Consider the following premises. For all x_10, if x_10 were a cashier, then x_10 is reading a book. For all x_10, if x_10 reads a book, then x_10 is working. For all x_10, if x_10 cooks, then x_10 is not sleeping. For all x_10, x_10 will sleep. For all x_10, if x_10 works, then x_10 is cooking. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is a cashier.
 From the fact that for all x_10, if x_10 cooks, then x_10 is not sleeping, and that for all x_10, x_10 will sleep we can infer that for all x_10, x_10 will not cook via universal modus tollens. From the fact that for all x_10, if x_10 were a cashier, then x_10 is reading a book, and that for all x_10, if x_10 reads a book, then x_10 is working we can infer that for all x_10, if x_10 were a cashier, then x_10 is working via universal transitivity. From the fact that for all x_10, if x_10 works, then x_10 is cooking, and that for all x_10, x_10 will not cook we can infer that for all x_10, x_10 will not work via universal modus tollens. Finally, from the fact that for all x_10, if x_10 were a cashier, then x_10 is working, and that for all x_10, x_10 will not work we can infer that for all x_10, x_10 is not a cashier via universal modus tollens, which contradicts that There is at least one x_10 for which x_10 is a cashier. Therefore, the answer is no.