What is the legal status of children born to a man who purchased a female slave believing she was legitimately owned by the seller, when it is later discovered the slave was usurped?

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If a man purchases a female slave believing her to be rightfully owned by the seller, and subsequently has children with her, those children are considered free if the ownership by the seller is later proven invalid (i.e., the slave was usurped). This is because the man's belief regarding the lineage establishes the freedom of the offspring based on his assumption of legitimate ownership.