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_13, x_13 is a carpenter if and only if x_13 is a janitor. For all x_13, x_13 is a carpenter if and only if x_13 is an office clerk. For all x_13, x_13 is an office clerk if and only if x_13 will take a plane. For all x_13, if x_13 listens to a song, then x_13 is a janitor. For all x_13, x_13 will not take a plane. For all x_13, if x_13 were a janitor, then x_13 is listening to a song.
For all x_13, x_13 will listen to a song if and only if x_13 is a janitor can be inferred via the universal biconditional introduction rule. For all x_13, x_13 is a janitor if and only if x_13 will listen to a song can be inferred via the universal biconditional introduction rule. For all x_13, if x_13 were a carpenter, then x_13 is a janitor can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were a carpenter, then x_13 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were an office clerk, then x_13 is taking a plane can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were a janitor, then x_13 is a carpenter can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were an office clerk, then x_13 is a carpenter can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 takes a plane, then x_13 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_13, x_13 is not an office clerk can be inferred via the universal biconditional elimination rule.