Consider the following premises. p_1 -> w. ~r_2. r_2 or ~w. Can we infer ~p_1 from them?
 From r_2 or ~w we can infer w -> r_2. From p_1 -> w, w -> r_2 we can infer p_1 -> r_2. Finally, from p_1 -> r_2, ~r_2 we can infer ~p_1. Therefore, the answer is yes.