"""
name: Nicholas Tamassia

Honor Code and Acknowledgments:

        This work complies with the JMU Honor Code.

       Comments here on your code and submission.
"""

from itertools import product
from typing import Callable

type Three_SAT = Callable[[bool, bool, bool], bool]


def three_sat_missing(x1: bool, x2: bool, x3: bool) -> bool:
    combos = product([x1, not x1], [x2, not x2], [x3, not x3])
    # Remove the last clause
    missing_combo = list(combos)[:-1]
    return all(a or b or c for a, b, c in missing_combo)


def three_sat(x1: bool, x2: bool, x3: bool) -> bool:
    return all(
        a or b or c for a, b, c in product([x1, not x1], [x2, not x2], [x3, not x3])
    )


# All modules for CS 412 must include a main method that allows it
# to imported and invoked from other python scripts
def main():
    settings = product([False, True], repeat=3)

    sentences_satisfied: dict[Three_SAT, bool] = {}
    sentences_satisfied[three_sat] = False
    sentences_satisfied[three_sat_missing] = False

    for setting in settings:
        for sentence in sentences_satisfied:
            if sentence(*setting):
                print(f"{setting} satisfied {sentence.__name__}")
                sentences_satisfied[sentence] = True

    for sentence, satisfied in sentences_satisfied.items():
        if not satisfied:
            print(f"{sentence.__name__} is not satisfiable")


if __name__ == "__main__":
    main()