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: There is at least one x_7 for which if x_7 plays a game, then x_7 is driving a car. For all x_7, x_7 will climb a mountain if and only if x_7 is an office clerk. For all x_7, if x_7 drives a car, then x_7 is climbing a mountain.
There is at least one x_7 for which if x_7 plays a game, then x_7 is climbing a mountain can be inferred via the existential transitivity rule. For all x_7, if x_7 climbs a mountain, then x_7 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_7, if x_7 were an office clerk, then x_7 is climbing a mountain can be inferred via the universal biconditional elimination rule.