Consider the following premises. q_11 or w_2. w_2 -> p. p -> q_11. p <-> q_11. Can we infer ~p from them?
 From p <-> q_11 we can infer q_11 -> p. From p -> q_11, q_11 -> p we can infer p <-> q_11. From p <-> q_11 we can infer q_11 -> p. Finally, from q_11 -> p, w_2 -> p, q_11 or w_2 we can infer p, which contradicts ~p. Therefore, the answer is no.