Consider the following premises. forall x_6: T_1(x_6) -> T(x_6). exists x_6: T(x_6) -> T_1(x_6). forall x_6: ~Q(x_6). forall x_6: T_1(x_6) -> Q(x_6). Can we infer exists x_6: ~T(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: T_1(x_6) -> T(x_6), exists x_6: T(x_6) -> T_1(x_6) we can infer exists x_6: T_1(x_6) <-> T(x_6) via existential biconditional introduction. From forall x_6: T_1(x_6) -> Q(x_6), forall x_6: ~Q(x_6) we can infer forall x_6: ~T_1(x_6) via universal modus tollens. Finally, from exists x_6: T_1(x_6) <-> T(x_6), forall x_6: ~T_1(x_6) we can infer exists x_6: ~T(x_6) via existential biconditional elimination. Therefore, the answer is yes.