Consider the following premises. forall z_3: T(z_3) -> Q(z_3). forall z_3: T(z_3) -> U(z_3). exists z_3: U(z_3) -> Q(z_3). forall z_3: Q(z_3) -> T(z_3). Can we infer forall z_3: ~(Q(z_3) <-> U(z_3)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.