%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET082-7 : 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 : n013.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 08:31:57 AM UTC 2026
% Result : Unsatisfiable 25.55s 3.75s
% Output : CNFRefutation 25.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 13 ( 7 unt; 6 nHn; 6 RR)
% Number of literals : 21 ( 10 equ; 4 neg)
% Maximal clause size : 3 ( 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; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair_equals_singleton1,axiom,
( 'unordered$upair'(X1,X0) = singleton(X1)
| member(X0,'universal$uclass') ) ).
cnf(null_unordered_pair,axiom,
( member(X1,'universal$uclass')
| member(X0,'universal$uclass')
| 'unordered$upair'(X0,X1) = 'null$uclass' ) ).
cnf(prove_singleton_is_null_class_1,negated_conjecture,
~ member(x,'universal$uclass') ).
cnf(prove_singleton_is_null_class_2,negated_conjecture,
singleton(x) != 'null$uclass' ).
cnf(c19,plain,
( 'unordered$upair'(X1,X0) = singleton(X1)
| member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair_equals_singleton1]) ).
cnf(c21,plain,
( member(X1,'universal$uclass')
| member(X0,'universal$uclass')
| 'unordered$upair'(X0,X1) = 'null$uclass' ),
inference(clausification,[status(esa)],[null_unordered_pair]) ).
cnf(c34,plain,
~ member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_singleton_is_null_class_1]) ).
cnf(c35,plain,
singleton(x) != 'null$uclass',
inference(clausification,[status(esa)],[prove_singleton_is_null_class_2]) ).
cnf(d0,plain,
'unordered$upair'(X0,x) = singleton(X0),
inference(resolution,[status(thm)],[c19,c34]) ).
cnf(d1,plain,
( member(X0,'universal$uclass')
| 'unordered$upair'(X0,x) = 'null$uclass' ),
inference(resolution,[status(thm)],[c21,c34]) ).
cnf(d2,plain,
( member(X0,'universal$uclass')
| singleton(X0) = 'null$uclass' ),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
singleton(x) = 'null$uclass',
inference(resolution,[status(thm)],[d2,c34]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c35,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET082-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n013.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:03:36 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.55/3.75 % SZS status Unsatisfiable for theBenchmark.p
% 25.55/3.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------