Consider the following premises. For all z, z will not climb a mountain. For all z, z is rich if and only if z will climb a mountain. There is at least one z for which if z cooks, then z is rich. For all z, if z were rich, then z is cooking. Can we infer the following from them? For all z, z will cook.
 From the fact that for all z, z is rich if and only if z will climb a mountain, and that for all z, z will not climb a mountain we can infer that for all z, z is not rich. From the fact that there is at least one z for which if z cooks, then z is rich, and that for all z, if z were rich, then z is cooking we can infer that there is at least one z for which z will cook if and only if z is rich. Finally, from the fact that there is at least one z for which z will cook if and only if z is rich, and that for all z, z is not rich we can infer that there is at least one z for which z will not cook, which contradicts that For all z, z will cook. Therefore, the answer is no.