This paper presents our system for SemEval-2026 Task 11 Subtask 1, which evaluates the formal validity of English syllogisms independently of semantic plausibility. To reduce content effects, we use a hybrid neuro-symbolic pipeline that separates natural-language abstraction from logical inference. The system maps each syllogism into categorical propositions using template rules and a learned parser, followed by explicit role mapping for the major, minor, and middle terms. If the abstraction is structurally complete, an exact Venn-style satisfiability solver checks validity; otherwise, the instance is routed to a learned fallback classifier. Our official submission achieved 71.73% accuracy, a Total Content Effect of 11.84, a Combined Score of 20.19, and a rank of 41st. Development analysis shows that symbolic inference is reliable on well-formed abstractions, while most remaining errors arise from paraphrase, multiword terms, and unstable term alignment.