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 a lawyer. For all y, y will not work. For all y, if y works, then y is an astronaut. For all y, if y were a lawyer, then y is an astronaut. For all y, if y were an astronaut, then y is working. Can we infer the following from them? There is at least one y for which y is not a lawyer.
 From the fact that for all y, if y works, then y is an astronaut, and that for all y, if y were an astronaut, then y is working we can infer that for all y, y will work if and only if y is an astronaut. From the fact that for all y, if y were an astronaut, then y is writing a letter, and that there is at least one y for which if y writes a letter, then y is a lawyer we can infer that there is at least one y for which if y were an astronaut, then y is a lawyer. From the fact that for all y, y will work if and only if y is an astronaut, and that for all y, y will not work we can infer that for all y, y is not an astronaut. From the fact that there is at least one y for which if y were an astronaut, then y is a lawyer, and that for all y, if y were a lawyer, then y is an astronaut we can infer that there is at least one y for which y is an astronaut if and only if y is a lawyer. Finally, from the fact that there is at least one y for which y is an astronaut if and only if y is a lawyer, and that for all y, y is not an astronaut we can infer that there is at least one y for which y is not a lawyer. Therefore, the answer is yes.