Consider the following premises. r -> p. w_2 <-> p. r. Can we infer ~p from them?
 From r we can infer r or w_2. From w_2 <-> p we can infer w_2 -> p. Finally, from r -> p, w_2 -> p, r or w_2 we can infer p, which contradicts ~p. Therefore, the answer is no.