File: LT-McKenzie-4basis.in

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formulas(assumptions).

% McKenzie's absorption 4-basis (self-dual, independent) for
% Lattice Theory (LT).

% Prover9 should produce a proof in a few seconds.

x v (y ^ (x ^ z)) = x         # label(McKenzie_1).
x ^ (y v (x v z)) = x         # label(McKenzie_2).
((y ^ x) v (x ^ z)) v x = x   # label(McKenzie_3).
((y v x) ^ (x v z)) ^ x = x   # label(McKenzie_4).

end_of_list.

formulas(goals).

(x ^ y) ^ z = x ^ (y ^ z)     # label(assoc_meet).

end_of_list.