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_13, x_13 will not play tennis. For all x_13, if x_13 were a janitor, then x_13 is curious. For all x_13, if x_13 were an astronaut, then x_13 is a janitor. For all x_13, if x_13 were curious, then x_13 is playing tennis. For all x_13, if x_13 were a janitor, then x_13 is an astronaut.
For all x_13, x_13 is not curious can be inferred via the universal modus tollens rule. For all x_13, if x_13 were a janitor, then x_13 is playing tennis can be inferred via the universal transitivity rule. For all x_13, if x_13 were an astronaut, then x_13 is curious can be inferred via the universal transitivity rule. For all x_13, x_13 is an astronaut if and only if x_13 is a janitor can be inferred via the universal biconditional introduction rule. For all x_13, x_13 is a janitor if and only if x_13 is an astronaut can be inferred via the universal biconditional introduction rule.