Entrants' System Descriptions


CARINE 0.72

Paul Haroun, Monty Newborn
McGill University Canada
pharoun@cs.mcgill.ca

Architecture

CARINE is a first-order classical logic ATP system intended for experimental purposes. It is based on ideas from THEO [
New01]. The inference rules implemented so far are binary resolution and binary factoring.

Implementation

CARINE is implemented in ANSI-C and currently runs under SunOS and Microsoft Windows. It has not yet been tested on Linux but it works in the Linux emulation layer: Cygwin. CARINE relies heavily on tables that are either 1) representations of graphs (i.e. dependency/adjacency matrices) or 2) lookup tables resulting from memoization and dynamic programming techniques. The graphs are relations that are formed from the information gathered from the base clauses. These relations are mainly groupings of the base clauses or their literals according to certain common characteristics. The tables are allocated dynamically based on the input and remain the same size throughout the search. A finite automaton, also implemented as a table, is used to store unit clauses.

The system will be available at:

    http://www.cs.mcgill.ca/~pharoun/atp_carine_site

Strategies

CARINE is based on a semi-linear resolution search. It performs the implemented inference rules in an iteratively deepening depth first search until a unit clause is obtained. The unit clause is then evaluated and if it passes the tests it is resolved with all the stored unit clauses and if none yields the empty clause then it is added to the unit clauses table. The main implemented strategies are delayed clause construction, time slicing, extended depth search and memoization.

Delayed clause construction is very useful when clauses contain many literals and/or many terms. Only an "interesting" clause is actually constructed. This strategy is the heart of the system.

Input parameters are used to control the search. Time slicing, if turned on, would calculate time slices based on the evaluation of the input clauses at the beginning of the search. Each time slice uses different parameters to control the search. Currently, only two time slices are applicable. In the first slice an aggressive search is performed and in the second time slice a more conservative search is performed.

Extended depth search is performed based on certain heuristics. Certain paths are explored deeper than the iteration depth when the heuristics apply.

Expected Competition Performance

CARINE is a system built mainly for experimental purposes. It is still in its elementary stage.

References

New01
Newborn M. (2001), Automated Theorem Proving: Theory and Practice, Springer.


CiME 2.01

Evelyne Contejean, Benjamin Monate
Université Paris-Sud, France
contejea@lri.fr monate@lix.polytechnique.fr

Architecture

CiME [
CM+00] is intended to be a toolkit, which contains nowadays the following features: The ordered completion of term rewriting systems will be used during the competion to attempt to solve unification problems, that is problems in the UEQ division [CM96].

Implementation

CiME2 is fully written in Objective CAML, a functional language of the ML family developed in the CRISTAL project at INRIA Rocquencourt. CiME2 is available at:
    http://cime.lri.fr/
as binaries for SPARC workstations running Solaris (at least version 2.6) and for pentium PCs running Linux, and its sources are available by read-only anynomous CVS.

Strategies

There are two distinct kinds of strategies to perform completion:

Expected Competition Performance

This will be the second participation of CiME2 in CASC, in the UEQ division.

References

CM+00
Contejean E., Marché C., Monate B., Urbain X. (2000), CiME version 2, http://cime.lri.fr.
CM96
Contejean E., Marché C. (1996), CiME: Completion Modulo E, Ganzinger H., Proceedings of the 7th International Conference on Rewriting Techniques and Applications (New Brunswick, USA), pp.416-419, Lecture Notes in Computer Science 1103, Springer-Verlag.

Acknowledgments: Claude Marché and Xavier Urbain contributed to the development of CiME 2.


DCTP 1.3 and 10.2p

Gernot Stenz
Max-Planck-Institut für Informatik, Germany
stenz@mpi-sb.mpg.de

Architecture

DCTP 1.3 [
Ste02a] is an automated theorem prover for first order clause logic. It is an implementation of the disconnection calculus described in [Bil96,LS01,Ste02b]. The disconnection calculus is a proof confluent and inherently cut-free tableau calculus with a weak connectedness condition. The inherently depth-first proof search is guided by a literal selection based on literal instantiatedness or literal complexity and a heavily parameterised link selection. The pruning mechanisms mostly rely on different forms of variant deletion and unit based strategies. Additionally the calculus has been augmented by full tableau pruning.

The new DCTP 1.3 has been enhanced with respect to clause preprocessing, selection functions and closure heuristics. Most prominent among the improvements is the introduction of a unification index for finding connections, which also replaces the connection graph hitherto used.

DCTP 10.2p is a strategy parallel version using the technology of E-SETHEO [SW99] to combine several different strategies based on DCTP 1.3.

Implementation

DCTP 1.3 has been implemented as a monolithic system in the Bigloo dialect of the Scheme language. The most important data structures are perfect discrimination trees, which are used in many variations. DCTP 10.2p has been derived of the Perl implementation of E-SETHEO and includes DCTP 1.3 as well as additional components written in Prolog and Shell tools. Both versions run under Solaris and Linux.

Strategies

DCTP 1.3 is a single strategy prover. Individual strategies are started by DCTP 10.2p using the schedule based resource allocation scheme known from the E-SETHEO system. Of course, different schedules have been precomputed for the syntactic problem classes. The problem classes are more or less identical with the sub-classes of the competition organisers. We have no idea whether or not this conflicts with the organisers' tuning restrictions.

Expected Competition Performance

We expect both DCTP 1.3 and DCTP 10.2p to perform reasonably well, in particular in the EPR (in any case) and SAT (depending on the selection of problems for the competition) categories.

