Consider the following premises. t -> w. w -> w_4. s -> t. w_4 -> s. Can we infer ~(w_4 -> t) from them? If possible, name the inference rules being used at each step.
 From t -> w, w -> w_4 we can infer t -> w_4 via transitivity. Finally, from w_4 -> s, s -> t we can infer w_4 -> t via transitivity, which contradicts ~(w_4 -> t). Therefore, the answer is no.