Consider the following premises. There is at least one x_10 for which if x_10 works, then x_10 is cooking. For all x_10, if x_10 makes tea, then x_10 is cooking. For all x_10, x_10 will make tea. Can we infer the following from them? There is at least one x_10 for which x_10 will cook or x_10 will listen to a song.
 From the fact that for all x_10, x_10 will make tea we can infer that for all x_10, x_10 will make tea or x_10 will work. From the fact that for all x_10, if x_10 makes tea, then x_10 is cooking, that there is at least one x_10 for which if x_10 works, then x_10 is cooking, and that for all x_10, x_10 will make tea or x_10 will work we can infer that there is at least one x_10 for which x_10 will cook. Finally, from the fact that there is at least one x_10 for which x_10 will cook we can infer that there is at least one x_10 for which x_10 will cook or x_10 will listen to a song. Therefore, the answer is yes.