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, if x plays a game, then x is working. For all x, x will not drive a car. For all x, if x works, then x is driving a car. There is at least one x for which if x drives a car, then x is playing a game. For all x, if x works, then x is driving a car.
For all x, x will not work can be inferred via the universal modus tollens rule. For all x, x will not work can be inferred via the universal modus tollens rule. For all x, if x plays a game, then x is driving a car can be inferred via the universal transitivity rule. For all x, if x plays a game, then x is driving a car can be inferred via the universal transitivity rule. There is at least one x for which if x drives a car, then x is working can be inferred via the existential transitivity rule. There is at least one x for which if x works, then x is playing a game can be inferred via the existential transitivity rule. There is at least one x for which if x works, then x is playing a game can be inferred via the existential transitivity rule.