Consider the following premises. forall x_18: P_18(x_18) <-> Q_18(x_18). forall x_18: P_18(x_18) or Q_12(x_18). forall x_18: ~Q_18(x_18). Can we infer exists y: Q_12(y) or T_1(y) from them?
 From forall x_18: P_18(x_18) <-> Q_18(x_18), forall x_18: ~Q_18(x_18) we can infer forall x_18: ~P_18(x_18). From forall x_18: P_18(x_18) or Q_12(x_18), forall x_18: ~P_18(x_18) we can infer forall x_18: Q_12(x_18). From forall x_18: Q_12(x_18) we can infer Q_12(a_10). From Q_12(a_10) we can infer exists y: Q_12(y). Finally, from exists y: Q_12(y) we can infer exists y: Q_12(y) or T_1(y). Therefore, the answer is yes.