Design a C++ program containing a class Fraction. The class data should have two variables numerator and denominator, both of type integer, to represent the fraction numerator/denominator. The fraction representation within the object must allow no simplification. That is, the numerator and denominator have to have no common divisor different from 1. For example, the fraction 4/6 must be represented as 2/3.
Be sure to implement the following features:
1. The class constructor must take two integers numbers (numerator and denominator).
2. For negative fractions, the numerator must be negative and denominator must be positive.
3. Include the method simplify that takes two numbers and returns a fraction object (representing a fraction that cannot be simplified).
4. Include a method add that takes two fraction objects and returns their sum (as a fraction object).
5. Include a method diff that takes two fraction objects and returns their difference (as a fraction object).
6. Implement overloaded operators + and - for addition and subtraction of fractions.
7. Implement overloaded comparison operators == and != for comparing two fraction objects.
Test your class in the main() method by creating several fractions, adding them, subtracting them, and printing the result by using the / sign (e.g., 2/3), not as decimal fractions. Also demonstrate usage of the overloaded operators.