Consider the following premises. For all z, if z sleeps, then z is driving a car. Robert is climbing a mountain. For all z, z is a poet or z will sleep. For all z, if z were a poet, then z is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all z, either z will drive a car or z will climb a mountain are not true.
 From the fact that for all z, if z were a poet, then z is driving a car, that for all z, if z sleeps, then z is driving a car, and that for all z, z is a poet or z will sleep we can infer that for all z, z will drive a car via universal disjunction elimination. From the fact that Robert is climbing a mountain we can infer that there is at least one z for which z will climb a mountain via existential generalization. Finally, from the fact that for all z, z will drive a car, and that there is at least one z for which z will climb a mountain we can infer that there is at least one z for which z will drive a car and z will climb a mountain via existential conjunction, which contradicts that For all z, either z will drive a car or z will climb a mountain are not true. Therefore, the answer is no.