In this paper we present an extension OMDoc to the Open-Math standard that allows to represent the semantics and structure of various kinds of mathematical documents, including articles, textbooks, interactive books, courses. It can serve as the content language for agent communication of mathematical services on a mathematical software bus.

Digital Library (FDL). We designed the system and assembled the prototype as part of a

The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. de Bruijn – more modest in its aims with respect to automation – showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proof-checked by a computer. Classical theorem proving procedures of today are based on ingenious search techniques to find a proof for a given theorem in very large search spaces – often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited. The shift

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Abstract. Freek Wiedijk proposed the well-known theorem about the irrationality of √ 2 as a case study and used this theorem for a comparison of fifteen (interactive) theorem proving systems, which were asked to present their solution (see [48]). This represents an important shift of emphasis in the field of automated deduction away from the somehow artificial problems of the past as represented, for example, in the test set of the TPTP library [45] back to real mathematical challenges. In this paper we present an overview of the Ωmega system as far as it is relevant for the purpose of this paper and show the development of a proof for this theorem. 1 Ωmega The Ωmega proof development system [40] is at the core of several related and well-integrated research projects of the Ωmega research group, whose aim is to develop system support for the working mathematician.