Consider the following premises. s -> u. w_1 -> w_2. ~u. s -> w_1. w_2 -> s. Can we infer w_2 from them?
 From s -> u, ~u we can infer ~s. From s -> w_1, w_1 -> w_2 we can infer s -> w_2. From s -> w_2, w_2 -> s we can infer s <-> w_2. Finally, from s <-> w_2, ~s we can infer ~w_2, which contradicts w_2. Therefore, the answer is no.