%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM144-1 : 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 : 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 08:10:48 AM UTC 2026
% Result : Unsatisfiable 119.40s 31.53s
% Output : CNFRefutation 119.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of clauses : 95 ( 41 unt; 30 nHn; 48 RR)
% Number of literals : 168 ( 61 equ; 52 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 : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_successor_of_proper_class_is_class_1,negated_conjecture,
~ member(x,'universal$uclass') ).
cnf(prove_successor_of_proper_class_is_class_2,negated_conjecture,
successor(x) != x ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(not_subclass_members2,axiom,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$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$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
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(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(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
~ member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_successor_of_proper_class_is_class_1]) ).
cnf(c1,plain,
successor(x) != x,
inference(clausification,[status(esa)],[prove_successor_of_proper_class_is_class_2]) ).
cnf(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c3,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c4,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c5,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
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$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c13,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
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(c25,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c26,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c27,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(clausification,[status(esa)],[union]) ).
cnf(c29,plain,
intersection(X0,'cross$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$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c44,plain,
union(X0,singleton(X0)) = successor(X0),
inference(clausification,[status(esa)],[successor]) ).
cnf(c67,plain,
( member(regular(X0),X0)
| X0 = 'null$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,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(d1,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(d3,plain,
( ~ member('not$usubclass$uelement'(complement(complement(X0)),X1),'universal$uclass')
| member('not$usubclass$uelement'(complement(complement(X0)),X1),X0)
| subclass(complement(complement(X0)),X1) ),
inference(resolution,[status(thm)],[d2,c26]) ).
cnf(d4,plain,
( subclass(complement(complement(X0)),X1)
| subclass(complement(complement(X0)),X1)
| member('not$usubclass$uelement'(complement(complement(X0)),X1),X0) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( subclass(complement(complement(X0)),X0)
| subclass(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c22,c3]) ).
cnf(d7,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( X0 = 'null$uclass'
| subclass('null$uclass',X0) ),
inference(superposition,[status(thm)],[c68,d7]) ).
cnf(d9,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass'
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
intersection('null$uclass',X0) = 'null$uclass',
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ subclass(X0,intersection(X0,X1))
| X0 = intersection(X0,X1) ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d12,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(d13,plain,
( subclass(X0,intersection(X0,X1))
| subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( subclass(X0,intersection(X0,'universal$uclass'))
| subclass(X0,intersection(X0,'universal$uclass')) ),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
X0 = intersection(X0,'universal$uclass'),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( ~ subclass('universal$uclass',X0)
| 'universal$uclass' = X0 ),
inference(resolution,[status(thm)],[c8,c5]) ).
cnf(d17,plain,
'null$uclass' = restrict('null$uclass',X0,X1),
inference(superposition,[status(thm)],[d10,c29]) ).
cnf(d18,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d17,c31]) ).
cnf(d19,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d19,c67]) ).
cnf(d21,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d19,d20]) ).
cnf(d22,plain,
( subclass(X0,complement(X1))
| ~ member('not$usubclass$uelement'(X0,complement(X1)),'universal$uclass')
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c26,c4]) ).
cnf(d23,plain,
( subclass(X0,complement(X1))
| subclass(X0,complement(X1))
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[d22,d1]) ).
cnf(d24,plain,
subclass(X0,complement('null$uclass')),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
'universal$uclass' = complement('null$uclass'),
inference(resolution,[status(thm)],[d24,d16]) ).
cnf(d26,plain,
( subclass(complement('universal$uclass'),X0)
| subclass(complement('universal$uclass'),X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d27,plain,
complement('universal$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d9,d26]) ).
cnf(d28,plain,
complement(intersection('null$uclass',complement(X0))) = union('universal$uclass',X0),
inference(superposition,[status(thm)],[d27,c27]) ).
cnf(d29,plain,
complement('null$uclass') = union('universal$uclass',X0),
inference(demodulation,[status(thm)],[d28,d10]) ).
cnf(d30,plain,
'universal$uclass' = union('universal$uclass',X0),
inference(demodulation,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
complement(intersection(complement(X2),union(X0,X1))) = union(X2,intersection(complement(X0),complement(X1))),
inference(superposition,[status(thm)],[c27,c27]) ).
cnf(d32,plain,
complement(intersection(complement(X0),union('universal$uclass',X1))) = union(X0,intersection('null$uclass',complement(X1))),
inference(superposition,[status(thm)],[d27,d31]) ).
cnf(d33,plain,
complement(intersection(complement(X1),'universal$uclass')) = union(X1,intersection('null$uclass',complement(X0))),
inference(demodulation,[status(thm)],[d32,d30]) ).
cnf(d34,plain,
complement(complement(X0)) = union(X0,intersection('null$uclass',complement(X1))),
inference(demodulation,[status(thm)],[d33,d15]) ).
cnf(d35,plain,
complement(complement(X1)) = union(X1,'null$uclass'),
inference(demodulation,[status(thm)],[d34,d10]) ).
cnf(d36,plain,
( member(regular(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c67,d0]) ).
cnf(d37,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d38,plain,
( singleton(X0) = 'null$uclass'
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[d37,c67]) ).
cnf(d39,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
singleton(x) = 'null$uclass',
inference(resolution,[status(thm)],[d39,c0]) ).
cnf(d41,plain,
union(x,'null$uclass') = successor(x),
inference(superposition,[status(thm)],[d40,c44]) ).
cnf(d42,plain,
complement(complement(x)) = successor(x),
inference(demodulation,[status(thm)],[d41,d35]) ).
cnf(d43,plain,
subclass(successor(x),x),
inference(superposition,[status(thm)],[d42,d5]) ).
cnf(d44,plain,
( ~ subclass(x,successor(x))
| x = successor(x) ),
inference(resolution,[status(thm)],[d43,c8]) ).
cnf(d45,plain,
( ~ member('not$usubclass$uelement'(X0,complement(complement(X1))),X1)
| subclass(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d23,c25]) ).
cnf(d46,plain,
( subclass(X0,complement(complement(X0)))
| subclass(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[d45,c3]) ).
cnf(d47,plain,
subclass(x,successor(x)),
inference(superposition,[status(thm)],[d42,d46]) ).
cnf(d48,plain,
x = successor(x),
inference(resolution,[status(thm)],[d47,d44]) ).
cnf(d49,plain,
x != x,
inference(demodulation,[status(thm)],[c1,d48]) ).
cnf(d50,plain,
( subclass(X0,intersection(X0,X0))
| subclass(X0,intersection(X0,X0)) ),
inference(resolution,[status(thm)],[d13,c3]) ).
cnf(d51,plain,
X0 = intersection(X0,X0),
inference(resolution,[status(thm)],[d50,d11]) ).
cnf(d52,plain,
( X0 = intersection(X0,X0)
| ~ subclass(X0,X0) ),
inference(superposition,[status(thm)],[d51,d11]) ).
cnf(d53,plain,
( ~ subclass(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d52,d51]) ).
cnf(d54,plain,
( subclass(X0,X0)
| subclass(X0,X0) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d55,plain,
X0 = X0,
inference(resolution,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
$false,
inference(resolution,[status(thm)],[d55,d49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM144-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 02:02:17 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 119.40/31.53 % SZS status Unsatisfiable for theBenchmark.p
% 119.40/31.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------