Consider the following premises. For all z_2, if z_2 climbs a mountain, then z_2 is a cashier. For all z_2, if z_2 were a cashier, then z_2 is happy. For all z_2, if z_2 were happy, then z_2 is climbing a mountain. For all z_2, z_2 is not happy. Can we infer the following from them? For all z_2, z_2 is not a cashier.
 From the fact that for all z_2, if z_2 were happy, then z_2 is climbing a mountain, and that for all z_2, if z_2 climbs a mountain, then z_2 is a cashier we can infer that for all z_2, if z_2 were happy, then z_2 is a cashier. From the fact that for all z_2, if z_2 were happy, then z_2 is a cashier, and that for all z_2, if z_2 were a cashier, then z_2 is happy we can infer that for all z_2, z_2 is happy if and only if z_2 is a cashier. Finally, from the fact that for all z_2, z_2 is happy if and only if z_2 is a cashier, and that for all z_2, z_2 is not happy we can infer that for all z_2, z_2 is not a cashier. Therefore, the answer is yes.