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_15, if x_15 were a janitor, then x_15 is writing a letter. For all x_15, x_15 will play a game if and only if x_15 will cook. For all x_15, if x_15 cooks, then x_15 is a janitor. There is at least one x_15 for which if x_15 writes a letter, then x_15 is playing a game.
For all x_15, if x_15 cooks, then x_15 is writing a letter can be inferred via the universal transitivity rule. There is at least one x_15 for which if x_15 were a janitor, then x_15 is playing a game can be inferred via the existential transitivity rule. For all x_15, if x_15 plays a game, then x_15 is cooking can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 cooks, then x_15 is playing a game can be inferred via the universal biconditional elimination rule.