%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM181-1 : 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 : n017.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 08:10:51 AM UTC 2026
% Result : Unsatisfiable 71.83s 18.15s
% Output : CNFRefutation 71.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 21
% Syntax : Number of clauses : 108 ( 44 unt; 21 nHn; 66 RR)
% Number of literals : 185 ( 49 equ; 65 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 : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 143 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_null_class_is_not_a_limit_ordinal_1,negated_conjecture,
member('null$uclass','limit$uordinals') ).
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$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$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$uclass') ) ).
cnf(union,axiom,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1) ).
cnf(restriction1,axiom,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,X1,X2) ).
cnf(domain1,axiom,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ) ).
cnf(successor,axiom,
union(X0,singleton(X0)) = successor(X0) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(ordinal_numbers2,axiom,
( subclass('sum$uclass'(X0),X0)
| ~ member(X0,'ordinal$unumbers') ) ).
cnf(kind_1_ordinals,axiom,
union(singleton('null$uclass'),image('successor$urelation','ordinal$unumbers')) = 'kind$u1$uordinals' ).
cnf(limit_ordinals,axiom,
intersection(complement('kind$u1$uordinals'),'ordinal$unumbers') = 'limit$uordinals' ).
cnf(c0,plain,
member('null$uclass','limit$uordinals'),
inference(clausification,[status(esa)],[prove_null_class_is_not_a_limit_ordinal_1]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c2,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c3,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c4,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c7,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c9,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c12,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c22,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c23,plain,
( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c24,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c25,plain,
( member(X0,X1)
| ~ member(X0,'universal$uclass')
| member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c26,plain,
union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
inference(clausification,[status(esa)],[union]) ).
cnf(c28,plain,
restrict(X0,X1,X2) = intersection(X0,'cross$uproduct'(X1,X2)),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c30,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c43,plain,
successor(X0) = union(X0,singleton(X0)),
inference(clausification,[status(esa)],[successor]) ).
cnf(c66,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(c135,plain,
( subclass('sum$uclass'(X0),X0)
| ~ member(X0,'ordinal$unumbers') ),
inference(clausification,[status(esa)],[ordinal_numbers2]) ).
cnf(c138,plain,
union(singleton('null$uclass'),image('successor$urelation','ordinal$unumbers')) = 'kind$u1$uordinals',
inference(clausification,[status(esa)],[kind_1_ordinals]) ).
cnf(c139,plain,
intersection(complement('kind$u1$uordinals'),'ordinal$unumbers') = 'limit$uordinals',
inference(clausification,[status(esa)],[limit_ordinals]) ).
cnf(d0,plain,
( member(X0,complement('kind$u1$uordinals'))
| ~ member(X0,'limit$uordinals') ),
inference(superposition,[status(thm)],[c139,c21]) ).
cnf(d1,plain,
( ~ member(X0,'kind$u1$uordinals')
| ~ member(X0,'limit$uordinals') ),
inference(resolution,[status(thm)],[d0,c24]) ).
cnf(d2,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c22,c2]) ).
cnf(d3,plain,
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( ~ subclass(X1,intersection(X0,X1))
| intersection(X0,X1) = X1 ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c1,c4]) ).
cnf(d6,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,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)],[c23,c3]) ).
cnf(d8,plain,
( subclass(X0,intersection('universal$uclass',X1))
| subclass(X0,intersection('universal$uclass',X1))
| ~ member('not$usubclass$uelement'(X0,intersection('universal$uclass',X1)),X1) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( subclass(X0,intersection('universal$uclass',X0))
| subclass(X0,intersection('universal$uclass',X0)) ),
inference(resolution,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
intersection('universal$uclass',X0) = X0,
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( ~ subclass('universal$uclass',X0)
| X0 = 'universal$uclass' ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d12,plain,
( member(regular(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c66,d5]) ).
cnf(d13,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c24,c66]) ).
cnf(d14,plain,
( complement('universal$uclass') = 'null$uclass'
| complement('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d14,c24]) ).
cnf(d16,plain,
( X0 = 'null$uclass'
| ~ member(regular(X0),'null$uclass') ),
inference(resolution,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
( intersection(X0,X1) = 'null$uclass'
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[c21,c66]) ).
cnf(d18,plain,
( intersection('null$uclass',X0) = 'null$uclass'
| intersection('null$uclass',X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(superposition,[status(thm)],[d18,c28]) ).
cnf(d20,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d19,c30]) ).
cnf(d21,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),'null$uclass') ),
inference(resolution,[status(thm)],[d15,d6]) ).
cnf(d22,plain,
( subclass('null$uclass',X0)
| subclass('null$uclass',X0) ),
inference(resolution,[status(thm)],[d21,c2]) ).
cnf(d23,plain,
( ~ subclass(X0,'null$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d22,c7]) ).
cnf(d24,plain,
( ~ member('null$uclass','ordinal$unumbers')
| 'null$uclass' = 'sum$uclass'('null$uclass') ),
inference(resolution,[status(thm)],[d23,c135]) ).
cnf(d25,plain,
( member(X0,'ordinal$unumbers')
| ~ member(X0,'limit$uordinals') ),
inference(superposition,[status(thm)],[c139,c22]) ).
cnf(d26,plain,
member('null$uclass','ordinal$unumbers'),
inference(resolution,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
'null$uclass' = 'sum$uclass'('null$uclass'),
inference(resolution,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
( ~ subclass(X0,'sum$uclass'(X0))
| 'sum$uclass'(X0) = X0
| ~ member(X0,'ordinal$unumbers') ),
inference(resolution,[status(thm)],[c135,c7]) ).
