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%------------------------------------------------------------------------------
% File : SET002+4 : TPTP v3.1.0. Released v2.2.0.
% Domain : Set Theory (Naive)
% Problem : Idempotency of union
% Version : [Pas99] axioms.
% English :
% Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% Source : [Pas99]
% Names :
% Status : Theorem
% Rating : 0.36 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.57 v2.5.0, 0.50 v2.4.0, 0.25 v2.3.0, 0.00 v2.2.1
% Syntax : Number of formulae : 12 ( 2 unit)
% Number of atoms : 30 ( 3 equality)
% Maximal formula depth : 7 ( 5 average)
% Number of connectives : 20 ( 2 ~ ; 2 |; 4 &)
% ( 10 <=>; 2 =>; 0 <=)
% ( 0 <~>; 0 ~|; 0 ~&)
% Number of predicates : 4 ( 0 propositional; 2-2 arity)
% Number of functors : 9 ( 1 constant; 0-2 arity)
% Number of variables : 29 ( 0 singleton; 28 !; 1 ?)
% Maximal term depth : 2 ( 1 average)
% Comments :
% : tptp2X -f dfg -t rm_equality:rstfp SET002+4.p
%------------------------------------------------------------------------------
begin_problem(TPTP_Problem).
list_of_descriptions.
name({*[ File : SET002+4 : TPTP v3.1.0. Released v2.2.0.],[ Names :]*}).
author({*[ Source : [Pas99]]*}).
status(unknown).
description({*[ Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe]*}).
end_of_list.
list_of_symbols.
functions[(difference,2), (empty_set,0), (intersection,2), (power_set,1), (product,1), (singleton,1), (sum,1), (union,2), (unordered_pair,2)].
predicates[(equal_set,2), (member,2), (subset,2)].
end_of_list.
list_of_formulae(axioms).
formula(
forall([A,B],
equiv(
subset(A,B),
forall([X],
implies(
member(X,A),
member(X,B))))),
subset ).
formula(
forall([A,B],
equiv(
equal_set(A,B),
and(
subset(A,B),
subset(B,A)))),
equal_set ).
formula(
forall([X,A],
equiv(
member(X,power_set(A)),
subset(X,A))),
power_set ).
formula(
forall([X,A,B],
equiv(
member(X,intersection(A,B)),
and(
member(X,A),
member(X,B)))),
intersection ).
formula(
forall([X,A,B],
equiv(
member(X,union(A,B)),
or(
member(X,A),
member(X,B)))),
union ).
formula(
forall([X],
not(
member(X,empty_set))),
empty_set ).
formula(
forall([B,A,E],
equiv(
member(B,difference(E,A)),
and(
member(B,E),
not(
member(B,A))))),
difference ).
formula(
forall([X,A],
equiv(
member(X,singleton(A)),
equal(X,A))),
singleton ).
formula(
forall([X,A,B],
equiv(
member(X,unordered_pair(A,B)),
or(
equal(X,A),
equal(X,B)))),
unordered_pair ).
formula(
forall([X,A],
equiv(
member(X,sum(A)),
exists([Y],
and(
member(Y,A),
member(X,Y))))),
sum ).
formula(
forall([X,A],
equiv(
member(X,product(A)),
forall([Y],
implies(
member(Y,A),
member(X,Y))))),
product ).
end_of_list.
%----NOTE WELL: conjecture has been negated
list_of_formulae(conjectures).
formula( %(conjecture)
forall([A],
equal_set(union(A,A),A)),
thI14 ).
end_of_list.
end_problem.
%------------------------------------------------------------------------------
|
