Consider the following premises. For all x_10, if x_10 were a janitor, then x_10 is driving a car. For all x_10, x_10 is sad. For all x_10, if x_10 drives a car, then x_10 is not sad. For all x_10, if x_10 plays tennis, then x_10 is a poet. For all x_10, if x_10 were a poet, then x_10 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will not play tennis.
 From the fact that for all x_10, if x_10 drives a car, then x_10 is not sad, and that for all x_10, x_10 is sad we can infer that for all x_10, x_10 will not drive a car via universal modus tollens. From the fact that for all x_10, if x_10 plays tennis, then x_10 is a poet, and that for all x_10, if x_10 were a poet, then x_10 is a janitor we can infer that for all x_10, if x_10 plays tennis, then x_10 is a janitor via universal transitivity. From the fact that for all x_10, if x_10 were a janitor, then x_10 is driving a car, and that for all x_10, x_10 will not drive a car we can infer that for all x_10, x_10 is not a janitor via universal modus tollens. Finally, from the fact that for all x_10, if x_10 plays tennis, then x_10 is a janitor, and that for all x_10, x_10 is not a janitor we can infer that for all x_10, x_10 will not play tennis via universal modus tollens. Therefore, the answer is yes.