> So we're already halfway done with the proof. Indeed the Cook-Levin theorem > https://en.wikipedia.org/wiki/Cook%E2%80%93Levin_theorem https://en.wikipedia.

> So we're already halfway done with the proof. Indeed the Cook-Levin theorem > https://en.wikipedia.org/wiki/Cook%E2%80%93Levin_theorem https://en.wikipedia.org/wiki/Cook%E2%80%93Levin_theorem which actually proves that there exist NP-complete problems in NP is not a trivial result (and was at that time a highly surprising one). So, indeed, "one half of the proof" has been done; the other half (which seems to be much harder) of P vs NP is still open.