formulas(sos).

% lattice theory

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

% This input is for Mace4, so we can include the following,
% because finite lattices always have 0 and 1.

x v 0 = x.
x ^ 1 = x.

end_of_list.

formulas(sos).
end_of_list.

% We want the following to be false, so we put it in the goals list.

formulas(goals).
x ^ (y v (x ^ z)) = x ^ (y v (z ^ ((x ^ (y v z)) v (y ^ z)))) # label(H2).
end_of_list.