Consider the following premises. For all z, z will not make tea. For all z, if z makes tea, then z is cooking. For all z, z will not read a book or z is a carpenter. For all z, if z cooks, then z is making tea. For all z, z will read a book or z will cook. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is a carpenter.
 From the fact that for all z, if z makes tea, then z is cooking, and that for all z, if z cooks, then z is making tea we can infer that for all z, z will make tea if and only if z will cook via universal biconditional introduction. From the fact that for all z, z will read a book or z will cook, and that for all z, z will not read a book or z is a carpenter we can infer that for all z, z will cook or z is a carpenter via universal resolution. From the fact that for all z, z will make tea if and only if z will cook, and that for all z, z will not make tea we can infer that for all z, z will not cook via universal biconditional elimination. Finally, from the fact that for all z, z will cook or z is a carpenter, and that for all z, z will not cook we can infer that for all z, z is a carpenter via universal disjunctive syllogism. Therefore, the answer is yes.