Consider the following premises. There is at least one z_1 for which if z_1 were a carpenter, then z_1 is cooking. For all z_1, if z_1 were a soldier, then z_1 is a carpenter. For all z_1, if z_1 cooks, then z_1 is a carpenter. Can we infer the following from them? There is at least one z_1 for which if z_1 were a soldier, then z_1 is cooking.
 From the fact that for all z_1, if z_1 cooks, then z_1 is a carpenter, and that there is at least one z_1 for which if z_1 were a carpenter, then z_1 is cooking we can infer that there is at least one z_1 for which z_1 will cook if and only if z_1 is a carpenter. From the fact that there is at least one z_1 for which z_1 will cook if and only if z_1 is a carpenter we can infer that there is at least one z_1 for which if z_1 were a carpenter, then z_1 is cooking. Finally, from the fact that for all z_1, if z_1 were a soldier, then z_1 is a carpenter, and that there is at least one z_1 for which if z_1 were a carpenter, then z_1 is cooking we can infer that there is at least one z_1 for which if z_1 were a soldier, then z_1 is cooking. Therefore, the answer is yes.