Consider the following premises. forall x_16: Q(x_16). forall x_16: T(x_16) <-> Q_16(x_16). exists x_16: Q(x_16) -> T(x_16). forall x_16: Q_16(x_16) -> S_3(x_16). Can we infer forall x_16: ~S_3(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: T(x_16) <-> Q_16(x_16) we can infer forall x_16: T(x_16) -> Q_16(x_16) via universal biconditional elimination. From forall x_16: T(x_16) -> Q_16(x_16), forall x_16: Q_16(x_16) -> S_3(x_16) we can infer forall x_16: T(x_16) -> S_3(x_16) via universal transitivity. From exists x_16: Q(x_16) -> T(x_16), forall x_16: Q(x_16) we can infer exists x_16: T(x_16) via existential modus ponens. Finally, from forall x_16: T(x_16) -> S_3(x_16), exists x_16: T(x_16) we can infer exists x_16: S_3(x_16) via existential modus ponens, which contradicts forall x_16: ~S_3(x_16). Therefore, the answer is no.