Consider the following premises. There is at least one x_17 for which x_17 is a politician. For all x_17, if x_17 were bored, then x_17 is climbing a mountain. For all x_17, if x_17 were a politician, then x_17 is bored. For all x_17, x_17 will listen to a song if and only if x_17 will climb a mountain. Can we infer the following from them? There is at least one x_17 for which x_17 will listen to a song.
 From the fact that for all x_17, x_17 will listen to a song if and only if x_17 will climb a mountain we can infer that for all x_17, if x_17 climbs a mountain, then x_17 is listening to a song. From the fact that for all x_17, if x_17 were bored, then x_17 is climbing a mountain, and that for all x_17, if x_17 climbs a mountain, then x_17 is listening to a song we can infer that for all x_17, if x_17 were bored, then x_17 is listening to a song. From the fact that for all x_17, if x_17 were a politician, then x_17 is bored, and that there is at least one x_17 for which x_17 is a politician we can infer that there is at least one x_17 for which x_17 is bored. Finally, from the fact that for all x_17, if x_17 were bored, then x_17 is listening to a song, and that there is at least one x_17 for which x_17 is bored we can infer that there is at least one x_17 for which x_17 will listen to a song. Therefore, the answer is yes.