],[d44,d42]) ).
cnf(d46,plain,
( subclass(X0,'set$ubuilder'('universal$uclass',X0))
| subclass(X0,'set$ubuilder'('universal$uclass',X0)) ),
inference(resolution,[status(thm)],[d45,c4]) ).
cnf(d47,plain,
( ~ subclass(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d23,c9]) ).
cnf(d48,plain,
( subclass(X0,intersection(X0,X1))
| subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d13,c4]) ).
cnf(d49,plain,
( subclass(X0,intersection(X0,'universal$uclass'))
| subclass(X0,intersection(X0,'universal$uclass')) ),
inference(resolution,[status(thm)],[d48,d2]) ).
cnf(d50,plain,
intersection(X0,'universal$uclass') = X0,
inference(resolution,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
union(X0,'null$uclass') = complement(intersection(complement(X0),'universal$uclass')),
inference(superposition,[status(thm)],[d39,c28]) ).
cnf(d52,plain,
union(X0,'null$uclass') = complement(complement(X0)),
inference(demodulation,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
union(X0,'null$uclass') = 'set$ubuilder'('universal$uclass',X0),
inference(demodulation,[status(thm)],[d52,d42]) ).
cnf(d54,plain,
'symmetric$udifference'(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)),
inference(demodulation,[status(thm)],[c29,c28]) ).
cnf(d55,plain,
'null$uclass' = intersection(X0,'null$uclass'),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d56,plain,
'symmetric$udifference'(X0,'null$uclass') = intersection(complement('null$uclass'),union(X0,'null$uclass')),
inference(superposition,[status(thm)],[d55,d54]) ).
cnf(d57,plain,
'symmetric$udifference'(X0,'null$uclass') = intersection('universal$uclass',union(X0,'null$uclass')),
inference(demodulation,[status(thm)],[d56,d39]) ).
cnf(d58,plain,
'symmetric$udifference'(X0,'null$uclass') = union(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d57,d16]) ).
cnf(d59,plain,
'symmetric$udifference'(X0,'null$uclass') = 'set$ubuilder'('universal$uclass',X0),
inference(demodulation,[status(thm)],[d58,d53]) ).
cnf(d60,plain,
'symmetric$udifference'(singleton(X0),'null$uclass') = intersection('universal$uclass','set$ubuilder'(X0,'null$uclass')),
inference(superposition,[status(thm)],[c0,d57]) ).
cnf(d61,plain,
'symmetric$udifference'(singleton(X0),'null$uclass') = 'set$ubuilder'(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d60,d16]) ).
cnf(d62,plain,
'set$ubuilder'('universal$uclass',singleton(X0)) = 'set$ubuilder'(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d61,d59]) ).
cnf(d63,plain,
subclass(singleton(X0),'set$ubuilder'(X0,'null$uclass')),
inference(superposition,[status(thm)],[d62,d46]) ).
cnf(d64,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c26,c4]) ).
cnf(d65,plain,
( member('not$usubclass$uelement'(X0,complement(intersection(X1,X2))),X2)
| subclass(X0,complement(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[d37,c24]) ).
cnf(d66,plain,
( subclass(complement(X0),complement(intersection(X1,X0)))
| subclass(complement(X0),complement(intersection(X1,X0))) ),
inference(resolution,[status(thm)],[d65,d64]) ).
cnf(d67,plain,
subclass(complement(complement(X1)),union(X0,X1)),
inference(superposition,[status(thm)],[c28,d66]) ).
cnf(d68,plain,
subclass('set$ubuilder'('universal$uclass',X0),union(X1,X0)),
inference(demodulation,[status(thm)],[d67,d42]) ).
cnf(d69,plain,
subclass('set$ubuilder'('universal$uclass',X1),'set$ubuilder'(X0,X1)),
inference(superposition,[status(thm)],[c0,d68]) ).
cnf(d70,plain,
'symmetric$udifference'('null$uclass',X0) = intersection(complement('null$uclass'),union('null$uclass',X0)),
inference(superposition,[status(thm)],[d24,d54]) ).
cnf(d71,plain,
'symmetric$udifference'('null$uclass',X0) = intersection('universal$uclass',union('null$uclass',X0)),
inference(demodulation,[status(thm)],[d70,d39]) ).
cnf(d72,plain,
'symmetric$udifference'('null$uclass',X0) = intersection('universal$uclass','set$ubuilder'('universal$uclass',X0)),
inference(demodulation,[status(thm)],[d71,d34]) ).
cnf(d73,plain,
'symmetric$udifference'('null$uclass',X0) = 'set$ubuilder'('universal$uclass',X0),
inference(demodulation,[status(thm)],[d72,d16]) ).
cnf(d74,plain,
( member('not$usubclass$uelement'(X0,complement(intersection(X1,X2))),X1)
| subclass(X0,complement(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[d37,c23]) ).
cnf(d75,plain,
( subclass(complement(X0),complement(intersection(X0,X1)))
| subclass(complement(X0),complement(intersection(X0,X1))) ),
inference(resolution,[status(thm)],[d74,d64]) ).
cnf(d76,plain,
subclass(complement(complement(X0)),union(X0,X1)),
inference(superposition,[status(thm)],[c28,d75]) ).
cnf(d77,plain,
subclass('set$ubuilder'('universal$uclass',X0),union(X0,X1)),
inference(demodulation,[status(thm)],[d76,d42]) ).