References

Bil96
Billon J-P. (1996), The Disconnection Method: A Confluent Integration of Unification in the Analytic Framework, Miglioli P., Moscato U., Mundici D., Ornaghi M., Proceedings of TABLEAUX'96: the 5th Workshop on Theorem Proving with Analytic Tableaux and Related Methods (Palermo, Italy), pp.110-126, Lecture Notes in Artificial Intelligence 1071, Springer-Verlag.
LS01
Letz R., Stenz G. (2001), Model Elimination and Connection Tableau Procedures, Robinson A., Voronkov A., Handbook of Automated Reasoning, pp.2015-2114, Elsevier Science.
SW99
Stenz G., Wolf A. (1999), E-SETHEO: Design, Configuration and Use of a Parallel Automated Theorem Prover, Foo N., Proceedings of AI'99: The 12th Australian Joint Conference on Artificial Intelligence (Sydney, Australia), pp.231-243, Lecture Notes in Artificial Intelligence 1747, Springer-Verlag.
Ste02a
Stenz G. (2002), DCTP 1.2 - System Abstract, Fermüller C., Egly U., Proceedings of TABLEAUX 2002: Automated Reasoning with Analytic Tableaux and Related Methods (Copenhagen, Denmark), pp.335-340, Lecture Notes in Artificial Intelligence 2381, Springer-Verlag.
Ste02b
Stenz G. (2002), The Disconnection Calculus, PhD thesis, Institut für Informatik, Technische Universität München, Munich, Germany.


E 0.8 and EP 0.8

Stephan Schulz
Technische Universität München, Germany, and RISC-Linz, Johannes Kepler Universität, Austria
schulz@informatik.tu-muenchen.de

Architecture

E 0.8 [
Sch01,Sch02] 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. E also implements AC redundancy elimination and AC simplification for dynamically recognized associative and commutative equational theories, as well as pseudo-splitting for clauses. It now also unfolds equational definitions in a preprocessing stage.

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 0.8 is just a combination of E 0.8 in verbose mode and a proof analysis tool extracting the used inference steps.

Implementation

E is implemented in ANSI C, using the GNU C compiler. The most outstanding feature is the global sharing of rewrite steps. Contrary to earlier version of E, which destructively changed all shared instances of a term, the latest version only adds a rewrite link from the rewritten to the new term. In effect, E is caching rewrite operations as long as sufficient memory is available. 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, MacOS-X, and various versions of Linux. Sources of the latest released version and a current snapshot are available freely from:

    http://www4.informatik.tu-muenchen.de/~schulz/WORK/eprover.html 
EP 0.8 is a simple Bourne shell script calling E and the postprocessor in a pipeline.

Strategies

E's automatic mode is optimized for performance on TPTP 2.5.1. 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. All test runs have been performed on SUN Ultra 60/300 machines with a time limit of 120 seconds (or roughly equivalent configurations). All individual strategies are general purpose, the worst one solves about 45% of TPTP 2.5.1, the best one 55%.

E distinguishes problem classes based on a number of features, all of which have between two and four possible values. These are:

Wherever there is a selection of few, some, and many of a certain entity, the limits are selected automatically with the aim of splitting the set of clauses into three sets of approximately equal size based on this one feature.

For each non-empty class, we assign the most general candidate heuristic that solves the same number of problems on this class as the best heuristic on this class does. Empty classes are assigned the globally best heuristic. Typically, most selected heuristics are assigned to more than one class.

Expected Competition Performance

In the last year, E performed well in the MIX category of CASC and came in third 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. In UEQ, E will probably be beaten only by Waldmeister, and, possibly E-SETHEO (which incorporates E).

EP 0.8 will be hampered by the fact that it has to analyse the inference step listing, an operation that typically is about as expensive as the proof search itself. Nevertheless, it should be competitive among the MIX* systems.

References

Sch01
Schulz S. (2001), System Abstract: E 0.61, Gore R., Leitsch A., Nipkow T., Proceedings of the International Joint Conference on Automated Reasoning (Siena, Italy), pp.370-375, Lecture Notes in Artificial Intelligence 2083, Springer-Verlag.
Sch02
Schulz S. (2002), E: A Brainiac Theorem Prover, AI Communications 15(2-3), pp.111-126.


E-SETHEO csp02

Reinhold Letz, Stephan Schulz, Gernot Stenz
Technische Universität München, Germany
{letz,schulz,stenz}@informatik.tu-muenchen.de

Architecture

E-SETHEO is a compositional theorem prover for formulae in first order clause logic, combining the systems E [
Sch01], DCTP [Ste02] and SETHEO [MI+97]. It incorporates different calculi and proof procedures like superposition, model elimination and semantic trees (the DPLL procedure). Furthermore, the system contains transformation techniques which may split the formula into independent subparts or which may perform a ground instantiation. Finally, advanced methods for controlling and optimizing the combination of the subsystems are applied. The first-order variant of E-SETHEO no longer uses Flotter [WGR96] as a preprocessing module for transforming non-clausal formulae to clausal form. Instead, a more primitive normal form transformation is employed.

Since version 99csp of E-SETHEO, the different strategies are run sequentially, one after the other. E-SETHEO csp02 incorporates the new version of the disconnection prover DCTP with integrated equality handling as a new strategy as well as a new version of the E prover. The new Scheme version of SETHEO that is in use features local unit failure caching [LS01] and lazy root paramodulation, an optimisation of lazy paramodulation which is complete in the Horn case [LS02].

Implementation

According to the diversity of the contained systems, the modules of E-SETHEO are implemented in different programming languages like C, Prolog, Scheme, and Shell tools.

The program runs under Solaris and, with a little luck, under Linux, too. Sources are available from the authors.

Strategies

Individual strategies are started by E-SETHEO depending on the allocation of resources to the different strategies, so-called schedules, which have been computed from experimental data using machine learning techniques as described in [SW99]. Schedule selection depends on syntactic characteristics of the input formula such as the Horn-ness of formulae, whether a problem contains equality literals or whether the formula is in the Bernays-Schönfinkel class. The problem classes are more or less identical with the sub-classes of the competition. We have no idea whether or not this conflicts with the organisers' tuning restrictions.

