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There are many problems that are easy to state but provably impossible to solve such as the halting problem and satisfiability of first order logic. How would that affect your hypothesis?
We're talking about solvable tasks, and concerned not about runtime complexity but instead about Kolmogorov complexity of the shortest possible solution
a counterexample wrt both runtime and kolmogorov complexity: 4-coloring
Both problem and solution have very small KC in this case (although solutions would have high runtime complexity)
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