What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? There is at least one z for which if z were happy, then z is listening to a song. For all z, z will listen to a song or z is not happy. For all z, z will not listen to a song. For all z, if z listens to a song, then z is happy.
There is at least one z for which z is not happy. For all z, if z were happy, then z is listening to a song. There is at least one z for which z is happy if and only if z will listen to a song. There is at least one z for which z will listen to a song if and only if z is happy.