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Mathematical proofs

Aristotle ✓

Autoformalize English into verified Lean4 proofs.

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

A quick read before you dig into the full page.

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Autoformalize English into verified Lean4 proofs
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Limited input formats (LaTeX, markdown)
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Vibe Proving

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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.

Aristotle website

Access & connections

Where you can use Aristotle.

Platforms

Web

Capabilities

What this tool accepts, produces, and is strongest at.

Input

  • API
  • Text

Output

  • Code
  • API

Pros & 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
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  • Aids in logical error identification
  • Detects overlooked edge cases
  • Pinpoints misformalizations
  • Advanced reasoning capabilities
  • Seamless project integration
  • Uses dependencies from Mathlib

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
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  • No error handling for correct statements
  • Possible project interruptions with integration

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Releases 1

Initial release July 29, 2025 Current
Initial release of Aristotle.

FAQ 12

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.
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.
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