Consider the following premises. If it is sunny, then Mary is driving a car. It is not cloudy or it is overcast. Susan is a soldier if and only if Mary is driving a car. It is cloudy or it is sunny. If it is overcast, then Mary is driving a car. Can we infer the following from them? If we can, name the inference rule being used: Susan is a soldier.
 From the fact that it is cloudy or it is sunny, and that it is not cloudy or it is overcast we can infer that it is sunny or it is overcast via resolution. From the fact that if it is sunny, then Mary is driving a car, that if it is overcast, then Mary is driving a car, and that it is sunny or it is overcast we can infer that Mary is driving a car via disjunction elimination. From the fact that Susan is a soldier if and only if Mary is driving a car we can infer that if Mary drives a car, then Susan is a soldier via biconditional elimination. Finally, from the fact that if Mary drives a car, then Susan is a soldier, and that Mary is driving a car we can infer that Susan is a soldier via modus ponens. Therefore, the answer is yes.