Consider the following premises. forall y: W(y) <-> U_4(y). forall y: W(y) -> Q(y). Can we infer exists y: ~(U_4(y) -> Q(y)) from them? If possible, name the inference rules being used at each step.
 From forall y: W(y) <-> U_4(y) we can infer forall y: U_4(y) -> W(y) via universal biconditional elimination. Finally, from forall y: U_4(y) -> W(y), forall y: W(y) -> Q(y) we can infer forall y: U_4(y) -> Q(y) via universal transitivity, which contradicts exists y: ~(U_4(y) -> Q(y)). Therefore, the answer is no.