Sindbad~EG File Manager

% test file for second-order unification

op(400, xfx, *). 
set(lambda).
set(demod_inf).
set(binary_res).
%set(very_verbose).
%set(knuth_bendix).

list(usable).
x = x.
% the universe is a group G and H is a subgroup of G
%-H(x) | -H(y) | H(x*y).
%-H(x) | H(i(x)).
(x * y) * z = x * (y * z).     % product is associative
%x*i(x) = 1.
%i(x) * x = 1.
%1*x = 1.
%x*1 = 1.
 -Ap(Z,w) | exists(lambda(x,Ap(Z,x))).
end_of_list.

list(demodulators).
f(w) = exists(lambda(x, and(H(x), x*a = w))).   % f is the characteristic function of Ha 
%i(i(x))= x.
end_of_list.

list(sos).
H(g(X)).                % c = g(X) is forbidden to X and belongs to H
-f(Ap(X,g(X))) | $ANS(X).         % negation of:  X(c) belongs to Ha.  Thus X maps H to Ha.   
end_of_list.