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: There is at least one x_13 for which if x_13 were a taxi driver, then x_13 is playing a game. For all x_13, if x_13 were a bartender, then x_13 is playing a game. For all x_13, x_13 will play a game if and only if x_13 is a bartender. For all x_13, x_13 is not a bartender. For all x_13, if x_13 were a poet, then x_13 is a taxi driver.
There is at least one x_13 for which if x_13 were a poet, then x_13 is playing a game can be inferred via the existential transitivity rule. For all x_13, if x_13 plays a game, then x_13 is a bartender can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were a bartender, then x_13 is playing a game can be inferred via the universal biconditional elimination rule. For all x_13, x_13 will not play a game can be inferred via the universal biconditional elimination rule.