In a two party coinjoin consists of Mr Seller and Mr Buyer. Mr Seller has set A of sender addresses/input and set B of receiver addresses (output) Mr Buyer has set C of sender addresses/input and set D of receiver addresses (Output) Assume all input/output are addresses (P2PK or P2PKH and none of them are script).
How does Mr Seller prove to others that set A and set B addresses belong to him? Is there any other way to prove than proving the address one by one which can be very long. On top of that set B addresses are hashes. Mr Seller also need to cooperation from Mr Buyer to provide proof that set C and Set D address belong to Mr Buyer. This is a requirement from IRS audit department who wanted proof of payment amount from the given invoice record.