Consider the following premises. w -> s_4. s_4 -> w. p_2 or w. ~s_4. Can we infer ~p_2 from them?
 From s_4 -> w, w -> s_4 we can infer s_4 <-> w. From s_4 <-> w, ~s_4 we can infer ~w. From p_2 or w we can infer ~w -> p_2. Finally, from ~w -> p_2, ~w we can infer p_2, which contradicts ~p_2. Therefore, the answer is no.