Consider the following premises. ~w. p_9 <-> w_1. p_9 -> p_12. p_12 -> w. Can we infer ~w_1 from them?
 From p_12 -> w, ~w we can infer ~p_12. From p_9 <-> w_1 we can infer w_1 -> p_9. From p_9 -> p_12, ~p_12 we can infer ~p_9. Finally, from w_1 -> p_9, ~p_9 we can infer ~w_1. Therefore, the answer is yes.