Animation, Verification and Visualisation of Prolog Transition Systems with ProB

Event-B is a formal method rooted in predicate logic and set theory. We encoded over 600 proof rules in Prolog, enabling a systematic, comprehensible proof analysis and construction. By integrating the proof rules into the Prolog-based validation tool ProB, we obtain an interactive proof system with proof tree visualisation. This has advantages in teaching, giving students direct control over the selection of proof rules. Our tool can import proof obligations from the Rodin platform and provides multiple exports: a trace file for proof replay in ProB, an interactive HTML document for tool-independent exploration of the proof tree, and an export back to Rodin, allowing the ProB prover to be used as second chain. Compared to the previous implementation of the proof rules in Java, the encoding in Prolog is more compact, maintainable and extensible. While a preliminary iterative deepening prover with simple heuristics is already available and useful for finding short proofs, we aim to obtain fast automatic provers in the future.

MerLean-Prover is an end-to-end Lean4 theorem prover that replaces sorry declarations with kernel-checkable proofs. It is built from three agent types (Planning, Check, and Lean) composed by a recursive outer loop whose unit of revision is the proof plan itself, and uses no fine-tuning, no custom RL objective, and no theorem-specific scaffolding. On FormalQualBench, a benchmark of 23 PhD-qualifying-exam theorems, MerLean-Prover solves 10/23, surpassing the strongest published open-source baseline (OpenGauss, 8/23). On Putnam2025, the same harness closes 12/12 with substantially lower total wall-clock than the next-best system that closes the full set. The harness also transfers to smaller models: Sonnet closes all four tested FormalQualBench problems, and Haiku closes the two short ones. These results suggest that harness design is a central factor in end-to-end Lean4 theorem proving, alongside raw model capability, and that a relatively simple harness can already be effective.

Reasoning models post-hoc rationalize answers they have already committed to internally, producing chains of reasoning theater: deliberative-looking steps that contribute nothing to correctness. This wastes inference tokens, pollutes interpretability, and obscures what the model actually computed. We introduce ProFIL (Probe-Filtered Reinforcement Learning) to reduce theater, increase chain-of-thought faithfulness, and shrink chain length in a single, drop-in extension to Group Relative Policy Optimization (GRPO). A multi-head attention probe is trained once on the frozen base model to detect post-commitment steps from internal activations alone; during GRPO, rollouts whose probe score exceeds a threshold have their advantage zeroed. Our central finding is that a probe trained on a frozen base, with verifier-derived labels and no human annotation, provides a stable signal that suppresses theater while resisting the RL-obfuscation failure mode predicted by prior work. Across four reasoning domains (GSM8K, LiveCodeBench, ToolUse, MMLU-Redux) and two model architectures (Llama-8B, Qwen-7B), ProFIL reduces post-commitment theater by 11--100%, raises faithful-fraction (e.g., +24pp on LiveCodeBench under an independent Claude 3.7 Sonnet judge), and shortens chains by 4--19%, all while preserving or improving task accuracy. ProFIL also beats a matched length-penalty GRPO baseline, isolating the gain as semantic commitment-detection rather than chain compression. Probe weights, training configurations, and rollouts are released across all four domains.