Consider the following premises. forall x_8: P_8(x_8) or Q_5(x_8). forall x_8: W_4(x_8). forall x_8: ~Q_8(x_8). forall x_8: P_8(x_8) -> Q_8(x_8). Can we infer Q_5(a_2) 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 Q_5(x_8), forall x_8: ~P_8(x_8) we can infer forall x_8: Q_5(x_8). From forall x_8: W_4(x_8), forall x_8: Q_5(x_8) we can infer forall x_8: W_4(x_8) and Q_5(x_8). From forall x_8: W_4(x_8) and Q_5(x_8) we can infer W_4(a_2) and Q_5(a_2). Finally, from W_4(a_2) and Q_5(a_2) we can infer Q_5(a_2). Therefore, the answer is yes.