Consider the following premises. For all z_2, if z_2 climbs a mountain, then z_2 is reading a book. For all z_2, if z_2 plays a game, then z_2 is a mechanic. For all z_2, if z_2 were a mechanic, then z_2 is a cashier. For all z_2, if z_2 reads a book, then z_2 is climbing a mountain. For all z_2, if z_2 reads a book, then z_2 is playing a game. Can we infer the following from them? There is at least one z_2 for which the fact that z_2 climbs a mountain does not imply that z_2 is a cashier.
 From the fact that for all z_2, if z_2 plays a game, then z_2 is a mechanic, and that for all z_2, if z_2 were a mechanic, then z_2 is a cashier we can infer that for all z_2, if z_2 plays a game, then z_2 is a cashier. From the fact that for all z_2, if z_2 reads a book, then z_2 is climbing a mountain, and that for all z_2, if z_2 climbs a mountain, then z_2 is reading a book we can infer that for all z_2, z_2 will read a book if and only if z_2 will climb a mountain. From the fact that for all z_2, z_2 will read a book if and only if z_2 will climb a mountain we can infer that for all z_2, if z_2 climbs a mountain, then z_2 is reading a book. From the fact that for all z_2, if z_2 climbs a mountain, then z_2 is reading a book, and that for all z_2, if z_2 reads a book, then z_2 is playing a game we can infer that for all z_2, if z_2 climbs a mountain, then z_2 is playing a game. Finally, from the fact that for all z_2, if z_2 climbs a mountain, then z_2 is playing a game, and that for all z_2, if z_2 plays a game, then z_2 is a cashier we can infer that for all z_2, if z_2 climbs a mountain, then z_2 is a cashier, which contradicts that There is at least one z_2 for which the fact that z_2 climbs a mountain does not imply that z_2 is a cashier. Therefore, the answer is no.