Consider the following premises. w -> w_3. ~p_5. p_5 <-> p. w_3 -> p. p -> w. Can we infer w_3 from them?
 From p -> w, w -> w_3 we can infer p -> w_3. From p_5 <-> p, ~p_5 we can infer ~p. From p -> w_3, w_3 -> p we can infer p <-> w_3. Finally, from p <-> w_3, ~p we can infer ~w_3, which contradicts w_3. Therefore, the answer is no.