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