D rejects (D), but then H accepted (D,(D)) and hence D accepted (D), contradiction! So D cannot exist, so H cannot exist either (D was built from H). This means that ATM is undecidable.

Is ATM complement undecidable?

Corollary 4.23: ATM is Turing-recognizable but not decidable, so its complement ATM is NOT Turing-recognizable.

Is ATM enumerable complete?

Corollary: ATM = {〈M,w〉 : M accepts w} is recursively enumerable.