And by "known", I don't mean "in the AI's knowledge-base"; the AI would properly at least be able to hunt down textbooks and journal papers, read them, and learn problem-solving approaches from them. In other words, the AI would at least be as able to "do science" in the way that a grad student is expected to "do science."
What relation an AGI has to NP hardness is unclear. I think that if P=NP in the sense that a practical algorithm exists for solving large (ie. 10^9 variables) NP complete problems then AGI (even super-AGI) would probably follow. However I don't necessarily think that's a necessary condition for AGI to exist.