%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET099-7 : 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 08:32:02 AM UTC 2026
% Result : Unsatisfiable 37.10s 13.70s
% Output : CNFRefutation 37.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 14 unt; 4 nHn; 23 RR)
% Number of literals : 45 ( 13 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(set_in_its_singleton,axiom,
( member(X0,singleton(X0))
| ~ member(X0,'universal$uclass') ) ).
cnf(number_of_elements_in_class,axiom,
( X0 = 'null$uclass'
| singleton('not$usubclass$uelement'(X0,'null$uclass')) = X0
| member('not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(X0,'null$uclass'))),X0),'null$uclass'),intersection(complement(singleton('not$usubclass$uelement'(X0,'null$uclass'))),X0)) ) ).
cnf(prove_corollary_2_to_number_of_elements_in_class_1,negated_conjecture,
'not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(x,'null$uclass'))),x),'null$uclass') = 'not$usubclass$uelement'(x,'null$uclass') ).
cnf(prove_corollary_2_to_number_of_elements_in_class_2,negated_conjecture,
singleton('not$usubclass$uelement'(x,'null$uclass')) != x ).
cnf(prove_corollary_2_to_number_of_elements_in_class_3,negated_conjecture,
x != 'null$uclass' ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(c30,plain,
( member(X0,singleton(X0))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[set_in_its_singleton]) ).
cnf(c49,plain,
( X0 = 'null$uclass'
| singleton('not$usubclass$uelement'(X0,'null$uclass')) = X0
| member('not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(X0,'null$uclass'))),X0),'null$uclass'),intersection(complement(singleton('not$usubclass$uelement'(X0,'null$uclass'))),X0)) ),
inference(clausification,[status(esa)],[number_of_elements_in_class]) ).
cnf(c50,plain,
'not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(x,'null$uclass'))),x),'null$uclass') = 'not$usubclass$uelement'(x,'null$uclass'),
inference(clausification,[status(esa)],[prove_corollary_2_to_number_of_elements_in_class_1]) ).
cnf(c51,plain,
singleton('not$usubclass$uelement'(x,'null$uclass')) != x,
inference(clausification,[status(esa)],[prove_corollary_2_to_number_of_elements_in_class_2]) ).
cnf(c52,plain,
x != 'null$uclass',
inference(clausification,[status(esa)],[prove_corollary_2_to_number_of_elements_in_class_3]) ).
cnf(c53,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c56,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c73,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c76,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(d0,plain,
( singleton('not$usubclass$uelement'(x,'null$uclass')) = x
| x = 'null$uclass'
| member('not$usubclass$uelement'(x,'null$uclass'),intersection(complement(singleton('not$usubclass$uelement'(x,'null$uclass'))),x)) ),
inference(superposition,[status(thm)],[c50,c49]) ).
cnf(d1,plain,
( member('not$usubclass$uelement'(x,'null$uclass'),intersection(complement(singleton('not$usubclass$uelement'(x,'null$uclass'))),x))
| singleton('not$usubclass$uelement'(x,'null$uclass')) = x ),
inference(resolution,[status(thm)],[c52,d0]) ).
cnf(d2,plain,
member('not$usubclass$uelement'(x,'null$uclass'),intersection(complement(singleton('not$usubclass$uelement'(x,'null$uclass'))),x)),
inference(resolution,[status(thm)],[c51,d1]) ).
cnf(d3,plain,
member('not$usubclass$uelement'(x,'null$uclass'),complement(singleton('not$usubclass$uelement'(x,'null$uclass')))),
inference(resolution,[status(thm)],[d2,c73]) ).
cnf(d4,plain,
~ member('not$usubclass$uelement'(x,'null$uclass'),singleton('not$usubclass$uelement'(x,'null$uclass'))),
inference(resolution,[status(thm)],[d3,c76]) ).
cnf(d5,plain,
~ member('not$usubclass$uelement'(x,'null$uclass'),'universal$uclass'),
inference(resolution,[status(thm)],[d4,c30]) ).
cnf(d6,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c53,c56]) ).
cnf(d7,plain,
member('not$usubclass$uelement'(x,'null$uclass'),'universal$uclass'),
inference(resolution,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n006.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 07:06:49 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.10/13.70 % SZS status Unsatisfiable for theBenchmark.p
% 37.10/13.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------