A method is devised to integrate reasoning by mathematical induction into saturation-based proof procedures based on resolution or superposition. The obtained calculi are capable of handling formulas in which some of the quantified variables range over inductively defined domains (which, as is well-known, cannot be expressed in first-order logic). The procedure is defined as a set of inference rules that generate inductive invariants incrementally and prove their validity. Although the considered logic itself is incomplete, it is shown that the invariant generation rules are complete, in the sense that if an invariant (of some specific form) is deducible from the considered clauses, then it is eventually generated.

中文翻译：

---

结合归纳和基于饱和的定理证明

设计了一种方法，将通过数学归纳法进行的推理整合到基于分解或叠加的基于饱和的证明程序中。获得的演算能够处理公式中的一些量化变量范围在归纳定义的域（众所周知，不能用一阶逻辑表示）。该过程被定义为一组推理规则，这些规则递增地生成归纳不变量并证明其有效性。尽管所考虑的逻辑本身是不完整的，但表明不变量生成规则是完整的，从某种意义上说，如果从所考虑的子句中可以推导出一个（某种特定形式的）不变量，那么它最终会被生成。