Consider the following premises. For all x_2, if x_2 were poor, then x_2 is not a poet. For all x_2, x_2 is a poet. For all x_2, if x_2 cooks, then x_2 is poor. For all x_2, if x_2 were poor, then x_2 is cooking. Can we infer the following from them? For all x_2, x_2 will not cook.
 From the fact that for all x_2, if x_2 cooks, then x_2 is poor, and that for all x_2, if x_2 were poor, then x_2 is cooking we can infer that for all x_2, x_2 will cook if and only if x_2 is poor. From the fact that for all x_2, if x_2 were poor, then x_2 is not a poet, and that for all x_2, x_2 is a poet we can infer that for all x_2, x_2 is not poor. Finally, from the fact that for all x_2, x_2 will cook if and only if x_2 is poor, and that for all x_2, x_2 is not poor we can infer that for all x_2, x_2 will not cook. Therefore, the answer is yes.