Consider the following premises. For all x_2, x_2 will drive a car or x_2 is not a janitor. For all x_2, if x_2 were excited, then x_2 is driving a car. There is at least one x_2 for which x_2 is excited or x_2 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will not drive a car.
 From the fact that for all x_2, x_2 will drive a car or x_2 is not a janitor we can infer that for all x_2, if x_2 were a janitor, then x_2 is driving a car via universal rewriting. Finally, from the fact that for all x_2, if x_2 were excited, then x_2 is driving a car, that for all x_2, if x_2 were a janitor, then x_2 is driving a car, and that there is at least one x_2 for which x_2 is excited or x_2 is a janitor we can infer that there is at least one x_2 for which x_2 will drive a car via existential disjunction elimination, which contradicts that For all x_2, x_2 will not drive a car. Therefore, the answer is no.