Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2406.17762

Solving Hard Mizar Problems with Instantiation and Strategy Invention

Jan Jakubův·Mikoláš Janota·Josef Urban
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we prove over 3000 previously ATP-unproved Mizar/MPTP problems by using several ATP and AI methods, raising the number of ATP-solved Mizar problems from 75\% to above 80\%. First, we start to experiment with the cvc5 SMT solver which uses several instantiation-based heuristics that differ from the superposition-based systems, that were previously applied to Mizar,and add many new solutions. Then we use automated strategy invention to develop cvc5 strategies that largely improve cvc5's performance on the hard problems. In particular, the best invented strategy solves over 14\% more problems than the best previously available cvc5 strategy. We also show that different clausification methods have a high impact on such instantiation-based methods, again producing many new solutions. In total, the methods solve 3021 (21.3\%) of the 14163 previously unsolved hard Mizar problems. This is a new milestone over the Mizar large-theory benchmark and a large strengthening of the hammer methods for Mizar.

Explore related subjects

cs.AIcs.LGcs.LOcs.SC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jan Jakubův, Mikoláš Janota, Josef Urban. 2024-06-25. Solving Hard Mizar Problems with Instantiation and Strategy Invention. https://arxiv.org/abs/2406.17762

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Small Language Models are the Future of Agentic AI

Large language models (LLMs) are often praised for exhibiting near-human performance on a wide range of tasks and valued for their ability to hold a general conversation. The rise of agentic AI systems is, however, ushering in a mass of applications in which language models perform a small number of specialized tasks repetitively and with little variation. Here we lay out the position that small language models (SLMs) are sufficiently powerful, inherently more suitable, and necessarily more economical for many invocations in agentic systems, and are therefore the future of agentic AI. Our argumentation is grounded in the current level of capabilities exhibited by SLMs, the common architectures of agentic systems, and the economy of LM deployment. We further argue that in situations where general-purpose conversational abilities are essential, heterogeneous agentic systems (i.e., agents invoking multiple different models) are the natural choice. We discuss the potential barriers for the adoption of SLMs in agentic systems and outline a general LLM-to-SLM agent conversion algorithm. Our position, formulated as a value statement, highlights the significance of the operational and economic impact even a partial shift from LLMs to SLMs is to have on the AI agent industry. We aim to stimulate the discussion on the effective use of AI resources and hope to advance the efforts to lower the costs of AI of the present day. Calling for both contributions to and critique of our position, we commit to publishing all such correspondence at https://research.nvidia.com/labs/lpr/slm-agents.

cs.AI↗
arXiv2026

EndoCogniAgent: Closed-Loop Agentic Reasoning with Self-Consistency Validation for Endoscopic Diagnosis

Endoscopic diagnosis is an iterative process in which clinicians acquire, compare, and verify local visual evidence before reaching a conclusion. Current AI systems do not adequately support this process because fine-grained evidence acquisition and multi-step reasoning remain weakly coupled, complicating reconciliation of image-derived findings with their textual interpretations. This gives rise to two failure modes, hallucinated evidence and uncorrected error accumulation, that undermine diagnostic reliability. We propose EndoCogniAgent, a closed-loop agentic framework that formulates endoscopic diagnosis as a controlled state update process for integrating complementary visual and textual evidence. At each reasoning round, a central planner selects an evidence acquisition action, specialized expert tools extract spatial and semantic observations as structured textual evidence, and a self-consistency validation mechanism examines this evidence along two dimensions, knowledge consistency against the input image and temporal consistency with prior validated findings, before updating the diagnostic state. Validated observations are admitted into the evolving state to condition subsequent planning, while insufficiently supported or conflicting findings are retained with corrective feedback that redirects the planner toward additional verification. We further introduce EndoAgentBench, a workflow-oriented benchmark comprising 6,132 question-answer pairs from 11 endoscopic datasets, to evaluate diagnostic agents across a comprehensive diagnostic chain, from fine-grained visual perception to high-level diagnostic reasoning. EndoCogniAgent achieves 85.23% overall accuracy on perception tasks and 71.13% clinical acceptance rate on reasoning tasks. Blinded clinician evaluation further shows consistent improvements in diagnostic response quality over the evaluated baselines.

cs.AI↗
arXiv2026

Navigating Taxonomic Expansions of Entity Sets Driven by Knowledge Bases

Recognizing similarities among entities is central to both human cognition and computational intelligence. Within this broader landscape, Entity Set Expansion is one prominent task aimed at taking an initial set of (tuples of) entities and identifying additional ones that share relevant semantic properties with the former, potentially repeating the process to form increasingly broader sets. However, this ``linear'' approach does not unveil the richer ``taxonomic'' structures present in knowledge resources. A recent logic-based framework introduces the notion of an expansion graph: a rooted directed acyclic graph where each node represents a semantic generalization labeled by a logical formula, and edges encode strict semantic inclusion. This structure supports taxonomic expansions of entity sets driven by knowledge bases. Yet, the potentially large size of such graphs may make full materialization impractical in real-world scenarios. To overcome this, we formalize reasoning tasks that check whether two tuples belong to comparable, incomparable, or the same nodes in the graph. Our results show that these tasks are intractable in general, that they remain intractable when the number of input tuples is bounded, and that they become solvable in polynomial time when the descriptions of the entities are small as well. The bounds we establish are tight. This enables local, incremental navigation of expansion graphs, supporting practical applications without requiring full graph construction.

cs.AI↗