Consider the following premises. p <-> q_4. ~w. p -> w. Can we infer q_4 from them?
 From p -> w, ~w we can infer ~p. From p <-> q_4 we can infer q_4 -> p. Finally, from q_4 -> p, ~p we can infer ~q_4, which contradicts q_4. Therefore, the answer is no.