R-calculus without the cut rule

R-calculus is an inference system for deducing all possible changes when a theory is refuted by the facts. In this paper, we try to eliminate the cut rule in R-calculus by modifying the existing rules and by introducing new rules. The result is the R-calculus without the cut rule, which still preserves the reachability, soundness and completeness as R-calculus does. R-calculus without the cut rule is a formal inference system of logical connective symbols and quantifier symbols solely. It can serve as the theoretical foundation of the automation of revision calculus.