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 sleeps, then x_10 is a janitor. For all x_10, x_10 is a musician if and only if x_10 will sleep. For all x_10, if x_10 were a janitor, then x_10 is a carpenter. There is at least one x_10 for which x_10 is not a carpenter.
There is at least one x_10 for which x_10 is not a janitor can be inferred via the existential modus tollens rule. For all x_10, if x_10 sleeps, then x_10 is a carpenter can be inferred via the universal transitivity rule. For all x_10, if x_10 were a musician, then x_10 is sleeping can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 sleeps, then x_10 is a musician can be inferred via the universal biconditional elimination rule.