Consider the following premises. q <-> q_11. ~q_11. p -> q. p or ~q. Can we infer ~p from them?
 From q <-> q_11, ~q_11 we can infer ~q. From p or ~q we can infer q -> p. From p -> q, q -> p we can infer p <-> q. Finally, from p <-> q, ~q we can infer ~p. Therefore, the answer is yes.