Expected Competition Performance

E-SETHEO csp02 was the CASC-18 EPR division winner.

References

LS01
Letz R., Stenz G. (2001), Model Elimination and Connection Tableau Procedures, Robinson A., Voronkov A., Handbook of Automated Reasoning, pp.2015-2114, Elsevier Science.
LS02
Letz R., Stenz G. (2002), Integration of Equality Reasoning into the Disconnection Calculus, Fermüller C., Egly U., Proceedings of TABLEAUX 2002: Automated Reasoning with Analytic Tableaux and Related Methods (Copenhagen, Denmark), pp.176-190, Lecture Notes in Artificial Intelligence 2381, Springer-Verlag.
MI+97
Moser M., Ibens O., Letz R., Steinbach J., Goller C., Schumann J., Mayr K. (1997), SETHEO and E-SETHEO: The CADE-13 Systems, Journal of Automated Reasoning 18(2), pp.237-246.
Sch01
Schulz S. (2001), System Abstract: E 0.61, Gore R., Leitsch A., Nipkow T., Proceedings of the International Joint Conference on Automated Reasoning (Siena, Italy), pp.370-375, Lecture Notes in Artificial Intelligence 2083, Springer-Verlag.
SW99
Stenz G., Wolf A. (1999), E-SETHEO: Design, Configuration and Use of a Parallel Automated Theorem Prover, Foo N., Proceedings of AI'99: The 12th Australian Joint Conference on Artificial Intelligence (Sydney, Australia), pp.231-243, Lecture Notes in Artificial Intelligence 1747, Springer-Verlag.
Ste02
Stenz G. (2002), DCTP 1.2 - System Abstract, Fermüller C., Egly U., Proceedings of TABLEAUX 2002: Automated Reasoning with Analytic Tableaux and Related Methods (Copenhagen, Denmark), pp.335-340, Lecture Notes in Artificial Intelligence 2381, Springer-Verlag.
WGR96
Weidenbach C., Gaede B., Rock G. (1996), SPASS and FLOTTER, McRobbie M., Slaney J.K., Proceedings of the 13th International Conference on Automated Deduction (New Brunswick, USA), pp.141-145, Lecture Notes in Artificial Intelligence 1104, Springer-Verlag.


E-SETHEO csp03

Reinhold Letz, Stephan Schulz, Gernot Stenz
Technische Universität München, Germany, Max-Planck-Institut für Informatik, Germany, and RISC-Linz, Johannes Kepler Universität, Austria
{letz,schulz,stenz}@informatik.tu-muenchen.de

Architecture

E-SETHEO is a compositional theorem prover for formulae in first order clause logic, combining the systems E [
Sch01], DCTP [Ste02] and SETHEO [MI+97]. It incorporates different calculi and proof procedures like superposition, model elimination and semantic trees (the DPLL procedure). Furthermore, the system contains transformation techniques which may split the formula into independent subparts or which may perform a ground instantiation. Finally, advanced methods for controlling and optimizing the combination of the subsystems are applied. The first-order variant of E-SETHEO no longer uses Flotter [WGR96] as a preprocessing module for transforming non-clausal formulae to clausal form. Instead, a more primitive normal form transformation is employed.

Since version 99csp of E-SETHEO, the different strategies are run sequentially, one after the other. E-SETHEO csp03 incorporates the new version of the disconnection prover DCTP with new preprocessing and heuristics as a new strategy, as well as a new version of the E prover. The new Scheme version of SETHEO that is in use features local unit failure caching [LS01] and lazy root paramodulation, an optimisation of lazy paramodulation which is complete in the Horn case [LS02]. Other than that (and a new resource distribution scheme), E-SETHEO csp03 is identical to E-SETHEO csp02.

Implementation

According to the diversity of the contained systems, the modules of E-SETHEO are implemented in different programming languages like C, Prolog, Scheme, and Shell tools.

The program runs under Solaris and Linux. Sources are available from the authors.

Strategies

Individual strategies are started by E-SETHEO depending on the allocation of resources to the different strategies, so-called schedules, which have been computed from experimental data using machine learning techniques as described in [SW99]. Schedule selection depends on syntactic characteristics of the input formula such as the Horn-ness of formulae, whether a problem contains equality literals, or whether the formula is in the Bernays-Schönfinkel class. The problem classes are more or less identical with the sub-classes of the competition. We have no idea whether or not this conflicts with the organisers' tuning restrictions.

Expected Competition Performance

We expect E-SETHEO to perform well in all categories it participates in.

References

LS01
Letz R., Stenz G. (2001), Model Elimination and Connection Tableau Procedures, Robinson A., Voronkov A., Handbook of Automated Reasoning, pp.2015-2114, Elsevier Science.
LS02
Letz R., Stenz G. (2002), Integration of Equality Reasoning into the Disconnection Calculus, Fermüller C., Egly U., Proceedings of TABLEAUX 2002: Automated Reasoning with Analytic Tableaux and Related Methods (Copenhagen, Denmark), pp.176-190, Lecture Notes in Artificial Intelligence 2381, Springer-Verlag.
MI+97
Moser M., Ibens O., Letz R., Steinbach J., Goller C., Schumann J., Mayr K. (1997), SETHEO and E-SETHEO: The CADE-13 Systems, Journal of Automated Reasoning 18(2), pp.237-246.
Sch01
Schulz S. (2001), System Abstract: E 0.61, Gore R., Leitsch A., Nipkow T., Proceedings of the International Joint Conference on Automated Reasoning (Siena, Italy), pp.370-375, Lecture Notes in Artificial Intelligence 2083, Springer-Verlag.
SW99
Stenz G., Wolf A. (1999), E-SETHEO: Design, Configuration and Use of a Parallel Automated Theorem Prover, Foo N., Proceedings of AI'99: The 12th Australian Joint Conference on Artificial Intelligence (Sydney, Australia), pp.231-243, Lecture Notes in Artificial Intelligence 1747, Springer-Verlag.
Ste02
Stenz G. (2002), DCTP 1.2 - System Abstract, Fermüller C., Egly U., Proceedings of TABLEAUX 2002: Automated Reasoning with Analytic Tableaux and Related Methods (Copenhagen, Denmark), pp.335-340, Lecture Notes in Artificial Intelligence 2381, Springer-Verlag.
WGR96
Weidenbach C., Gaede B., Rock G. (1996), SPASS and FLOTTER, McRobbie M., Slaney J.K., Proceedings of the 13th International Conference on Automated Deduction (New Brunswick, USA), pp.141-145, Lecture Notes in Artificial Intelligence 1104, Springer-Verlag.


