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A sharp threshold in proof complexity
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For each k ≤ 4, we give τk 0 such that a random k-CNF formula F with n variables and ⌊rkn⌋ clauses is satisfiable with high probability, but ORDERED-DLL takes exponential time on F with uniformly positive probability. Using results of [2], this can be strengthened to a high probability result for certain natural backtracking schemes and extended to many other DPLL algorithms.