Consider the following premises. forall y: T(y) or R_2(y). forall y: T(y) <-> S(y). forall y: R_2(y) -> S(y). forall x_5: S(x_5) -> S_5(x_5). Can we infer S_5(j) from them?
 From forall y: T(y) <-> S(y) we can infer forall y: T(y) -> S(y). From forall y: T(y) -> S(y), forall y: R_2(y) -> S(y), forall y: T(y) or R_2(y) we can infer forall y: S(y). From forall y: S(y) we can infer S(j). From forall x_5: S(x_5) -> S_5(x_5) we can infer S(j) -> S_5(j). Finally, from S(j) -> S_5(j), S(j) we can infer S_5(j). Therefore, the answer is yes.