Basically: - If you can solve k-sat in time (2-eps)^n, you've refuted SETH. - If you can solve 3-sat in time (1+o(1))^n, you've refuted ETH. - If you can sol

Basically: - If you can solve k-sat in time (2-eps)^n, you've refuted SETH. - If you can solve 3-sat in time (1+o(1))^n, you've refuted ETH. - If you can solve 3-sat in time n^O(1), you've refuted P!=NP. Since general k-sat is at least as hard as 3-sat, it follows that SETH is the strongest hypothesis (hence the name) and thus the most likely to fall. P!=NP is the weakest hypothesis and thus the most likely of the three to be true.