Consider the following premises. t <-> r. s -> r. r -> t. Can we infer ~(s -> t) from them?
 From t <-> r we can infer t -> r. From r -> t, t -> r we can infer r <-> t. From r <-> t we can infer r -> t. Finally, from s -> r, r -> t we can infer s -> t, which contradicts ~(s -> t). Therefore, the answer is no.