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_10, if x_10 were a taxi driver, then x_10 is not a carpenter. For all x_10, if x_10 were happy, then x_10 is a taxi driver. For all x_10, x_10 is excited if and only if x_10 will sleep. For all x_10, x_10 is happy if and only if x_10 is excited. For all x_10, x_10 is a carpenter.
For all x_10, x_10 is not a taxi driver can be inferred via the universal modus tollens rule. For all x_10, if x_10 were excited, then x_10 is sleeping can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 were happy, then x_10 is excited can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 sleeps, then x_10 is excited can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 were excited, then x_10 is happy can be inferred via the universal biconditional elimination rule.