Consider the following premises. For all x_10, if x_10 listens to a song, then x_10 is not a police officer. For all x_10, if x_10 were a police officer, then x_10 is driving a car. For all x_10, if x_10 drives a car, then x_10 is a police officer. For all x_10, if x_10 were a cashier, then x_10 is a police officer. For all x_10, x_10 will drive a car or x_10 will play squash. For all x_10, if x_10 plays squash, then x_10 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will not listen to a song.
 From the fact that for all x_10, if x_10 plays squash, then x_10 is a cashier, and that for all x_10, if x_10 were a cashier, then x_10 is a police officer we can infer that for all x_10, if x_10 plays squash, then x_10 is a police officer via universal transitivity. From the fact that for all x_10, if x_10 were a police officer, then x_10 is driving a car, and that for all x_10, if x_10 drives a car, then x_10 is a police officer we can infer that for all x_10, x_10 is a police officer if and only if x_10 will drive a car via universal biconditional introduction. From the fact that for all x_10, x_10 is a police officer if and only if x_10 will drive a car we can infer that for all x_10, if x_10 drives a car, then x_10 is a police officer via universal biconditional elimination. From the fact that for all x_10, if x_10 drives a car, then x_10 is a police officer, that for all x_10, if x_10 plays squash, then x_10 is a police officer, and that for all x_10, x_10 will drive a car or x_10 will play squash we can infer that for all x_10, x_10 is a police officer via universal disjunction elimination. Finally, from the fact that for all x_10, if x_10 listens to a song, then x_10 is not a police officer, and that for all x_10, x_10 is a police officer we can infer that for all x_10, x_10 will not listen to a song via universal modus tollens. Therefore, the answer is yes.