Consider the following premises. ~r_3. u_1 -> r_3. r_3 -> p. p -> u_1. Can we infer p from them?
 From p -> u_1, u_1 -> r_3 we can infer p -> r_3. From p -> r_3, r_3 -> p we can infer p <-> r_3. Finally, from p <-> r_3, ~r_3 we can infer ~p, which contradicts p. Therefore, the answer is no.