Autoformalize English into verified Lean4 proofs.

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December 10, 2025

Aristotle

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Autoformalize English into verified Lean4 proofs.

Autoformalization lean4 Proofs Formal Verification Theorem Proving Mathematical Problem Solving IMO Level Intelligence

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Overview

Aristotle Lean API is an artificial intelligence tool designed particularly to provide a new era of 'Vibe Proving' which aids users in addressing complex reasoning problems.

It adopts the IMO (International Mathematics Olympiad) Gold Medal Level Intelligence engine to develop robust solutions to these problems. One of the main features of this API is the ability to 'autoformalize' English statements and proofs into a formally verified Lean4 proofs.

It has the ability to adapt to various modes of inputs like LaTeX, markdown, or general questions, and it responds by furnishing formally verified Lean4 proofs as explanations.

Aristotle Lean API smoothly integrates with user projects without causing disruptions. It leverages all available resources from the users' theorem and definition libraries along with other dependencies.

Another significant attribute of this API is its capability to generate counterexamples when a statement is incorrect. This feature aids the users in identifying logical errors, overlooked edge cases, or even misformalizations.

Furthermore, Aristotle Lean API is an important tool for autoformalization and formal verification tasks. Overall, it's an advanced tool that combines automatic theorem proving with the functionality of problem-solving and counterexample identification.

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July 29, 2025

Initial release of Aristotle.

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Mathematical proofs Aristotle

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Pros and Cons

Pros

Vibe Proving

IMO Gold Level Intelligence

Autoformalizing English to Lean4

Supports LaTeX, markdown inputs

Produces verified Lean4 proofs

No disruption API integration

Utilizes user's theorem libraries

Generates counterexamples for false statements

Aids in logical error identification

Detects overlooked edge cases

Pinpoints misformalizations

Advanced reasoning capabilities

Seamless project integration

Uses dependencies from Mathlib

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Cons

Lacks support for other languages

Reliant on user's theorem libraries

Limited to mathematical domain

Not for casual users

Optimization for Lean4 only

Overlooks ambiguous English phrases

Limited input formats (LaTeX, markdown)

No customization settings provided

No error handling for correct statements

Possible project interruptions with integration

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Q&A

What is Aristotle Lean API?

Aristotle Lean API is an artificial intelligence tool specifically designed for 'Vibe Proving'. It helps users address complex reasoning problems by autoformalizing English statements and proofs into formally verified Lean4 proofs. It also generates counterexamples when a statement is incorrect, and integrates seamlessly into user projects.

How does Aristotle Lean API work?

Aristotle Lean API works by adopting the Intelligence engine of the IMO Gold Medal Level. It autoformalizes English statements and proofs into formally verified Lean4 proofs. It handles various modes of inputs like LaTeX, markdown, and general questions, providing the responses as verified Lean4 proofs. It can also generate counterexamples when a statement is incorrect, aiding in identifying logical errors, edge cases, and misformalizations.

What is 'Vibe Proving' in Aristotle Lean API?

'Vibe Proving' in Aristotle Lean API relates to the advanced problem-solving abilities it provides to users. The term stands for its features including auto formalization English statement into Lean4 proofs, counterexamples generation for incorrect statements and seamless integration into user projects.

How does Aristotle Lean API use IMO Gold Medal Level Intelligence?

Aristotle Lean API uses IMO Gold Medal Level Intelligence by integrating it into its AI engine. This engine enables Aristotle to tackle complex reasoning problems, potentially of the same difficulty faced in the International Mathematical Olympiad.

How does the autoformalization feature in Aristotle Lean API work?

The autoformalization feature in Aristotle Lean API works by converting English statements and proofs into formally verified Lean4 proofs. This process assists in addressing complex reasoning problems effectively.

What types of input does Aristotle Lean API accept?

Aristotle Lean API accepts various modes of inputs including LaTeX, markdown, and general questions.

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In what format does Aristotle Lean API provide proofs?

Aristotle Lean API provides the proofs in the format of formally verified Lean4 proofs.

How does Aristotle Lean API integrate with my projects?

Aristotle Lean API integrates seamlessly into your projects without causing disruptions. It works by leveraging all available resources from your theorem and definition libraries along with other dependencies.

How does Aristotle Lean API utilize theorem and definition libraries?

Aristotle Lean API utilizes theorem and definition libraries by leveraging all available resources from these libraries during its operations. This utilization enhances the efficiency of its problem-solving capabilities.

Can Aristotle Lean API generate counterexamples?

Yes, Aristotle Lean API can generate counterexamples when a statement is incorrect. This feature assists users in identifying logical errors, overlooked edge cases, or even misformalizations.

How can Aristotle Lean API aid in identifying logical errors?

Aristotle Lean API aids in identifying logical errors through its ability to generate counterexamples. By doing so, users can identify errors, overlooked edge cases, and misformulations.

What is the purpose of Aristotle Lean API in formal verification tasks?

Aristotle Lean API plays a significant role in formal verification tasks. It can autoformalize English statements and proofs into formally verified Lean4 proofs, thereby aiding in the validation of these statements and proofs.

What advanced functionalities does Aristotle Lean API offer?

Advanced functionalities offered by Aristotle Lean API include autoformalization of English statements and proofs into formally verified Lean4 proofs, ability to adapt to multiple modes of inputs, seamless project integration, counterexample generation when a statement is incorrect, and the ability to leverage theorem and definition libraries.

Can Aristotle Lean API diagnose misformalizations?

Yes, Aristotle Lean API can diagnose misformalizations. It achieves this through its ability to generate counterexamples when a statement is incorrect, assisting users in identifying potential misformalizations.

How is Aristotle Lean API useful in problem-solving?

Aristotle Lean API is useful in problem-solving by providing rigorous, formally-verified proofs to complex reasoning problems. It also helps identify overlooked edge cases or logical errors by generating counterexamples when a statement is wrong.

Does Aristotle Lean API support LaTeX and Markdown inputs?

Yes, Aristotle Lean API does support LaTeX and Markdown as input methods alongside general questions.

What is the role of Aristotle Lean API in Mathematical Olympiad?

In the context of the Mathematical Olympiad, Aristotle Lean API’s role could be likened to the reasoning ability of an IMO Gold Medal Level Intelligence. This metaphor represents the API's advanced problem-solving capabilities and its ability to handle complex reasoning tasks.

How do I integrate Aristotle Lean API into my project?

Aristotle Lean API can be integrated into your project seamlessly. It operates without disruptions and leverages all available resources from your theorem and definition libraries, along with other dependencies.

What is the process to access Aristotle Lean API?

The exact process for accessing Aristotle Lean API is not specified on their website. However, the page does provide an option for 'Get access now', indicating there is a process for gaining access to the API.

Who can use the Aristotle Lean API?

The specific target audience for Aristotle Lean API is not identified on their website. However, given its advanced problem-solving, theorem proving, and formal verification capabilities, it is likely aimed at individuals or organizations dealing with complex reasoning tasks, such as researchers, mathematicians, or even software developers.

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