Cool, I did not know that SETH and PvNP were different
- 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.
It doesn't have to by hyperpolynomial, if you solve ETH in linear time, you also refute it :-)