Consider the following premises. For all x_15, if x_15 were happy, then x_15 is running. For all x_15, x_15 will go running if and only if x_15 will listen to a song. For all x_15, x_15 is happy if and only if x_15 is a soldier. For all x_15, if x_15 were an artist, then x_15 is listening to a song. For all x_15, x_15 is a soldier or x_15 is an artist. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will listen to a song.
 From the fact that for all x_15, x_15 will go running if and only if x_15 will listen to a song we can infer that for all x_15, if x_15 goes running, then x_15 is listening to a song via universal biconditional elimination. From the fact that for all x_15, x_15 is happy if and only if x_15 is a soldier we can infer that for all x_15, if x_15 were a soldier, then x_15 is happy via universal biconditional elimination. From the fact that for all x_15, if x_15 were happy, then x_15 is running, and that for all x_15, if x_15 goes running, then x_15 is listening to a song we can infer that for all x_15, if x_15 were happy, then x_15 is listening to a song via universal transitivity. From the fact that for all x_15, if x_15 were a soldier, then x_15 is happy, and that for all x_15, if x_15 were happy, then x_15 is listening to a song we can infer that for all x_15, if x_15 were a soldier, then x_15 is listening to a song via universal transitivity. Finally, from the fact that for all x_15, if x_15 were a soldier, then x_15 is listening to a song, that for all x_15, if x_15 were an artist, then x_15 is listening to a song, and that for all x_15, x_15 is a soldier or x_15 is an artist we can infer that for all x_15, x_15 will listen to a song via universal disjunction elimination. Therefore, the answer is yes.