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: Joseph is listening to a song if and only if it is cloudy. Joseph is listening to a song if and only if David is sleeping. If it is cloudy, then David is sleeping.
If Joseph listens to a song, then it is cloudy can be inferred via the biconditional elimination rule. If Joseph listens to a song, then David is sleeping can be inferred via the biconditional elimination rule. If it is cloudy, then Joseph is listening to a song can be inferred via the biconditional elimination rule. If David sleeps, then Joseph is listening to a song can be inferred via the biconditional elimination rule.