Consider the following premises. w_4 <-> S_12(h). t. forall x_12: P(x_12) <-> S_12(x_12). w_4 -> ~t. Can we infer P(h) from them? If possible, name the inference rules being used at each step.
 From forall x_12: P(x_12) <-> S_12(x_12) we can infer P(h) <-> S_12(h) via universal instantiation. From w_4 -> ~t, t we can infer ~w_4 via modus tollens. From w_4 <-> S_12(h), ~w_4 we can infer ~S_12(h) via biconditional elimination. Finally, from P(h) <-> S_12(h), ~S_12(h) we can infer ~P(h) via biconditional elimination, which contradicts P(h). Therefore, the answer is no.