Consider the following premises. forall y: T_3(y) -> R_4(y). forall y: T_3(y) or ~Q(y). forall y: R_4(y) -> Q(y). Can we infer exists y: ~(T_3(y) <-> R_4(y)) from them? If possible, name the inference rules being used at each step.
 From forall y: T_3(y) or ~Q(y) we can infer forall y: Q(y) -> T_3(y) via universal rewriting. From forall y: R_4(y) -> Q(y), forall y: Q(y) -> T_3(y) we can infer forall y: R_4(y) -> T_3(y) via universal transitivity. Finally, from forall y: T_3(y) -> R_4(y), forall y: R_4(y) -> T_3(y) we can infer forall y: T_3(y) <-> R_4(y) via universal biconditional introduction, which contradicts exists y: ~(T_3(y) <-> R_4(y)). Therefore, the answer is no.