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_6, x_6 is a cashier if and only if x_6 will cook. For all x_6, if x_6 listens to a song, then x_6 is cooking. For all x_6, if x_6 cooks, then x_6 is a police officer. For all x_6, x_6 is not a cashier. For all x_6, if x_6 were a police officer, then x_6 is listening to a song.
For all x_6, if x_6 listens to a song, then x_6 is a police officer can be inferred via the universal transitivity rule. For all x_6, if x_6 cooks, then x_6 is listening to a song can be inferred via the universal transitivity rule. For all x_6, if x_6 were a police officer, then x_6 is cooking can be inferred via the universal transitivity rule. For all x_6, if x_6 were a cashier, then x_6 is cooking can be inferred via the universal biconditional elimination rule. For all x_6, if x_6 cooks, then x_6 is a cashier can be inferred via the universal biconditional elimination rule. For all x_6, x_6 will not cook can be inferred via the universal biconditional elimination rule.