A hypothetical reasoning, which can find an explanation for a given set of observation by assuming some hypothetical sets, is a useful knowledge processing framework because of its theoretical basis and usefulness for practical problems such as diagnostics, scheduling, and design. It is, however, known to be computationally very expensive for large problems because it must deal with incomplete knowledge. Predicate-logic allows powerful and compact knowledge representation compared to propositional-logic. Efficient methods to proceed reasoning have been developed for propositional-logic. However it would be desirable to develop similar methods for predicate-logic, but this has so far proved difficult. “KICK-HOPE” is one of hypothetical reasoning systems for predicate-logic. KICK-HOPE, which is based on a deductive database technique called the QSQR method and a basic fast hypothetical reasoning system called ATMS(Assumption-based Truth Maintenance System), made advances in the speed of reasoning. However, for a practical knowledge base, ‘the inconsistent process’ and ‘the subsumption process’ still consume much calculation time. In this paper, we investigate an e.cient method of the inconsistent and subsumption processes of KICK-HOPE. First, we show most of these processes are vain and omissible. Second, to omit vain processes, we introduce bit-vector(check-vector) to represent what hypotheses include in hypothetical sets. And, we improve that vain processes will be reduced to check the check-vector. Finally, we examine the proposed system with two examples, a diagnostic problem of a logic circuit and a scheduling problem. It is shown to be more efficient than the original KICK-HOPE for all problems.