Consider the following premises. For all z_1, if z_1 were a writer, then z_1 is working. For all z_1, z_1 is a writer or z_1 will not work. For all z_1, z_1 will not work. Can we infer the following from them? For all z_1, z_1 is not a writer.
 From the fact that for all z_1, z_1 is a writer or z_1 will not work we can infer that for all z_1, if z_1 works, then z_1 is a writer. From the fact that for all z_1, if z_1 works, then z_1 is a writer, and that for all z_1, if z_1 were a writer, then z_1 is working we can infer that for all z_1, z_1 will work if and only if z_1 is a writer. Finally, from the fact that for all z_1, z_1 will work if and only if z_1 is a writer, and that for all z_1, z_1 will not work we can infer that for all z_1, z_1 is not a writer. Therefore, the answer is yes.