Consider the following premises. Susan is not a police officer. For all y, y is a police officer if and only if y will sleep. For all y, y is a police officer if and only if y will sleep. Can we infer the following from them? Susan is not sleeping.
 From the fact that for all y, y is a police officer if and only if y will sleep we can infer that for all y, if y were a police officer, then y is sleeping. From the fact that for all y, y is a police officer if and only if y will sleep we can infer that for all y, if y sleeps, then y is a police officer. From the fact that for all y, if y were a police officer, then y is sleeping, and that for all y, if y sleeps, then y is a police officer we can infer that for all y, y is a police officer if and only if y will sleep. From the fact that for all y, y is a police officer if and only if y will sleep we can infer that Susan is a police officer if and only if Susan is sleeping. Finally, from the fact that Susan is a police officer if and only if Susan is sleeping, and that Susan is not a police officer we can infer that Susan is not sleeping. Therefore, the answer is yes.