A general game player is a system that can play previously unknown games given nothing but their rules. A key to success in this endeavour is the ability to automatically gain knowledge about new games that follows from the rules without being explicitly given. In this paper, we show how a recently developed, theoretical method for automated theorem proving in general game playing can be put into practice. To this end, we extend the method so as to allow a general game player to systematically search and verify multiple temporal game properties at once. We formally prove this extension to be correct, and we report on extensive experiments that show how this improvement helps to significantly enhance the ability of a successful general game player to infer new properties about a previously unknown game.