Consider the following premises. If Patricia sleeps, then William is not climbing a mountain. William is climbing a mountain. For all x_8, if x_8 sleeps, then x_8 is a police officer. For all x_8, if x_8 were a police officer, then x_8 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: Patricia is not a police officer.
 From the fact that for all x_8, if x_8 were a police officer, then x_8 is sleeping, and that for all x_8, if x_8 sleeps, then x_8 is a police officer we can infer that for all x_8, x_8 is a police officer if and only if x_8 will sleep via universal biconditional introduction. From the fact that for all x_8, x_8 is a police officer if and only if x_8 will sleep we can infer that Patricia is a police officer if and only if Patricia is sleeping via universal instantiation. From the fact that if Patricia sleeps, then William is not climbing a mountain, and that William is climbing a mountain we can infer that Patricia is not sleeping via modus tollens. Finally, from the fact that Patricia is a police officer if and only if Patricia is sleeping, and that Patricia is not sleeping we can infer that Patricia is not a police officer via biconditional elimination. Therefore, the answer is yes.