I've always thought about it this way.
A car factory in 1950 employed so many people to make X cars. The factory of today employs far less people to make the same amount of stuff. Up until now we've all bought every increasing quantities of stuff so we've been able to absorb that extra productivity.
What happens then if our capacity to consume extra stuff is met? Or what happens when some proportion of the populace is now unemployed due to automation. They're kind of 2 sides to the same coin. Once consumption capacity is met, productivity increases just lead to increasing unemployment.
Of course you could leave them to rot. Or you could distribute the benefits of increased productivity to everyone.
Are we there yet? No, but we're using more resources than we should so we should probably hope that we reach that limit sooner rather than later.
So to answer your question, there wouldn't be extra inflation, because there wouldn't be extra consumption.