%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET078-6 : 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 : n001.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 08:31:55 AM UTC 2026
% Result : Unsatisfiable 13.07s 2.35s
% Output : CNFRefutation 13.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 4 RR)
% Number of literals : 13 ( 2 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 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 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_1_to_singletons_are_sets_1,negated_conjecture,
~ member(singleton(y),'unordered$upair'(x,singleton(y))) ).
cnf(unordered_pair3,axiom,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ) ).
cnf(unordered_pairs_in_universal,axiom,
member('unordered$upair'(X0,X1),'universal$uclass') ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(c0,plain,
~ member(singleton(y),'unordered$upair'(x,singleton(y))),
inference(clausification,[status(esa)],[prove_corollary_1_to_singletons_are_sets_1]) ).
cnf(c10,plain,
( member(X0,'unordered$upair'(X1,X0))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair3]) ).
cnf(c11,plain,
member('unordered$upair'(X0,X1),'universal$uclass'),
inference(clausification,[status(esa)],[unordered_pairs_in_universal]) ).
cnf(c12,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(d0,plain,
~ member(singleton(y),'universal$uclass'),
inference(resolution,[status(thm)],[c10,c0]) ).
cnf(d1,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[d1,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET078-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:09:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.07/2.35 % SZS status Unsatisfiable for theBenchmark.p
% 13.07/2.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------