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, x_9 will write a letter. For all x_9, x_9 is a musician or x_9 is a carpenter. For all x_9, if x_9 were a carpenter, then x_9 is taking a plane. For all x_9, if x_9 were a musician, then x_9 is taking a plane. For all x_9, if x_9 takes a plane, then x_9 is playing a game.
For all x_9, if x_9 were a carpenter, then x_9 is playing a game can be inferred via the universal transitivity rule. For all x_9, if x_9 were a musician, then x_9 is playing a game can be inferred via the universal transitivity rule. For all x_9, x_9 will take a plane can be inferred via the universal disjunction elimination rule.