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