Gandalf c-2.5

Tanel Tammet
Tallinn Technical University, Estonia
Safelogic AB, Sweden
tammet@cc.ttu.ee

Architecture

Gandalf [
Tam97,Tam98] is a family of automated theorem provers, including classical, type theory, intuitionistic and linear logic provers, plus finite a model builder. The version c-2.5 contains the classical logic prover for clause form input and the finite model builder. One distinguishing feature of Gandalf is that it contains a large number of different search strategies and is capable of automatically selecting suitable strategies and experimenting with these strategies.

Gandalf is available under GPL. There exists a separate commercial version of Gandalf, called G, developed and distributed by Safelogic AB (www.safelogic.se), which contains numerous additions, strategies, and optimisations, aimed specifically at verification of large systems.

The finite model building component of Gandalf uses the Zchaff propositional logic solver by L.Zhang [MM+01] as an external program called by Gandalf. Zchaff is not free, although it can be used freely for research purposes. Gandalf is not optimised for Zchaff or linked together with it: Zchaff can be freely replaced by other satisfiability checkers.

Implementation

Gandalf is implemented in Scheme and compiled to C using the Hobbit Scheme-to-C compiler. Version scm5d6 of the Scheme interpreter scm by A.Jaffer is used as the underlying Scheme system.

Gandalf has been tested on Linux, Solaris and MS Windows under Cygwin.

The propositional satisifiability checker Zchaff used by Gandalf during finite model building is implemented by L.Zhang in C++.

Gandalf should be publicly available at:

    http://www.ttu.ee/it/gandalf

Strategies

One of the basic ideas used in Gandalf is time-slicing: Gandalf typically runs a number of searches with different strategies one after another, until either the proof is found or time runs out. Also, during each specific run Gandalf typically modifies its strategy as the time limit for this run starts coming closer. Selected clauses from unsuccessful runs are sometimes used in later runs.

In the normal mode Gandalf attempts to find only unsatisfiability. It has to be called with a -sat flag to find satisfiability. Gandalf selects the strategy list according to the following criteria:

Expected Competition Performance

Gandalf c-2.5-SAT was the CASC-18 SAT division winner.

References

MM+01
Moskewicz M., Madigan C., Zhao Y., Zhang L., Malik S. (2001), Chaff: Engineering an Efficient SAT Solver, Blaauw D., Lavagno L., Proceedings of the 39th Design Automation Conference (Las Vegas, USA), pp.530-535.
Tam97
Tammet T. (1997), Gandalf, Journal of Automated Reasoning 18(2), pp.199-204.
Tam98
Tammet T. (1998), Towards Efficient Subsumption, Kirchner C., Kirchner H., Proceedings of the 15th International Conference on Automated Deduction (Lindau, Germany), pp.427-440, Lecture Notes in Artificial Intelligence 1421, Springer-Verlag.

Gandalf c-2.6

Tanel Tammet
Tallinn Technical University, Estonia
tammet@cc.ttu.ee

Architecture

Gandalf [
Tam97,Tam98] is a family of automated theorem provers, including classical, type theory, intuitionistic and linear logic provers, plus finite a model builder. The version c-2.6 contains the classical logic prover for clause form input and the finite model builder. One distinguishing feature of Gandalf is that it contains a large number of different search strategies and is capable of automatically selecting suitable strategies and experimenting with these strategies.

The finite model building component of Gandalf uses the Zchaff propositional logic solver by L.Zhang [MM+01] as an external program called by Gandalf. Zchaff is not free, although it can be used freely for research purposes. Gandalf is not optimised for Zchaff or linked together with it: Zchaff can be freely replaced by other satisfiability checkers.

Implementation

Gandalf is implemented in Scheme and compiled to C using the Hobbit Scheme-to-C compiler. Version scm5d6 of the Scheme interpreter scm by A.Jaffer is used as the underlying Scheme system. Zchaff is implemented in C++.

Gandalf has been tested on Linux, Solaris, and MS Windows under Cygwin.

Gandalf is available under GPL from:

    http://www.ttu.ee/it/gandalf

Strategies

One of the basic ideas used in Gandalf is time-slicing: Gandalf typically runs a number of searches with different strategies one after another, until either the proof is found or time runs out. Also, during each specific run Gandalf typically modifies its strategy as the time limit for this run starts coming closer. Selected clauses from unsuccessful runs are sometimes used in later runs.

In the normal mode Gandalf attempts to find only unsatisfiability. It has to be called with a -sat flag to find satisfiability. Gandalf selects the strategy list according to the following criteria:

Expected Competition Performance

We expect Gandalf to be among the best provers in most of the main categories it competes in.

References

MM+01
Moskewicz M., Madigan C., Zhao Y., Zhang L., Malik S. (2001), Chaff: Engineering an Efficient SAT Solver, Blaauw D., Lavagno L., Proceedings of the 39th Design Automation Conference (Las Vegas, USA), pp.530-535.
Tam97
Tammet T. (1997), Gandalf, Journal of Automated Reasoning 18(2), pp.199-204.
Tam98
Tammet T. (1998), Towards Efficient Subsumption, Kirchner C., Kirchner H., Proceedings of the 15th International Conference on Automated Deduction (Lindau, Germany), pp.427-440, Lecture Notes in Artificial Intelligence 1421, Springer-Verlag.

