Consider the following premises. exists y_1: ~T_2(y_1). forall y_1: P_2(y_1) <-> T_2(y_1). forall y_1: P_2(y_1) or S(y_1). Can we infer exists y_1: S(y_1) or T(y_1) from them? If possible, name the inference rules being used at each step.
 From forall y_1: P_2(y_1) <-> T_2(y_1), exists y_1: ~T_2(y_1) we can infer exists y_1: ~P_2(y_1) via existential biconditional elimination. From forall y_1: P_2(y_1) or S(y_1), exists y_1: ~P_2(y_1) we can infer exists y_1: S(y_1) via existential disjunctive syllogism. Finally, from exists y_1: S(y_1) we can infer exists y_1: S(y_1) or T(y_1) via existential addition. Therefore, the answer is yes.