Consider the following premises. exists x_17: ~W(x_17). forall x_17: U_4(x_17) -> T(x_17). forall x_17: T_4(x_17) -> U_4(x_17). forall x_17: T(x_17) -> ~Q_4(x_17). forall x_17: W(x_17) or Q_4(x_17). Can we infer exists x_17: ~T_4(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: W(x_17) or Q_4(x_17), exists x_17: ~W(x_17) we can infer exists x_17: Q_4(x_17) via existential disjunctive syllogism. From forall x_17: T_4(x_17) -> U_4(x_17), forall x_17: U_4(x_17) -> T(x_17) we can infer forall x_17: T_4(x_17) -> T(x_17) via universal transitivity. From forall x_17: T(x_17) -> ~Q_4(x_17), exists x_17: Q_4(x_17) we can infer exists x_17: ~T(x_17) via existential modus tollens. Finally, from forall x_17: T_4(x_17) -> T(x_17), exists x_17: ~T(x_17) we can infer exists x_17: ~T_4(x_17) via existential modus tollens. Therefore, the answer is yes.