A group of mutually trusting clients outsources a computation service to a remote server, which they do not fully trust and that may be subject to attacks. The clients do not communicate with each other and would like to verify the correctness of the remote computation and the consistency of the server's responses. This paper presents the Conflict-free Operation verification Protocol (COP) that ensures linearizability when the server is correct and preserves fork-linearizability in any other case. All clients that observe each other's operations are consistent, in the sense that their own operations and those operations of other clients that they see are linearizable. If the server forks two clients by hiding an operation, these clients never again see operations of each other. COP supports wait-free client operations in the sense that when executed with a correct server, non-conflicting operations can run without waiting for other clients, allowing more parallelism than earlier protocols. A conflict arises when an operation causes a subsequent operation to produce a different output value for the client who runs it. The paper gives a precise model for the guarantees of COP and includes a formal analysis that these are achieved.