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 were a janitor, then x_9 is playing tennis. There is at least one x_9 for which if x_9 plays tennis, then x_9 is a janitor. For all x_9, x_9 is an office clerk. For all x_9, if x_9 were an office clerk, then x_9 is playing tennis.
For all x_9, x_9 will play tennis can be inferred via the universal modus ponens rule. There is at least one x_9 for which if x_9 were an office clerk, then x_9 is a janitor can be inferred via the existential transitivity rule. There is at least one x_9 for which x_9 will play tennis if and only if x_9 is a janitor can be inferred via the existential biconditional introduction rule. There is at least one x_9 for which x_9 is a janitor if and only if x_9 will play tennis can be inferred via the existential biconditional introduction rule.