Large language model (LLM) based assertion generation is making formal verification more accessible for Register Transfer Level (RTL) designs, but three practical issues remain. Generated properties can pass for the wrong reason, proof cost can vary widely from one design to another, and failing traces are hard to interpret. This paper presents a lightweight, open-source framework that addresses these issues in one loop. Our method combines mutation-guided refinement to reject weak assertions, including vacuous ones and those that fail to distinguish faulty behaviour, a solver-selection stage that chooses among candidate Satisfiability Modulo Theories (SMT) backends using RTL structure, and causal narrative synthesis to explain why a proof failed. Across diverse RTL designs, the framework improves confidence in generated assertions, reduces runtime variability over fixed-solver choices, and produces failure explanations that remain grounded in the counterexample trace. The results suggest that quality-aware closure, rather than assertion generation alone, is the missing step for practical LLM-assisted formal verification.

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