Consider the following premises. There is at least one x_2 for which if x_2 were excited, then x_2 is cooking. For all x_2, if x_2 were a carpenter, then x_2 is not cooking. For all x_2, x_2 is excited. Can we infer the following from them? There is at least one x_2 for which x_2 is not a carpenter.
 From the fact that there is at least one x_2 for which if x_2 were excited, then x_2 is cooking, and that for all x_2, x_2 is excited we can infer that there is at least one x_2 for which x_2 will cook. Finally, from the fact that for all x_2, if x_2 were a carpenter, then x_2 is not cooking, and that there is at least one x_2 for which x_2 will cook we can infer that there is at least one x_2 for which x_2 is not a carpenter. Therefore, the answer is yes.