cnf(d29,plain,
( ~ member('null$uclass','ordinal$unumbers')
| 'sum$uclass'('null$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
( ~ member('null$uclass','ordinal$unumbers')
| 'null$uclass' = 'null$uclass' ),
inference(demodulation,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
'null$uclass' = 'null$uclass',
inference(resolution,[status(thm)],[d26,d30]) ).
cnf(d32,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(resolution,[status(thm)],[d31,d20]) ).
cnf(d33,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d32,c66]) ).
cnf(d34,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d32,d33]) ).
cnf(d35,plain,
( subclass(X0,complement(X1))
| ~ member('not$usubclass$uelement'(X0,complement(X1)),'universal$uclass')
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(d36,plain,
( subclass(X0,complement(X1))
| subclass(X0,complement(X1))
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[d35,d6]) ).
cnf(d37,plain,
subclass(X0,complement('null$uclass')),
inference(resolution,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
complement('null$uclass') = 'universal$uclass',
inference(resolution,[status(thm)],[d37,d11]) ).
cnf(d39,plain,
union('universal$uclass',X0) = complement(intersection('null$uclass',complement(X0))),
inference(superposition,[status(thm)],[d14,c26]) ).
cnf(d40,plain,
union('universal$uclass',X0) = complement('null$uclass'),
inference(demodulation,[status(thm)],[d39,d18]) ).
cnf(d41,plain,
union('universal$uclass',X0) = 'universal$uclass',
inference(demodulation,[status(thm)],[d40,d38]) ).
cnf(d42,plain,
union(intersection(complement(X0),complement(X1)),X2) = complement(intersection(union(X0,X1),complement(X2))),
inference(superposition,[status(thm)],[c26,c26]) ).
cnf(d43,plain,
union(intersection('null$uclass',complement(X0)),X1) = complement(intersection(union('universal$uclass',X0),complement(X1))),
inference(superposition,[status(thm)],[d14,d42]) ).
cnf(d44,plain,
union('null$uclass',X1) = complement(intersection(union('universal$uclass',X0),complement(X1))),
inference(demodulation,[status(thm)],[d43,d18]) ).
cnf(d45,plain,
union('null$uclass',X1) = complement(intersection('universal$uclass',complement(X1))),
inference(demodulation,[status(thm)],[d44,d41]) ).
cnf(d46,plain,
union('null$uclass',X0) = complement(complement(X0)),
inference(demodulation,[status(thm)],[d45,d10]) ).
cnf(d47,plain,
successor('null$uclass') = complement(complement(singleton('null$uclass'))),
inference(superposition,[status(thm)],[d46,c43]) ).
cnf(d48,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c24,c2]) ).
cnf(d49,plain,
( member('not$usubclass$uelement'(X0,complement(intersection(X1,X2))),X1)
| subclass(X0,complement(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[d36,c21]) ).
cnf(d50,plain,
( subclass(complement(X0),complement(intersection(X0,X1)))
| subclass(complement(X0),complement(intersection(X0,X1))) ),
inference(resolution,[status(thm)],[d49,d48]) ).
cnf(d51,plain,
subclass(complement(complement(X0)),union(X0,X1)),
inference(superposition,[status(thm)],[c26,d50]) ).
cnf(d52,plain,
subclass(complement(complement(singleton('null$uclass'))),'kind$u1$uordinals'),
inference(superposition,[status(thm)],[c138,d51]) ).
cnf(d53,plain,
subclass(successor('null$uclass'),'kind$u1$uordinals'),
inference(demodulation,[status(thm)],[d52,d47]) ).
cnf(d54,plain,
( ~ member(X0,successor('null$uclass'))
| member(X0,'kind$u1$uordinals') ),
inference(resolution,[status(thm)],[d53,c1]) ).
cnf(d55,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c12,c9]) ).
cnf(d56,plain,
( ~ member('not$usubclass$uelement'(X0,complement(complement(X1))),X1)
| subclass(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d36,c24]) ).
cnf(d57,plain,
( subclass(X0,complement(complement(X0)))
| subclass(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[d56,c2]) ).
cnf(d58,plain,
subclass(singleton('null$uclass'),successor('null$uclass')),
inference(superposition,[status(thm)],[d47,d57]) ).
cnf(d59,plain,
( ~ member(X0,singleton('null$uclass'))
| member(X0,successor('null$uclass')) ),
inference(resolution,[status(thm)],[d58,c1]) ).
cnf(d60,plain,
( ~ member('null$uclass','universal$uclass')
| member('null$uclass',successor('null$uclass')) ),
inference(resolution,[status(thm)],[d59,d55]) ).
cnf(d61,plain,
member('null$uclass','universal$uclass'),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d62,plain,
member('null$uclass',successor('null$uclass')),
inference(resolution,[status(thm)],[d61,d60]) ).
cnf(d63,plain,
member('null$uclass','kind$u1$uordinals'),
inference(resolution,[status(thm)],[d62,d54]) ).
cnf(d64,plain,
~ member('null$uclass','limit$uordinals'),
inference(resolution,[status(thm)],[d63,d1]) ).
cnf(d65,plain,
$false,
inference(resolution,[status(thm)],[c0,d64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM181-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 02:05:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.83/18.15 % SZS status Unsatisfiable for theBenchmark.p
% 71.83/18.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------