Consider the following premises. r -> p_4. p_4 <-> r_1. r_1 or r. Can we infer ~p_4 from them?
 From p_4 <-> r_1 we can infer r_1 -> p_4. Finally, from r_1 -> p_4, r -> p_4, r_1 or r we can infer p_4, which contradicts ~p_4. Therefore, the answer is no.