Consider the following premises. P(d_2) -> W(d_2). forall x_2: P(x_2) <-> W(x_2). ~W(d_2). Can we infer ~P(d_2) from them?
 From forall x_2: P(x_2) <-> W(x_2) we can infer P(d_2) <-> W(d_2). From P(d_2) <-> W(d_2) we can infer W(d_2) -> P(d_2). From P(d_2) -> W(d_2), W(d_2) -> P(d_2) we can infer P(d_2) <-> W(d_2). Finally, from P(d_2) <-> W(d_2), ~W(d_2) we can infer ~P(d_2). Therefore, the answer is yes.