Consider the following premises. forall z: W(z) <-> T_3(z). exists z: W(z) <-> R_1(z). Can we infer forall z: ~(T_3(z) -> R_1(z)) from them? If possible, name the inference rules being used at each step.
 From exists z: W(z) <-> R_1(z) we can infer exists z: W(z) -> R_1(z) via existential biconditional elimination. Finally, from forall z: W(z) <-> T_3(z) we can infer forall z: T_3(z) -> W(z) via universal biconditional elimination, which contradicts forall z: ~(T_3(z) -> R_1(z)). Therefore, the answer is no.