Consider the following premises. forall x_7: Q_7(x_7). forall x_7: P_7(x_7) -> ~Q_7(x_7). P_7(a_5) <-> r_1. Can we infer r_1 from them?
 From forall x_7: P_7(x_7) -> ~Q_7(x_7), forall x_7: Q_7(x_7) we can infer forall x_7: ~P_7(x_7). From forall x_7: ~P_7(x_7) we can infer ~P_7(a_5). Finally, from P_7(a_5) <-> r_1, ~P_7(a_5) we can infer ~r_1, which contradicts r_1. Therefore, the answer is no.