Consider the following premises. s_4 <-> p. p <-> s_2. s_4 or s_2. Can we infer ~p from them?
 From s_4 <-> p we can infer s_4 -> p. From p <-> s_2 we can infer s_2 -> p. Finally, from s_4 -> p, s_2 -> p, s_4 or s_2 we can infer p, which contradicts ~p. Therefore, the answer is no.