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David Geffen is firing back at his estranged husband ... he says the guy's claims that Geffen promised to financially support him for life are bogus and a textbook shakedown attempt.

The billionaire just responded to a lawsuit filed by his estranged husband, David Andrew Armstrong (AKA Donovan Michaels ) ... and Geffen flat out denies ever making assurances to take care of Armstrong financially for the rest of his life.

In the docs, obtained by TMZ, Geffen says Armstrong's claims are ludicrous and part of a contrived attempt to humiliate Geffen in public and extract a financial settlement. Getty

Geffen says it's clearly a shakedown but insists it won't work. He says during their relationship, he was happy to provide Armstrong with anything he asked for, putti

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