Mr. Mann,
Your argument reminds me of a very nice fellow who once tried to sell me a used car.
But a con-job in logic cannot be covered up by the lies and damned lies of statistics.
You may try to photo-shop that dent in the logic of your used inequality car with a paintjob of statistics, but the fact remains that there is a 500-pound canary sitting in the final offer you are making; namely
n(A, B-NOT) n(B, C-NOT) >= n(A, C-NOT).
You can't fool Nature with your final offer. It contains a conjunction in the place where Nature demands a disjunction. Your final offer claims
n(A, B-NOT) and n(B, C-NOT)
when Nature permits only
n(A, B-NOT) or n(B, C-NOT).
No wonder your used inequality car is not selling even after 50 years of trying.
Every experiment ever done to sell it has rejected it outright.
Perhaps it is time again for you to learn that "or" is not the same as "and."