Consider the following premises. For all x_9, if x_9 were a poet, then x_9 is cooking. For all x_9, x_9 is a mechanic. There is at least one x_9 for which if x_9 cooks, then x_9 is not a mechanic. For all x_9, if x_9 cooks, then x_9 is a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is not a poet.
 From the fact that for all x_9, if x_9 were a poet, then x_9 is cooking, and that for all x_9, if x_9 cooks, then x_9 is a poet we can infer that for all x_9, x_9 is a poet if and only if x_9 will cook via universal biconditional introduction. From the fact that there is at least one x_9 for which if x_9 cooks, then x_9 is not a mechanic, and that for all x_9, x_9 is a mechanic we can infer that there is at least one x_9 for which x_9 will not cook via existential modus tollens. Finally, from the fact that for all x_9, x_9 is a poet if and only if x_9 will cook, and that there is at least one x_9 for which x_9 will not cook we can infer that there is at least one x_9 for which x_9 is not a poet via existential biconditional elimination. Therefore, the answer is yes.