Fewer people working fewer hours = lower productivity = fewer things to buy with your money. The average standard of living has to drop.
The problem being that you are attempting to demonstrate the effects of UBI, using mathematics that
doesn't mention UBI.
You assume that a UBI leads to "fewer people working fewer hours", but this is one if the major points in question, so you don't get to use it as an assumption in your proof.
Even if your assumption were valid, the first part of your equation is demonstrably false; Since the industrial revolution, the entire economic system has been one long and continuous demonstration of increased productivity in which fewer people work fewer hours.
Without a UBI, a large fraction of the population are too busy working shit jobs for poor wages to do anything else.
Freeing up people to get educated, and to have the free time to innovate, and the safety net to take risks such as setting up new busineses, was (and remains) the major driver of those productivity increases - increased productivity leads to more free time, and more wealth, to make that free time itself generate further productivity increases.
A UBI would further multiply this virtuous circle, and your assumption that it would not, is unwarranted.
Economics hadn't been a zero sum game, or even close to it, since the Middle Ages.
Innovation = Fewer people working fewer hours = Higher productivity = A higher innovation to drudgery ratio + Higher real incomes for less work.
At some point, such an innovative society gets productive enough to feed, house, and clothe everybody, even those who can't or won't work, such as the elderly, clergymen, children, aristocrats, and the unemployed.
This is NOT a bad outcome.