Consider the following premises. For all z, z is a carpenter if and only if z will play squash. For all z, if z were a carpenter, then z is playing squash. For all z, if z makes tea, then z is playing squash. There is at least one z for which z is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z will not make tea.
 From the fact that for all z, z is a carpenter if and only if z will play squash we can infer that for all z, if z plays squash, then z is a carpenter via universal biconditional elimination. From the fact that for all z, if z were a carpenter, then z is playing squash, and that for all z, if z plays squash, then z is a carpenter we can infer that for all z, z is a carpenter if and only if z will play squash via universal biconditional introduction. From the fact that for all z, z is a carpenter if and only if z will play squash, and that there is at least one z for which z is not a carpenter we can infer that there is at least one z for which z will not play squash via existential biconditional elimination. Finally, from the fact that for all z, if z makes tea, then z is playing squash, and that there is at least one z for which z will not play squash we can infer that there is at least one z for which z will not make tea via existential modus tollens. Therefore, the answer is yes.