
formulas(assumptions).

% A problem from Norm Megill, on weak orthomodular lattices (WOM).

% Mace4 should produce a counterexample in a few seconds.

% Lattice Axioms

x ^ y = y ^ x.
(x ^ y) ^ z = x ^ (y ^ z).
x v y = y v x.
(x v y) v z = x v (y v z).
x v (x ^ y) = x.
x ^ (x v y) = x.

% The following gives us ortholattices.

x' ^ x = 0.
x' v x = 1.
x'' = x.
x ^ y = (x' v y')'.

% Ortholattice lemmas.

% 1 v x = 1.
% 1 ^ x = x.

% 0 ^ x = 0.
% 0 v x = x.

% Weak orthomodular law (*1 of mail 68).

(x' ^ (x v y)) v (y' v (x ^ y)) = 1  # label(mail_68_1).

end_of_list.

formulas(goals).

% Equation in question (*3 of mail 68).

x ^ (y v (x ^ (x' v (x ^ y)))) = x ^ (x' v (x ^ y)) # label(mail_68_3).

end_of_list.

