Consider the following premises. p_4 -> u. u -> p_4. p_4 <-> p_1. Can we infer ~(u -> p_1) from them?
 From p_4 <-> p_1 we can infer p_4 -> p_1. From p_4 -> u, u -> p_4 we can infer p_4 <-> u. From p_4 <-> u we can infer u -> p_4. Finally, from u -> p_4, p_4 -> p_1 we can infer u -> p_1, which contradicts ~(u -> p_1). Therefore, the answer is no.