Consider the following premises. p_12 <-> u_2. p -> p_12. ~q. u_2 -> q. Can we infer ~p from them?
 From u_2 -> q, ~q we can infer ~u_2. From p_12 <-> u_2 we can infer p_12 -> u_2. From p_12 -> u_2, ~u_2 we can infer ~p_12. Finally, from p -> p_12, ~p_12 we can infer ~p. Therefore, the answer is yes.