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, if x were a janitor, then x is playing squash. There is at least one x for which x will not play squash. For all x, x is a janitor if and only if x will play squash.
There is at least one x for which x is not a janitor can be inferred via the existential modus tollens rule. For all x, if x were a janitor, then x is playing squash can be inferred via the universal biconditional elimination rule. For all x, if x plays squash, then x is a janitor can be inferred via the universal biconditional elimination rule. There is at least one x for which x is not a janitor can be inferred via the existential biconditional elimination rule.