Consider the following premises. For all z, z is an artist if and only if z will go running. For all z, if z were an artist, then z is writing a letter. For all z, if z writes a letter, then z is running. For all z, if z were an artist, then z is running. Can we infer the following from them? There is at least one z for which if is not true that z is an artist if and only if z will go running.
 From the fact that for all z, if z were an artist, then z is writing a letter, and that for all z, if z writes a letter, then z is running we can infer that for all z, if z were an artist, then z is running. From the fact that for all z, z is an artist if and only if z will go running we can infer that for all z, if z goes running, then z is an artist. From the fact that for all z, if z were an artist, then z is running, and that for all z, if z goes running, then z is an artist we can infer that for all z, z is an artist if and only if z will go running. From the fact that for all z, z is an artist if and only if z will go running we can infer that for all z, if z goes running, then z is an artist. Finally, from the fact that for all z, if z were an artist, then z is running, and that for all z, if z goes running, then z is an artist we can infer that for all z, z is an artist if and only if z will go running, which contradicts that There is at least one z for which if is not true that z is an artist if and only if z will go running. Therefore, the answer is no.