Recent years have seen the emergence of a new generation of heavily-optimised modal decision procedures. Several systems based on such procedures are now available and have proved to be much more effective than the previous generation of modal decision procedures. As both computational complexity and algorithm complexity are generally unchanged, neither is useful in analysing and comparing these new systems and their various optimisations. Instead, empirical testing has been widely used, both for comparison and as a tool for tuning systems and identifying their strengths and weaknesses. However, the very effectiveness of the new systems has revealed serious weaknesses in existing empirical test suites and methodologies. This paper provides a detailed survey of empirical testing methodologies, analyses the current state of the art and presents new results obtained with a recently developed test method.

Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like l-calculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] with two remarkable features inherited from its object-oriented coding in C++: it is easily tunable for our needs, and it is efficient. We have made it even more reduced, removing any operand in the instruction set, even for the loop operations. We have only three registers which are AX (the accumulator), BX and CX. The operations Q b we have used for our experiment are in Table 1: LOOPTOP Decrements CX. If it is not equal to the first element jump to the program top.

. We present two learning inference control heuristics for equational deduction. Based on data about facts that contributed to previous proofs, evaluation functions learn to select equations that are likely to be of use in new situations. The first evaluation function works by symbolic retrieval of generalized patterns from a knowledge base, the second function compiles the knowledge into abstract term evaluation trees. We analyze the performance of the two heuristics on a set of examples and demonstrate their usefulness. We also show that these strategies are well suited for cooperation in the framework of the knowledge based distribution method teamwork. 1 Introduction The last years have seen a steady increase in the power of automatic theorem provers. There are a couple of reasons for this trend. The most significant ones are hardware improvements, refined inference engines, and stronger guiding heuristics. However, despite these advances, theorem provers still cannot ri...

One of the major problems in clausal theorem proving is the control of the proof search. In the presence of equality, this problem is particularly hard, since nearly all state-of-the-art systems perform the proof search by saturating a mostly unstructured set of clauses. We describe an approach that enables a superposition-based prover to pick good clauses for generating inferences based on experiences from previous successful proof searches for other problems. Information about good and bad search decisions (useful and superfluous clauses) is automatically collected from search protocols and represented in the form of annotated clause patterns. At run time, new clauses are compared with stored patterns and evaluated according to the associated information found. We describe our implementation of the system. Experimental results demonstrate that a learned heuristic significantly outperforms the conventional base strategy, especially in domains where enough training examples are available.

Many implementations of model elimination perform proof search by iteratively increasing a bound on the total size of the proof. We propose an optimized version of this search mode using a simple divide-and-conquer refinement. Optimized and unoptimized modes are compared, together with depth-bounded and best-first search, over the entire TPTP problem library. The optimized size-bounded mode seems to be the overall winner, but for each strategy there are problems on which it performs best. Some attempt is made to analyze why. We emphasize that our optimization, and other implementation techniques like caching, are rather general: they are not dependent on the details of model elimination, or even that the search is concerned with theorem proving. As such, we believe that this study is a useful complement to research on extending the model elimination calculus.

Abstract. St˚almarck’s algorithm is a patented technique for tautology-checking which has been used successfully for industrial-scale problems. Here we describe the algorithm and explore its implementation as a HOL derived rule. 1

. This is description of TPS, a theorem-proving system for classical type theory (Church's typed #-calculus). TPS has been designed to be a general research tool for manipulating wffs of first- and higher-order logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higher-order logic. AMS Subject Classification: 03-04, 68T15, 03B35, 03B15, 03B10. Key words: higher-order logic, type theory, mating, connection, expansion proof, natural deduction. 1. Introduction TPS is a theorem-proving system for classical type theory ## (Church's typed #-calculus [20]) which has been under development at Carnegie Mellon University for a number years. This paper gives a general...

We present a collection of simple but powerful techniques for enhancing the efficiency of tableau-based model generators such as Satchmo. The central ideas are to compile a clausal first order theory into a procedural Prolog program and to avoid redundant work of a naive implementation. We have compared various combinations of our techniques among each other and with theorem provers based on various calculi, using the TPTP Problem Library as a benchmark. Our implementation has turned out to be the most efficient for range-restricted problems and for a class of problems we call "non-nesting".

One of the key issues in Automated Theorem Proving is the search for optimal proof strategies. Since there is not one uniform strategy which works optimal on all proof tasks, one is faced with the difficult problem of selecting a good strategy for a given task. In this paper, we discuss a way of circumventing this strategy selection problem by using strategy parallelism. In this approach, a proof task is attempted in parallel by a set of uniform strategies while distributing the given amount of computing resources according to a certain schedule. We discuss important issues of strategy parallelism like search space partitioning, schedule computation, and scalability. In order to evaluate the potential of the method experimentally, we have implemented the strategy parallel theorem prover p-SETHEO, which is also described in the paper. The experimental results obtained with the system justify our approach. 1 Introduction Automated Theorem Proving (ATP) is the subfield of theoretical co...

this paper we first introduce the TEAMWORK method and the DISCOUNT