Consider the following premises. forall x_16: P_16(x_16) -> S(x_16). forall x_16: Q_4(x_16) -> P_2(x_16). forall x_16: P_2(x_16) or ~Q_6(x_16). forall x_16: P_16(x_16) or Q_16(x_16). forall x_16: Q_6(x_16) or Q_4(x_16). exists x_16: Q_16(x_16) -> S(x_16). Can we infer exists x_16: P_2(x_16) and S(x_16) from them?
 From forall x_16: P_16(x_16) -> S(x_16), exists x_16: Q_16(x_16) -> S(x_16), forall x_16: P_16(x_16) or Q_16(x_16) we can infer exists x_16: S(x_16). From forall x_16: P_2(x_16) or ~Q_6(x_16) we can infer forall x_16: Q_6(x_16) -> P_2(x_16). From forall x_16: Q_6(x_16) -> P_2(x_16), forall x_16: Q_4(x_16) -> P_2(x_16), forall x_16: Q_6(x_16) or Q_4(x_16) we can infer forall x_16: P_2(x_16). Finally, from forall x_16: P_2(x_16), exists x_16: S(x_16) we can infer exists x_16: P_2(x_16) and S(x_16). Therefore, the answer is yes.