% We received this problem from Norm Megill on July 13, 2001 (message 98). % % Does the equation in questio below hold in all ortholattices? % % Mike Rose and Kristin Wilkinson found (with SEM 1.7) found a % countermodel of size 16 (July 2001). % % NOTE: If we replace constants D and E with 0 and 1, SEM fails % to find a countermodel in reasonable time. 16. % Lattice Axioms m(x,y) = m(y,x). m(m(x,y),z) = m(x,m(y,z)). j(x,y) = j(y,x). j(j(x,y),z) = j(x,j(y,z)). j(x,m(x,y)) = x. m(x,j(x,y)) = x. % Idempotence (follows from the lattice axioms) m(x,x) = x. j(x,x) = x. % The following gives us ortholattices. m(c(x),x) = D. j(c(x),x) = E. c(c(x)) = x. m(x,y) = c(j(c(x),c(y))). % Denial of equation in question. j(A,m(c(B),j(c(A),m(c(B),j(A,m(c(B),c(A))))))) != j(A,m(c(B),j(c(A),m(c(B),j(A,m(c(B),j(c(A),m(c(B),A)))))))).