Consider the following premises. There is at least one x_13 for which if x_13 works, then x_13 is a janitor. For all x_13, x_13 will not write a letter. For all x_13, x_13 will read a book if and only if x_13 will work. For all x_13, if x_13 were a janitor, then x_13 is reading a book. For all x_13, x_13 will write a letter if and only if x_13 is a janitor. Can we infer the following from them? There is at least one x_13 for which x_13 will not work.
 From the fact that for all x_13, x_13 will read a book if and only if x_13 will work we can infer that for all x_13, if x_13 reads a book, then x_13 is working. From the fact that for all x_13, if x_13 were a janitor, then x_13 is reading a book, and that for all x_13, if x_13 reads a book, then x_13 is working we can infer that for all x_13, if x_13 were a janitor, then x_13 is working. From the fact that for all x_13, x_13 will write a letter if and only if x_13 is a janitor, and that for all x_13, x_13 will not write a letter we can infer that for all x_13, x_13 is not a janitor. From the fact that for all x_13, if x_13 were a janitor, then x_13 is working, and that there is at least one x_13 for which if x_13 works, then x_13 is a janitor we can infer that there is at least one x_13 for which x_13 is a janitor if and only if x_13 will work. Finally, from the fact that there is at least one x_13 for which x_13 is a janitor if and only if x_13 will work, and that for all x_13, x_13 is not a janitor we can infer that there is at least one x_13 for which x_13 will not work. Therefore, the answer is yes.