Consider the following premises. There is at least one y_3 for which if y_3 were a cashier, then y_3 is sleeping. For all y_3, y_3 will sleep if and only if y_3 is rich. For all y_3, if y_3 sleeps, then y_3 is a cashier. For all y_3, y_3 is not rich. Can we infer the following from them? For all y_3, y_3 is a cashier.
 From the fact that there is at least one y_3 for which if y_3 were a cashier, then y_3 is sleeping, and that for all y_3, if y_3 sleeps, then y_3 is a cashier we can infer that there is at least one y_3 for which y_3 is a cashier if and only if y_3 will sleep. From the fact that for all y_3, y_3 will sleep if and only if y_3 is rich, and that for all y_3, y_3 is not rich we can infer that for all y_3, y_3 will not sleep. Finally, from the fact that there is at least one y_3 for which y_3 is a cashier if and only if y_3 will sleep, and that for all y_3, y_3 will not sleep we can infer that there is at least one y_3 for which y_3 is not a cashier, which contradicts that For all y_3, y_3 is a cashier. Therefore, the answer is no.