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