Consider the following premises. There is at least one z for which if z were rich, then z is cooking. For all z, if z cooks, then z is a soldier. For all z, if z cooks, then z is rich. For all z, if z were a soldier, then z is cooking. For all z, z is not a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is rich.
 From the fact that for all z, if z cooks, then z is a soldier, and that for all z, if z were a soldier, then z is cooking we can infer that for all z, z will cook if and only if z is a soldier via universal biconditional introduction. From the fact that for all z, if z cooks, then z is rich, and that there is at least one z for which 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 via existential biconditional introduction. From the fact that for all z, z will cook if and only if z is a soldier, and that for all z, z is not a soldier we can infer that for all z, z will not cook via universal biconditional elimination. 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 will not cook we can infer that there is at least one z for which z is not rich via existential biconditional elimination, which contradicts that For all z, z is rich. Therefore, the answer is no.