Consider the following premises. For all z_3, z_3 is a mechanic. There is at least one z_3 for which z_3 will go running and z_3 will work. Can we infer the following from them? If we can, name the inference rule being used: For all z_3, z_3 will not go running.
 From the fact that there is at least one z_3 for which z_3 will go running and z_3 will work we can infer that there is at least one z_3 for which z_3 will go running via existential simplification. From the fact that for all z_3, z_3 is a mechanic, and that there is at least one z_3 for which z_3 will go running we can infer that some mechanics will go running via existential conjunction. Finally, from the fact that some mechanics will go running we can infer that there is at least one z_3 for which z_3 is a mechanic via existential simplification, which contradicts that For all z_3, z_3 will not go running. Therefore, the answer is no.