MUSCADET 2.4

D. Pastre
Université René Descartes (Paris 5), France
pastre@math-info.univ-paris5.fr

Architecture

The MUSCADET theorem prover is a knowledge-based system. It is based on Natural Deduction, following the terminology of [
Ble71] and [Pas78], and uses methods that resemble those used by humans. It is composed of an inference engine, which interprets and executes rules, and of one or several bases of facts, which are the internal representation of "theorems to be proved". Rules are either universal and put into the system, or built by the system itself by metarules from data (definitions and lemmas). Rules may add new hypotheses, modify the conclusion, create objects, split theorems into two or more subtheorems, or build new rules which are local for a (sub-)theorem.

Implementation

MUSCADET 2 [Pas02b] is implemented in SWI-Prolog. Rules are written as declarative Prolog clauses. Metarules are written as sets of Prolog clauses, more or less declarative. The inference engine includes the Prolog interpreter and some procedural Prolog clauses. MUSCADET 2.4 is available from:
      http://www.math-info.univ-paris5.fr/~pastre/muscadet/muscadet.html 

Strategies

There are specific strategies for existential, universal, conjunctive or disjunctive hypotheses, and conclusions. Functional symbols may be used, but an automatic creation of intermediate objects allows deep subformulae to be flattened and treated as if the concepts were defined by predicate symbols. The successive steps of a proof may be forward deduction (deduce new hypotheses from old ones), backward deduction (replace the conclusion by a new one) or refutation (only if the conclusion is a negation).

The system is also able to work with second order statements. It may also receive knowledge and know-how for a specific domain from a human user; see [Pas89] and [Pas93]. These two possibilities are not used while working with the TPTP Library.

Expected Competition Performance

The best performances of MUSCADET will be for problems manipulating many concepts in which all statements (conjectures, definitions, axioms) are expressed in a manner similar to the practice of humans, especially of mathematicians. It will have poor performances for problems using few concepts but large and deep formulas leading to many splittings.

References

Ble71
Bledsoe W.W. (1971), Splitting and Reduction Heuristics in Automatic Theorem Proving, Artificial Intelligence 2, pp.55-77.
Pas78
Pastre D. (1978), Automatic Theorem Proving in Set Theory, Artificial Intelligence 10, pp.1-27.
Pas89
Pastre D. (1989), MUSCADET : An Automatic Theorem Proving System using Knowledge and Metaknowledge in Mathematics, Artificial Intelligence 38, pp.257-318.
Pas93
Pastre D. (1993), Automated Theorem Proving in Mathematics, Annals of Mathematics and Artificial Intelligence 8, pp.425-447.
Pas01a
Pastre D. (2001), Muscadet2.3 : A Knowledge-based Theorem Prover based on Natural Deduction, Gore R., Leitsch A., Nipkow T., Proceedings of the International Joint Conference on Automated Reasoning (Siena, Italy), pp.685-689, Lecture Notes in Artificial Intelligence 2083, Springer-Verlag.
Pas01b
Pastre D. (2001), Implementation of Knowledge Bases for Natural Deduction, Nieuwenhuis R., Voronkov A., Proceedings of the 8th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (Havana, Cuba), pp.29-68, Lecture Notes in Artificial Intelligence 2250, Springer-Verlag.
Pas02a
Pastre D. (2002), Strong and Weak Points of the MUSCADET Theorem Prover, AI Communications 15(2-3), pp.147-160.
Pas02b
Pastre D. (2002), MUSCADET version 2.4 : User's Manual, http://www.math-info.univ-paris5.fr/~pastre/muscadet/manual-en.ps.


Octopus N

Monty Newborn, Zongyan Wang
McGill University, Canada
newborn@cs.mcgill.ca

Architecture

Octopus is a parallel ATP system. It is an improved version of the single-processor ATP system Theo [
New01]. Inference rules used by Octopus include binary resolution, binary factoring, instantiation, demodulation, and hash table resolutions. Octopus performs 3000-10000 inferences/second on each processor.

Implementation

Octopus is implemented in C and currently runs under Linux. It runs on a network of 20-40 PCs housed in a laboratory at McGill University's School of Computer Science. The processors communicate using PVM [GB+94].

Strategies

Octopus begins by determining a number of weakened versions of the given theorem, and then assigns one such version to each computer. Each computer then attempts to prove the weakened version of the theorem assigned to it. If successful, the computer then uses the proof found to weakened theorem to help prove the given theorem. In essence, Octopus combines learning and parallel theorem proving.

In the current version of Octopus, a weakened version of a theorem consists of the same clauses of the given theorem except for one. In that one clause, a constant is replaced by a variable that doesn't appear elsewhere in the clause. If a proof exists to the given theorem, a proof exists to the weakened version, and often, though far from always, the proof of the weakened version is easier to find.

When a proof is found to a weakened version, certain clauses in the proof are added to the base clauses of the given theorem. Octopus then tries to prove the given theorem with the augmented set of base clauses.

Each processor in the system also uses different values for the maximum number of literals and terms in inferences generated when looking for a proof. Thus while two computers may try to solve the same weakened version of the given theorem, they do it with different values for the maximum number of literals and terms in derived inferences.

Expected Competition Performance

Octopus should do somewhat better than its predecessors that competed in the competition in the late 1990s, though it is not likely to finish among the top perfomers.

References

New01
Newborn M. (2001), Automated Theorem Proving: Theory and Practice, Springer.
GB+94
Geist A., Beguelin A., Dongarra J., Jiang W., Manchek R., and Sunderam V. (1994), PVM: Parallel Virtual Machine: A Users Guide and Tutorial for Network Parallel Computing, MIT Press.

