Consider the following premises. For all y, if y were a sailor, then y is a mechanic. For all y, if y were a mechanic, then y is working. For all y, if y were an astronaut, then y is a sailor. There is at least one y for which y is an astronaut if and only if y will work. Can we infer the following from them? There is at least one y for which if y were a sailor, then y is working.
 From the fact that there is at least one y for which y is an astronaut if and only if y will work we can infer that there is at least one y for which if y works, then y is an astronaut. From the fact that for all y, if y were a sailor, then y is a mechanic, and that for all y, if y were a mechanic, then y is working we can infer that for all y, if y were a sailor, then y is working. From the fact that there is at least one y for which if y works, then y is an astronaut, and that for all y, if y were an astronaut, then y is a sailor we can infer that there is at least one y for which if y works, then y is a sailor. From the fact that there is at least one y for which if y works, then y is a sailor, and that for all y, if y were a sailor, then y is working we can infer that there is at least one y for which y will work if and only if y is a sailor. Finally, from the fact that there is at least one y for which y will work if and only if y is a sailor we can infer that there is at least one y for which if y were a sailor, then y is working. Therefore, the answer is yes.