gene 0.7.2

use std::collections::HashMap;

use lazy_static::lazy_static;

#[cfg(test)]
mod test {
    use super::*;
    use crate::rules::condition::*;

    #[test]
    fn test_condition_computation() {
        TEST_CONDITIONS.iter().for_each(|(condition, result)| {
            let cond = Expr::from_str(condition).unwrap();
            assert_eq!(cond.compute(&OPERANDS).unwrap(), *result)
        });
    }
}

// Below are just defined structures used for tests, no need to scroll down

lazy_static! {
    static ref OPERANDS: HashMap<&'static str, bool> = {
        let mut m = HashMap::new();
        m.insert("$a", true);
        m.insert("$b", false);
        m
    };
    static ref TEST_CONDITIONS: Vec<(&'static str, bool)> = vec![
    ("$a",true),
    ("$b",false),
    ("!$a",false),
    ("!$b",true),
    ("$a or $b",true),
    ("$a and $b",false),
    ("($a and !$b)",true),
    ("((($a and !$b)))",true),
    ("$a and ($b or !$b)",true),
    ("!($a or $b) or $a",true),
    ("$a && !$b && !$a",false),
    ("!($a and $b or !($a and $b))",false),
    ("!($a or $b) and ($a or ($b and !$a)) and !$a",false),
    ("!$b or (!($a or $b) and ($a or ($b and !$a)))",true),
    ("(!($a or $b) and ($a or ($b and !$a)))",false),
    ("(($a and !$b) and $a)",true),
    ("(!($a and $b) and $b)",false),
    ("(!($a and $b) and $b) or (($a and !$b) and $a)",true),
    ("!(!($a || $b)) && !(!$a and !$b)",true),
    ("!(($b and $a) or $a)",false),
    ("!($a or ($b and $a))",false),
    ("(($a or $b) and $b)",false),
    ("$a or $b or ( $b and ($a or $b) and $b)",true),
    ("$a and ($a or $b) and !($a or $b or $a or $b or $a or $b or $a or (($a or $b) and $b))",false),
    ("$a and !($a or ($a and $b))",false),
    ("$a and !$b",true),
    ("$a and !(($a and $b))",true),
    ("$a and !( ($b and $b) or ($b and $a) or $a )",false),
    ("$a and !(($b) or ($b) or $a)",false),
    ("!(($b) or ($b) or $a)",false),
    ("!( $a and ( $a or !$a and !$b and $b and ( $a and ( $a and !$a or $b or !$a or $b ) ) ) )",false),
    ("!$a or !$a or ($b or $a and !$a or !$a) or ($b and $a and !$b and $a) and ($a)",false),
    ("$a or $a or !$a or !$a or !($a and !$b or ($b) or !$a or ($b or !$a and !$b))",true),
    ("!$b or !$b and (($b or !$b or ($b and $b or $b) or $b) and ($b or !$b) and !$b)",true),
    ("$b and !$b and ($a or !($a and $b or !($a) and !$b)) and !$a and !$a and !(($b or !$a))",false),
    ("!$a or $a or !$a or !($a or ($a or $b and !$a and $a) and !($b and $b or !$b))",true),
    ("($b or $b) and !$b and !($b or !($b and $a or !$a or !$b and $b or !$b or $b))",false),
    ("!($b or !$b and $a and !$b or !$b and ($a and !$b or $b or !($a or $b or !$b)))",false),
    ("!$a or !$a and !$b or !$b and !$b and $a or $b or !$a and !$a and $a and ($a)",true),
    ("!($a or $a or $a or $a or ($a or !$b and ($b) or $a and $a or !$a) and $b)",false),
    ("!(($b and $b or !$a) and !$b and $b or !$b and !($b and !($b) and !$a or !$b and !$a))",false),
    ("$a and !$a and !$b and $b and $a or !($b or !($b or !$b and $a and !$a and !$a))",false),
    ("($b and !$b or !$a) and ($a or ($b and !$a and $a) and !$b or $b or !($b and !$b))",false),
    ("$b or $b or $a or $b or ($b or (($b or !$a) or !$b and $a or $a) and !(($b)))",true),
    ("!$b or !$b and !$b and !$b and !$a and !$a or $b or $a or !$b or ($b and !($b))",true),
    ("($b and !($b or (($a and $b) and ($a and $a and !($b) or !$a) or ($a) and ($b or !($b)))))",false),
    ("!($a and $a) and !($a and !$b and ($a or !$a or !($b and !$b and ($b and ((($a) or !$a))))))",false),
    ("!$b or $b and !$b and $a and ($b or $a or !$a and !($b or $a) and ($b and !$b))",true),
