Consider the following premises. forall x_8: S(x_8) and Q_3(x_8). exists x_8: S(x_8) <-> T(x_8). Can we infer forall x_8: ~T(x_8) from them? If possible, name the inference rules being used at each step.
 From exists x_8: S(x_8) <-> T(x_8) we can infer exists x_8: S(x_8) -> T(x_8) via existential biconditional elimination. From forall x_8: S(x_8) and Q_3(x_8) we can infer forall x_8: S(x_8) via universal simplification. Finally, from exists x_8: S(x_8) -> T(x_8), forall x_8: S(x_8) we can infer exists x_8: T(x_8) via existential modus ponens, which contradicts forall x_8: ~T(x_8). Therefore, the answer is no.