Relation extraction in the equipment domain often exhibits asymmetric patterns, where entities participate in multiple overlapping relations that break the expected structural symmetry of semantic associations. Such asymmetry increases task complexity and reduces extraction accuracy in conventional approaches. To address this issue, we propose a symmetry- and asymmetry-aware dual-path retrieval and in-context learning-based large language model. Specifically, the BGE-M3 embedding model is fine-tuned for domain-specific adaptation, and a multi-level retrieval database is constructed to capture both global semantic symmetry at the sentence level and local asymmetric interactions at the relation level. A dual-path retrieval strategy, combined with Reciprocal Rank Fusion, integrates these complementary perspectives, while task-specific prompt templates further enhance extraction accuracy. Experimental results demonstrate that our method not only mitigates the challenges posed by overlapping and asymmetric relations but also leverages the latent symmetry of semantic structures to improve performance. Experimental results show that our approach effectively mitigates challenges from overlapping and asymmetric relations while exploiting latent semantic symmetry, achieving an F1-score of 88.53%, a 1.86% improvement over the strongest baseline (GPT-RE).