Consider the following premises. For all x_7, x_7 is not happy. For all x_7, if x_7 listens to a song, then x_7 is happy. There is at least one x_7 for which if x_7 were happy, then x_7 is listening to a song. For all x_7, if x_7 were happy, then x_7 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will listen to a song.
 From the fact that for all x_7, if x_7 listens to a song, then x_7 is happy, and that for all x_7, if x_7 were happy, then x_7 is listening to a song we can infer that for all x_7, x_7 will listen to a song if and only if x_7 is happy via universal biconditional introduction. From the fact that for all x_7, x_7 will listen to a song if and only if x_7 is happy we can infer that for all x_7, if x_7 listens to a song, then x_7 is happy via universal biconditional elimination. From the fact that there is at least one x_7 for which if x_7 were happy, then x_7 is listening to a song, and that for all x_7, if x_7 listens to a song, then x_7 is happy we can infer that there is at least one x_7 for which x_7 is happy if and only if x_7 will listen to a song via existential biconditional introduction. Finally, from the fact that there is at least one x_7 for which x_7 is happy if and only if x_7 will listen to a song, and that for all x_7, x_7 is not happy we can infer that there is at least one x_7 for which x_7 will not listen to a song via existential biconditional elimination, which contradicts that For all x_7, x_7 will listen to a song. Therefore, the answer is no.