Consider the following premises. ~r. r <-> w. w -> p_1. p_1 -> w. Can we infer ~p_1 from them?
 From r <-> w, ~r we can infer ~w. From p_1 -> w, w -> p_1 we can infer p_1 <-> w. Finally, from p_1 <-> w, ~w we can infer ~p_1. Therefore, the answer is yes.