Consider the following premises. For all x_8, x_8 will write a letter or x_8 will listen to a song. For all x_8, if x_8 were a soldier, then x_8 is bored. There is at least one x_8 for which if x_8 writes a letter, then x_8 is a soldier. For all x_8, x_8 will listen to a song if and only if x_8 is bored. Can we infer the following from them? For all x_8, x_8 is not bored.
 From the fact that for all x_8, x_8 will listen to a song if and only if x_8 is bored we can infer that for all x_8, if x_8 listens to a song, then x_8 is bored. From the fact that there is at least one x_8 for which if x_8 writes a letter, then x_8 is a soldier, and that for all x_8, if x_8 were a soldier, then x_8 is bored we can infer that there is at least one x_8 for which if x_8 writes a letter, then x_8 is bored. Finally, from the fact that there is at least one x_8 for which if x_8 writes a letter, then x_8 is bored, that for all x_8, if x_8 listens to a song, then x_8 is bored, and that for all x_8, x_8 will write a letter or x_8 will listen to a song we can infer that there is at least one x_8 for which x_8 is bored, which contradicts that For all x_8, x_8 is not bored. Therefore, the answer is no.