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: David is sleeping if and only if Barbara is running. David is sleeping or Barbara is a carpenter. For all x_12, x_12 is a carpenter if and only if x_12 will go running.
If Barbara plays a game, then David is sleeping can be inferred via the rewriting rule. If David sleeps, then Barbara is running can be inferred via the biconditional elimination rule. If Barbara goes running, then David is sleeping can be inferred via the biconditional elimination rule. For all x_12, if x_12 were a carpenter, then x_12 is running can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 goes running, then x_12 is a carpenter can be inferred via the universal biconditional elimination rule.