Consider the following premises. w or ~p_4. p_4 or p_3. p_3 <-> w. Can we infer ~w from them?
 From w or ~p_4 we can infer p_4 -> w. From p_3 <-> w we can infer p_3 -> w. Finally, from p_4 -> w, p_3 -> w, p_4 or p_3 we can infer w, which contradicts ~w. Therefore, the answer is no.