Flagging use of C# operator possible?

I am quite new to ReSharper, so please forgive my noobness.  I would like to know if it is possible to flag C# code that uses an operator that has not been overridden as an error or warning.  For example, in C# the equals operator (==) provided by the Object class performs reference equality.  If I were to define a new class based off of Object that does not override the equals operator, would it be possible for ReSharper to examine all code that uses that class to determine if the equals operator is being used with that class and flag that code as an error or warning?

A more general question would be - can ReSharper be used to validate virtual methods and operators with the following options:
1. Flag as an error or warning code that does not override certain base class virtual methods or operators.
2. Flag as an error or warning code that attempts to use a virtual base class method or operator that is not overridden by the most derived class.

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