Consider the following premises. forall y_1: U(y_1). forall y_1: P(y_1). Can we infer exists y_1: ~P(y_1) from them? If possible, name the inference rules being used at each step.
 From forall y_1: P(y_1), forall y_1: U(y_1) we can infer forall y_1: P(y_1) and U(y_1) via universal conjunction. Finally, from forall y_1: P(y_1) and U(y_1) we can infer forall y_1: P(y_1) via universal simplification, which contradicts exists y_1: ~P(y_1). Therefore, the answer is no.