%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET079-6 : 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 : n006.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 08:31:56 AM UTC 2026
% Result : Unsatisfiable 9.60s 4.36s
% Output : CNFRefutation 9.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 12 unt; 10 nHn; 24 RR)
% Number of literals : 71 ( 14 equ; 26 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_to_set_in_its_singleton_1,negated_conjecture,
member(x,'universal$uclass') ).
cnf(prove_corollary_to_set_in_its_singleton_2,negated_conjecture,
singleton(x) = 'null$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$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$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(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_corollary_to_set_in_its_singleton_1]) ).
cnf(c1,plain,
singleton(x) = 'null$uclass',
inference(clausification,[status(esa)],[prove_corollary_to_set_in_its_singleton_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$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c8,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c10,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c13,plain,
'unordered$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(c25,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c68,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity2]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c13,c10]) ).
cnf(d1,plain,
( ~ member(x,'universal$uclass')
| member(x,'null$uclass') ),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
member(x,'null$uclass'),
inference(resolution,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(d4,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(d5,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),'universal$uclass') ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
( subclass(complement('universal$uclass'),X0)
| subclass(complement('universal$uclass'),X0) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c22,c3]) ).
cnf(d8,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( X0 = 'null$uclass'
| subclass('null$uclass',X0) ),
inference(superposition,[status(thm)],[c68,d8]) ).
cnf(d10,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass'
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d9,c8]) ).
cnf(d11,plain,
complement('universal$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ member(X0,'universal$uclass')
| ~ member(X0,'null$uclass') ),
inference(superposition,[status(thm)],[d11,c25]) ).
cnf(d13,plain,
~ member(x,'universal$uclass'),
inference(resolution,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c0,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET079-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n006.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 07:03:40 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.60/4.36 % SZS status Unsatisfiable for theBenchmark.p
% 9.60/4.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------