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 David were a musician, then William is taking a plane. William is taking a plane or Barbara is a bartender. If Barbara plays squash, then David is a musician. For all z, if z were a bartender, then z is playing squash. If William takes a plane, then David is a musician.
If Barbara plays squash, then William is taking a plane can be inferred via the transitivity rule. If Barbara listens to a song, then William is taking a plane can be inferred via the rewriting rule. David is a musician if and only if William is taking a plane can be inferred via the biconditional introduction rule. William is taking a plane if and only if David is a musician can be inferred via the biconditional introduction rule.