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