Consider the following premises. For all y_4, y_4 will work or y_4 is excited. For all y_4, if y_4 works, then y_4 is driving a car. There is at least one y_4 for which if y_4 were excited, then y_4 is driving a car. For all y_4, y_4 will drive a car if and only if y_4 will work. Can we infer the following from them? If we can, name the inference rule being used: For all y_4, y_4 will not drive a car.
 From the fact that for all y_4, y_4 will drive a car if and only if y_4 will work we can infer that for all y_4, if y_4 drives a car, then y_4 is working via universal biconditional elimination. From the fact that for all y_4, if y_4 drives a car, then y_4 is working, and that for all y_4, if y_4 works, then y_4 is driving a car we can infer that for all y_4, y_4 will drive a car if and only if y_4 will work via universal biconditional introduction. From the fact that for all y_4, y_4 will drive a car if and only if y_4 will work we can infer that for all y_4, if y_4 works, then y_4 is driving a car via universal biconditional elimination. Finally, from the fact that for all y_4, if y_4 works, then y_4 is driving a car, that there is at least one y_4 for which if y_4 were excited, then y_4 is driving a car, and that for all y_4, y_4 will work or y_4 is excited we can infer that there is at least one y_4 for which y_4 will drive a car via existential disjunction elimination, which contradicts that For all y_4, y_4 will not drive a car. Therefore, the answer is no.