Consider the following premises. For all z_3, z_3 will work or z_3 is not bored. There is at least one z_3 for which z_3 will not work. Can we infer the following from them? If we can, name the inference rule being used: For all z_3, z_3 is bored.
 From the fact that for all z_3, z_3 will work or z_3 is not bored we can infer that for all z_3, if z_3 were bored, then z_3 is working via universal rewriting. Finally, from the fact that for all z_3, if z_3 were bored, then z_3 is working, and that there is at least one z_3 for which z_3 will not work we can infer that there is at least one z_3 for which z_3 is not bored via existential modus tollens, which contradicts that For all z_3, z_3 is bored. Therefore, the answer is no.