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Actually modal logic proved Gods existence over 40 years ago. This was proven by Gödel's ontological proofIt has now been tested and proven further with the use of a super computer by two scientists. https://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof http://www.spiegel.de/international/germany/scientists-use-computer-to-mathematically-prove-goedel-god-theorem-a-928668.html
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Axiom 3 assumes the existence of God, by forcing any model of the logic to feature a god-like entity. The proof therefore assumes god and is vacuous.