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_1, x_1 will listen to a song if and only if x_1 is a bartender. For all x_1, x_1 is an astronaut or x_1 will not listen to a song. For all x_1, if x_1 were a bartender, then x_1 is listening to a song.
For all x_1, if x_1 listens to a song, then x_1 is an astronaut can be inferred via the universal rewriting rule. For all x_1, if x_1 listens to a song, then x_1 is a bartender can be inferred via the universal biconditional elimination rule. For all x_1, if x_1 were a bartender, then x_1 is listening to a song can be inferred via the universal biconditional elimination rule.