Consider the following premises. For all x_9, if x_9 were a janitor, then x_9 is a poet. For all x_9, x_9 is a carpenter if and only if x_9 is a janitor. For all x_9, x_9 is a carpenter. There is at least one x_9 for which if x_9 cooks, then x_9 is a poet. Can we infer the following from them? There is at least one x_9 for which x_9 is a poet.
 From the fact that for all x_9, x_9 is a carpenter if and only if x_9 is a janitor we can infer that for all x_9, if x_9 were a carpenter, then x_9 is a janitor. From the fact that for all x_9, if x_9 were a carpenter, then x_9 is a janitor, and that for all x_9, x_9 is a carpenter we can infer that for all x_9, x_9 is a janitor. From the fact that for all x_9, x_9 is a janitor we can infer that for all x_9, x_9 is a janitor or x_9 will cook. Finally, from the fact that for all x_9, if x_9 were a janitor, then x_9 is a poet, that there is at least one x_9 for which if x_9 cooks, then x_9 is a poet, and that for all x_9, x_9 is a janitor or x_9 will cook we can infer that there is at least one x_9 for which x_9 is a poet. Therefore, the answer is yes.