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: It is cloudy. It is late if and only if Barbara is playing a game. If it is late, then John is listening to a song. If it is cloudy, then John is listening to a song.
John is listening to a song can be inferred via the modus ponens rule. If it is late, then Barbara is playing a game can be inferred via the biconditional elimination rule. If Barbara plays a game, then it is late can be inferred via the biconditional elimination rule.