This sounds like a fair and reasonable criticism of the the paper, it says that there are factual errors that should be addresses and it echo's comments by othe

This sounds like a fair and reasonable criticism of the the paper, it says that there are factual errors that should be addresses and it echo's comments by others here on HN (i.e. that a real solution is not sufficient, the solutions should be integral). Believe me, I've had a far less helpful and much more antagonistic reviews for a paper that was eventually accepted (after much revision). If you address the concerns, either with proofs or with references to other papers, you could resubmit. Another approach might be an experimental one. As they say "the proof is in the pudding". There are plenty of SAT solvers out there and plenty of SAT benchmarks and tests that they run on. Implement your approach and run it against the benchmarks for varying size of benchmark and against other SAT solvers. If your approach gets the same answers and consistently outperforms other implementations (especially for large N, where the non-poly terms will dominate) then you have an empirical proof. I would guess that a sufficiently large problem that takes 2-3 days to solve should be solvable by your approach within minutes. Assuming this works and you get the same answer, open source the solution and the tests so that others can play with it. If others can reproduce your results, then you have applied the scientific method, although through usual ways, to prove your point.