Consider the following premises. There is at least one z_2 for which z_2 will take a plane if and only if z_2 will go running. For all z_2, if z_2 takes a plane, then z_2 is a cashier. For all z_2, z_2 will not go running. For all z_2, if z_2 were a cashier, then z_2 is running. Can we infer the following from them? For all z_2, z_2 will take a plane.
 From the fact that for all z_2, if z_2 takes a plane, then z_2 is a cashier, and that for all z_2, if z_2 were a cashier, then z_2 is running we can infer that for all z_2, if z_2 takes a plane, then z_2 is running. From the fact that there is at least one z_2 for which z_2 will take a plane if and only if z_2 will go running we can infer that there is at least one z_2 for which if z_2 goes running, then z_2 is taking a plane. From the fact that for all z_2, if z_2 takes a plane, then z_2 is running, and that there is at least one z_2 for which if z_2 goes running, then z_2 is taking a plane we can infer that there is at least one z_2 for which z_2 will take a plane if and only if z_2 will go running. Finally, from the fact that there is at least one z_2 for which z_2 will take a plane if and only if z_2 will go running, and that for all z_2, z_2 will not go running we can infer that there is at least one z_2 for which z_2 will not take a plane, which contradicts that For all z_2, z_2 will take a plane. Therefore, the answer is no.