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_9, if x_9 listens to a song, then x_9 is playing a game. For all x_9, x_9 will cook or x_9 is a cashier. For all x_9, x_9 will not cook or x_9 will listen to a song. For all x_9, if x_9 were a cashier, then x_9 is climbing a mountain. For all x_9, if x_9 climbs a mountain, then x_9 is sleeping. There is at least one x_9 for which if x_9 sleeps, then x_9 is playing a game.
For all x_9, if x_9 were a cashier, then x_9 is sleeping can be inferred via the universal transitivity rule. There is at least one x_9 for which if x_9 climbs a mountain, then x_9 is playing a game can be inferred via the existential transitivity rule. For all x_9, x_9 is a cashier or x_9 will listen to a song can be inferred via the universal resolution rule.