FOL Prover Server

An MCP (Model Context Protocol) server for First-Order Logic theorem proving using Vampire, E, and Prover9.

Features

• Multiple Provers: Support for Vampire, E (eprover), Prover9, and built-in simple prover
• Built-in Prover: Simple resolution-based prover requires no external installation
• FOL Parsing: Parse and validate first-order logic formulas with Unicode notation
• Session Management: Build proofs incrementally with named sessions
• TPTP Export: Convert problems to standard TPTP format
• Automatic Fallback: Try multiple provers if one fails

Installation

Prerequisites

The server includes a built-in simple prover that works without any external installation. For more complex proofs, install one of the following theorem provers:

Vampire (recommended):

# Linux (Ubuntu/Debian)
sudo apt-get install vampire

# macOS (with Homebrew)
brew install vampire

# Or download from: https://github.com/vprover/vampire

E Prover:

# Linux (Ubuntu/Debian)
sudo apt-get install eprover

# macOS
brew install eprover

# Or download from: https://wwwlehre.dhbw-stuttgart.de/~sschulz/E/E.html

Prover9:

# Download from: https://www.cs.unm.edu/~mccune/prover9/

Install the MCP Server

pip install folprover-mcp

Or install from source:

git clone https://github.com/folprover-mcp/folprover-mcp
cd folprover-mcp
pip install -e .

Configuration

Add to your MCP client configuration:

Claude Desktop

Add to ~/.config/claude/claude_desktop_config.json (Linux/macOS) or %APPDATA%\Claude\claude_desktop_config.json (Windows):

{
  "mcpServers": {
    "folprover": {
      "command": "folprover-mcp"
    }
  }
}

VS Code with Continue

Add to your Continue configuration:

{
  "mcpServers": {
    "folprover": {
      "command": "folprover-mcp"
    }
  }
}

Usage

FOL Notation

The server supports standard FOL notation with Unicode operators:

Symbol	Meaning	Example
∀	Universal quantifier	∀x P(x)
∃	Existential quantifier	∃x P(x)
∧	Conjunction (AND)	P(x) ∧ Q(x)
∨	Disjunction (OR)	P(x) ∨ Q(x)
→	Implication	P(x) → Q(x)
↔	Biconditional	P(x) ↔ Q(x)
¬	Negation	¬P(x)
⊕	Exclusive OR	P(x) ⊕ Q(x)

You can also use ASCII alternatives:

• forall or all for ∀
• exists for ∃
• & or and for ∧
• | or or for ∨
• -> or implies for →
• <-> or iff for ↔
• ~ or not for ¬

Tools

prove

Execute a FOL proof directly:

{
  "premises": [
    "∀x (Human(x) → Mortal(x))",
    "Human(socrates)"
  ],
  "conclusion": "Mortal(socrates)",
  "prover": "vampire"
}

add_premise

Add a premise to the current session:

{
  "premise": "∀x (Human(x) → Mortal(x))"
}

set_conclusion

Set the conclusion to prove:

{
  "conclusion": "Mortal(socrates)"
}

prove_session

Prove using the current session's premises and conclusion:

{
  "prover": "vampire"
}

parse_formula

Parse and validate a FOL formula:

{
  "formula": "∀x (P(x) → Q(x))"
}

convert_to_tptp

Convert a problem to TPTP format:

{
  "premises": ["∀x (P(x) → Q(x))", "P(a)"],
  "conclusion": "Q(a)"
}

list_provers

List available theorem provers:

{}

Session Management

• create_session: Create a new named session
• list_sessions: List all active sessions
• switch_session: Switch to a different session
• get_session: Get current session state
• clear_session: Clear all premises and conclusion
• remove_premise: Remove a premise by index

Examples

Example 1: Classic Syllogism

Premises:

1. All humans are mortal: ∀x (Human(x) → Mortal(x))
2. Socrates is human: Human(socrates)

Conclusion: Socrates is mortal: Mortal(socrates)

Result: Theorem (True)

Example 2: Set Theory

Premises:

1. If x is a subset of y and y is a subset of z, then x is a subset of z: ∀x ∀y ∀z ((Subset(x,y) ∧ Subset(y,z)) → Subset(x,z))
2. A is a subset of B: Subset(a, b)
3. B is a subset of C: Subset(b, c)

Conclusion: A is a subset of C: Subset(a, c)

Result: Theorem (True)

Example 3: With Counter-model

Premises:

1. Some birds can fly: ∃x (Bird(x) ∧ CanFly(x))

Conclusion: All birds can fly: ∀x (Bird(x) → CanFly(x))

Result: Not a theorem (False - there's a counter-model where some bird can't fly)

Architecture

folprover-mcp/
├── src/folprover_mcp/
│   ├── __init__.py
│   ├── server.py          # MCP server implementation
│   ├── provers.py         # Prover interfaces (Vampire, E, Prover9, Simple)
│   ├── simple_prover.py   # Built-in resolution prover
│   ├── fol_parser.py      # FOL formula parser
│   └── tptp_converter.py  # TPTP format converter
├── tests/                 # Test suite
├── examples/              # Example proof problems
├── pyproject.toml
└── README.md

References

• Vampire Theorem Prover
• E Theorem Prover
• Prover9
• TPTP Problem Library
• Logic-LLM - Original inspiration
• MCP Specification

License

MIT License