%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM172-1 : 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 : n005.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 08:10:50 AM UTC 2026
% Result : Unsatisfiable 95.43s 41.79s
% Output : CNFRefutation 95.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of clauses : 86 ( 26 unt; 27 nHn; 51 RR)
% Number of literals : 166 ( 46 equ; 59 neg)
% Maximal clause size : 4 ( 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 : 132 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_successor_is_different_1,negated_conjecture,
member(x,'universal$uclass') ).
cnf(prove_successor_is_different_2,negated_conjecture,
successor(x) = x ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$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$upair'(X1,X2)) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$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(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_successor_is_different_1]) ).
cnf(c1,plain,
successor(x) = x,
inference(clausification,[status(esa)],[prove_successor_is_different_2]) ).
cnf(c2,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c3,plain,
( subclass(X0,X1)
| member('not$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,
( X2 = X1
| ~ member(X1,'unordered$upair'(X0,X2))
| X0 = X1 ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c10,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c13,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c22,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c23,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c24,plain,
( member(X0,intersection(X2,X1))
| ~ 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,'universal$uclass')
| member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c27,plain,
union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
inference(clausification,[status(esa)],[union]) ).
cnf(c29,plain,
restrict(X0,X1,X2) = intersection(X0,'cross$uproduct'(X1,X2)),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c31,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c44,plain,
successor(X0) = union(X0,singleton(X0)),
inference(clausification,[status(esa)],[successor]) ).
cnf(c67,plain,
( member(regular(X0),X0)
| X0 = 'null$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,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c13,c10]) ).
cnf(d1,plain,
( X0 = X1
| X0 = X1
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d2,plain,
( singleton(X0) = 'null$uclass'
| X0 = regular(singleton(X0)) ),
inference(resolution,[status(thm)],[d1,c67]) ).
cnf(d3,plain,
( singleton(X0) = 'null$uclass'
| singleton(X0) = 'null$uclass'
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[d2,c67]) ).
cnf(d4,plain,
( X0 = 'null$uclass'
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| member(X1,'null$uclass') ),
inference(superposition,[status(thm)],[c68,c24]) ).
cnf(d5,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(d6,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
( member(regular(X0),'universal$uclass')
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c67,d5]) ).
cnf(d8,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c25,c67]) ).
cnf(d9,plain,
( complement('universal$uclass') = 'null$uclass'
| complement('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d9,c25]) ).
cnf(d11,plain,
( subclass('null$uclass',X0)
| ~ member('not$usubclass$uelement'('null$uclass',X0),'universal$uclass') ),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
( subclass('null$uclass',X0)
| subclass('null$uclass',X0) ),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( ~ subclass(X0,'null$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d12,c8]) ).
cnf(d14,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c22,c3]) ).
cnf(d15,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
'null$uclass' = intersection('null$uclass',X0),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(superposition,[status(thm)],[d16,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,
( ~ member(X1,regular(X0))
| ~ member(X1,X0)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d21,d4]) ).
cnf(d23,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X1,singleton(X0))
| singleton(X0) = 'null$uclass'
| ~ member(X1,X0) ),
inference(superposition,[status(thm)],[d2,d22]) ).
cnf(d24,plain,
( singleton(X0) = 'null$uclass'
| ~ member(X0,X0)
| singleton(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d23,d3]) ).
cnf(d25,plain,
( subclass(X0,complement(X1))
| ~ member('not$usubclass$uelement'(X0,complement(X1)),'universal$uclass')
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c26,c4]) ).
cnf(d26,plain,
( subclass(X0,complement(X1))
| subclass(X0,complement(X1))
| member('not$usubclass$uelement'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[d25,d6]) ).
cnf(d27,plain,
( ~ member('not$usubclass$uelement'(X0,complement(complement(X1))),X1)
| subclass(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d26,c25]) ).
cnf(d28,plain,
( subclass(X0,complement(complement(X0)))
| subclass(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[d27,c3]) ).
cnf(d29,plain,
( ~ member(X0,X1)
| member(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d28,c2]) ).
cnf(d30,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(d31,plain,
( member('not$usubclass$uelement'(X0,complement(intersection(X1,X2))),X2)
| subclass(X0,complement(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[d26,c23]) ).
cnf(d32,plain,
( subclass(complement(X0),complement(intersection(X1,X0)))
| subclass(complement(X0),complement(intersection(X1,X0))) ),
inference(resolution,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
subclass(complement(complement(X1)),union(X0,X1)),
inference(superposition,[status(thm)],[c27,d32]) ).
cnf(d34,plain,
subclass(complement(complement(singleton(X0))),successor(X0)),
inference(superposition,[status(thm)],[c44,d33]) ).
cnf(d35,plain,
subclass(complement(complement(singleton(x))),x),
inference(superposition,[status(thm)],[c1,d34]) ).
cnf(d36,plain,
( ~ member(X0,complement(complement(singleton(x))))
| member(X0,x) ),
inference(resolution,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
( ~ member(X0,singleton(x))
| member(X0,x) ),
inference(resolution,[status(thm)],[d36,d29]) ).
cnf(d38,plain,
( ~ member(x,'universal$uclass')
| member(x,x) ),
inference(resolution,[status(thm)],[d37,d0]) ).
cnf(d39,plain,
member(x,x),
inference(resolution,[status(thm)],[c0,d38]) ).
cnf(d40,plain,
singleton(x) = 'null$uclass',
inference(resolution,[status(thm)],[d39,d24]) ).
cnf(d41,plain,
( ~ member(x,'universal$uclass')
| member(x,'null$uclass') ),
inference(superposition,[status(thm)],[d40,d0]) ).
cnf(d42,plain,
member(x,'null$uclass'),
inference(resolution,[status(thm)],[c0,d41]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d21,d42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM172-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.66 % Computer : n005.cluster.edu
% 0.18/0.66 % Model : x86_64 x86_64
% 0.18/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.66 % Memory : 8046.5625MB
% 0.18/0.66 % OS : Linux 6.8.0-71-generic
% 0.18/0.66 % CPULimit : 300
% 0.18/0.66 % WCLimit : 300
% 0.18/0.66 % DateTime : Sat Sep 26 02:09:18 UTC 2026
% 0.18/0.66 % CPUTime :
% 0.18/0.66 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.43/41.79 % SZS status Unsatisfiable for theBenchmark.p
% 95.43/41.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------