Consider the following premises. ~p_13. p_13 <-> r_1. ~r_1 -> w. Can we infer w from them?
 From p_13 <-> r_1 we can infer r_1 -> p_13. From r_1 -> p_13, ~p_13 we can infer ~r_1. Finally, from ~r_1 -> w, ~r_1 we can infer w. Therefore, the answer is yes.