Consider the following premises. For all x_2, x_2 is a cashier. There is at least one x_2 for which if x_2 were a cashier, then x_2 is a carpenter. For all x_2, if x_2 drives a car, then x_2 is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will drive a car.
 From the fact that there is at least one x_2 for which if x_2 were a cashier, then x_2 is a carpenter, and that for all x_2, x_2 is a cashier we can infer that there is at least one x_2 for which x_2 is a carpenter via existential modus ponens. Finally, from the fact that for all x_2, if x_2 drives a car, then x_2 is not a carpenter, and that there is at least one x_2 for which x_2 is a carpenter we can infer that there is at least one x_2 for which x_2 will not drive a car via existential modus tollens, which contradicts that For all x_2, x_2 will drive a car. Therefore, the answer is no.