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: For all x_12, x_12 will listen to a song if and only if x_12 is happy. James is not happy. Sarah is sleeping if and only if Charles is a carpenter. James is listening to a song if and only if Sarah is sleeping.
If Sarah sleeps, then Charles is a carpenter can be inferred via the biconditional elimination rule. If James listens to a song, then Sarah is sleeping can be inferred via the biconditional elimination rule. If Charles were a carpenter, then Sarah is sleeping can be inferred via the biconditional elimination rule. If Sarah sleeps, then James is listening to a song can be inferred via the biconditional elimination rule. For all x_12, if x_12 listens to a song, then x_12 is happy can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were happy, then x_12 is listening to a song can be inferred via the universal biconditional elimination rule.