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