Consider the following premises. p <-> t. forall y_4: ~S_3(y_4). S_3(e) <-> p. Can we infer t from them? If possible, name the inference rules being used at each step.
 From forall y_4: ~S_3(y_4) we can infer ~S_3(e) via universal instantiation. From S_3(e) <-> p, ~S_3(e) we can infer ~p via biconditional elimination. Finally, from p <-> t, ~p we can infer ~t via biconditional elimination, which contradicts t. Therefore, the answer is no.