Consider the following premises. For all x_9, if x_9 cooks, then x_9 is a carpenter. For all x_9, x_9 will cook if and only if x_9 will work. For all x_9, if x_9 were a carpenter, then x_9 is cooking. For all x_9, x_9 will not work. Can we infer the following from them? There is at least one x_9 for which x_9 is a carpenter.
 From the fact that for all x_9, if x_9 were a carpenter, then x_9 is cooking, and that for all x_9, if x_9 cooks, then x_9 is a carpenter we can infer that for all x_9, x_9 is a carpenter if and only if x_9 will cook. From the fact that for all x_9, x_9 will cook if and only if x_9 will work, and that for all x_9, x_9 will not work we can infer that for all x_9, x_9 will not cook. From the fact that for all x_9, x_9 is a carpenter if and only if x_9 will cook we can infer that for all x_9, if x_9 were a carpenter, then x_9 is cooking. Finally, from the fact that for all x_9, if x_9 were a carpenter, then x_9 is cooking, and that for all x_9, x_9 will not cook we can infer that for all x_9, x_9 is not a carpenter, which contradicts that There is at least one x_9 for which x_9 is a carpenter. Therefore, the answer is no.