If you change the tail end of your code to this:
C.c_method_
puts self.inspect
puts "----"
include C
c_method_
you should help you see what's going on. That will give you this output:
a_method_
main
----
a_method_
c_method_
b_method_
So what is this main
business? Chuck has a nice summary over in this answer:
Everything in Ruby occurs in the context of some object. The object at the top level is called "main". It's basically an instance of Object with the special property that any methods defined there are added as instance methods of Object (so they're available everywhere).
That means that saying this at the top level:
include C
is the same as saying:
Object.send(:include, C)
Adding things to Object
pollutes everything.