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, x is an office clerk or x is not a scientist. For all x, x will take a plane if and only if x is an office clerk. For all x, if x were an office clerk, then x is a scientist. There is at least one x for which x is not a scientist.
There is at least one x for which x is not an office clerk can be inferred via the existential modus tollens rule. For all x, if x were a scientist, then x is an office clerk can be inferred via the universal rewriting rule. For all x, if x takes a plane, then x is an office clerk can be inferred via the universal biconditional elimination rule. For all x, if x were an office clerk, then x is taking a plane can be inferred via the universal biconditional elimination rule.