Consider the following premises. For all x_5, if x_5 goes running, then x_5 is driving a car. For all x_5, if x_5 plays tennis, then x_5 is working. For all x_5, x_5 will read a book or x_5 will play tennis. There is at least one x_5 for which if x_5 reads a book, then x_5 is running. For all x_5, if x_5 works, then x_5 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will drive a car.
 From the fact that there is at least one x_5 for which if x_5 reads a book, then x_5 is running, and that for all x_5, if x_5 goes running, then x_5 is driving a car we can infer that there is at least one x_5 for which if x_5 reads a book, then x_5 is driving a car via existential transitivity. From the fact that for all x_5, if x_5 plays tennis, then x_5 is working, and that for all x_5, if x_5 works, then x_5 is driving a car we can infer that for all x_5, if x_5 plays tennis, then x_5 is driving a car via universal transitivity. Finally, from the fact that there is at least one x_5 for which if x_5 reads a book, then x_5 is driving a car, that for all x_5, if x_5 plays tennis, then x_5 is driving a car, and that for all x_5, x_5 will read a book or x_5 will play tennis we can infer that there is at least one x_5 for which x_5 will drive a car via existential disjunction elimination. Therefore, the answer is yes.