What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all x_8, if x_8 listens to a song, then x_8 is not excited. For all x_8, if x_8 writes a letter, then x_8 is sleeping. There is at least one x_8 for which if x_8 sleeps, then x_8 is listening to a song. For all x_8, x_8 is excited. For all x_8, if x_8 listens to a song, then x_8 is writing a letter.
For all x_8, x_8 will not listen to a song can be inferred via the universal modus tollens rule. For all x_8, if x_8 listens to a song, then x_8 is sleeping can be inferred via the universal transitivity rule. There is at least one x_8 for which if x_8 sleeps, then x_8 is writing a letter can be inferred via the existential transitivity rule. There is at least one x_8 for which if x_8 writes a letter, then x_8 is listening to a song can be inferred via the existential transitivity rule.