E 0.62 and EP 0.62

S. Schulz
Institut für Informatik, Technische Universität München, Germany
schulz@informatik.tu-muenchen.de

Architecture

E 0.62[Sch2001] is a purely equational theorem prover. The calculus used by E combines superposition (with selection of negative literals) and rewriting. No special rules for non-equational literals have been implemented, i.e. resolution is simulated via paramodulation and equality resolution. New additions to the calculus since E 0.6 include AC redundancy elimination and AC simplification for dynamically recognized associative and commutative equational theories, as well as simulated clause splitting (inspired by Vampire).

E is based on the DISCOUNT-loop variant of the given-clause algorithm, i.e. a strict separation of active and passive facts. Proof search in E is primarily controlled by a literal selection strategy, a clause evaluation heuristic, and a simplification ordering. The prover supports a large number of preprogrammed literal selection strategies, many of which are only experimental. Clause evaluation heuristics can be constructed on the fly by combining various parameterized primitive evaluation functions, or can be selected from a set of predefined heuristics. Supported term orderings are several parameterized instances of Knuth-Bendix-Ordering (KBO) and Lexicographic Path Ordering (LPO).

An automatic mode can select literal selection strategy, term ordering (different versions of KBO and LPO), and search heuristic based on simple problem characteristics.

EP 0.62 is just a combination of E 0.62 in full verbose mode and a proof generation tool. Proof object generation is handled by complex postprocessing of the full search protocol.

Implementation

E is implemented in ANSI C, using the GNU C compiler. The most unique feature of the implementation is the maximally shared term representation. This includes parallel rewriting for all instances of a particular subterm. A second important feature is the use of perfect discrimination trees with age and size constraints for rewriting and unit-subsumption.

The program has been successfully installed under SunOS 4.3.x, Solaris 2.x, HP-UX B 10.20, and various versions of Linux. Sources of the latest released version and a current snapshot are available freely from:

    http://wwwjessen.informatik.tu-muenchen.de/~schulz/WORK/eprover.html

EP 0.62 is a simple Bourne shell script calling E and the postprocessor in a pipeline.

Expected Competition Performance

In the last year, E won the MIX category of CASC and came in fourth in the UEQ division. We believe that E will again be among the strongest provers in the MIX category, in particular due to its good performance for Horn problems. We also hope to improve in the UEQ category, although we probably will not nearly reach the performance of Waldmeister.

EP 0.62 will be hampered by the fact that it has to reconstruct proofs in a post-processing step that typically usually uses at least the same amount of time as the proof search itself. This is particularly grave because E is able to find a relatively large number of proofs late in the proof search.

E's auto mode is optimized for performance on the TPTP 2.3.0. The optimization is based on a fairly large number of test runs and consists of the selection of one of about 50 different strategies for each problem.

References

Sch2001: Schulz S. (2001), System Abstract: E 0.61, Proceedings of the 1st IJCAR, (Sienna, Italy), Lecture Notes in Artificial Intelligence Springer-Verlag