Consider the following premises. For all x_16, if x_16 were a soldier, then x_16 is bored. For all x_16, x_16 is a lawyer. There is at least one x_16 for which if x_16 were bored, then x_16 is listening to a song. For all x_16, x_16 will climb a mountain if and only if x_16 will listen to a song. For all x_16, if x_16 were a lawyer, then x_16 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_16 for which x_16 will climb a mountain.
 From the fact that for all x_16, if x_16 were a soldier, then x_16 is bored, and that there is at least one x_16 for which if x_16 were bored, then x_16 is listening to a song we can infer that there is at least one x_16 for which if x_16 were a soldier, then x_16 is listening to a song via existential transitivity. From the fact that for all x_16, x_16 will climb a mountain if and only if x_16 will listen to a song we can infer that for all x_16, if x_16 listens to a song, then x_16 is climbing a mountain via universal biconditional elimination. From the fact that there is at least one x_16 for which if x_16 were a soldier, then x_16 is listening to a song, and that for all x_16, if x_16 listens to a song, then x_16 is climbing a mountain we can infer that there is at least one x_16 for which if x_16 were a soldier, then x_16 is climbing a mountain via existential transitivity. From the fact that for all x_16, if x_16 were a lawyer, then x_16 is a soldier, and that there is at least one x_16 for which if x_16 were a soldier, then x_16 is climbing a mountain we can infer that there is at least one x_16 for which if x_16 were a lawyer, then x_16 is climbing a mountain via existential transitivity. Finally, from the fact that there is at least one x_16 for which if x_16 were a lawyer, then x_16 is climbing a mountain, and that for all x_16, x_16 is a lawyer we can infer that there is at least one x_16 for which x_16 will climb a mountain via existential modus ponens. Therefore, the answer is yes.