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