Consider the following premises. For all x_15, x_15 will not climb a mountain. For all x_15, if x_15 were a cashier, then x_15 is climbing a mountain. There is at least one x_15 for which x_15 will play a game. For all x_15, x_15 is a cashier if and only if x_15 will play a game. Can we infer the following from them? For all x_15, x_15 is not rich.
 From the fact that for all x_15, x_15 is a cashier if and only if x_15 will play a game we can infer that for all x_15, if x_15 plays a game, then x_15 is a cashier. From the fact that for all x_15, if x_15 plays a game, then x_15 is a cashier, and that for all x_15, if x_15 were a cashier, then x_15 is climbing a mountain we can infer that for all x_15, if x_15 plays a game, then x_15 is climbing a mountain. From the fact that there is at least one x_15 for which x_15 will play a game we can infer that there is at least one x_15 for which x_15 will play a game or x_15 is rich. From the fact that for all x_15, if x_15 plays a game, then x_15 is climbing a mountain, and that for all x_15, x_15 will not climb a mountain we can infer that for all x_15, x_15 will not play a game. Finally, from the fact that there is at least one x_15 for which x_15 will play a game or x_15 is rich, and that for all x_15, x_15 will not play a game we can infer that there is at least one x_15 for which x_15 is rich, which contradicts that For all x_15, x_15 is not rich. Therefore, the answer is no.