Consider the following premises. For all x_9, if x_9 cooks, then x_9 is not a scientist. For all x_9, x_9 is rich if and only if x_9 will cook. Barbara is a scientist. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is rich.
 From the fact that Barbara is a scientist we can infer that there is at least one x_9 for which x_9 is a scientist via existential generalization. From the fact that for all x_9, if x_9 cooks, then x_9 is not a scientist, and that there is at least one x_9 for which x_9 is a scientist we can infer that there is at least one x_9 for which x_9 will not cook via existential modus tollens. Finally, from the fact that for all x_9, x_9 is rich if and only if x_9 will cook, and that there is at least one x_9 for which x_9 will not cook we can infer that there is at least one x_9 for which x_9 is not rich via existential biconditional elimination, which contradicts that For all x_9, x_9 is rich. Therefore, the answer is no.