Consider the following premises. r or ~p. u -> r. r -> u. Can we infer ~(p -> u) from them?
 From u -> r, r -> u we can infer u <-> r. From u <-> r we can infer r -> u. From r or ~p we can infer p -> r. Finally, from p -> r, r -> u we can infer p -> u, which contradicts ~(p -> u). Therefore, the answer is no.