Consider the following premises. For all x_9, x_9 is a police officer or x_9 will not write a letter. For all x_9, if x_9 were a cashier, then x_9 is an astronaut. For all x_9, if x_9 were a police officer, then x_9 is a cashier. For all x_9, if x_9 were an astronaut, then x_9 is playing a game. Can we infer the following from them? There is at least one x_9 for which the fact that x_9 writes a letter does not imply that x_9 is playing a game.
 From the fact that for all x_9, if x_9 were a police officer, then x_9 is a cashier, and that for all x_9, if x_9 were a cashier, then x_9 is an astronaut we can infer that for all x_9, if x_9 were a police officer, then x_9 is an astronaut. From the fact that for all x_9, x_9 is a police officer or x_9 will not write a letter we can infer that for all x_9, if x_9 writes a letter, then x_9 is a police officer. From the fact that for all x_9, if x_9 writes a letter, then x_9 is a police officer, and that for all x_9, if x_9 were a police officer, then x_9 is an astronaut we can infer that for all x_9, if x_9 writes a letter, then x_9 is an astronaut. Finally, from the fact that for all x_9, if x_9 writes a letter, then x_9 is an astronaut, and that for all x_9, if x_9 were an astronaut, then x_9 is playing a game we can infer that for all x_9, if x_9 writes a letter, then x_9 is playing a game, which contradicts that There is at least one x_9 for which the fact that x_9 writes a letter does not imply that x_9 is playing a game. Therefore, the answer is no.