Consider the following premises. For all z, z will play tennis or z will climb a mountain. There is at least one z for which if z climbs a mountain, then z is a carpenter. For all z, if z plays tennis, then z is a carpenter. For all z, z will go running. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is not a carpenter.
 From the fact that for all z, if z plays tennis, then z is a carpenter, that there is at least one z for which if z climbs a mountain, then z is a carpenter, and that for all z, z will play tennis or z will climb a mountain we can infer that there is at least one z for which z is a carpenter via existential disjunction elimination. From the fact that there is at least one z for which z is a carpenter, and that for all z, z will go running we can infer that some carpenters will go running via existential conjunction. Finally, from the fact that some carpenters will go running we can infer that there is at least one z for which z is a carpenter via existential simplification, which contradicts that For all z, z is not a carpenter. Therefore, the answer is no.