Before proceeding, I'd recommend becoming more familiar with the prerequisites to being papabilie; as it stands, your syllogism rests on an irrelevant premise because a man doesn't require holy orders to be validly and lawfully elected.
To be pope, one must be a baptized male, and a Catholic in the narrow sense-- that is, he must be a member of the Catholic Church, professing the Catholic faith. If a man meets these conditions he is, in the narrowest sense, eligible to be pope. If lawful electors were to select him in a conclave, that man would become pope as soon as he accepted the Office.
Once you've adjusted your conclusion to rest on relevant premises, you will likely find more eagerness to discuss the issue.