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: William is not a carpenter. For all x_10, if x_10 were a carpenter, then x_10 is listening to a song. For all x_10, if x_10 listens to a song, then x_10 is a carpenter.
For all x_10, x_10 is a carpenter if and only if x_10 will listen to a song can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will listen to a song if and only if x_10 is a carpenter can be inferred via the universal biconditional introduction rule.