Consider the following premises. p <-> w_3. p_12 <-> u. w_3 -> u. ~p_12. Can we infer ~p from them?
 From p_12 <-> u, ~p_12 we can infer ~u. From w_3 -> u, ~u we can infer ~w_3. Finally, from p <-> w_3, ~w_3 we can infer ~p. Therefore, the answer is yes.