Consider the following premises. For all x, x is an office clerk if and only if x will make tea. For all x, if x were an office clerk, then x is a scientist. There is at least one x for which if x were a scientist, then x is making tea. For all x, x is not a scientist. Can we infer the following from them? There is at least one x for which x is not an office clerk.
 From the fact that for all x, x is an office clerk if and only if x will make tea we can infer that for all x, if x makes tea, then x is an office clerk. From the fact that there is at least one x for which if x were a scientist, then x is making tea, and that for all x, if x makes tea, then x is an office clerk we can infer that there is at least one x for which if x were a scientist, then x is an office clerk. From the fact that for all x, if x were an office clerk, then x is a scientist, and that there is at least one x for which if x were a scientist, then x is an office clerk we can infer that there is at least one x for which x is an office clerk if and only if x is a scientist. Finally, from the fact that there is at least one x for which x is an office clerk if and only if x is a scientist, and that for all x, x is not a scientist we can infer that there is at least one x for which x is not an office clerk. Therefore, the answer is yes.