Consider the following premises. For all x_9, x_9 will write a letter if and only if x_9 is a soldier. For all x_9, if x_9 writes a letter, then x_9 is an astronaut. There is at least one x_9 for which x_9 is not an astronaut. For all x_9, if x_9 were an astronaut, then x_9 is writing a letter. Can we infer the following from them? For all x_9, x_9 is a soldier.
 From the fact that for all x_9, if x_9 were an astronaut, then x_9 is writing a letter, and that for all x_9, if x_9 writes a letter, then x_9 is an astronaut we can infer that for all x_9, x_9 is an astronaut if and only if x_9 will write a letter. From the fact that for all x_9, x_9 is an astronaut if and only if x_9 will write a letter, and that there is at least one x_9 for which x_9 is not an astronaut we can infer that there is at least one x_9 for which x_9 will not write a letter. Finally, from the fact that for all x_9, x_9 will write a letter if and only if x_9 is a soldier, and that there is at least one x_9 for which x_9 will not write a letter we can infer that there is at least one x_9 for which x_9 is not a soldier, which contradicts that For all x_9, x_9 is a soldier. Therefore, the answer is no.