Consider the following premises. For all x_9, x_9 will not climb a mountain. For all x_9, x_9 will listen to a song if and only if x_9 is a soldier. For all x_9, if x_9 were a soldier, then x_9 is climbing a mountain. There is at least one x_9 for which if x_9 climbs a mountain, then x_9 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 will not listen to a song.
 From the fact that there is at least one x_9 for which if x_9 climbs a mountain, then x_9 is a soldier, and that for all x_9, if x_9 were a soldier, then x_9 is climbing a mountain we can infer that there is at least one x_9 for which x_9 will climb a mountain if and only if x_9 is a soldier via existential biconditional introduction. From the fact that there is at least one x_9 for which x_9 will climb a mountain if and only if x_9 is a soldier, and that for all x_9, x_9 will not climb a mountain we can infer that there is at least one x_9 for which x_9 is not a soldier via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will listen to a song if and only if x_9 is a soldier, and that there is at least one x_9 for which x_9 is not a soldier we can infer that there is at least one x_9 for which x_9 will not listen to a song via existential biconditional elimination. Therefore, the answer is yes.