C# Online Compiler | .NET Fiddle

using System;
using System.Collections.Generic;
					
public class Program
{
	public static void Main()
	{
		Console.WriteLine("-------BEGIN-------");
		
		Base b1 = new Base(1);
		Base b2 = new Base(2);
		Base b3 = new Base(3);
		Base b4 = new Base(4);
		Base b5 = new Base(1);
		Derived d1 = new Derived(1,"d1");
		Derived d2 = new Derived(2,"d2");
		Derived d3 = new Derived(3,"d3");
		Derived d4 = new Derived(4,"d4");
		Derived d5 = new Derived(1,"d5");
		
		object ob1 = b1;
		object ob2 = b2;
		object ob3 = b3;
		object ob4 = b4;
		object ob5 = b5;
		object od1 = d1;
		object od2 = d2;
		object od3 = d3;
		object od4 = d4;
		object od5 = d5;
		
		List<object> lo = new List<object>();
		lo.Add(b1);
		lo.Add(b2);
		lo.Add(b3);
		lo.Add(d1);
		lo.Add(d2);
		lo.Add(d3);
		//PrintList(lo);
		
		List<object> lob = new List<object>();
		lob.Add(ob1);
		lob.Add(ob2);
		lob.Add(ob3);
		lob.Add(od1);
		lob.Add(od2);
		lob.Add(od3);
		//PrintList(lob);
		
		Console.WriteLine("Is " + ob1.ToString() + " Equals " + od5.ToString() + "? : " + ob1.Equals(od5).ToString());
		Console.WriteLine("Is " + od5.ToString() + " Equals " + b1.ToString() + "? : " + od5.Equals(b1).ToString());
		
		Console.WriteLine(PrintFind(lob,d3));
		
		Console.WriteLine("--------END--------");
	}
	
	public static void PrintList(List<object> lo)
	{
		Console.WriteLine("Printing a List of objects :");
		
		foreach(var o in lo)
		{
			Console.WriteLine(o.ToString());
		}
	}
	
	public static int FindIdx(List<object> lo, object o)
	{
		return lo.FindIndex(ob=>ob.Equals(o));
	}
	
	public static string PrintFind(List<object> lo, object o)
	{
		string res = "\nTrying to find index of : "+o.ToString()+" in a List<object> :\n -> ";
		int index = FindIdx(lo,o);
		if(index < 0)
			res += "Cannot find it.";
		else
			res += "Index is "+index;
		res += "\n";
		return res;
	}
}

public class Base : IEquatable<Base>
{
	public int ID {get; set;}
	
	public Base(int id)
	{ID = id;}
	
	public virtual bool Equals(Base other)
	{
		Console.WriteLine("Begin Base.Equals(Base other);");
		
		if (other == null) return false;
		if (ReferenceEquals(this, other)) return true;
		if (GetType() != other.GetType()) return false;
		
		return ID == other.ID;
	}
	
	public override bool Equals(object other)
	{
		return this.Equals(other as Base);
	}
	
	public override int GetHashCode()
    {
        unchecked
    	{
        	// Choose large primes to avoid hashing collisions
        	const int HashingBase = (int) 2166136261;
        	const int HashingMultiplier = 16777619;

        	int hash = HashingBase;
        	hash = (hash * HashingMultiplier) ^ (!Object.ReferenceEquals(null, ID) ? ID.GetHashCode() : 0);        
        	return hash;
    	}
    }
	
	public override string ToString()
	{
		return "A Base object with ["+ID+"] as ID";
	}
}

public class Derived : Base, IEquatable<Derived>
{
	public string Name {get; set;}
	
	public Derived(int id, string name) : base(id)
	{Name = name;}
	
	public bool Equals(Derived other)
	{	
		Console.WriteLine("Begin Derived.Equals(Derived other);");		
		
		if (!base.Equals(other)) return false;
		
		return Name == other.Name;
	}
	
	public override bool Equals(object other)
	{
		return this.Equals(other as Derived);
	}	
	
	public override int GetHashCode()
    {
        unchecked
    	{
        	// Choose large primes to avoid hashing collisions
        	const int HashingBase = (int) 2166136261;
        	const int HashingMultiplier = 16777619;

        	int hash = HashingBase;
        	hash = (hash * HashingMultiplier) ^ base.GetHashCode();
        	hash = (hash * HashingMultiplier) ^ (!Object.ReferenceEquals(null, Name) ? Name.GetHashCode() : 0);        
        	return hash;
    	}
    }
	
	public override string ToString()
	{
		return "A Derived object with '" + Name + "' as Name, and also " + base.ToString();
	}
}

            hash = (hash * HashingMultiplier) ^ (!Object.ReferenceEquals(null, Name) ? Name.GetHashCode() : 0);        
 
using System;
using System.Collections.Generic;
                    
public class Program
{
    public static void Main()
    {
        Console.WriteLine("-------BEGIN-------");
        
        Base b1 = new Base(1);
        Base b2 = new Base(2);
        Base b3 = new Base(3);
        Base b4 = new Base(4);
        Base b5 = new Base(1);
        Derived d1 = new Derived(1,"d1");
        Derived d2 = new Derived(2,"d2");
        Derived d3 = new Derived(3,"d3");
        Derived d4 = new Derived(4,"d4");
        Derived d5 = new Derived(1,"d5");
        
        object ob1 = b1;
        object ob2 = b2;
        object ob3 = b3;
        object ob4 = b4;

Cached Result

Source: [{"a":"new"}]
Result: [{"a":"new"}]
Equal? False
Source: [{"a":"old"}]
Result: [{"a":"old"}]
Result: [{"a":"old"}]
Equal? False