Consider the following premises. p_2 <-> s. p_2. ~s. Can we infer w_1 from them?
 From p_2 <-> s, ~s we can infer ~p_2. From p_2 we can infer p_2 or w_1. Finally, from p_2 or w_1, ~p_2 we can infer w_1. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.