Consider the following premises. There is at least one x for which if x reads a book, then x is a doctor. For all x, if x were an astronaut, then x is a bartender. For all x, if x were a janitor, then x is reading a book. For all x, if x were a doctor, then x is an astronaut. Can we infer the following from them? There is at least one x for which if x were a janitor, then x is a bartender.
 From the fact that there is at least one x for which if x reads a book, then x is a doctor, and that for all x, if x were a doctor, then x is an astronaut we can infer that there is at least one x for which if x reads a book, then x is an astronaut. From the fact that for all x, if x were a janitor, then x is reading a book, and that there is at least one x for which if x reads a book, then x is an astronaut we can infer that there is at least one x for which if x were a janitor, then x is an astronaut. Finally, from the fact that there is at least one x for which if x were a janitor, then x is an astronaut, and that for all x, if x were an astronaut, then x is a bartender we can infer that there is at least one x for which if x were a janitor, then x is a bartender. Therefore, the answer is yes.