An Improved Upper Bound for SAT

We show that the CNF satisfiability problem can be solved O * (1.2226 m ) time, where m is the number of clauses in the formula, improving the known upper bounds O * (1.234 m ) given by Yamamoto 15 years ago and O * (1.239 m ) given by Hirsch 22 years ago. By using an amortized technique and careful case analysis, we successfully avoid the bottlenecks in previous algorithms and get the improvement.