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_13, if x_13 were a carpenter, then x_13 is sleeping. For all x_13, if x_13 were a carpenter, then x_13 is sleeping. For all x_13, if x_13 were a carpenter, then x_13 is not driving a car. For all x_13, x_13 will drive a car. There is at least one x_13 for which if x_13 sleeps, then x_13 is a carpenter.
For all x_13, x_13 is not a carpenter can be inferred via the universal modus tollens rule. There is at least one x_13 for which x_13 will sleep if and only if x_13 is a carpenter can be inferred via the existential biconditional introduction rule. There is at least one x_13 for which x_13 will sleep if and only if x_13 is a carpenter can be inferred via the existential biconditional introduction rule. There is at least one x_13 for which x_13 is a carpenter if and only if x_13 will sleep can be inferred via the existential biconditional introduction rule. There is at least one x_13 for which x_13 is a carpenter if and only if x_13 will sleep can be inferred via the existential biconditional introduction rule.