Large language models are increasingly used in inventive problem-solving, but effective support requires more than open-ended idea generation. Inventive problem-solving requires improving one aspect of a technical system without unintentionally worsening another. TRIZ (Theory of Inventive Problem Solving) provides a unique and structured framework for this setting by representing engineering trade-offs as contradictions and linking them to standardized inventive principles. However, prior TRIZ–LLM evaluations are typically small-scale, case studies in focused areas of technology, and rarely grounded in patent text, which makes it difficult to assess structured reasoning at scale. We introduce TRIZBench, a dataset and benchmark for TRIZ reasoning grounded in open technical sources and U.S. patents. TRIZBench evaluates the core TRIZ workflow through three tasks: contradiction prediction, inventive principle prediction, and grounded TRIZ reasoning. Experiments with multiple LLM baselines show that detecting contradictions is easier than recovering correct trade-off pairs, while principle prediction benefits from explicitly exploiting TRIZ structure. Our findings further underscore the importance of grounding. We show that semantic retrieval enables evidence-based justifications and helps explain why LLMs fail. Dataset and code are available at https://github.com/ellenzhuwang/trizbench.