Consider the following premises. For all x, if x takes a plane, then x is working. There is at least one x for which if x takes a plane, then x is writing a letter. For all x, if x writes a letter, then x is taking a plane. For all x, x will not work. Can we infer the following from them? There is at least one x for which x will not write a letter.
 From the fact that there is at least one x for which if x takes a plane, then x is writing a letter, and that for all x, if x writes a letter, then x is taking a plane we can infer that there is at least one x for which x will take a plane if and only if x will write a letter. From the fact that for all x, if x takes a plane, then x is working, and that for all x, x will not work we can infer that for all x, x will not take a plane. Finally, from the fact that there is at least one x for which x will take a plane if and only if x will write a letter, and that for all x, x will not take a plane we can infer that there is at least one x for which x will not write a letter. Therefore, the answer is yes.