%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET098-7 : 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 : n012.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 24.56s 20.33s
% Output : CNFRefutation 24.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 8 unt; 4 nHn; 11 RR)
% Number of literals : 23 ( 13 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uclass'))),X0)) ) ).
cnf(prove_corollary_1_to_number_of_elements_in_class_1,negated_conjecture,
~ member('not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(x,'null$uclass'))),x),'null$uclass'),x) ).
cnf(prove_corollary_1_to_number_of_elements_in_class_2,negated_conjecture,
singleton('not$usubclass$uelement'(x,'null$uclass')) != x ).
cnf(prove_corollary_1_to_number_of_elements_in_class_3,negated_conjecture,
x != 'null$uclass' ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(c49,plain,
( X0 = 'null$uclass'
| member('not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(X0,'null$uclass'))),X0),'null$uclass'),intersection(complement(singleton('not$usubclass$uelement'(X0,'null$uclass'))),X0))
| singleton('not$usubclass$uelement'(X0,'null$uclass')) = X0 ),
inference(clausification,[status(esa)],[number_of_elements_in_class]) ).
cnf(c50,plain,
~ member('not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(x,'null$uclass'))),x),'null$uclass'),x),
inference(clausification,[status(esa)],[prove_corollary_1_to_number_of_elements_in_class_1]) ).
cnf(c51,plain,
singleton('not$usubclass$uelement'(x,'null$uclass')) != x,
inference(clausification,[status(esa)],[prove_corollary_1_to_number_of_elements_in_class_2]) ).
cnf(c52,plain,
x != 'null$uclass',
inference(clausification,[status(esa)],[prove_corollary_1_to_number_of_elements_in_class_3]) ).
cnf(c74,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(d0,plain,
( singleton('not$usubclass$uelement'(X0,'null$uclass')) = X0
| X0 = 'null$uclass'
| member('not$usubclass$uelement'(intersection(complement(singleton('not$usubclass$uelement'(X0,'null$uclass'))),X0),'null$uclass'),X0) ),
inference(resolution,[status(thm)],[c74,c49]) ).
cnf(d1,plain,
( singleton('not$usubclass$uelement'(x,'null$uclass')) = x
| x = 'null$uclass' ),
inference(resolution,[status(thm)],[d0,c50]) ).
cnf(d2,plain,
singleton('not$usubclass$uelement'(x,'null$uclass')) = x,
inference(resolution,[status(thm)],[c52,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c51,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/15.37 % Computer : n012.cluster.edu
% 0.08/15.37 % Model : x86_64 x86_64
% 0.08/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/15.37 % Memory : 8046.5625MB
% 0.08/15.37 % OS : Linux 6.8.0-71-generic
% 0.08/15.37 % CPULimit : 300
% 0.08/15.37 % WCLimit : 300
% 0.08/15.37 % DateTime : Sat Sep 26 07:07:07 UTC 2026
% 0.08/15.37 % CPUTime :
% 0.08/15.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.56/20.33 % SZS status Unsatisfiable for theBenchmark.p
% 24.56/20.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------