Consider the following premises. exists x_18: P(x_18) or ~Q_12(x_18). forall x_18: P(x_18) <-> Q_18(x_18). forall x_18: Q_18(x_18) or Q_12(x_18). Can we infer exists x_18: P(x_18) or S(x_18) from them?
 From forall x_18: P(x_18) <-> Q_18(x_18) we can infer forall x_18: Q_18(x_18) -> P(x_18). From exists x_18: P(x_18) or ~Q_12(x_18) we can infer exists x_18: Q_12(x_18) -> P(x_18). From forall x_18: Q_18(x_18) -> P(x_18), exists x_18: Q_12(x_18) -> P(x_18), forall x_18: Q_18(x_18) or Q_12(x_18) we can infer exists x_18: P(x_18). Finally, from exists x_18: P(x_18) we can infer exists x_18: P(x_18) or S(x_18). Therefore, the answer is yes.