## SEKI Report

- 94,4
- Goal oriented equational theorem proving using team work (1999)
- The team work method is a concept for distributing automated theoremprovers and so to activate several experts to work on a given problem. We haveimplemented this for pure equational logic using the unfailing KnuthADBendixcompletion procedure as basic prover. In this paper we present three classes ofexperts working in a goal oriented fashion. In general, goal oriented experts perADform their job "unfair" and so are often unable to solve a given problem alone.However, as a team member in the team work method they perform highly effiADcient, even in comparison with such respected provers as Otter 3.0 or REVEAL,as we demonstrate by examples, some of which can only be proved using teamwork.The reason for these achievements results from the fact that the team workmethod forces the experts to compete for a while and then to cooperate by exADchanging their best results. This allows one to collect "good" intermediate resultsand to forget "useless" ones. Completion based proof methods are frequently reADgarded to have the disadvantage of being not goal oriented. We believe that ourapproach overcomes this disadvantage to a large extend.

- 94,2
- The application of goal-oriented heuristics for prooving equational theorems via the unfailing Knuth-Bendix completion procedure A case study: lattice ordered groups (1999)
- In this report we present a case study of employing goal-oriented heuristics whenproving equational theorems with the (unfailing) Knut-Bendix completion proce-dure. The theorems are taken from the domain of lattice ordered groups. It will bedemonstrated that goal-oriented (heuristic) criteria for selecting the next critical paircan in many cases significantly reduce the search effort and hence increase per-formance of the proving system considerably. The heuristic, goalADoriented criteriaare on the one hand based on so-called "measures" measuring occurrences andnesting of function symbols, and on the other hand based on matching subterms.We also deal with the property of goal-oriented heuristics to be particularly helpfulin certain stages of a proof. This fact can be addressed by using them in a frame-work for distributed (equational) theorem proving, namely the "teamwork-method".