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_5, x_5 is a scientist or x_5 will play a game. For all x_5, if x_5 were a scientist, then x_5 is listening to a song. There is at least one x_5 for which if x_5 listens to a song, then x_5 is sleeping. For all x_5, if x_5 plays a game, then x_5 is listening to a song. For all x_5, if x_5 sleeps, then x_5 is an office clerk.
There is at least one x_5 for which if x_5 listens to a song, then x_5 is an office clerk can be inferred via the existential transitivity rule. There is at least one x_5 for which if x_5 were a scientist, then x_5 is sleeping can be inferred via the existential transitivity rule. There is at least one x_5 for which if x_5 plays a game, then x_5 is sleeping can be inferred via the existential transitivity rule. For all x_5, x_5 will listen to a song can be inferred via the universal disjunction elimination rule.