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, x will climb a mountain or x is not an astronaut. There is at least one x for which if x climbs a mountain, then x is taking a plane. For all x, x will take a plane if and only if x will listen to a song.
For all x, if x were an astronaut, then x is climbing a mountain can be inferred via the universal rewriting rule. For all x, if x takes a plane, then x is listening to a song can be inferred via the universal biconditional elimination rule. For all x, if x listens to a song, then x is taking a plane can be inferred via the universal biconditional elimination rule.