Consider the following premises. For all x_8, x_8 is not a janitor. For all x_8, if x_8 were a janitor, then x_8 is a doctor. For all x_8, if x_8 were a janitor, then x_8 is a doctor. There is at least one x_8 for which if x_8 were a doctor, then x_8 is a janitor. Can we infer the following from them? There is at least one x_8 for which x_8 is not a doctor.
 From the fact that there is at least one x_8 for which if x_8 were a doctor, then x_8 is a janitor, and that for all x_8, if x_8 were a janitor, then x_8 is a doctor we can infer that there is at least one x_8 for which x_8 is a doctor if and only if x_8 is a janitor. From the fact that there is at least one x_8 for which x_8 is a doctor if and only if x_8 is a janitor we can infer that there is at least one x_8 for which if x_8 were a doctor, then x_8 is a janitor. From the fact that there is at least one x_8 for which if x_8 were a doctor, then x_8 is a janitor, and that for all x_8, if x_8 were a janitor, then x_8 is a doctor we can infer that there is at least one x_8 for which x_8 is a doctor if and only if x_8 is a janitor. Finally, from the fact that there is at least one x_8 for which x_8 is a doctor if and only if x_8 is a janitor, and that for all x_8, x_8 is not a janitor we can infer that there is at least one x_8 for which x_8 is not a doctor. Therefore, the answer is yes.