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_2, x_2 is not rich. There is at least one x_2 for which if x_2 climbs a mountain, then x_2 is rich. For all x_2, if x_2 plays a game, then x_2 is climbing a mountain.
There is at least one x_2 for which x_2 will not climb a mountain can be inferred via the existential modus tollens rule. There is at least one x_2 for which if x_2 plays a game, then x_2 is rich can be inferred via the existential transitivity rule.