bpo-25732: Make functools.total_ordering implementing __ne__. (#3748)

Patch by Raymond Hettinger.
diff --git a/Lib/functools.py b/Lib/functools.py
index 53680b8..5d755d4 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -55,23 +55,28 @@
     convert = {
         '__lt__': [('__gt__', lambda self, other: not (self < other or self == other)),
                    ('__le__', lambda self, other: self < other or self == other),
+                   ('__ne__', lambda self, other: not self == other),
                    ('__ge__', lambda self, other: not self < other)],
         '__le__': [('__ge__', lambda self, other: not self <= other or self == other),
                    ('__lt__', lambda self, other: self <= other and not self == other),
+                   ('__ne__', lambda self, other: not self == other),
                    ('__gt__', lambda self, other: not self <= other)],
         '__gt__': [('__lt__', lambda self, other: not (self > other or self == other)),
                    ('__ge__', lambda self, other: self > other or self == other),
+                   ('__ne__', lambda self, other: not self == other),
                    ('__le__', lambda self, other: not self > other)],
         '__ge__': [('__le__', lambda self, other: (not self >= other) or self == other),
                    ('__gt__', lambda self, other: self >= other and not self == other),
+                   ('__ne__', lambda self, other: not self == other),
                    ('__lt__', lambda self, other: not self >= other)]
     }
-    roots = set(dir(cls)) & set(convert)
+    defined_methods = set(dir(cls))
+    roots = defined_methods & set(convert)
     if not roots:
         raise ValueError('must define at least one ordering operation: < > <= >=')
     root = max(roots)       # prefer __lt__ to __le__ to __gt__ to __ge__
     for opname, opfunc in convert[root]:
-        if opname not in roots:
+        if opname not in defined_methods:
             opfunc.__name__ = opname
             opfunc.__doc__ = getattr(int, opname).__doc__
             setattr(cls, opname, opfunc)