Consider the following premises. forall x_17: T_3(x_17) -> T(x_17). exists x_17: T_3(x_17) -> ~Q_14(x_17). forall x_17: P_14(x_17) or Q_14(x_17). forall x_17: ~P_14(x_17). forall x_17: T(x_17) -> T_3(x_17). Can we infer exists x_17: ~T(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: T(x_17) -> T_3(x_17), forall x_17: T_3(x_17) -> T(x_17) we can infer forall x_17: T(x_17) <-> T_3(x_17) via universal biconditional introduction. From forall x_17: P_14(x_17) or Q_14(x_17), forall x_17: ~P_14(x_17) we can infer forall x_17: Q_14(x_17) via universal disjunctive syllogism. From forall x_17: T(x_17) <-> T_3(x_17) we can infer forall x_17: T(x_17) -> T_3(x_17) via universal biconditional elimination. From exists x_17: T_3(x_17) -> ~Q_14(x_17), forall x_17: Q_14(x_17) we can infer exists x_17: ~T_3(x_17) via existential modus tollens. Finally, from forall x_17: T(x_17) -> T_3(x_17), exists x_17: ~T_3(x_17) we can infer exists x_17: ~T(x_17) via existential modus tollens. Therefore, the answer is yes.