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: If Mary takes a plane, then William is sleeping. If William sleeps, then Barbara is listening to a song. Mary is taking a plane if and only if Barbara is listening to a song.
If Mary takes a plane, then Barbara is listening to a song can be inferred via the transitivity rule. If Mary takes a plane, then Barbara is listening to a song can be inferred via the biconditional elimination rule. If Barbara listens to a song, then Mary is taking a plane can be inferred via the biconditional elimination rule.