Software

Database of Existing Mechanized Reasoning Systems - A list (>50 entries) of automatic resolution provers (like Otter), interactive provers (like PVS) and other mechanized reasoning tools.
http://www-formal.stanford.edu/clt/ARS/systems.html

MUltlog - Takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and clause formation rules for this logic.
http://www.logic.at/multlog/

j'Imp Theorem Prover - An automatic theorem prover based on set of support and ordered resolution for first-order logic. j'Imp is part of the Orbital library. This library is a Java class providing object-oriented representations and algorithms for logic, mathematics, and artificial intelligence.
http://www.functologic.com/logic/jImp.html

Isabelle - A generic theorem proving environment developed at Cambridge University (Larry Paulson) and TU Munich (Tobias Nipkow). Includes logic, documentation and free download.
http://www.cl.cam.ac.uk/Research/HVG/Isabelle/

LWB - Logics Workbench.
http://www.lwb.unibe.ch/

Automated Reasoning Project - Web resource provided by research group. Includes access to software developed by the team, coverering such projects as FINDER (Finite Domain Enumerator), MaGIC (Matrix Generator for Implication Connectives) and Kripke (A theorem prover for the relevant logic LR).
http://cslab.anu.edu.au/ar/

VeriFun - A semi-automated system for the verification of statements about programs written in a functional programming language. The system is capable of following fully-automated routines for theorem proving and hypotheses formation, as well as operating interactively when these reoutines fail.
http://www.informatik.tu-darmstadt.de/pm/verifun/

MUltseq - A generic sequent prover for propositional finitely-valued logics.
http://www.logic.at/multseq/

Tree Proof Generator - An implementation of the semantic tableaux method for classical propositional and predicate logic, written in JavaScript/DOM.
http://www.umsu.de/logik/trees

WinKE - An interactive proof assistant based on analytic tableaux, and designed for the teaching of deductive reasoning. Ordering information is available at this site, as are academic papers on the design of the software.
http://staff.science.uva.nl/~ulle/WinKE/

PVS - The PVS Specification and Verification System. Available for Sparc machines with Solaris 2 and Intel x86 Machines with Linux compatible with Redhat 5 or later. Required is Emacs (version 19 or later), recommended LaTeX and Tcl/Tk. Download by FTP.
http://pvs.csl.sri.com/

CrocoPat: Simple and Efficient Relational Programming - CrocoPat manipulates relations of any arity, including graphs (which are binary relations). Its simple and expressive query and manipulation language is based on first-order predicate calculus. The implementation is based on the data structure binary decision diagram (BDD).
http://mtc.epfl.ch/~beyer/CrocoPat/

DELORES - A forward-chaining reasoning engine for defeasible logic, a less expressive but more efficient nonmonotonic logic.
http://www.dfki.uni-kl.de/~miller/delores/

LOOM - A language and environment for constructing intelligent applications. It is a research project in the Artificial Intelligence research group at the University of Southern California's Information Sciences Institute. The goal of the project is to develop and field advanced tools for knowledge representation and reasoning in Artificial Intelligence.
http://www.isi.edu/isd/LOOM/LOOM-HOME.html

Logic Software from CSLI - By Jon Barwise and John Etchemendy.
http://www-csli.stanford.edu/hp/Logic-software.html

Paradox - A tool that processes first-order logic problems and tries to find finite-domain models for them; written by Koen Claessen and Niklas Sörensson. Haskell and C++; free download under GPL.
http://www.cs.chalmers.se/~koen/paradox/

The Coq Project - Deals with effectively machine-checked formal mathematics. In practice, this includes the study of mathematical formalisms well-suited for implementations, the implementations themselves and the use of these for various applications. Focuses on software correctness proofs.
http://pauillac.inria.fr/coq/

Church - Program understands the different types of lambda expressions, can extract lists of variables (both free and bound) and subterms, and can simplify complicated expressions. Uses Python.
http://www.alcyone.com/software/church/

Spreadsheet Logic - Free Microsoft Excel add-in for processing and evaluating logic in your spreadhseet.
http://members.lycos.co.uk/jbusar/

Gateway to Logic - A collection of web-based logic programs offering a number of logical functions: interactively or automatically build proofs, check theorems, and operate on propositional logic formulae.
http://logik.phl.univie.ac.at/~chris/formular-uk.html

Proof General - Comprehensive Gnu-Emacs and XEmacs interface for several theorem provers including Coq, Isabelle, Lego, and Phox.
http://proofgeneral.inf.ed.ac.uk

Bertrand - Bertrand solves sets of first-order predicate logic statements for satisfiability (consistency), validity, and equivalence. It also checks single statements for "logical truth" (tautology) and "logical falsity" (self-contradiction). Subject-identity is supported. User can "step through" the solution algorithm as Bertrand solves a problem, and/or check the graphic tree produced.
http://www.uwosh.edu/faculty_staff/herzberg/Bertrand.html

ModLeanTAP: Lean Tableau-based Deduction for Propositional Modal Logics - Lean Tableau-based Deduction for Propositional Modal Logics. By Bernhard Beckert.
http://i12www.ira.uka.de/modlean/

PROTEIN - A PROver with a Theory Extension INterface. Theorem prover for first-order clause logic, written in ECRC's Prolog-dialect ECLiPSe. Free download, documentation.
http://www.uni-koblenz.de/ag-ki/Implementierungen/Protein/

ACL2 Version 2.7 - A programming language in which you can model computer systems and a tool to help prove properties of those models. Available under GPL and runs on various platforms. Includes related download links.
http://www.cs.utexas.edu/users/moore/acl2/

llprover - A linear logic prover that searches a cut-free proof for the given two-sided sequent of first-order linear logic.
http://bach.scitec.kobe-u.ac.jp/llprover/

ProofPower - A suite of tools supporting specification and proof in Higher Order Logic (HOL) and in Z notation.
http://www.lemma-one.com/ProofPower/index/

DC Proof Online - New proof-writing software to teach the fundamentals of logic and proof. Enables users/students to write error-free proofs by selecting rules of inference, axioms, etc. from convenient drop-down menus. Includes tutorial and exercises.
http://www.dcproof.com