Okay, I decided to humor you, but lets change the language a little. Instead of God the Father, God the Son and God the Holy Spirit, lets use the words Being, Consciousness and Mind. This is fair because it gives us one essence (Being) with three aspects, faces or hypostases not at all different than either the Christian concept or the Hindu concept of Being, Bliss and Intelligence. In order to logically disprove such a God, you have to show that consciousness is not intrinsic to the nature of Being itself. (Never mind that you have to use mind to do so.) But heres the problem: in order to do so you either have to disprove the science that suggests consciousness is intrinsic or prove such interpretations of scientific experiments are invalid.
Quite frankly, I dont think youre up to the task.