Consider the following premises. For all x_3, if x_3 climbs a mountain, then x_3 is listening to a song. There is at least one x_3 for which if x_3 listens to a song, then x_3 is a musician. For all x_3, if x_3 were a musician, then x_3 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which if x_3 listens to a song, then x_3 is climbing a mountain.
We can infer this via the existential transitivity rule. Therefore, the answer is yes.