Consider the following premises. forall x_5: T_1(x_5) -> Q_5(x_5). forall x_5: ~Q_5(x_5). exists x_5: T(x_5) <-> S(x_5). forall x_5: T(x_5) <-> T_1(x_5). Can we infer forall x_5: S(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: T_1(x_5) -> Q_5(x_5), forall x_5: ~Q_5(x_5) we can infer forall x_5: ~T_1(x_5) via universal modus tollens. From forall x_5: T(x_5) <-> T_1(x_5), forall x_5: ~T_1(x_5) we can infer forall x_5: ~T(x_5) via universal biconditional elimination. Finally, from exists x_5: T(x_5) <-> S(x_5), forall x_5: ~T(x_5) we can infer exists x_5: ~S(x_5) via existential biconditional elimination, which contradicts forall x_5: S(x_5). Therefore, the answer is no.