Consider the following premises. u -> p_6. p_6 -> u. ~w. u -> w. w -> u. Can we infer ~p_6 from them?
 From u -> w, w -> u we can infer u <-> w. From p_6 -> u, u -> p_6 we can infer p_6 <-> u. From u <-> w, ~w we can infer ~u. Finally, from p_6 <-> u, ~u we can infer ~p_6. Therefore, the answer is yes.