Consider the following premises. forall x_6: S(x_6) -> Q(x_6). forall x_6: T_1(x_6) -> ~Q(x_6). forall x_6: ~P_6(x_6). forall x_6: P_6(x_6) or S(x_6). Can we infer forall x_6: ~T_1(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) or S(x_6), forall x_6: ~P_6(x_6) we can infer forall x_6: S(x_6) via universal disjunctive syllogism. From forall x_6: S(x_6) -> Q(x_6), forall x_6: S(x_6) we can infer forall x_6: Q(x_6) via universal modus ponens. Finally, 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. Therefore, the answer is yes.