Abstract: The Winograd Schema Challenge (WSC) serves as a prominent benchmark for evaluating machine understanding. While Large Language Models (LLMs) excel at answering WSC questions, their ability to generate such questions remains less explored. In this work, we propose Tree-of-Experts (ToE), a novel prompting method which enhances the generation of WSC instances (50% valid cases vs. 10% in recent methods). Using this approach, we introduce WSC+, a novel dataset comprising 3,026 LLM-generated sentences. Notably, we extend the WSC framework by incorporating new 'ambiguous' and 'offensive' categories, providing a deeper insight into model overconfidence and bias. Our analysis reveals nuances in generation-evaluation consistency, suggesting that LLMs may not always outperform in evaluating their own generated questions when compared to those crafted by other models. On WSC+, GPT-4, the top-performing LLM, achieves an accuracy of 68.7%, significantly below the human benchmark of 95.1%.