Consider the following premises. p_1 -> r_1. r_1 -> p_1. ~r_1. Can we infer p_1 from them?
 From p_1 -> r_1, r_1 -> p_1 we can infer p_1 <-> r_1. Finally, from p_1 <-> r_1, ~r_1 we can infer ~p_1, which contradicts p_1. Therefore, the answer is no.