Consider the following premises. forall x_8: P_8(x_8) <-> Q_8(x_8). forall x_8: ~Q_8(x_8). forall x_8: P_8(x_8) or P(x_8). forall x_8: S_2(x_8). Can we infer forall x_8: P(x_8) and S_2(x_8) from them?
 From forall x_8: P_8(x_8) <-> Q_8(x_8), forall x_8: ~Q_8(x_8) we can infer forall x_8: ~P_8(x_8). From forall x_8: P_8(x_8) or P(x_8), forall x_8: ~P_8(x_8) we can infer forall x_8: P(x_8). Finally, from forall x_8: P(x_8), forall x_8: S_2(x_8) we can infer forall x_8: P(x_8) and S_2(x_8). Therefore, the answer is yes.