Bahá'i is a distinct monotheism that nevertheless has certain roots in primarily the Abrahamic faiths (roots that cause some people to consider it a syncretism). It's theistic scriptures were relatively recently authored by the prophet Báh'u'lláh during a tumultuous period of religious upheaval in nineteenth century Persia, although they have been extended by others since.
To some extent Bahá'i inherits the contradiction of the theorem above from its associated Abrahamic ancestry. It portrays a standard model of monotheistic God as e.g. omnipotent, omnipresent, omniscient, and the dualistic creator of all things in the Universe. As we have seen, this directly contradicts the definition of Universe (God must be a subset of the Universe and therefore cannot create it) and any dualism between God separate from Universe with ``knowledge'' of the latter in the form of any sort of high level symbolic decomposition necessarily being compressive and violating omniscience and ensuring the certainty that God Itself cannot be certain of the completeness or truth of God's knowledge. However, the faith is considerably more mystical than e.g. Judaism, Christianity, or Islam, and claims that the specific attributes of God that it asserts are really just a metaphor intended to guide humans along a path of spiritual enlightenment21.
As world religions go, Bahá'i actually exhibits a surprising degree of rationality and enlightenment in its teachings. For example, it has more or less completely moderated the ``heaven and hell'' meme of its parent faiths into poles of an ordinal metric of nearness to God in terms of the harmony of one's life practices with God's divinely expressed will, not as reward or punishment inflicted on hapless humans by the angry Allah portrayed by Muhammed, or the God whose name is Jealous in the Old Testament, or the Jesus who teaches one to cut off one's own hand if `it' sins or else count on experiencing the fires of eternal torment. This is far more in accord with the Hindu or Buddhist concept of God than with the Abrahamic faiths, although Bahá'i appears to stop short of endorsing serial immortality in human incarnations - it leaves what happens to one's ``rational soul'' after death mystical and unknown. Indeed, Bahá'i, in its attempt to become the Universal world religion, has co-opted connections to Hinduism and Buddhism as well.
Some of the really good things in the tenets of Bahá'i include:
I will take Bahá'i at its own word - it asserts that it seeks a harmony between religion and reason, that its system of beliefs is rational. It makes specific provision for the serial appearance of messengers that communicate great truths about the Universe, although as far as I know it hasn't recognized Galileo, Descartes, Newton, Gauss, Riemmann, Lorentz, Darwin, Einstein, Bohr, Schrödinger, Hume, Russell, Gödel, Whitehead, Dirac, Feynman or the cast of millions of scientists, historians, and philosophers worldwide who over the last five hundred years as having contributed more to the enlightenment of the world than all of the religious prophets of the world combined over the course of recorded human history.
I hereby pronounce myself just such a messenger22. In order for Bahá'i to not be in conflict with the theorem above (and hence be arguably conditionally rational on a precisely equal footing with e.g. atheism) it needs to explicitly shift its core assertion about God so that God is explicitly identified with the Universe and not a dualistically separate entity, so that ``creation'' no longer means what all the world religions assert that it does - an act of an outsider to create a cosmos, but rather means ``cause'' in the precise sense used in physics - the ongoing evolution of ``stuff'' (mass-energy) in interaction according to natural law. If God exists at all, the Universe is necessarily God's self-encoded mind. If God does not exist, the Universe is still very much a self-encoded sytem with exactly the same rules.
Does making this shift really matter? I think that it does. For one thing, it shifts the burden or responsibility onto us for making the human world whatever it is we want it to be. We cannot but do God's will, because that Will is built into the laws of physics that utterly dictate our actions right down to the last twitch of the last elementary particle - `sin' exists only as we define it to exist, and our definition will ultimately be practical and not a matter of divine revelation. I like Bahá'i because the rules above seem entirely practical - they satisfy the intuitive test of goodness and `taste sweet' where so much of theism tastes like leftover shit from a brutal age, written down by self-aggrandizing charlatans who were not content laying out their intellectual wares in a bazaar to be considered with reason and free will but had to incorporate extortionist violence of an angry and punitive God who would get you, my pretty23 if you didn't buy into every word of their tripe.
Sweetness, however, is not enough. Any religion that asserts the inflexible truth of its theistic prescription on the basis of some sort of divine authority granted a specific ``messenger'' to whom truths are revealed as preternatural knowledge is rotten at the core. Reason as a path to knowledge of the real world is one of successive approximation, progressive discovery. It requires the flexibility to ascribe to any set of assertions not ``perfect truth'' as ``divinely revealed'' but provisional truth, plausible truth, things that make sense as of our knowledge right now, where the degree of belief we ascribe to them can vary as new evidence and arguments come to light.
Right now I believe very strongly in gravity, for example, not because God has Revealed the Truth About Gravity to Newton, or to Einstein, but because there is a large body of consistent evidence in the greater connected system of modern physics that strongly supports the assertions of certain mathematical laws in context. Is it fundamentally true? I don't know - probably not. One day we will put salt on the tail of gravitons, or somebody will make string theory or supersymmetry work as a better theory of gravitation, one that supercedes and perhaps fundamentally changes the way we think of it. That won't make Newton's Law of Gravitation suddenly false in context, it will simply explain and predict more, and better, the Universe we can observe.
As a ``messenger'' to Bahá'i, let me therefore add one other change to its tenets. The tenets of any reason based religion must be capable of varying over time as better arguments and evidence comes along or they will inevitably be revealed as false! So let's throw away any and all of the silly assertions like the one that there won't be any more messengers for 1000 years, that the tenets of the religion are perfect as they stand, and so on. Why not make a religion that really does try to use reason to infer or deduce properties of God (as does the theorem above) instead of the false methodology of direct revelation? Why not lay religion out in the bazaar of human ideas not as a mandatory set of theistic writings but in the same sense that physics is laid out (and indeed, any such set will necessarily have physics exactly as it stands as a subset).
Bahá'i is therefore arguably the second closest to being in compliance with the theorem above behind Vedantic Hinduism, and by virtue of being put together well into the age of reason, it has a social and moral structure that is far better attuned to the needs of the modern world. All it needs is to acknowledge that God and the Universe are one (so that each of us is a part of God, not something distinct from It in any sense), the ability to change, to loosen up its own dogma and constantly subject it to the ongoing test of reason and argument, to stop asserting its own tenets as being divinely inspired any more than any discovery of the human mind is divinely inspired. Every scientist, every seeker of truth on this planet then becomes a source of non-divine, purely mundane, revelation, revelation of the trustworthy sort, contributing authors to a system of imperfect, incomplete beliefs that we can accept because they are arguably the best set of beliefs (given the evidence) that we have come up with - so far. I would then give it my blessing as being a rational pandeism with positive social value not in immediate contradiction of its own ``infinite claims'' for the Deity it worships through study.