Consider the following premises. Michael is not cooking. For all x_12, if x_12 were a soldier, then x_12 is cooking. If Thomas reads a book, then Michael is a soldier. If Michael cooks, then Thomas is reading a book. Can we infer the following from them? If we can, name the inference rule being used: Thomas is reading a book.
 From the fact that for all x_12, if x_12 were a soldier, then x_12 is cooking we can infer that if Michael were a soldier, then Michael is cooking via universal instantiation. From the fact that if Thomas reads a book, then Michael is a soldier, and that if Michael were a soldier, then Michael is cooking we can infer that if Thomas reads a book, then Michael is cooking via transitivity. From the fact that if Thomas reads a book, then Michael is cooking, and that if Michael cooks, then Thomas is reading a book we can infer that Thomas is reading a book if and only if Michael is cooking via biconditional introduction. Finally, from the fact that Thomas is reading a book if and only if Michael is cooking, and that Michael is not cooking we can infer that Thomas is not reading a book via biconditional elimination, which contradicts that Thomas is reading a book. Therefore, the answer is no.