Large language models are increasingly asked to treat the input context as the source of task-specific rules, procedures, and evidence. A difficult case arises when this context contradicts pretrained priors: models may mention the local rule but still execute familiar semantic, commonsense, positional, or operator shortcuts. We study this failure mode as prior-dominated reasoning, where either the final answer or the intermediate trajectory follows a plausible prior-consistent path rather than the current context. We propose Anti-Prior Reinforcement Learning, a post-training framework that constructs executable context-prior conflict tasks and trains with a gated verifier reward. The reward gives positive credit for answer correctness, context anchoring, and step-wise local rule use, while penalizing prior-consistent answers and reasoning steps. On Qwen3-8B, Anti-Prior RL improves controlled validation accuracy from 51.7% to 74.5% and controlled OOD accuracy from 46.4% to 73.4%, while reducing OOD prior-answer/prior-step hit rates from 15.9%/40.2% to 1.5%/8.9%. It also improves over SFT and LongRLVR on downstream CL-Bench, RULER-QA, and LongBench v2 across both Qwen3-8B and Qwen2.5-7B-1M, and outperforms outcome-only RL on Qwen3-8B. Together, these results provide complementary evidence that the learned behavior transfers beyond the constructed prior-conflict setting to broader context-learning and reasoning benchmarks.