Consider the following premises. forall x_16: Q(x_16) <-> S(x_16). forall x_16: T_4(x_16) <-> S(x_16). exists x_16: ~Q_16(x_16). forall x_16: Q(x_16) <-> Q_16(x_16). Can we infer exists x_16: ~T_4(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: Q(x_16) <-> Q_16(x_16), exists x_16: ~Q_16(x_16) we can infer exists x_16: ~Q(x_16) via existential biconditional elimination. From forall x_16: Q(x_16) <-> S(x_16), exists x_16: ~Q(x_16) we can infer exists x_16: ~S(x_16) via existential biconditional elimination. Finally, from forall x_16: T_4(x_16) <-> S(x_16), exists x_16: ~S(x_16) we can infer exists x_16: ~T_4(x_16) via existential biconditional elimination. Therefore, the answer is yes.