Consider the following premises. forall x_4: T_3(x_4). forall x_4: S_1(x_4) -> ~T_3(x_4). exists x_4: S_1(x_4) or U(x_4). Can we infer forall x_4: ~(U(x_4) or S_2(x_4)) from them?
 From forall x_4: S_1(x_4) -> ~T_3(x_4), forall x_4: T_3(x_4) we can infer forall x_4: ~S_1(x_4). From exists x_4: S_1(x_4) or U(x_4), forall x_4: ~S_1(x_4) we can infer exists x_4: U(x_4). Finally, from exists x_4: U(x_4) we can infer exists x_4: U(x_4) or S_2(x_4), which contradicts forall x_4: ~(U(x_4) or S_2(x_4)). Therefore, the answer is no.