Otter: An Automated Deduction System

Contents

Description

Computational Environment

Availability Version 3.3

Documentation

Example Inputs and Outputs

Accomplishments

Performance on the TPTP Problems

Bugs and Fixes

Mailing Lists

Copyrights and License

Related Pages

Try Otter right now with Son of BirdBrain

A sample Otter proof

New Results obtained with Otter and related programs

Mace searches for small models

EQP, a prover for equational logic with associative unification

Automated Reasoning at Argonne

External Work

Some of the Otter and Mace users

Description

Our current automated deduction system Otter is designed to prove theorems stated in first-order logic with equality. Otter's inference rules are based on resolution and paramodulation, and it includes facilities for term rewriting, term orderings, Knuth-Bendix completion, weighting, and strategies for directing and restricting searches for proofs. Otter can also be used as a symbolic calculator and has an embedded equational programming system. Otter is a fourth-generation Argonne National Laboratory deduction system whose ancestors (dating from the early 1960s) include the TP series, NIUTP, AURA, and ITP.
Currently, the main application of Otter is research in abstract algebra and formal logic. Otter and its predecessors have been used to answer many open questions in the areas of finite semigroups, ternary Boolean algebra, logic calculi, combinatory logic, group theory, lattice theory, and algebraic geometry.

Computational Environment

Otter is coded in ANSI C and is portable, easy to install, and fast. It has been used mostly on Unix-like systems, but limited versions also run in Microsoft Windows.

Availability

The current version is Otter 3.3, and the distribution package includes Mace 2.2.
Download Otter 3.3 / Mace 2.2.

Documentation

The Otter distribution package contains all source code, installation instructions, users guides in PDF and PostScript formats, and a collection of test problems.
Otter 3.3 Reference Manual

Several books on Otter and its applications are available.

Automated Reasoning and the Discovery of Missing and Elegant Proofs, by L. Wos and G. W. Pieper, Rinton Press (2003).

Automated Reasoning with Otter, by J. A. Kalman, Rinton Press (2001).

A Fascinating Country in the World of Computing: Your Guide to Automated Reasoning , by Larry Wos, with Gail Pieper, World Scientific (2000).

Automated Deduction in Equational Logic and Cubic Curves, by W. McCune and R. Padmanabhan, Springer-Verlag LNCS #1095 (1996).

The Automation of Reasoning: An Experimenter's Notebook with Otter Tutorial, by Larry Wos, Academic Press (1996).

Automated Development of Fundamental Mathematical Theories, by Art Quaife, Kluwer Acadamic Publishers (1992).

Example Inputs and Outputs

Here are the test problems from the distribution package.

Otter 3.3 test problems.

Mace 2.2 test problems.

Accomplishments

See the New Results Page (way out of date) for a summary of new results that have been obtained with Otter and other Argonne deduction programs.

Performance on the TPTP Problems

TPTP is a large problem set for testing first-order automated theorem-proving programs. Otter has been run on all of the TPTP problems, and the following results are available.
Otter 3.1 and MACE 1.4 on TPTP v2.3.0 (table created May 22, 2000).

Bugs and Fixes

See the Change-log File.
These changes have been made in the development version of Otter. We don't retain the source code for the intermediate versions (e.g., Otter-3.2d).

If you need any of these changes, we can give you a snapshot of the current version (source code), which should contain all of the updates listed in the Change-log (and then some).

Mailing Lists

The mailing lists

otter-announce

otter-help

otter-development

have been discontinued.

Copyrights and License

See the Otter/MACE Legal Page. These activities are projects of the Mathematics and Computer Science Division of Argonne National Laboratory.