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