%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET101-7 : 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 08:32:03 AM UTC 2026
% Result : Unsatisfiable 24.57s 3.50s
% Output : CNFRefutation 24.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 4 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_unordered_pair,axiom,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
cnf(corollary_1_to_singletons_are_sets,axiom,
member(singleton(X0),'unordered$upair'(X1,singleton(X0))) ).
cnf(prove_singleton_member_of_ordered_pair_1,negated_conjecture,
~ member(singleton(x),'ordered$upair'(x,y)) ).
cnf(ordered_pair,axiom,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1) ).
cnf(c16,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_unordered_pair]) ).
cnf(c29,plain,
member(singleton(X0),'unordered$upair'(X1,singleton(X0))),
inference(clausification,[status(esa)],[corollary_1_to_singletons_are_sets]) ).
cnf(c54,plain,
~ member(singleton(x),'ordered$upair'(x,y)),
inference(clausification,[status(esa)],[prove_singleton_member_of_ordered_pair_1]) ).
cnf(c67,plain,
'unordered$upair'(singleton(X0),'unordered$upair'(X0,singleton(X1))) = 'ordered$upair'(X0,X1),
inference(clausification,[status(esa)],[ordered_pair]) ).
cnf(d0,plain,
member(singleton(X1),'unordered$upair'(singleton(X1),X0)),
inference(superposition,[status(thm)],[c16,c29]) ).
cnf(d1,plain,
member(singleton(X0),'ordered$upair'(X0,X1)),
inference(superposition,[status(thm)],[c67,d0]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[d1,c54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET101-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 07:07:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.57/3.50 % SZS status Unsatisfiable for theBenchmark.p
% 24.57/3.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------