Consider the following premises. It is not raining. If it is cloudy, then Jennifer is running. It is raining if and only if it is overcast. It is overcast if and only if Jennifer is running. It is cloudy or Jennifer is not running. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that it is raining if and only if it is overcast, and that it is not raining we can infer that it is not overcast via biconditional elimination. From the fact that it is overcast if and only if Jennifer is running, and that it is not overcast we can infer that Jennifer is not running via biconditional elimination. From the fact that it is cloudy or Jennifer is not running we can infer that if Jennifer goes running, then it is cloudy via rewriting. From the fact that if Jennifer goes running, then it is cloudy, and that if it is cloudy, then Jennifer is running we can infer that Jennifer is running if and only if it is cloudy via biconditional introduction. Finally, from the fact that Jennifer is running if and only if it is cloudy, and that Jennifer is not running we can infer that it is not cloudy via biconditional elimination. Therefore, the answer is yes.