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Greenlight Capital President David Einhorn clapped back at recent criticism from Elon Musk on Friday.

Einhorn, a well-known Tesla short, also called out the company's shaky record of profitability, contrasting it with his firm's history of positive returns.

He also referred to Tesla's "alien dreadnought factory" in a letter published on Twitter.

Musk had published a letter earlier Friday addressing Einhorn as "Mr. Unicorn" and accusing the hedge fund of making false statements about Tesla in a recent investor letter.

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David Einhorn, the Greenlight Capital president and well-known Tesla short-seller, snapped back at Elon Musk's recent criticism on Friday, stepping up a long-running feud between the two.

Einhorn published a letter responding to Musk's post earlier Friday addressing Einhorn as "Mr. Unicorn" and accusing Greenlight of making "numerous false allegations against Tesla" in a recent letter to investors.

"We certainly are capable of making mistakes and if we said anything false, we will correct it for the record," Einhorn wrote.

He added: "I can't imagine how it would feel to have entire websites like https://elonmusk.today chronicling your untruths."

The two have battled it out numerous times, with Musk famously sending Einhorn a box of shorts last year to make fun of his position against Tesla.

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Einhorn took his letter a step further on Friday, calling out Tesla's volatile profitability over the past decade and contrasting it with Greenlight's history of positive returns.

In his letter, Musk invited Einhorn to meet with him to learn more about Tesla and tour some facilities.

"We welcome your offer to learn more about Tesla and will take you up on it. This is a stark contrast from Tesla's prior position," Einhorn said.

He continued: "I think some facility visits would be fun (can we start in Buffalo?). I might learn the difference between your alien dreadnought factory and cars made by hand in a tent."

Greenlight had reportedly sent its note to address Tesla's better-than-expected third-quarter earnings, which sent the company's share price soaring 20%.

Shares of Tesla were up about 1% year-to-date on Friday.

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