Consider the following premises. forall x_1: ~S_3(x_1). forall x_1: U_3(x_1) <-> R(x_1). exists x_1: S_3(x_1) <-> U_2(x_1). forall x_1: U_2(x_1) <-> U_3(x_1). Can we infer exists x_1: ~R(x_1) from them?
 From exists x_1: S_3(x_1) <-> U_2(x_1), forall x_1: ~S_3(x_1) we can infer exists x_1: ~U_2(x_1). From forall x_1: U_2(x_1) <-> U_3(x_1), exists x_1: ~U_2(x_1) we can infer exists x_1: ~U_3(x_1). Finally, from forall x_1: U_3(x_1) <-> R(x_1), exists x_1: ~U_3(x_1) we can infer exists x_1: ~R(x_1). Therefore, the answer is yes.