Consider the following premises. ~s_1. w -> s_1. s <-> t. w <-> t. Can we infer ~s from them?
 From w <-> t we can infer t -> w. From t -> w, w -> s_1 we can infer t -> s_1. From t -> s_1, ~s_1 we can infer ~t. Finally, from s <-> t, ~t we can infer ~s. Therefore, the answer is yes.