Otter 3.2

William McCune
Argonne National Laboratory, USA
mccune@mcs.anl.gov

Architecture

Otter 3.2 [
McC94] is an ATP system for statements in first-order (unsorted) logic with equality. Otter is based on resolution and paramodulation applied to clauses. An Otter search uses the "given clause algorithm", and typically involves a large database of clauses; subsumption and demodulation play an important role.

Implementation

Otter is written in C. Otter uses shared data structures for clauses and terms, and it uses indexing for resolution, paramodulation, forward and backward subsumption, forward and backward demodulation, and unit conflict. Otter is available from:
    http://www-unix.mcs.anl.gov/AR/otter/ 

Strategies

Otter's original automatic mode, which reflects no tuning to the TPTP problems, will be used.

Expected Competition Performance

Otter has been entered into CASC-19 as a stable benchmark against which progress can be judged (there have been only minor changes to Otter since 1996 [MW97], nothing that really affects its performace in CASC). This is not an ordinary entry, and we do not hope for Otter to do well in the competition.

References

McC94
McCune W.W. (1994), Otter 3.0 Reference Manual and Guide, ANL-94/6, Argonne National Laboratory, Argonne, USA.
MW97
McCune W.W., Wos L. (1997), Otter: The CADE-13 Competition Incarnations, Journal of Automated Reasoning 18(2), pp.211-220.

Acknowledgments: Ross Overbeek, Larry Wos, Bob Veroff, and Rusty Lusk contributed to the development of Otter.


Paradox 1.0

Koen Claessen, Niklas Sörensson
Chalmers University of Technology and Gothenburg University, Sweden
{koen,nik}@cs.chalmers.se

Architecture

Paradox 1.0 [
CS03] is a finite-domain model generator. It is based on a MACE-style [McC94] flattening and instantiating of the FO clauses into propositional clauses, and then the use of a SAT solver to solve the resulting problem.

Paradox incorporates the following novel features: New polynomial-time clause splitting heuristics, the use of incremental SAT, static symmetry reduction techniques, and the use of sort inference.

Implementation

The main part of Paradox is implemented in Haskell using the GHC compiler. Paradox also has a built-in incremental SAT solver which is written in C++. The two parts are linked together on the object level using Haskell's Foreign Function Interface. Paradox uses the following non-standard Haskell extensions: local universal type quantification and hash-consing.

Strategies

There is only one strategy in Paradox:
  1. Analyze the problem, finding an upper bound N on the domain size of models, where N is possibly infinite. A finite such upper bound can for example be found for EPR problems.
  2. Flatten the problem, and split clauses and simplify as much as possible.
  3. Instantiate the problem for domain sizes 1 up to N, applying the SAT solver incrementally for each size. Report "SATISFIABLE" when a model is found.
  4. When no model of sizes smaller or equal to N is found, report "CONTRADICTION".
In this way, Paradox can be used both as a model finder and as an EPR solver.

Expected Competition Performance

Paradox will enter the CASC competition in two categories: SAT and EPR. Paradox beats last year's winner (2002) in the SAT category, and has also solved a number of "unknown" problems from TPTP within a short time limit. So it should have some chance of winning this year's SAT competition. Paradox is not optimized at all for the EPR category, but should perform reasonably well.

References

CS03
Claessen K., Sorensson N. (2003), New Techniques that Improve MACE-style Finite Model Finding, Baumgartner P., Fermueller C., Proceedings of the CADE-19 Workshop: Model Computation - Principles, Algorithms, Applications (Miami, USA).
McC94
McCune W.W. (1994), A Davis-Putnam Program and its Application to Finite First-Order Model Search: Quasigroup Existence Problems, ANL/MCS-TM-194, Argonne National Laboratory, Argonne, USA.


THEO J2003

Monty Newborn
McGill University, Canada
newborn@cs.mcgill.ca

Architecture

THEO [
New01] is a resolution-refutation theorem prover for first order clause logic. It uses binary resolution, binary factoring, instantiation, demodulation, and hash table resolutions.

Implementation

Theo is written in C and runs under both LINUX and FREEBSD. It contains about 35000 lines of source code. Originally it was called The Great Theorem Prover.

Strategies

THEO uses a large hash table (16 megaentries) to store clauses. This permits complex proofs to be found, some as long as 500 inferences. It uses what might be called a brute-force iteratively deepening depth-first search for a contradiction while storing information about clauses - unit clauses in particular - in its hash table.

Expected Competition Performance

THEO should perform slightly better than it has in the past.

References

New01
Newborn M. (2001), Automated Theorem Proving: Theory and Practice, Springer.


Vampire 5.0

Alexandre Riazanov, Andrei Voronkov
University of Manchester, England
{riazanoa,voronkov}@cs.man.ac.uk

Architecture

Vampire [
RV01, RV02] 5.0 is an automatic theorem prover for first-order classical logic. Its kernel implements the calculi of ordered binary resolution and superposition for handling equality. The splitting rule is simulated by introducing new predicate symbols. A number of standard redundancy criteria and simplification techniques are used for pruning the search space: subsumption, tautology deletion, subsumption resolution and rewriting by ordered unit equalities. The only term ordering used in Vampire at the moment is a special non-recursive version of the Knuth-Bendix ordering that allows efficient approximation algorithms for solving ordering constraints. By the system installation deadline we may implement the standard Knuth-Bendix ordering. A number of efficient indexing techniques are used to implement all major operations on sets of terms and clauses. Although the kernel of the system works only with clausal normal forms, the preprocessor component accepts a problem in the full first-order logic syntax, clausifies it and performs a number of useful transformations before passing the result to the kernel.

