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Is the usage of that is correct here? And why is it correct? (main reason for the asking: I have not seen a sentence that is joined by that is)

Out of the experiments, only one is successful, that is, produces same same output in both set of input.

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In your question, that is is only a different way of saying: i.e.

"The actual term i.e. is an abbreviation of id est in Latin, which literally means "that is". In fact, when I see i.e., I cannot help but say "that is" in my head."

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The words "that is" might be replaced with "in other words" or "let me explain that some more".

The usage you mentioned is correct.

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