Consider the following premises. For all x_16, x_16 is a police officer if and only if x_16 will sleep. Robert is a police officer or it is cloudy. If it rains, then Robert is not sleeping. If it is cloudy, then Robert is sleeping. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that for all x_16, x_16 is a police officer if and only if x_16 will sleep we can infer that Robert is a police officer if and only if Robert is sleeping via universal instantiation. From the fact that Robert is a police officer if and only if Robert is sleeping we can infer that if Robert were a police officer, then Robert is sleeping via biconditional elimination. From the fact that if Robert were a police officer, then Robert is sleeping, that if it is cloudy, then Robert is sleeping, and that Robert is a police officer or it is cloudy we can infer that Robert is sleeping via disjunction elimination. Finally, from the fact that if it rains, then Robert is not sleeping, and that Robert is sleeping we can infer that it is not raining via modus tollens. Therefore, the answer is yes.