Consider the following premises. For all x_8, if x_8 were bored, then x_8 is a sailor. For all x_8, x_8 is a soldier or x_8 is bored. For all x_8, if x_8 were a sailor, then x_8 is listening to a song. There is at least one x_8 for which x_8 is a soldier if and only if x_8 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not listen to a song.
 From the fact that there is at least one x_8 for which x_8 is a soldier if and only if x_8 will listen to a song we can infer that there is at least one x_8 for which if x_8 were a soldier, then x_8 is listening to a song via existential biconditional elimination. From the fact that for all x_8, if x_8 were bored, then x_8 is a sailor, and that for all x_8, if x_8 were a sailor, then x_8 is listening to a song we can infer that for all x_8, if x_8 were bored, then x_8 is listening to a song via universal transitivity. Finally, from the fact that there is at least one x_8 for which if x_8 were a soldier, then x_8 is listening to a song, that for all x_8, if x_8 were bored, then x_8 is listening to a song, and that for all x_8, x_8 is a soldier or x_8 is bored we can infer that there is at least one x_8 for which x_8 will listen to a song via existential disjunction elimination, which contradicts that For all x_8, x_8 will not listen to a song. Therefore, the answer is no.