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The paper explores several ways to improve the speed and capacity of combinational equivalence checking based on Boolean satisfiability (SAT). State-of-the-art methods use simulation and BDD/SAT sweeping on the input side (i.e. proving equivalence of some internal nodes in a topological order), interleaved with attempts to run SAT on the output (i.e. proving equivalence of the output to constant 0). This paper improves on this method by (a) using more intelligent simulation, (b) using CNF-based SAT with circuit-based decision heuristics, and (c) interleaving SAT with low-effort logic synthesis. Experimental results on public and industrial benchmarks demonstrate substantial reductions in runtime, compared to the current methods. In several cases, the new solver succeeded in solving previously unsolved problems.