Consider the following premises. r_4 <-> r_1. r_1 or ~r_4. r. ~r_1. Can we infer ~r_4 and r from them?
 From r_4 <-> r_1 we can infer r_1 -> r_4. From r_1 or ~r_4 we can infer r_4 -> r_1. From r_4 -> r_1, r_1 -> r_4 we can infer r_4 <-> r_1. From r_4 <-> r_1, ~r_1 we can infer ~r_4. Finally, from ~r_4, r we can infer ~r_4 and r. Therefore, the answer is yes.