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