Consider the following premises. exists x_18: ~Q_18(x_18). forall x_18: P_18(x_18) <-> Q_18(x_18). forall x_18: P_18(x_18) <-> W(x_18). forall x_18: W(x_18). Can we infer exists x_18: S(x_18) from them?
 From forall x_18: P_18(x_18) <-> Q_18(x_18), exists x_18: ~Q_18(x_18) we can infer exists x_18: ~P_18(x_18). From forall x_18: P_18(x_18) <-> W(x_18), exists x_18: ~P_18(x_18) we can infer exists x_18: ~W(x_18). From forall x_18: W(x_18) we can infer forall x_18: W(x_18) or S(x_18). Finally, from forall x_18: W(x_18) or S(x_18), exists x_18: ~W(x_18) we can infer exists x_18: S(x_18). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.