Consider the following premises. For all x_6, if x_6 were a politician, then x_6 is a cashier. For all x_6, if x_6 were a cashier, then x_6 is a janitor. For all x_6, if x_6 were a janitor, then x_6 is reading a book. There is at least one x_6 for which if x_6 reads a book, then x_6 is a politician. Can we infer the following from them? For all x_6, if is not true that x_6 is a janitor if and only if x_6 is a politician.
 From the fact that for all x_6, if x_6 were a janitor, then x_6 is reading a book, and that there is at least one x_6 for which if x_6 reads a book, then x_6 is a politician we can infer that there is at least one x_6 for which if x_6 were a janitor, then x_6 is a politician. From the fact that for all x_6, if x_6 were a politician, then x_6 is a cashier, and that for all x_6, if x_6 were a cashier, then x_6 is a janitor we can infer that for all x_6, if x_6 were a politician, then x_6 is a janitor. Finally, from the fact that there is at least one x_6 for which if x_6 were a janitor, then x_6 is a politician, and that for all x_6, if x_6 were a politician, then x_6 is a janitor we can infer that there is at least one x_6 for which x_6 is a janitor if and only if x_6 is a politician, which contradicts that For all x_6, if is not true that x_6 is a janitor if and only if x_6 is a politician. Therefore, the answer is no.