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