Consider the following premises. For all y_1, y_1 is a bartender or y_1 will not sleep. For all y_1, if y_1 were a bartender, then y_1 is a nurse. For all y_1, if y_1 were a nurse, then y_1 is poor. There is at least one y_1 for which y_1 is poor if and only if y_1 will sleep. Can we infer the following from them? For all y_1, if is not true that y_1 will sleep if and only if y_1 is poor.
 From the fact that for all y_1, y_1 is a bartender or y_1 will not sleep we can infer that for all y_1, if y_1 sleeps, then y_1 is a bartender. From the fact that for all y_1, if y_1 sleeps, then y_1 is a bartender, and that for all y_1, if y_1 were a bartender, then y_1 is a nurse we can infer that for all y_1, if y_1 sleeps, then y_1 is a nurse. From the fact that there is at least one y_1 for which y_1 is poor if and only if y_1 will sleep we can infer that there is at least one y_1 for which if y_1 were poor, then y_1 is sleeping. From the fact that for all y_1, if y_1 sleeps, then y_1 is a nurse, and that for all y_1, if y_1 were a nurse, then y_1 is poor we can infer that for all y_1, if y_1 sleeps, then y_1 is poor. Finally, from the fact that for all y_1, if y_1 sleeps, then y_1 is poor, and that there is at least one y_1 for which if y_1 were poor, then y_1 is sleeping we can infer that there is at least one y_1 for which y_1 will sleep if and only if y_1 is poor, which contradicts that For all y_1, if is not true that y_1 will sleep if and only if y_1 is poor. Therefore, the answer is no.