Rep. Matt Gaetz, R-Fla., stumped the head of the Air Force Academy on Wednesday during a tense hearing about race and gender-based admissions practices at military colleges and universities.

Lt. Gen. Richard M. Clark was unable to define gender identity terms like "agender" and "demigender" that were listed in eligibility guidelines for a fellowship that’s open to Air Force cadets and other Americans, something Gaetz noted during their heated exchange.

"You’re literally pushing a program in the academies that says, ‘If you’re a cisgender woman, a transgender woman, a non-binary, agender, bigender, two-spirit, demigender…' What’s ‘demigender’?" Gaetz asked.

"Sir, that's a term of the people that are eligible for that particular scholarship, that is available to," Clarke said.

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Rep. Matt Gaetz Air Force Academy superintendent

Rep. Matt Gaetz, R-Fla., right, grilled Air Force Academy Superintendent Lt. Gen. Richard M. Clark at a heated Armed Services subcommittee hearing Wednesday. (Getty Images)

"It's a person who looks at their gender in a different way than I do, sir," Clarke said when the congressman cut him off to further question him.

"Well, sure. That's all of these people. You're a cisgender man, you don't even get to apply. Do you know what 'demigender' really means?" Gaetz asked.

"I’m not really sure, sir," Clark said. Gaetz then asked if he knew what "agender" meant, and the general again said he didn't know.

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Brooke Owens Fellowship

A screenshot of the Brooke Owens fellowship website outlines some of the eligibility terms.

"Right. So, here we are, pushing a fellowship calling for people that you don't even know what the words mean," Gaetz said. "And the No. 1 group of people, the cisgender men, are excluded. In the name of diversity, equity and inclusion, should we be pushing programs that we can't define, that exclude the largest group of service members?"

The Brooke Owens fellowship that Gaetz was referring to is open to "women and gender-minority students in aerospace," according to its website.

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Under its eligibility requirements, the site says, "If you are a cisgender woman, a transgender woman, non-binary, agender, bigender, two-spirit, demigender, genderfluid, genderqueer, or another form of gender minority, this program is for you."

Rep. Jim Banks in Indiana

Rep. Jim Banks, R-Ind., is the chairman of the Armed Services subcommittee holding Wednesday's hearing. (Rep. Jim Banks campaign)

Clark clarified when pressed that it is not an Air Force Academy program but rather is one that students are allowed to apply for "because it’s an opportunity for us to develop them as warfighters."

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"I mean, how can you use this as a way to develop the warfighters if you don't know what it means?" Gaetz asked.