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