Consider the following premises. For all x_8, x_8 will sleep if and only if x_8 will work. For all x_8, x_8 will drink water or x_8 is a police officer. For all x_8, if x_8 drinks water, then x_8 is driving a car. For all x_8, if x_8 works, then x_8 is not driving a car. For all x_8, if x_8 were a police officer, then x_8 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not sleep.
 From the fact that for all x_8, if x_8 drinks water, then x_8 is driving a car, that for all x_8, if x_8 were a police officer, then x_8 is driving a car, and that for all x_8, x_8 will drink water or x_8 is a police officer we can infer that for all x_8, x_8 will drive a car via universal disjunction elimination. From the fact that for all x_8, if x_8 works, then x_8 is not driving a car, and that for all x_8, x_8 will drive a car we can infer that for all x_8, x_8 will not work via universal modus tollens. Finally, from the fact that for all x_8, x_8 will sleep if and only if x_8 will work, and that for all x_8, x_8 will not work we can infer that for all x_8, x_8 will not sleep via universal biconditional elimination. Therefore, the answer is yes.