Consider the following premises. forall z_4: ~S_3(z_4). exists z_4: S_3(z_4) <-> U(z_4). Can we infer exists z_4: ~U(z_4) from them? If possible, name the inference rules being used at each step.
We can infer exists z_4: ~U(z_4) via the existential biconditional elimination rule. Therefore, the answer is yes.