Consider the following premises. For all z_1, z_1 is bored or z_1 will not work. For all z_1, z_1 is not bored. Can we infer the following from them? There is at least one z_1 for which z_1 will work.
 From the fact that for all z_1, z_1 is bored or z_1 will not work we can infer that for all z_1, if z_1 works, then z_1 is bored. Finally, from the fact that for all z_1, if z_1 works, then z_1 is bored, and that for all z_1, z_1 is not bored we can infer that for all z_1, z_1 will not work, which contradicts that There is at least one z_1 for which z_1 will work. Therefore, the answer is no.