hwayne

    from z3 import \*

    a, b, c = Ints('a b c')
    x, y = Ints('x y')
    s = Solver()

    s.add(a > 5)
    s.add(a % 2 == 0)
    theorem = Exists([b, c],
                     And(
                         a == b + c,
                         And(
                             Not(Exists([x, y], And(x > 1, y > 1, x \* y == b))),
                             Not(Exists([x, y], And(x > 1, y > 1, x \* y == c))),
                             )
                         )
                     )

    if s.check(Not(theorem)) == sat:
        print(f"Counterexample: {s.model()}")
    else:
        print("Theorem true")