%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET101-6 : 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 : 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 15.84s 3.77s
% Output : CNFRefutation 15.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 4 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_singleton_member_of_ordered_pair_1,negated_conjecture,
~ member(singleton(x),'ordered$upair'(x,y)) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ 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(ordered_pair,axiom,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1) ).
cnf(c0,plain,
~ member(singleton(x),'ordered$upair'(x,y)),
inference(clausification,[status(esa)],[prove_singleton_member_of_ordered_pair_1]) ).
cnf(c9,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c11,plain,
member('unordered$upair'(X0,X1),'universal$uclass'),
inference(clausification,[status(esa)],[unordered_pairs_in_universal]) ).
cnf(c12,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c13,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(d0,plain,
( ~ member(singleton(X0),'universal$uclass')
| member(singleton(X0),'ordered$upair'(X0,X1)) ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d1,plain,
member(singleton(X0),'universal$uclass'),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(d2,plain,
member(singleton(X0),'ordered$upair'(X0,X1)),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET101-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 07:07:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.84/3.77 % SZS status Unsatisfiable for theBenchmark.p
% 15.84/3.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------