EDIT: Thanks everyone, I wasn't aware that the F22 had a higher price and additional export restrictions.
One F-22 vs one F-35 is a contest obviously in favor of the F-22. One F-22 vs. three F-35s becomes a lot more ambiguous, particularly when we are not at war and there's no guarantee that any of these planes will do anything more than force projection.
(The F-35 very much seems like a peacetime fighter to me, and that may be exactly what the U.S. needs right now. History has shown that basically all your assumptions about how the next war will unfold go out the window once the next war actually starts. Under those conditions, it may make more sense to try out a bunch of new technologies, keep the defense contractors alive and the aeronautical engineers employed, contain costs, and build enough numbers that you don't get completely steamrolled in the early days of a war. Then when war actually does break out, you rapidly adjust and build the planes that you actually need, when you have real data about what's winning on the battlefield.)
Also, don't forget that nuclear weapons still exist. Nuclear powers shooting down squadrons of each others fighters to achieve "victory" does not seem likely.
Other controversial opinion: I think that the assumption that the next major war will be between nation-states is a likely candidate for one that'll go out the window. In my view, the next major war will be like Syria but on a global scale, with many semi-organized subnational groups duking it out in exceptionally nasty urban & guerilla warfare.
2. F22's are only fighter jets. F35 for better and worse is designed to do just about everything.
But to be fair, as the other comments have pointed out the F-35 is lower cost, a decent peace time machine and is has flexible configurations.
The F-22 also can't be sold as an export.