Consider the following premises. For all z_3, z_3 will not climb a mountain. There is at least one z_3 for which if z_3 cooks, then z_3 is a poet. For all z_3, if z_3 were a poet, then z_3 is cooking. For all z_3, z_3 will climb a mountain if and only if z_3 will cook. Can we infer the following from them? If we can, name the inference rule being used: For all z_3, z_3 is a poet.
 From the fact that for all z_3, if z_3 were a poet, then z_3 is cooking, and that there is at least one z_3 for which if z_3 cooks, then z_3 is a poet we can infer that there is at least one z_3 for which z_3 is a poet if and only if z_3 will cook via existential biconditional introduction. From the fact that for all z_3, z_3 will climb a mountain if and only if z_3 will cook, and that for all z_3, z_3 will not climb a mountain we can infer that for all z_3, z_3 will not cook via universal biconditional elimination. Finally, from the fact that there is at least one z_3 for which z_3 is a poet if and only if z_3 will cook, and that for all z_3, z_3 will not cook we can infer that there is at least one z_3 for which z_3 is not a poet via existential biconditional elimination, which contradicts that For all z_3, z_3 is a poet. Therefore, the answer is no.