This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...

In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for a hierarchical planning of proofs. Also rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. 1 Introduction In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling ...

During the last decade a variety of industrial strength formal methods has emerged and has been applied to industrial test cases to demonstrate their adequacy and scalability. Formal techniques require a sufficient tool support especially when dealing with proof obligations. The size and the complexity of the arising problems demand for techniques to structure the deduction. In this paper we present techniques to realize a general divide-and-conquer approach in the framework of proof planning. In order to tackle different subgoals by different proof methods we propose the use of the color-calculus as an underlying constraint mechanism to resolve possible threats. 1 Introduction The application of formal methods in an industrial setting (cf. [6]) results in an increased complexity of the specification and the correspondent verification. While various techniques have been developed to decompose specifications of large systems into modules of reasonable size (e.g. enrichment, parameteri...

After introducing the basic notions of reflective logic and internal strategies, we discuss in detail how reflection can be systematically exploited to design a strategy language internal to a reflective logic in the concrete case of rewriting logic and Maude; and we illustrate the advantages of this new approach to strategies by showing how the rules of inference for Knuth-Bendix completion can be given strategies corresponding to completion procedures in a completely modular way, not requiring any change whatsoever to the inference rules themselves.