Consider the following premises. There is at least one z for which if z makes tea, then z is a poet. For all z, z will read a book if and only if z is a poet. For all z, z will make tea or z is not a taxi driver. For all z, if z reads a book, then z is a taxi driver. Can we infer the following from them? For all z, if is not true that z is a poet if and only if z is a taxi driver.
That contradicts the premises. Therefore the answer is no.