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: Thomas is not listening to a song. David is not excited. It is late if and only if Thomas is listening to a song. David is excited if and only if it is cloudy.
Thomas is not listening to a song and David is not excited can be inferred via the conjunction rule. David is not excited and Thomas is not listening to a song can be inferred via the conjunction rule. If it is late, then Thomas is listening to a song can be inferred via the biconditional elimination rule. If David were excited, then it is cloudy can be inferred via the biconditional elimination rule. If Thomas listens to a song, then it is late can be inferred via the biconditional elimination rule. If it is cloudy, then David is excited can be inferred via the biconditional elimination rule. It is not cloudy can be inferred via the biconditional elimination rule. It is not late can be inferred via the biconditional elimination rule.