Consider the following premises. There is at least one z_4 for which z_4 will write a letter if and only if z_4 is a soldier. For all z_4, if z_4 were bored, then z_4 is climbing a mountain. For all z_4, if z_4 climbs a mountain, then z_4 is a soldier. For all z_4, z_4 will not write a letter. Can we infer the following from them? For all z_4, z_4 is bored.
 From the fact that for all z_4, if z_4 were bored, then z_4 is climbing a mountain, and that for all z_4, if z_4 climbs a mountain, then z_4 is a soldier we can infer that for all z_4, if z_4 were bored, then z_4 is a soldier. From the fact that there is at least one z_4 for which z_4 will write a letter if and only if z_4 is a soldier, and that for all z_4, z_4 will not write a letter we can infer that there is at least one z_4 for which z_4 is not a soldier. Finally, from the fact that for all z_4, if z_4 were bored, then z_4 is a soldier, and that there is at least one z_4 for which z_4 is not a soldier we can infer that there is at least one z_4 for which z_4 is not bored, which contradicts that For all z_4, z_4 is bored. Therefore, the answer is no.