Consider the following premises. ~u. p_10 -> u. w or p. p -> p_10. ~w or r_2. Can we infer r_2 from them?
 From p_10 -> u, ~u we can infer ~p_10. From p -> p_10, ~p_10 we can infer ~p. From w or p, ~w or r_2 we can infer p or r_2. Finally, from p or r_2, ~p we can infer r_2. Therefore, the answer is yes.