In this paper, stepwise and nearly stepwise simulation results for a number of first-order proof calculi are presented and an overview is given that illustrates the relations between these calculi. For this purpose, we modify the consolution calculus in such a way that it can be instantiated to resolution, tableaux model elimination, a connection method and Loveland's model elimination.

This thesis explores the relative complexity of proofs produced by the automatic theorem proving procedures of analytic tableaux, linear resolution, the connection method, tree resolution and the Davis-Putnam procedure. It is shown that tree resolution simulates the improved tableau procedure and that SL-resolution and the connection method are equivalent to restrictions of the improved tableau method. The theorem by Tseitin that the Davis-Putnam Procedure cannot be simulated by tree resolution is given an explicit and simplified proof. The hard examples for tree resolution are contradictions constructed from simple Tseitin graphs.

Prime implicants/implicates (PIs) have been shown to be a useful tool in several problem domains. In Model-Based Diagnosis (MBD), [de Kleer et al. 90] have used PIs to characterize diagnoses. We present a PI generation algorithm which, although based on the general SE-tree-based search framework, is effectively an improvement of a particular PI generation algorithm proposed by [Slagle et al. 70]. The improvement is achieved via a decomposition tactic which is boosted by the SE-tree-based framework. The new algorithm is also more flexible in a number of ways. We present empirical results comparing the new algorithm to the old one, as well as to current PI generation algorithms. 1 Introduction Prime implicates/implicants (PIs) were a topic of great interest to researchers in the early days of computer science, in part because of their use in procedures for boolean function minimization [Quine 52]. A number of algorithms were developed, including [Quine 52], [Karnaugh 53], [McCluskey 56]...