%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET071-7 : 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 : n011.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 08:31:53 AM UTC 2026
% Result : Unsatisfiable 33.37s 4.76s
% Output : CNFRefutation 33.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of clauses : 56 ( 23 unt; 21 nHn; 32 RR)
% Number of literals : 97 ( 38 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(equality1,axiom,
( member('not$usubclass$uelement'(X1,X0),X1)
| member('not$usubclass$uelement'(X0,X1),X0)
| X0 = X1 ) ).
cnf(special_classes_lemma,axiom,
~ member(X0,intersection(complement(X1),X1)) ).
cnf(existence_of_null_class,axiom,
~ member(X0,'null$uclass') ).
cnf(corollary_of_null_class_is_subclass,axiom,
( X0 = 'null$uclass'
| ~ subclass(X0,'null$uclass') ) ).
cnf(null_class_is_unique,axiom,
( member('not$usubclass$uelement'(X0,'null$uclass'),X0)
| X0 = 'null$uclass' ) ).
cnf(unordered_pair_equals_singleton1,axiom,
( 'unordered$upair'(X1,X0) = singleton(X1)
| member(X0,'universal$uclass') ) ).
cnf(prove_null_unordered_pair_1,negated_conjecture,
'unordered$upair'(x,y) != 'null$uclass' ).
cnf(prove_null_unordered_pair_2,negated_conjecture,
~ member(x,'universal$uclass') ).
cnf(prove_null_unordered_pair_3,negated_conjecture,
~ member(y,'universal$uclass') ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$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(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(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(c6,plain,
( member('not$usubclass$uelement'(X1,X0),X1)
| member('not$usubclass$uelement'(X0,X1),X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[equality1]) ).
cnf(c10,plain,
~ member(X0,intersection(complement(X1),X1)),
inference(clausification,[status(esa)],[special_classes_lemma]) ).
cnf(c11,plain,
~ member(X0,'null$uclass'),
inference(clausification,[status(esa)],[existence_of_null_class]) ).
cnf(c13,plain,
( X0 = 'null$uclass'
| ~ subclass(X0,'null$uclass') ),
inference(clausification,[status(esa)],[corollary_of_null_class_is_subclass]) ).
cnf(c14,plain,
( member('not$usubclass$uelement'(X0,'null$uclass'),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[null_class_is_unique]) ).
cnf(c19,plain,
( 'unordered$upair'(X1,X0) = singleton(X1)
| member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair_equals_singleton1]) ).
cnf(c21,plain,
'unordered$upair'(x,y) != 'null$uclass',
inference(clausification,[status(esa)],[prove_null_unordered_pair_1]) ).
cnf(c22,plain,
~ member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_null_unordered_pair_2]) ).
cnf(c23,plain,
~ member(y,'universal$uclass'),
inference(clausification,[status(esa)],[prove_null_unordered_pair_3]) ).
cnf(c24,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c25,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c26,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c27,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c31,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c35,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c44,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c47,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c89,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c24,c27]) ).
cnf(d1,plain,
( member('not$usubclass$uelement'(X0,'null$uclass'),X0)
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(d2,plain,
( member('not$usubclass$uelement'(X0,'null$uclass'),'universal$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( X1 = X0
| X1 = X0
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c35,c31]) ).
cnf(d4,plain,
( 'null$uclass' = singleton(X0)
| 'not$usubclass$uelement'(singleton(X0),'null$uclass') = X0 ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( 'null$uclass' = singleton(X0)
| 'null$uclass' = singleton(X0)
| member(X0,'universal$uclass') ),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'null$uclass' = singleton(x),
inference(resolution,[status(thm)],[d5,c22]) ).
cnf(d7,plain,
'unordered$upair'(X0,y) = singleton(X0),
inference(resolution,[status(thm)],[c19,c23]) ).
cnf(d8,plain,
singleton(x) != 'null$uclass',
inference(demodulation,[status(thm)],[c21,d7]) ).
cnf(d9,plain,
'null$uclass' != 'null$uclass',
inference(demodulation,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c44,c25]) ).
cnf(d11,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d10,c26]) ).
cnf(d12,plain,
intersection('null$uclass',X0) = 'null$uclass',
inference(resolution,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
intersection(complement(X0),X0) = 'null$uclass',
inference(resolution,[status(thm)],[c14,c10]) ).
cnf(d14,plain,
( ~ member(regular(complement(X0)),X0)
| complement(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[c89,c47]) ).
cnf(d15,plain,
( X0 = 'null$uclass'
| member(regular(X0),'universal$uclass') ),
inference(resolution,[status(thm)],[d0,c89]) ).
cnf(d16,plain,
( complement('universal$uclass') = 'null$uclass'
| complement('universal$uclass') = 'null$uclass' ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
intersection('null$uclass','universal$uclass') = 'null$uclass',
inference(superposition,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
'null$uclass' = 'null$uclass',
inference(demodulation,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET071-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 07:03:13 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.37/4.76 % SZS status Unsatisfiable for theBenchmark.p
% 33.37/4.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------