Implementation

Vampire 5.0 is implemented in C++. The main supported compiler version is gcc 2.95.3, although in the nearest future we are going to move to gcc 3.x. The system has been successfully compiled for Linux and Solaris. It is available from:
    http://www.cs.man.ac.uk/~riazanoa/Vampire/

Strategies

The Vampire kernel provides a fairly large number of features for strategy selection. The most important ones are: The standalone executables for Vampire 5.0 and Vampire 5.0-CASC use very simple time slicing to make sure that several kernel strategies are tried on a given problem.

The automatic mode of Vampire 5.0 is primitive. Seven problem classes are distinguished corresponding to the competition divisions HNE, HEQ, NNE, NEQ, PEQ, UEQ and EPR. Every class is assigned a fixed schedule consisting of a number of kernel strategies called one by one with different time limits.

Expected Competition Performance

Vampire 5.0 is the CASC-18 MIX and FOF divisions winner.

References

RV01
Riazanov A., Voronkov A. (2001), Vampire 1.1 (System Description), Gore R., Leitsch A., Nipkow T., Proceedings of the International Joint Conference on Automated Reasoning (Siena, Italy), pp.376-380, Lecture Notes in Artificial Intelligence 2083, Springer-Verlag.
RV02
Riazanov A., Voronkov A. (2002), The Design and Implementation of Vampire, AI Communications, To appear.

Vampire 6.0

Alexandre Riazanov, Andrei Voronkov
University of Manchester, England
{riazanoa,voronkov}@cs.man.ac.uk

Architecture

Vampire [
RV02] 6.0 is an automatic theorem prover for first-order classical logic. Its kernel implements the calculi of ordered binary resolution, superposition for handling equality and ordered chaining for transitive predicates. The splitting rule is simulated by introducing new predicate symbols. A number of standard redundancy criteria and simplification techniques are used for pruning the search space: subsumption, tautology deletion, subsumption resolution and rewriting by ordered unit equalities. The reduction orderings used are the standard Knuth-Bendix ordering and a special non-recursive version of the Knuth-Bendix ordering that allows efficient approximation algorithms for solving ordering constraints. A number of efficient indexing techniques are used to implement all major operations on sets of terms and clauses. Although the kernel of the system works only with clausal normal forms, the preprocessor component accepts a problem in the full first-order logic syntax, clausifies it and performs a number of useful transformations before passing the result to the kernel.

Implementation

Vampire 6.0 is implemented in C++. The supported compilers are gcc 2.95.3, 3.x and Microsoft Visual C++. The system has been successfully compiled for Linux, Solaris and Win32. It is available (conditions apply) from:
    http://www.cs.man.ac.uk/~riazanoa/Vampire/

Strategies

The Vampire kernel provides a fairly large number of features for strategy selection. The most important ones are: The standalone executable for Vampire 6.0 uses very simple time slicing to make sure that several kernel strategies are tried on a given problem.

The automatic mode of Vampire 6.0 is primitive. Seven problem classes are distinguished corresponding to the competition divisions HNE, HEQ, NNE, NEQ, PEQ, UEQ and EPR. Every class is assigned a fixed schedule consisting of a number of kernel strategies called one by one with different time limits.

Expected Competition Performance

We have made many, mostly cosmetic, changes since version 5.0, but they are unlikely to affect the performance drastically. We hope that Vampire 6.0 will perform at least as well as Vampire 5.0.

References

RV02
Riazanov A., Voronkov A. (2002), The Design and Implementation of Vampire, AI Communications 15(2-3), pp.91-110.

Waldmeister 702

Thomas Hillenbrand1, Bernd Löchner2
1Max-Planck-Institut für Informatik Saarbrücken, Germany, 2Universität Kaiserslautern, Germany
waldmeister@informatik.uni-kl.de

Architecture

Waldmeister 702 is an implementation of unfailing Knuth-Bendix completion [
BDP89] with extensions towards ordered completion (see [AHL00]) and basicness [BG+92, NR92]. The system saturates the input axiomatization, distinguishing active facts, which induce a rewrite relation, and passive facts, which are the one-step conclusions of the active ones up to redundancy. The saturation process is parameterized by a reduction ordering and a heuristic assessment of passive facts.

Only recently, we have designed a thorough refinement of the system architecture concerning the representation of passive facts [HL02]. The aim of that work - the next Waldmeister loop - is, besides gaining more structural clarity, to cut down memory consumption especially for long-lasting proof attempts, and hence less relevant in the CASC setting.

Implementation

The system is implemented in ANSI-C and runs under Solaris and Linux. The central data strucures are: perfect discrimination trees for the active facts; element-wise compressions for the passive ones; and sets of rewrite successors for the conjectures. Waldmeister can be found on the Web at
    http://www-avenhaus.informatik.uni-kl.de/waldmeister

Strategies

Our approach to control the proof search is to choose the search parameters according to the algebraic structure given in the problem specification [HJL99]. This is based on the observation that proof tasks sharing major parts of their axiomatization often behave similar. Hence, for a number of domains, the influence of different reduction orderings and heuristic assessments has been analyzed experimentally; and in most cases it has been possible to distinguish a strategy uniformly superior on the whole domain. In essence, every such strategy consists of an instantiation of the first parameter to a Knuth-Bendix ordering or to a lexicographic path ordering, and an instantiation of the second parameter to one of the weighting functions addweight, gtweight, or mixweight, which, if called on an equation s = t, return |s| + |t|, |max>(s,t)|, or |max>(s,t)| · (|s| + |t| + 1) + |s| + |t|, respectively, where |s| denotes the number of symbols in s.

Expected Competition Performance

Waldmeister 702 is the CASC-18 UEQ division winner.

