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