Consider the following premises. forall y: T_3(y) -> R(y). forall y: U_4(y). forall y: T(y). forall y: T(y) -> R(y). Can we infer exists y: ~(R(y) and U_4(y)) from them? If possible, name the inference rules being used at each step.
 From forall y: T(y) we can infer forall y: T(y) or T_3(y) via universal addition. From forall y: T(y) -> R(y), forall y: T_3(y) -> R(y), forall y: T(y) or T_3(y) we can infer forall y: R(y) via universal disjunction elimination. Finally, from forall y: R(y), forall y: U_4(y) we can infer forall y: R(y) and U_4(y) via universal conjunction, which contradicts exists y: ~(R(y) and U_4(y)). Therefore, the answer is no.