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Elon Musk and Billie Eilish are officially at war -- at least online -- after the billionaire clapped back at the singer on the heels of her calling him a "f***ing pathetic p***y b**** coward."

ICYMI ... last Thursday, Billie went on a tirade against the tech mogul on her IG story -- listing a slew of global issues Elon could single-handedly tackle after a new Tesla pay package put him on track to become the world's first trillionaire . Gallery Launch Gallery Getty

Billie shares claims arguing Elon could end world hunger, save critically endangered species or even rebuild all of Gaza with his fortune ... but instead, accuses him of hoarding his wealth.

Fast-forward to Wednesday night ... Elon took to this own platform, X, to hit back -- reacting to a screenshots of Bil

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