Consider the following premises. forall x_4: S_1(x_4) -> U(x_4). ~s. s <-> U(e_1). S_1(e_1) or ~U(e_1). Can we infer ~S_1(e_1) from them?
 From forall x_4: S_1(x_4) -> U(x_4) we can infer S_1(e_1) -> U(e_1). From S_1(e_1) or ~U(e_1) we can infer U(e_1) -> S_1(e_1). From s <-> U(e_1), ~s we can infer ~U(e_1). From U(e_1) -> S_1(e_1), S_1(e_1) -> U(e_1) we can infer U(e_1) <-> S_1(e_1). Finally, from U(e_1) <-> S_1(e_1), ~U(e_1) we can infer ~S_1(e_1). Therefore, the answer is yes.