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_10, if x_10 plays a game, then x_10 is a lawyer. For all x_10, if x_10 were a janitor, then x_10 is a poet. For all x_10, if x_10 were a lawyer, then x_10 is a janitor. There is at least one x_10 for which x_10 will sleep or x_10 is a lawyer. For all x_10, if x_10 were a janitor, then x_10 is playing a game. For all x_10, if x_10 sleeps, then x_10 is a poet.
For all x_10, if x_10 plays a game, then x_10 is a janitor can be inferred via the universal transitivity rule. For all x_10, if x_10 were a lawyer, then x_10 is a poet can be inferred via the universal transitivity rule. For all x_10, if x_10 were a lawyer, then x_10 is playing a game can be inferred via the universal transitivity rule. For all x_10, if x_10 were a janitor, then x_10 is a lawyer can be inferred via the universal transitivity rule.