Consider the following premises. For all z, z will not read a book. For all z, z will read a book or z is not a mechanic. For all z, z will make tea if and only if z is a mechanic. For all z, if z were a mechanic, then z is making tea. 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 make tea.
 From the fact that for all z, z will make tea if and only if z is a mechanic we can infer that for all z, if z makes tea, then z is a mechanic via universal biconditional elimination. From the fact that for all z, if z makes tea, then z is a mechanic, and that for all z, if z were a mechanic, then z is making tea we can infer that for all z, z will make tea if and only if z is a mechanic via universal biconditional introduction. From the fact that for all z, z will read a book or z is not a mechanic we can infer that for all z, if z were a mechanic, then z is reading a book via universal rewriting. From the fact that for all z, if z were a mechanic, then z is reading a book, and that for all z, z will not read a book we can infer that for all z, z is not a mechanic via universal modus tollens. Finally, from the fact that for all z, z will make tea if and only if z is a mechanic, and that for all z, z is not a mechanic we can infer that for all z, z will not make tea via universal biconditional elimination, which contradicts that There is at least one z for which z will make tea. Therefore, the answer is no.