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