Let's determine if an expression is tautological or not and let's try this expression: ((a ⊼ b) ∨ c) ↔ (¬a ∨ ¬b ∨ c). We can turn this problem into CIRCUIT-SAT decision problem by asking if the expression ((a ⊼ b) ∨ c) ⊕ (¬a ∨ ¬b ∨ c) is satisfiable. Note that we repalced the universal gate with its inverse (by "universal" I mean the gate that be computed the last). And now since we figured out that this expression isn't satisfiable then we can say that its (inverse) is tautological. Isn't this enough to conclude that NP = co-NP? Isn't UNSAT simply is where we take the answer to SAT and we apply an inverter on it?
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