Excuse me, but how do you expect to compute a private key of some point, when the only property you have is something that applies to all the points on the curve?

You have A, from which you compute -B. Obviously P is their addition. So zero useful information.

BTW all three points belong to the same endo class, so their field X Y values are directly derived one from another, without any need of point multiplication: So there's not something to "find" other than the key itself of one of the points, otherwise everything is just running in a circular logic. Nothing to compute.

A + B + C = 0 is satisfied for any possible private key and all three points have the same Y. The sum of their X's is also 0. This is basic number theory in action due to the curve equation and the roots of unity.

Excuse me, but how do you expect to compute a private key of some point, when the only property you have is something that applies to all the points on the curve?