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: exists x: U(x) -> S(x). forall x: S(x) -> U(x). forall x: ~S(x). forall x: S(x) or ~U(x).
exists x: ~U(x) can be inferred via the existential modus tollens rule. forall x: U(x) -> S(x) can be inferred via the universal rewriting rule. exists x: U(x) <-> S(x) can be inferred via the existential biconditional introduction rule. exists x: S(x) <-> U(x) can be inferred via the existential biconditional introduction rule.