Consider the following premises. forall y: S_1(y) -> W_2(y). exists y: ~T(y) or T_3(y). forall y: W_2(y) -> S_1(y). forall y: T(y) or S_1(y). forall y: ~W_2(y). Can we infer forall y: ~T_3(y) from them? If possible, name the inference rules being used at each step.
 From forall y: T(y) or S_1(y), exists y: ~T(y) or T_3(y) we can infer exists y: S_1(y) or T_3(y) via existential resolution. From forall y: S_1(y) -> W_2(y), forall y: W_2(y) -> S_1(y) we can infer forall y: S_1(y) <-> W_2(y) via universal biconditional introduction. From forall y: S_1(y) <-> W_2(y), forall y: ~W_2(y) we can infer forall y: ~S_1(y) via universal biconditional elimination. Finally, from exists y: S_1(y) or T_3(y), forall y: ~S_1(y) we can infer exists y: T_3(y) via existential disjunctive syllogism, which contradicts forall y: ~T_3(y). Therefore, the answer is no.