Consider the following premises. forall x_8: Q_1(x_8) -> T(x_8). exists x_8: T(x_8) <-> Q_8(x_8). forall x_8: ~Q_8(x_8). forall x_8: T(x_8) -> Q_1(x_8). Can we infer forall x_8: Q_1(x_8) from them? If possible, name the inference rules being used at each step.
 From exists x_8: T(x_8) <-> Q_8(x_8), forall x_8: ~Q_8(x_8) we can infer exists x_8: ~T(x_8) via existential biconditional elimination. From forall x_8: T(x_8) -> Q_1(x_8), forall x_8: Q_1(x_8) -> T(x_8) we can infer forall x_8: T(x_8) <-> Q_1(x_8) via universal biconditional introduction. Finally, from forall x_8: T(x_8) <-> Q_1(x_8), exists x_8: ~T(x_8) we can infer exists x_8: ~Q_1(x_8) via existential biconditional elimination, which contradicts forall x_8: Q_1(x_8). Therefore, the answer is no.