The classical TRIZ contradiction matrix omits self-contradictory cases, situations where a single technical parameter must satisfy conflicting demands, leaving its diagonal cells undefined. Such self-referential physical contradictions are increasingly relevant in modern engineering systems, where adaptability, dual-functionality, and dynamic optimization are essential. This paper addresses this gap by formalizing self-contradictions as a distinct class of design conflicts and proposing new inventive principles tailored to them. Using a semantic AI-driven discovery method and case-based reasoning, nine solution strategies were identified, several of which extend beyond the original 40 TRIZ principles. These were validated against real-world design challenges in robotics, aerospace, and cyber-physical systems. The study culminates in a reformulated contradiction matrix with populated diagonal entries, marking a conceptual and practical extension of TRIZ logic. This work repositions self-referential physical contradictions as fertile ground for innovation and demonstrates the role of AI in expanding the boundaries of systematic inventive thinking.