This directory contains some command files of RRL. RRL is an interactive 
theorem prover, you may talk to it by type rrl commands.
The file with the suffix ".cmd" contains a sequence of rrl commands. To execute
the commands in such a file, use the rrl command "auto". For example, if
you want to execute the commands in the file named "try.cmd", do it as follows:
        % rrl
        ... ...
        RRL-> auto try

Below we describe shortly some ".cmd" files in this directory:

Testing RRL:

demo-test.cmd: this is a concatenation of several "cmd" files to show 
  different features of RRL: producing canonical systems for free groups,
  free abelian groups, free rings; finding solutions by narrowing;
  inductionless induction proofs; testing sufficient completeness
  of equational specifications; first order propositional calculus using 
  the Grobner basis approach; first order predicate calculus using
  conditional rewrite rules.
  This file is used by the author to test RRL each time a change is made
  to the code.


Illustrations of Generating Canonical Rewriting Systems:

demo-ring.cmd: generating a canonical rewriting system for free rings.
demo-g1.cmd: generating a canonical rewriting system from a single axiom
  of free groups.


Proofs of Ring Commutativity Problems:

demo-x3x.cmd: proving x^3 = x implies the ring commutativity.
demo-x3xp.cmd: using the polynomial representation.
demo-x3xpc.cmd: generating a canonical system for the ring plus x^3 = x.
demo-x4x.cmd: proving x^4 = x implies the ring commutativity.
demo-x6x.cmd: proving x^6 = x implies the ring commutativity.


Illustration of Narrowing:

demo-narrow.cmd: finding solutions for a map connection problem.


Illustrations of Clausal Superposition and Conditional Rewriting:

demo-steam.cmd:	prove steamroller problem.
demo-set.cmd: prove a lemma from the set theory.
demo-sam.cmd: prove SAM's lemma.
demo-line.cmd: prove a lemma about hardware specification.


Illustrations of Cover Set Induction Method:

demo-gcd.cmd: proving gcd is commutative.
demo-queue.cmd:	proving the validity of ADT implementation.
demo-sort.cmd: proving the correctness of quick-sort algorithm.
demo-prime.cmd:	proving the unique prime factorization in number theory.
