Consider the following premises. For all x, x is excited. For all x_13, x_13 will drive a car and x_13 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is excited and x will drive a car.
 From the fact that for all x_13, x_13 will drive a car and x_13 is a carpenter we can infer that for all x_13, x_13 will drive a car via universal simplification. From the fact that for all x_13, x_13 will drive a car we can infer that William is driving a car via universal instantiation. From the fact that William is driving a car we can infer that there is at least one x for which x will drive a car via existential generalization. Finally, from the fact that for all x, x is excited, and that there is at least one x for which x will drive a car we can infer that there is at least one x for which x is excited and x will drive a car via existential conjunction. Therefore, the answer is yes.