Consider the following premises. If Charles sleeps, then Thomas is bored. If Charles climbs a mountain, then Charles is sleeping. Thomas is not bored. Sarah is a soldier if and only if Michael is a lawyer. If Michael were a lawyer, then Charles is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: Sarah is a soldier.
 From the fact that if Michael were a lawyer, then Charles is climbing a mountain, and that if Charles climbs a mountain, then Charles is sleeping we can infer that if Michael were a lawyer, then Charles is sleeping via transitivity. From the fact that if Michael were a lawyer, then Charles is sleeping, and that if Charles sleeps, then Thomas is bored we can infer that if Michael were a lawyer, then Thomas is bored via transitivity. From the fact that if Michael were a lawyer, then Thomas is bored, and that Thomas is not bored we can infer that Michael is not a lawyer via modus tollens. Finally, from the fact that Sarah is a soldier if and only if Michael is a lawyer, and that Michael is not a lawyer we can infer that Sarah is not a soldier via biconditional elimination, which contradicts that Sarah is a soldier. Therefore, the answer is no.