Collusion resistant computing of same function by two servers
It sounds like what you really want is a Proof of Replication, where you can have multiple servers prove that they each have their own copy of a file.

The servers must each prove that they've been hosting their own redundant copy of file the whole time, and that they haven't just downloaded it just-in-time in order to create the proof. If you upload a file to a cloud service that claims they'll host N redundant copies of the file, they can use proofs of replication in order to confirm that they are in fact keeping N copies and not just one.

Protocol Labs (developer of IPFS and Filecoin) has developed a strategy for proofs of replication. Page 8 of the Filecoin Primer has a short description and diagram overviewing the strategy, and their Proof of Replication paper is more in-depth.

The basic idea is that each server is given a unique "sealed" replica of the data. The data may be easily recoverable from the sealed version. Creating (or recreating) the sealed version takes a predictable amount of time and may be done by anyone. The verifier can issue a challenge to a server that can only be answered by using that server's uniquely-sealed version of the data, and the verifier expects the server to answer within a timeout period that's shorter than the amount of time it would take for the server to download the data from another server and recreate the seal.