cnf(d78,plain,
subclass('set$ubuilder'(X0,'null$uclass'),union(singleton(X0),X1)),
inference(superposition,[status(thm)],[d62,d77]) ).
cnf(d79,plain,
subclass('set$ubuilder'(X0,'null$uclass'),'set$ubuilder'(X0,X1)),
inference(demodulation,[status(thm)],[d78,c0]) ).
cnf(d80,plain,
subclass('set$ubuilder'(x,'null$uclass'),'null$uclass'),
inference(superposition,[status(thm)],[c2,d79]) ).
cnf(d81,plain,
'null$uclass' = 'set$ubuilder'(x,'null$uclass'),
inference(resolution,[status(thm)],[d80,d9]) ).
cnf(d82,plain,
subclass(singleton(x),'null$uclass'),
inference(superposition,[status(thm)],[d81,d63]) ).
cnf(d83,plain,
'null$uclass' = singleton(x),
inference(resolution,[status(thm)],[d82,d9]) ).
cnf(d84,plain,
subclass('symmetric$udifference'(X0,X1),union(X0,X1)),
inference(superposition,[status(thm)],[d54,d11]) ).
cnf(d85,plain,
subclass('symmetric$udifference'(singleton(X0),X1),'set$ubuilder'(X0,X1)),
inference(superposition,[status(thm)],[c0,d84]) ).
cnf(d86,plain,
subclass('symmetric$udifference'(singleton(x),'set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))),'null$uclass'),
inference(superposition,[status(thm)],[c2,d85]) ).
cnf(d87,plain,
( ~ subclass('null$uclass','symmetric$udifference'(singleton(x),'set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))))
| 'symmetric$udifference'(singleton(x),'set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))) = 'null$uclass' ),
inference(resolution,[status(thm)],[d86,c9]) ).
cnf(d88,plain,
( ~ subclass('null$uclass','symmetric$udifference'(singleton(x),'set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))))
| 'symmetric$udifference'('null$uclass','set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))) = 'null$uclass' ),
inference(demodulation,[status(thm)],[d87,d83]) ).
cnf(d89,plain,
( ~ subclass('null$uclass','symmetric$udifference'(singleton(x),'set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))))
| 'set$ubuilder'('universal$uclass','set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))) = 'null$uclass' ),
inference(demodulation,[status(thm)],[d88,d73]) ).
cnf(d90,plain,
( ~ subclass('null$uclass','symmetric$udifference'('null$uclass','set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))))
| 'set$ubuilder'('universal$uclass','set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))) = 'null$uclass' ),
inference(demodulation,[status(thm)],[d89,d83]) ).
cnf(d91,plain,
( ~ subclass('null$uclass','set$ubuilder'('universal$uclass','set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))))
| 'set$ubuilder'('universal$uclass','set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))) = 'null$uclass' ),
inference(demodulation,[status(thm)],[d90,d73]) ).
cnf(d92,plain,
'set$ubuilder'('universal$uclass','set$ubuilder'(y,'set$ubuilder'(u,'null$uclass'))) = 'null$uclass',
inference(resolution,[status(thm)],[d8,d91]) ).
cnf(d93,plain,
subclass('set$ubuilder'(y,'set$ubuilder'(u,'null$uclass')),'null$uclass'),
inference(superposition,[status(thm)],[d92,d46]) ).
cnf(d94,plain,
'null$uclass' = 'set$ubuilder'(y,'set$ubuilder'(u,'null$uclass')),
inference(resolution,[status(thm)],[d93,d9]) ).
cnf(d95,plain,
subclass('set$ubuilder'('universal$uclass','set$ubuilder'(u,'null$uclass')),'null$uclass'),
inference(superposition,[status(thm)],[d94,d69]) ).
cnf(d96,plain,
'null$uclass' = 'set$ubuilder'('universal$uclass','set$ubuilder'(u,'null$uclass')),
inference(resolution,[status(thm)],[d95,d9]) ).
cnf(d97,plain,
subclass('set$ubuilder'(u,'null$uclass'),'null$uclass'),
inference(superposition,[status(thm)],[d96,d46]) ).
cnf(d98,plain,
'null$uclass' = 'set$ubuilder'(u,'null$uclass'),
inference(resolution,[status(thm)],[d97,d9]) ).
cnf(d99,plain,
subclass(singleton(u),'null$uclass'),
inference(superposition,[status(thm)],[d98,d63]) ).
cnf(d100,plain,
'null$uclass' = singleton(u),
inference(resolution,[status(thm)],[d99,d9]) ).
cnf(d101,plain,
( ~ member(u,'universal$uclass')
| member(u,'null$uclass') ),
inference(superposition,[status(thm)],[d100,d0]) ).
cnf(d102,plain,
member(u,'null$uclass'),
inference(resolution,[status(thm)],[c1,d101]) ).
cnf(d103,plain,
$false,
inference(resolution,[status(thm)],[d29,d102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET136-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.58 % Computer : n001.cluster.edu
% 0.18/5.58 % Model : x86_64 x86_64
% 0.18/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.58 % Memory : 8046.5625MB
% 0.18/5.58 % OS : Linux 6.8.0-71-generic
% 0.18/5.58 % CPULimit : 300
% 0.18/5.58 % WCLimit : 300
% 0.18/5.58 % DateTime : Sat Sep 26 07:18:02 UTC 2026
% 0.18/5.59 % CPUTime :
% 0.18/5.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 116.64/28.86 % SZS status Unsatisfiable for theBenchmark.p
% 116.64/28.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------