Consider the following premises. p_1 -> p_8. p_8 <-> u. ~u. Can we infer p_1 from them?
 From p_8 <-> u we can infer p_8 -> u. From p_1 -> p_8, p_8 -> u we can infer p_1 -> u. Finally, from p_1 -> u, ~u we can infer ~p_1, which contradicts p_1. Therefore, the answer is no.