Consider the following premises. forall y_4: W_2(y_4) <-> Q_4(y_4). forall y_4: R(y_4). forall y_4: W_2(y_4). Can we infer exists y_4: ~(R(y_4) and Q_4(y_4)) from them? If possible, name the inference rules being used at each step.
 From forall y_4: W_2(y_4) <-> Q_4(y_4) we can infer forall y_4: W_2(y_4) -> Q_4(y_4) via universal biconditional elimination. From forall y_4: W_2(y_4) -> Q_4(y_4), forall y_4: W_2(y_4) we can infer forall y_4: Q_4(y_4) via universal modus ponens. Finally, from forall y_4: R(y_4), forall y_4: Q_4(y_4) we can infer forall y_4: R(y_4) and Q_4(y_4) via universal conjunction, which contradicts exists y_4: ~(R(y_4) and Q_4(y_4)). Therefore, the answer is no.