Consider the following premises. For all x_14, x_14 is a cashier. For all x_14, if x_14 were an astronaut, then x_14 is a doctor. For all x_14, if x_14 were a cashier, then x_14 is working. There is at least one x_14 for which if x_14 sleeps, then x_14 is a doctor. For all x_14, x_14 will work if and only if x_14 will sleep. Can we infer the following from them? There is at least one x_14 for which x_14 is a doctor.
 From the fact that for all x_14, x_14 will work if and only if x_14 will sleep we can infer that for all x_14, if x_14 works, then x_14 is sleeping. From the fact that for all x_14, if x_14 were a cashier, then x_14 is working, and that for all x_14, if x_14 works, then x_14 is sleeping we can infer that for all x_14, if x_14 were a cashier, then x_14 is sleeping. From the fact that for all x_14, if x_14 were a cashier, then x_14 is sleeping, and that there is at least one x_14 for which if x_14 sleeps, then x_14 is a doctor we can infer that there is at least one x_14 for which if x_14 were a cashier, then x_14 is a doctor. From the fact that for all x_14, x_14 is a cashier we can infer that for all x_14, x_14 is a cashier or x_14 is an astronaut. Finally, from the fact that there is at least one x_14 for which if x_14 were a cashier, then x_14 is a doctor, that for all x_14, if x_14 were an astronaut, then x_14 is a doctor, and that for all x_14, x_14 is a cashier or x_14 is an astronaut we can infer that there is at least one x_14 for which x_14 is a doctor. Therefore, the answer is yes.