Consider the following premises. forall z: R_1(z) or ~Q_1(z). forall z: R_1(z) -> Q_1(z). Can we infer exists z: ~(Q_1(z) <-> R_1(z)) from them? If possible, name the inference rules being used at each step.
 From forall z: R_1(z) or ~Q_1(z) we can infer forall z: Q_1(z) -> R_1(z) via universal rewriting. Finally, from forall z: Q_1(z) -> R_1(z), forall z: R_1(z) -> Q_1(z) we can infer forall z: Q_1(z) <-> R_1(z) via universal biconditional introduction, which contradicts exists z: ~(Q_1(z) <-> R_1(z)). Therefore, the answer is no.