Predicates are foundational components in data analysis systems. However, modern workloads increasingly involve unstructured documents, which demands semantic understanding, beyond traditional value-based predicates. Given enormous documents and ad-hoc queries, while Large Language Models (LLMs) demonstrate powerful zero-shot capabilities, their high inference cost leads to unacceptable overhead. Therefore, we introduce \textsc{ScaleDoc}, a novel system that addresses this by decoupling predicate execution into an offline representation phase and an optimized online filtering phase. In the offline phase, \textsc{ScaleDoc} leverages a LLM to generate semantic representations for each document. Online, for each query, it trains a lightweight proxy model on these representations to filter the majority of documents, forwarding only the ambiguous cases to the LLM for final decision. Furthermore, \textsc{ScaleDoc} proposes two core innovations to achieve significant efficiency: (1) a contrastive-learning-based framework that trains the proxy model to generate reliable predicating decision scores; (2) an adaptive cascade mechanism that determines the effective filtering policy while meeting specific accuracy targets. Our evaluations across three datasets demonstrate that \textsc{ScaleDoc} achieves over a 2$\times$ end-to-end speedup and reduces expensive LLM invocations by up to 85\%, making large-scale semantic analysis practical and efficient.