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_6, if x_6 plays a game, then x_6 is reading a book. For all x_6, if x_6 reads a book, then x_6 is listening to a song. There is at least one x_6 for which if x_6 listens to a song, then x_6 is reading a book. For all x_6, x_6 will play a game or x_6 will listen to a song.
For all x_6, if x_6 plays a game, then x_6 is listening to a song can be inferred via the universal transitivity rule. There is at least one x_6 for which x_6 will read a book can be inferred via the existential disjunction elimination rule. There is at least one x_6 for which x_6 will listen to a song if and only if x_6 will read a book can be inferred via the existential biconditional introduction rule. There is at least one x_6 for which x_6 will read a book if and only if x_6 will listen to a song can be inferred via the existential biconditional introduction rule.