Consider the following premises. For all x_3, x_3 is not a mechanic. For all x_3, x_3 will work if and only if x_3 is a janitor. For all x_3, if x_3 were a mechanic, then x_3 is a janitor. For all x_3, if x_3 were a janitor, then x_3 is a mechanic. Can we infer the following from them? There is at least one x_3 for which x_3 will work.
 From the fact that for all x_3, if x_3 were a janitor, then x_3 is a mechanic, and that for all x_3, if x_3 were a mechanic, then x_3 is a janitor we can infer that for all x_3, x_3 is a janitor if and only if x_3 is a mechanic. From the fact that for all x_3, x_3 is a janitor if and only if x_3 is a mechanic, and that for all x_3, x_3 is not a mechanic we can infer that for all x_3, x_3 is not a janitor. Finally, from the fact that for all x_3, x_3 will work if and only if x_3 is a janitor, and that for all x_3, x_3 is not a janitor we can infer that for all x_3, x_3 will not work, which contradicts that There is at least one x_3 for which x_3 will work. Therefore, the answer is no.