Consider the following premises. For all z, z is not a poet. There is at least one z for which z is a poet or z is not a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is a mechanic.
 From the fact that there is at least one z for which z is a poet or z is not a mechanic we can infer that there is at least one z for which if z were a mechanic, then z is a poet via existential rewriting. Finally, from the fact that there is at least one z for which if z were a mechanic, then z is a poet, and that for all z, z is not a poet we can infer that there is at least one z for which z is not a mechanic via existential modus tollens, which contradicts that For all z, z is a mechanic. Therefore, the answer is no.