Consider the following premises. u or w_1. p_12 <-> w_1. ~p_12. Can we infer u from them?
 From p_12 <-> w_1, ~p_12 we can infer ~w_1. From u or w_1 we can infer ~w_1 -> u. Finally, from ~w_1 -> u, ~w_1 we can infer u. Therefore, the answer is yes.