%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET084-7 : 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 : n002.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 08:31:58 AM UTC 2026
% Result : Unsatisfiable 15.32s 2.51s
% Output : CNFRefutation 15.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 13 unt; 2 nHn; 20 RR)
% Number of literals : 31 ( 11 equ; 13 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 10 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_null_class,axiom,
~ member(X0,'null$uclass') ).
cnf(set_in_its_singleton,axiom,
( member(X0,singleton(X0))
| ~ member(X0,'universal$uclass') ) ).
cnf(only_member_in_singleton,axiom,
( X0 = X1
| ~ member(X0,singleton(X1)) ) ).
cnf(singleton_is_null_class,axiom,
( singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ) ).
cnf(prove_singleton_identified_by_element2_1,negated_conjecture,
singleton(x) = singleton(y) ).
cnf(prove_singleton_identified_by_element2_2,negated_conjecture,
member(y,'universal$uclass') ).
cnf(prove_singleton_identified_by_element2_3,negated_conjecture,
x != y ).
cnf(c11,plain,
~ member(X0,'null$uclass'),
inference(clausification,[status(esa)],[existence_of_null_class]) ).
cnf(c30,plain,
( member(X0,singleton(X0))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[set_in_its_singleton]) ).
cnf(c33,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[only_member_in_singleton]) ).
cnf(c34,plain,
( singleton(X0) = 'null$uclass'
| member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[singleton_is_null_class]) ).
cnf(c35,plain,
singleton(x) = singleton(y),
inference(clausification,[status(esa)],[prove_singleton_identified_by_element2_1]) ).
cnf(c36,plain,
member(y,'universal$uclass'),
inference(clausification,[status(esa)],[prove_singleton_identified_by_element2_2]) ).
cnf(c37,plain,
x != y,
inference(clausification,[status(esa)],[prove_singleton_identified_by_element2_3]) ).
cnf(d0,plain,
( ~ member(x,'universal$uclass')
| member(x,singleton(y)) ),
inference(superposition,[status(thm)],[c35,c30]) ).
cnf(d1,plain,
( x = y
| ~ member(x,'universal$uclass') ),
inference(resolution,[status(thm)],[d0,c33]) ).
cnf(d2,plain,
~ member(x,'universal$uclass'),
inference(resolution,[status(thm)],[c37,d1]) ).
cnf(d3,plain,
singleton(x) = 'null$uclass',
inference(resolution,[status(thm)],[d2,c34]) ).
cnf(d4,plain,
'null$uclass' = singleton(y),
inference(demodulation,[status(thm)],[c35,d3]) ).
cnf(d5,plain,
( ~ member(y,'universal$uclass')
| member(y,'null$uclass') ),
inference(superposition,[status(thm)],[d4,c30]) ).
cnf(d6,plain,
~ member(y,'universal$uclass'),
inference(resolution,[status(thm)],[c11,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c36,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET084-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 07:07:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.32/2.51 % SZS status Unsatisfiable for theBenchmark.p
% 15.32/2.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------