Consider the following premises. ~u_1. p_2 -> p. w -> u_1. p -> p_2. p_2 -> w. Can we infer ~p from them?
 From p -> p_2, p_2 -> p we can infer p <-> p_2. From p <-> p_2 we can infer p -> p_2. From p_2 -> w, w -> u_1 we can infer p_2 -> u_1. From p_2 -> u_1, ~u_1 we can infer ~p_2. Finally, from p -> p_2, ~p_2 we can infer ~p. Therefore, the answer is yes.