Consider the following premises. exists x_2: W(x_2) -> S(x_2). forall x_2: U(x_2) -> W(x_2). forall x_2: S_2(x_2) <-> S(x_2). forall x_2: U(x_2). Can we infer forall x_2: ~S_2(x_2) from them?
 From forall x_2: U(x_2) -> W(x_2), exists x_2: W(x_2) -> S(x_2) we can infer exists x_2: U(x_2) -> S(x_2). From forall x_2: S_2(x_2) <-> S(x_2) we can infer forall x_2: S(x_2) -> S_2(x_2). From exists x_2: U(x_2) -> S(x_2), forall x_2: U(x_2) we can infer exists x_2: S(x_2). Finally, from forall x_2: S(x_2) -> S_2(x_2), exists x_2: S(x_2) we can infer exists x_2: S_2(x_2), which contradicts forall x_2: ~S_2(x_2). Therefore, the answer is no.