Consider the following premises. exists x_2: T_2(x_2) -> U(x_2). forall x_2: W_2(x_2) or ~U(x_2). forall x_2: ~W_2(x_2). Can we infer exists x_2: ~T_2(x_2) from them?
 From forall x_2: W_2(x_2) or ~U(x_2) we can infer forall x_2: U(x_2) -> W_2(x_2). From forall x_2: U(x_2) -> W_2(x_2), forall x_2: ~W_2(x_2) we can infer forall x_2: ~U(x_2). Finally, from exists x_2: T_2(x_2) -> U(x_2), forall x_2: ~U(x_2) we can infer exists x_2: ~T_2(x_2). Therefore, the answer is yes.