Z3 Prover

MCP server exposing Z3 solver API

PyPI Python Ruff

Install

pip install mcp-z3-prover

Usage

from mcp_z3_prover import mcp

# Run the server
mcp.run()

Or from command line:

mcp-z3-prover

MCP Tools

The server exposes the following tools:

• create_bool_var - Create a Boolean variable
• create_int_var - Create an Integer variable
• create_real_var - Create a Real variable
• create_int_constant - Create an integer constant
• create_real_constant - Create a real constant
• add_constraint - Add a constraint to the solver
• solve - Solve the current problem
• get_model_value - Get value of a variable from the model
• optimize - Solve with optimization objective
• reset_solver - Reset the solver state
• list_variables - List all created variables

Example

# Create variables
create_int_var("x")
create_int_var("y")

# Add constraints
add_constraint("int:x + int:y == 10")
add_constraint("int:x > 0")
add_constraint("int:y > 0")

# Solve
result = solve()
# Returns: {"status": "sat", "model": {"x": "5", "y": "5"}}

# Get specific values
x_val = get_model_value("int:x")

Integer Factorization Example

# Factor n = 4295229443 where n = p * q with q <= sqrt(n)
create_int_var("p")
create_int_var("q")

# Add constraints
add_constraint("int:p * int:q == 4295229443")
add_constraint("4295229443 > int:p")
add_constraint("4295229443 > int:q")
add_constraint("int:q <= 65537")  # sqrt(4295229443) ≈ 65537
add_constraint("int:q > 1")
add_constraint("int:p > 1")
add_constraint("int:q % 2 != 0")  # q is odd
add_constraint("int:p % 2 != 0")  # p is odd

# Solve
result = solve()
# Returns: {"status": "sat", "model": {"p": "65539", "q": "65537"}}
# Verification: 65537 * 65539 = 4295229443

Development

git clone https://github.com/daedalus/mcp-z3-prover.git
cd mcp-z3-prover
pip install -e ".[test]"

# run tests
pytest

# format
ruff format src/ tests/

# lint
ruff check src/ tests/

# type check
mypy src/

MCP Registration

mcp-name: io.github.daedalus/mcp-z3-prover