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 scientist, then x_10 is working. For all x_10, if x_10 works, then x_10 is a nurse. For all x_10, if x_10 were a nurse, then x_10 is a janitor. For all x_10, if x_10 were a janitor, then x_10 is a scientist. There is at least one x_10 for which x_10 is not a nurse.
There is at least one x_10 for which x_10 will not work can be inferred via the existential modus tollens rule. For all x_10, if x_10 were a scientist, then x_10 is a nurse can be inferred via the universal transitivity rule. For all x_10, if x_10 works, then x_10 is a janitor can be inferred via the universal transitivity rule. For all x_10, if x_10 were a nurse, then x_10 is a scientist can be inferred via the universal transitivity rule. For all x_10, if x_10 were a janitor, then x_10 is working can be inferred via the universal transitivity rule.