Stock market indices have nothing to do with inflation.
Do we have more money chasing the same or fewer stocks? That is inflation.
You don't appear to have an clue as to how the CPI is calculated.
Why don't you go to the Bureau of Labor Statistics and read up on it before spewing out garbage?
It's right here at the BLS site. It's explained in great detail. :
https://www.bls.gov/cpi/