Consider the following premises. For all x_5, x_5 will listen to a song or x_5 will not climb a mountain. For all x_5, if x_5 cooks, then x_5 is climbing a mountain. There is at least one x_5 for which if x_5 writes a letter, then x_5 is cooking. Can we infer the following from them? There is at least one x_5 for which if x_5 writes a letter, then x_5 is listening to a song.
 From the fact that there is at least one x_5 for which if x_5 writes a letter, then x_5 is cooking, and that for all x_5, if x_5 cooks, then x_5 is climbing a mountain we can infer that there is at least one x_5 for which if x_5 writes a letter, then x_5 is climbing a mountain. From the fact that for all x_5, x_5 will listen to a song or x_5 will not climb a mountain we can infer that for all x_5, if x_5 climbs a mountain, then x_5 is listening to a song. Finally, from the fact that there is at least one x_5 for which if x_5 writes a letter, then x_5 is climbing a mountain, and that for all x_5, if x_5 climbs a mountain, then x_5 is listening to a song we can infer that there is at least one x_5 for which if x_5 writes a letter, then x_5 is listening to a song. Therefore, the answer is yes.