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_9, if x_9 listens to a song, then x_9 is a sailor. For all x_9, x_9 is a sailor if and only if x_9 will work. For all x_9, x_9 will not work. For all x_9, if x_9 were a poet, then x_9 is listening to a song. For all x_9, if x_9 were a sailor, then x_9 is listening to a song.
For all x_9, if x_9 were a poet, then x_9 is a sailor can be inferred via the universal transitivity rule. For all x_9, x_9 will listen to a song if and only if x_9 is a sailor can be inferred via the universal biconditional introduction rule. For all x_9, x_9 is a sailor if and only if x_9 will listen to a song can be inferred via the universal biconditional introduction rule. For all x_9, if x_9 were a sailor, then x_9 is working can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 works, then x_9 is a sailor can be inferred via the universal biconditional elimination rule. For all x_9, x_9 is not a sailor can be inferred via the universal biconditional elimination rule.