References

AHL00
Avenhaus J., Hillenbrand T., Löchner B. (2000), On Using Ground Joinable Equations in Equational Theorem Proving, Baumgartner P., Zhang H., Proceedings of the 3rd International Workshop on First Order Theorem Proving (St Andrews, Scotland), pp.33-43.
BDP89
Bachmair L., Dershowitz N., Plaisted D.A. (1989), Completion Without Failure, Ait-Kaci H., Nivat M., Resolution of Equations in Algebraic Structures, pp.1-30, Academic Press.
BG+92
Bachmair L., Ganzinger H., Lynch C., Snyder W. (1992), Basic Paramodulation and Superposition, Kapur D., Proceedings of the 11th International Conference on Automated Deduction (Saratoga Springs, USA), pp.462-476, Lecture Notes in Artificial Intelligence 607, Springer-Verlag.
HJL99
Hillenbrand T., Jaeger A., Löchner B. (1999), Waldmeister - Improvements in Performance and Ease of Use, Ganzinger H., Proceedings of the 16th International Conference on Automated Deduction (Trento, Italy), pp.232-236, Lecture Notes in Artificial Intelligence 1632, Springer-Verlag.
HL02
Hillenbrand T., Löchner B. (2002), The Next Waldmeister Loop, Voronkov A., Proceedings of the 18th International Conference on Automated Deduction (Copenhagen, Denmark), pp.486-500, Lecture Notes in Artificial Intelligence 2392, Springer-Verlag.
NR92
Nieuwenhuis R., Rivero J.M. (1992), Basic Superposition is Complete, Krieg-Brückner B., Proceedings of the 4th European Symposium on Programming (Rennes, France), pp.371-390, Lecture Notes in Computer Science 582, Springer-Verlag.

Waldmeister 703

Jean-Marie Gaillourdet1, Thomas Hillenbrand2, Bernd Löchner1
1Universität Kaiserslautern, Germany, 2Max-Planck-Institut für Informatik Saarbrücken, Germany
waldmeister@informatik.uni-kl.de

Architecture

Waldmeister is a system for unit equational deduction. Its theoretical basis is unfailing completion in the sense of [
BDP89] with refinements towards ordered completion (cf. [AHL03]). The system saturates the input axiomatization, distinguishing active facts, which induce a rewrite relation, and passive facts, which are the one-step conclusions of the active ones up to redundancy. The saturation process is parameterized by a reduction ordering and a heuristic assessment of passive facts [HJL99]. For an in-depth description of the system, see [Hil03].

Since last year's competition, the "new Waldmeister loop" has been implemented, and is now operational [GH+03]. This notion captures a novel organization of the saturation-based proof procedure into a system architecture [HL02], featuring a highly compact representation of the search state which exploits its inherent structure. The revealed structure also paves the way to an easily implemented parallelization of the prover with modest communication requirements and rewarding speed-ups. With the new architecture it is now possible to solve problems that were previously out of reach, for example deriving Boolean from the second Winker Lemma (ROB007-1). The proof is found with a standard strategy just in a parallel overnight run. Over 70,000 active facts and 500,000,000 passive ones are represented in no more than 200 MBytes. This foils the common belief that provers succeed either within five minutes or not all.

Implementation

The prover is coded in ANSI-C. It runs on Solaris, Linux, and newly also on MacOS X. In addition, it is now available for Windows users via the Cygwin platform. The central data strucures are: perfect discrimination trees for the active facts; group-wise compressions for the passive ones; and sets of rewrite successors for the conjectures. Visit the thoroughly rewritten Waldmeister Web pages at:
    http://www.mpi-sb.mpg.de/~hillen/waldmeister/

Strategies

The approach taken to control the proof search is to choose the search parameters according to the algebraic structure given in the problem specification [HJL99]. This is based on the observation that proof tasks sharing major parts of their axiomatization often behave similarly. Hence, for a number of domains, the influence of different reduction orderings and heuristic assessments has been analyzed experimentally; and in most cases it has been possible to distinguish a strategy uniformly superior on the whole domain. In essence, every such strategy consists of an instantiation of the first parameter to a Knuth-Bendix ordering or to a lexicographic path ordering, and an instantiation of the second parameter to one of the weighting functions addweight, gtweight, or mixweight, which, if called on an equation s = t, return |s| + |t|, |max>(s,t)|, or |max>(s,t)| · (|s| + |t| + 1) + |s| + |t|, respectively, where |s| denotes the number of symbols in s.

Expected Competition Performance

The focus of recent developments has been on coping with large search states; so we hope that this year's system version will be competitive with last year's.

References

AHL03
Avenhaus J., Hillenbrand T., Löchner B. (2003), On Using Ground Joinable Equations in Equational Theorem Proving, Journal of Symbolic Computation 36(1-2), pp.217-233, Elsevier Science.
BDP89
Bachmair L., Dershowitz N., Plaisted D.A. (1989), Completion Without Failure, Ait-Kaci H., Nivat M., Resolution of Equations in Algebraic Structures, pp.1-30, Academic Press.
GH+03
Gaillourdet J-M., Hillenbrand T., Löchner B., Spies H. (2003), The New Waldmeister Loop at Work, Baader F., Proceedings of the 19th International Conference on Automated Deduction (Miami, USA), pp.To appear, Lecture Notes in Artificial Intelligence, Springer-Verlag.
HJL99
Hillenbrand T., Jaeger A., Löchner B. (1999), Waldmeister - Improvements in Performance and Ease of Use, Ganzinger H., Proceedings of the 16th International Conference on Automated Deduction (Trento, Italy), pp.232-236, Lecture Notes in Artificial Intelligence 1632, Springer-Verlag.
HL02
Hillenbrand T., Löchner B. (2002), The Next Waldmeister Loop, Voronkov A., Proceedings of the 18th International Conference on Automated Deduction (Copenhagen, Denmark), pp.486-500, Lecture Notes in Artificial Intelligence 2392, Springer-Verlag.
Hil03
Hillenbrand T. (2003), Citius altius fortius: Lessons Learned from the Theorem Prover Waldmeister, Dahn I., Vigneron L., Proceedings of the 4th International Workshop on First-Order Theorem Proving (Valencia, Spain), Electronic Notes in Theoretical Computer Science 86.1, Elsevier Science.