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: If Susan plays a game, then Barbara is taking a plane. Susan is not playing a game. If John were a janitor, then Patricia is not sleeping. If Barbara takes a plane, then Susan is playing a game. If Barbara doesn't take a plane, then Patricia is sleeping.
Barbara is not taking a plane can be inferred via the modus tollens rule. Susan is playing a game if and only if Barbara is taking a plane can be inferred via the biconditional introduction rule. Barbara is taking a plane if and only if Susan is playing a game can be inferred via the biconditional introduction rule.