"I don't know" is the right answer. There are over 20 towns named Hamburg around the world, many of them in the USA.
However, GPT4 is really struggling with this even if you assure it that by Hamburg, we mean the original one in Germany.
GPT4 gets it if you explain that this is a logic problem, and not a query about some actual person named Alice, and if you put all the relevant info into a single prompt.
But event then, if you use the successful prompt in a completely new chat, GPT4 is lost at sea:
Human: Assume that Hamburg is a town in Germany. Alice was not born in Germany. Was she born in Hamburg? This is a logic problem, nothing more; do not think about any famous people named Alice in connection with Hamburg.
GPT4: The answer to this question cannot be determined from the provided context. While it is clear that Hamburg is a town in Germany and that Alice was not born in Germany, there is no information given about where Alice was actually born. Therefore, it is impossible to say whether or not Alice was born in Hamburg.
Human: Please try harder. The answer can be entirely determined; this is purely a logic problem. We do not require information about where Alice was born; knowing that Alice was not born in Germany suffices.
GPT4: Based on the information provided in the context, we can answer the question. Alice was not born in Germany, which means she was not born in Hamburg. Therefore, Alice was not born in Hamburg. It is important to note that the answer to this question is purely based on logic. The context provides no additional information about Alice or any famous people named Alice.
After this, it was a real struggle to get GPT4 to identify the logically redudant sentence, "Therefore, Alice was not born in Hamburg.". Even after I narrowed it down to being one of those two sentences, it insisted that the second sentence is useful because it summarizes what was concluded in the deductive sentence before it. I brow-beat it into admitting that it's entirely redundant, like "X, therefore X".