Consider the following premises. r_2 -> p_5. p_5 <-> r_2. ~p_5. Can we infer r_2 from them?
 From p_5 <-> r_2 we can infer p_5 -> r_2. From p_5 -> r_2, r_2 -> p_5 we can infer p_5 <-> r_2. Finally, from p_5 <-> r_2, ~p_5 we can infer ~r_2, which contradicts r_2. Therefore, the answer is no.