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.