Consider the following premises. There is at least one x_5 for which if x_5 cooks, then x_5 is a mechanic. For all x_5, if x_5 were poor, then x_5 is cooking. For all x_5, if x_5 cooks, then x_5 is poor. Can we infer the following from them? There is at least one x_5 for which if x_5 were poor, then x_5 is a mechanic.
 From the fact that for all x_5, if x_5 were poor, then x_5 is cooking, and that for all x_5, if x_5 cooks, then x_5 is poor we can infer that for all x_5, x_5 is poor if and only if x_5 will cook. From the fact that for all x_5, x_5 is poor if and only if x_5 will cook we can infer that for all x_5, if x_5 were poor, then x_5 is cooking. Finally, from the fact that for all x_5, if x_5 were poor, then x_5 is cooking, and that there is at least one x_5 for which if x_5 cooks, then x_5 is a mechanic we can infer that there is at least one x_5 for which if x_5 were poor, then x_5 is a mechanic. Therefore, the answer is yes.