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 John drives a car, then David is an astronaut. John is driving a car. If David were an astronaut, then Michael is playing a game. If Michael plays a game, then John is driving a car. If William climbs a mountain, then David is an astronaut.
David is an astronaut can be inferred via the modus ponens rule. If John drives a car, then Michael is playing a game can be inferred via the transitivity rule. If David were an astronaut, then John is driving a car can be inferred via the transitivity rule. If Michael plays a game, then David is an astronaut can be inferred via the transitivity rule. If William climbs a mountain, then Michael is playing a game can be inferred via the transitivity rule.