Consider the following premises. forall y: R_4(y) or ~W_3(y). forall y: R_1(y) -> P(y). forall y: P(y) -> W_3(y). Can we infer exists y: ~(R_1(y) -> R_4(y)) from them? If possible, name the inference rules being used at each step.
 From forall y: R_4(y) or ~W_3(y) we can infer forall y: W_3(y) -> R_4(y) via universal rewriting. From forall y: R_1(y) -> P(y), forall y: P(y) -> W_3(y) we can infer forall y: R_1(y) -> W_3(y) via universal transitivity. Finally, from forall y: R_1(y) -> W_3(y), forall y: W_3(y) -> R_4(y) we can infer forall y: R_1(y) -> R_4(y) via universal transitivity, which contradicts exists y: ~(R_1(y) -> R_4(y)). Therefore, the answer is no.