Consider the following premises. exists y_3: T(y_3) or ~W(y_3). forall y_3: W(y_3). forall y_3: T_1(y_3) -> ~T(y_3). Can we infer exists y_3: ~T_1(y_3) from them? If possible, name the inference rules being used at each step.
 From exists y_3: T(y_3) or ~W(y_3) we can infer exists y_3: W(y_3) -> T(y_3) via existential rewriting. From exists y_3: W(y_3) -> T(y_3), forall y_3: W(y_3) we can infer exists y_3: T(y_3) via existential modus ponens. Finally, from forall y_3: T_1(y_3) -> ~T(y_3), exists y_3: T(y_3) we can infer exists y_3: ~T_1(y_3) via existential modus tollens. Therefore, the answer is yes.