Consider the following premises. There is at least one z for which if z were an office clerk, then z is an astronaut. For all z, z will go running if and only if z is an astronaut. For all z, z is an office clerk or z will not go running. Can we infer the following from them? There is at least one z for which z is an office clerk if and only if z will go running.
 From the fact that for all z, z is an office clerk or z will not go running we can infer that for all z, if z goes running, then z is an office clerk. From the fact that for all z, z will go running if and only if z is an astronaut we can infer that for all z, if z were an astronaut, then z is running. From the fact that there is at least one z for which if z were an office clerk, then z is an astronaut, and that for all z, if z were an astronaut, then z is running we can infer that there is at least one z for which if z were an office clerk, then z is running. Finally, from the fact that there is at least one z for which if z were an office clerk, then z is running, and that for all z, if z goes running, then z is an office clerk we can infer that there is at least one z for which z is an office clerk if and only if z will go running. Therefore, the answer is yes.