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: T(x) -> S_1(x). forall x: S_1(x) -> T(x). forall x: ~S_1(x). forall x: T(x) <-> P(x).
exists x: ~T(x) can be inferred via the existential modus tollens rule. exists x: T(x) <-> S_1(x) can be inferred via the existential biconditional introduction rule. exists x: S_1(x) <-> T(x) can be inferred via the existential biconditional introduction rule. forall x: T(x) -> P(x) can be inferred via the universal biconditional elimination rule. forall x: P(x) -> T(x) can be inferred via the universal biconditional elimination rule.