Consider the following premises. r -> p. t. t -> p. r <-> u_2. Can we infer ~p from them?
 From r <-> u_2 we can infer u_2 -> r. From u_2 -> r, r -> p we can infer u_2 -> p. From t we can infer t or u_2. Finally, from t -> p, u_2 -> p, t or u_2 we can infer p, which contradicts ~p. Therefore, the answer is no.