  In their 1936 founding paper on quantum logic, Birkhoff and von Neumann
postulated that the lattice describing the experimental propositions concerning
a quantum system is orthocomplemented. We prove that this postulate fails for
the lattice L_sep describing a compound system consisting of so called
separated quantum systems. By separated we mean two systems prepared in
different ``rooms'' of the lab, and before any interaction takes place. In that
case the state of the compound system is necessarily a product state. As a
consequence, Dirac's superposition principle fails, and therefore L_sep cannot
satisfy all Piron's axioms. In previous works, assuming that L_sep is
orthocomplemented, it was argued that L_sep is not orthomodular and fails to
have the covering property. Here we prove that L_sep cannot admit and
orthocomplementation. Moreover, we propose a natural model for L_sep which has
the covering property.
