Consider the following premises. forall y_1: T_4(y_1) or ~Q(y_1). forall y_1: T(y_1) -> S_3(y_1). exists y_1: T(y_1) <-> W(y_1). forall y_1: T_4(y_1) -> W(y_1). Can we infer exists y_1: Q(y_1) -> S_3(y_1) from them? If possible, name the inference rules being used at each step.
 From exists y_1: T(y_1) <-> W(y_1) we can infer exists y_1: W(y_1) -> T(y_1) via existential biconditional elimination. From exists y_1: W(y_1) -> T(y_1), forall y_1: T(y_1) -> S_3(y_1) we can infer exists y_1: W(y_1) -> S_3(y_1) via existential transitivity. From forall y_1: T_4(y_1) -> W(y_1), exists y_1: W(y_1) -> S_3(y_1) we can infer exists y_1: T_4(y_1) -> S_3(y_1) via existential transitivity. From forall y_1: T_4(y_1) or ~Q(y_1) we can infer forall y_1: Q(y_1) -> T_4(y_1) via universal rewriting. Finally, from forall y_1: Q(y_1) -> T_4(y_1), exists y_1: T_4(y_1) -> S_3(y_1) we can infer exists y_1: Q(y_1) -> S_3(y_1) via existential transitivity. Therefore, the answer is yes.