Consider the following premises. forall x_8: T(x_8) <-> S(x_8). exists x_8: ~Q_8(x_8). forall x_8: T(x_8) <-> Q_8(x_8). Can we infer exists x_8: ~S(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: T(x_8) <-> Q_8(x_8), exists x_8: ~Q_8(x_8) we can infer exists x_8: ~T(x_8) via existential biconditional elimination. Finally, from forall x_8: T(x_8) <-> S(x_8), exists x_8: ~T(x_8) we can infer exists x_8: ~S(x_8) via existential biconditional elimination. Therefore, the answer is yes.