We are invited to deal with mathematical activity in a sys­ tematic way [ ... ] one does expect and look for pleasant surprises in this requirement of a novel combination of psy­ chology, logic, mathematics and technology. Hao Wang, 1970, quoted from(Wang, 1970). The field of mathematics has been a key application area for automated theorem proving from the start, in fact the very first automatically found the­ orem was that the sum of two even numbers is even (Davis, 1983). The field of automated deduction has witnessed considerable progress and in the last decade, automated deduction methods have made their way into many areas of research and product development in computer science. For instance, deduction systems are increasingly used in software and hardware verification to ensure the correctness of computer hardware and computer programs with respect to a given specification. Logic programming, while still falling somewhat short of its expectations, is now widely used, deduc­ tive databases are well-developed and logic-based description and analysis of hard-and software is commonplace today. | Automated Deduction - A Basis for Applications Volume I Foundations | Indigo Chapters