Sindbad~EG File Manager

% This file finds a proof of Cantor's theorem, when the result is interpreted using the 
% implicit typings mentioned in comments below.  Or, it finds a proof of Russell's paradox,
% if interpreted as an untyped result, i.e., there is a fixed point of "not".   


set(lambda).
set(demod_inf).
set(hyper_res).
set(binary_res).
set(very_verbose).
assign(max_distinct_vars,4).
assign(max_weight,24).
assign(pick_given_ratio,4).

% typings: 
% Prop Ap(P(alpha),alpha).
% P(alpha) Ap(beta,alpha)  where beta is the type of c
% so polymorphically,  something Ap(something, alpha);  the second arg always has type alpha
% Prop not(Prop).
% P(Alpha) c(alpha).
% alpha J(P(alpha)).


list(usable).
x=x.
w != not(w).
end_of_list.

list(demodulators).
not(not(x)) = x.
end_of_list.

list(sos).
Ap(Ap(c,J(x)),z) = Ap(x,z)    |$ANS(x) | $ANS(z).   % "negated" goal.  Says every x of type P(alpha) is extensionally equal to  c(J(x)).
end_of_list.