Cheat Engine

[Icklorfin]

I need help on this game and need help on solving it, can someone help me solve this?

The Letter Game:

Undefined terms: Letters M,I, and U
Definition: x means any string of I's and U's
Postulates:
1. IF a string of letters end in I, you may add U at the end.
2. If you have Mx, then you may add x to get Mxx.
3.If 3 I's occur, that is III, then you may substitute U in their place.
4. If UU occurs, you drop it.

Objective: Given one string, you are to derice or prove some other string.

Example:
Given: MI
Prove: MIIU

Statement_____________________Reason
1.MI Given
2.MII Rule 2
3.MIIU Rule 1

Prove the following theorems:
3.Given: MI
Prove: MUI

4.
Given: MI
Prove:MIUIU

5.Given: MI
Prove: MIIUIIU

6.Given:MIIIUII
Prove: MIIUIIU

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3.