Consider the following premises. For all z, if z works, then z is drinking water. For all z, if z drinks water, then z is a carpenter. For all z, if z were a carpenter, then z is working. For all z, z will drink water or z will not work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which if is not true that z will work if and only if z will drink water.
 From the fact that for all z, z will drink water or z will not work we can infer that for all z, if z works, then z is drinking water via universal rewriting. From the fact that for all z, if z drinks water, then z is a carpenter, and that for all z, if z were a carpenter, then z is working we can infer that for all z, if z drinks water, then z is working via universal transitivity. From the fact that for all z, if z drinks water, then z is working, and that for all z, if z works, then z is drinking water we can infer that for all z, z will drink water if and only if z will work via universal biconditional introduction. From the fact that for all z, z will drink water if and only if z will work we can infer that for all z, if z drinks water, then z is working via universal biconditional elimination. Finally, from the fact that for all z, if z works, then z is drinking water, and that for all z, if z drinks water, then z is working we can infer that for all z, z will work if and only if z will drink water via universal biconditional introduction, which contradicts that There is at least one z for which if is not true that z will work if and only if z will drink water. Therefore, the answer is no.