Dependent Type Semantics (DTS) provides a highly rigorous framework for natural language inference (NLI), yet its scalability is severely bottlenecked by the need for manually created world knowledge. To overcome this knowledge acquisition bottleneck, we present a novel neuro-symbolic NLI system that integrates Hyperbolic Entailment Cones for automated conceptual hierarchy discovery. By exploiting the geometric properties of hyperbolic space, our model efficiently learns lexical entailment relations and dynamically injects them as logical axioms during the DTS proof-search process. Evaluations on our constructed diagnostic dataset show that our hybrid approach broadens the coverage of complex lexical variations and paraphrases without manual engineering.