I. The Atheistic Premise
The first premise is the atheistic premise, which it assumes in order to show that it ultimately leads to a contradiction: the greatest conceivable being exists as a concept, but NOT in reality
II.The Greatness Premise
If you have a hundred dollar bill that exists as a thought and also in reality, then this hundred dollar bill is greater than one that exists only as a thought. So the second premise is: existence as both a concept AND in reality is greater than existence as just a concept alone.
III. Conclusion from I and II
From the combination of I and II, it follows: therefore, if the greatest conceivable being exists as both a concept AND in reality, then it is greater than if it exists only as a concept
IV. The Conceivability Premise
It is logically coherent, and thus conceivable, that the greatest conceivable being exists both as a concept AND in reality. So the third and final premise is: it is conceivable that the greatest conceivable being exists both as a concept AND in reality
V. Conclusion from III and IV
From the combination of III and IV, we get the following conclusion: therefore, it is conceivable that there is a being greater than the greatest conceivable being. This is a logical contradiction.
VI. Final Conclusion
Therefore, it is false that the greatest conceivable being exists as a concept but NOT in reality.