Consider the following premises. ~u. t -> s_4. s -> t. s_4 -> u. Can we infer s from them? If possible, name the inference rules being used at each step.
 From s_4 -> u, ~u we can infer ~s_4 via modus tollens. From s -> t, t -> s_4 we can infer s -> s_4 via transitivity. Finally, from s -> s_4, ~s_4 we can infer ~s via modus tollens, which contradicts s. Therefore, the answer is no.