Consider the following premises. For all x_1, if x_1 writes a letter, then x_1 is taking a plane. There is at least one x_1 for which x_1 is a janitor if and only if x_1 will write a letter. For all x_1, x_1 will not take a plane. Can we infer the following from them? For all x_1, x_1 is a janitor.
 From the fact that for all x_1, if x_1 writes a letter, then x_1 is taking a plane, and that for all x_1, x_1 will not take a plane we can infer that for all x_1, x_1 will not write a letter. Finally, from the fact that there is at least one x_1 for which x_1 is a janitor if and only if x_1 will write a letter, and that for all x_1, x_1 will not write a letter we can infer that there is at least one x_1 for which x_1 is not a janitor, which contradicts that For all x_1, x_1 is a janitor. Therefore, the answer is no.