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Proof that P && !P (apenantology) is always false
//I propose an apenantology can be represented as P && !P such that this expression is always false
P || !P // Tautology, always true
=> !(P || !P) // Inverse of tautological statement, always false
=> !P && P // Distributive property of &&
=> P && !P // Commutitive property of &&
=> P && !P <=> false
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