    ("(($b and !$b or ($a or !$a and !$a or !$b and $a) or !(($b) and !($b or !$a) and !($a))))",true),
    ("($b and !$b or !$a and $a and $a or !($a and $a and !($a or !($b and !$b and !$b))))",true),
    ("(($a and !($a or ($b or !(($b and ($b) and ($b) and $b and !$b and $a and !($a or !($b))))))))",false),
    ("(($a and (($a or !($a or $a and (($a or $a and !$a or !$a) and !$b and $a and !($b)))))))",true),
    ("$a and !($a or $a or $a and $b or !$a and $a or $b and !($b or $a or $a))",false),
    ("!$a and $a and $b and !($a and !$b and !$b and $a or !$b or $a or (($a and !($a))))",false),
    ("($b or $b or $b and !($a or (($a) or !$b) and !($b and $a and !$b or !$a and !$a)))",false),
    ("($a or $a and !$b or ($b and !$a or $a and $a and !($a and $b and $a) or !$a))",true),
    ("!$b or $b or !$b and $a and ($b or !$b or !$b or !(($b or !$a and $a or $b)))",true),
    ("(($b or ($b) and ($b or ($a or $b and !$b or $b) or $a and !(($b and $a or !$b)))))",false),
    ("!$b or !($b or !($a or !$b and !$b or !$a) or $a or $a) and !$b or !($b and $a)",true),
    ("!$b and $b or ($a and !($a or !$a or !$b) and $a or (($a and !$a) or !($a)) or (($a)))",true),
    ("$b or $b or !$a and ($b or !$a and $a and !($b) or $b or !$b or !($b or !$b))",false),
    ("$a or !$a or !$b or !(($b or !$a and ($b) or !($a) and ($a and !$b or !$a or $b)))",true),
    ("($a or ($a or !($b and !($b) and ($b)) or ($a or !(($a or $a) or $a) and (($a or $a)))))",true),
    ("$a and !$a or ($a or !$a or !$a or $b or $a) or !($b and !$b) or !$b and ($b)",true),
    ("$a and !$a and $b and !($a and $a and $b and $b and !$a and $a or !$a or !(($a)))",false),
    ("!$b or ($b and !$a and !($a or $a or !$b or !($a and !$a and !($a or ($b and !$a)))))",true),
    ("$a and (($a and ($b or !($a) or !$b or !($b) and ($b and ($b and !$a)) and $a and !($a))))",true),
    ("($b and $b or !$a) or $a or (($a or !(($a or ($a) or !$b and $b and !$a and $a))))",true),
    ("!($b or ($b or !$a and !$b or !$b and !(($a) or !$b and !$a or $b or !$b and $a)))",true),
    ("!$a or !($a or ($b and !$a and !$b or ($a and $a) or $b and !($a and $a) or !$b))",false),
    ("!$a or !$a or $b and !((($a or ($a and $b and ($b and ($a and !$a or !($b or $a)))))))",false),
    ("$a or !$a or !$b or !$b or !($b and !($a or $a and !$a) or ($a or $a or !$b))",true),
    ("($b and !($b or $a) or $b or $a and $a or $a and $b or $b and !($a or !$a))",true),
    ("$b or !($b and ($a or !($a or !$a or !$b or !$a or $b and !$a and $a or $a)))",true),
    ("$b or (($b or $a or !($a or !($a or ($a or !$b or !$b and !$a and $b or $b)))))",true),
    ("!($a and $a or !$b or !$a and !$b and $a or ($b and ($a) and !$a or !($b and !$a)))",false),
    ("$a and !$a or !($a and $b or $b and !$a and !$a or $a and $a or !$a) or (($b))",false),
    ("!($b and !($b and $a and $b) or $b or !$b or !$b and !(($b and !$b and !($a or !$b))))",false),
    ("$b or !(($b and $a or !$a or !$b and (($a and !$b and $b) or (($b or !($b) and !($b))))))",false),
    ("($b and !$b) or !$b or !($b or !$b or $b and ($b and !($b and !$b or !($b and $b))))",true),
    ("(($b or !($b and !$a or $a and $b or !(($b or ($b and $a and !($a)) and !$a) and $b))))",false),
    ("(($a or !($a or ($b and $a and ($a)) or $b) and $b) and !($b or ($a and !$b and !($a))))",true),
    ("$a and !$a and $b or !(((($a and !(($b and $a or ($a) and !$a)) or $b or !$a and !($a)))))",false),
    ("$b or $b or !$a or $a and ($b or !$b or $a and !($a or !$a and ($b and !$b)))",true),
    ("!(($a and $a and !(($a or !$a or $a or !$a and !$a) and !($a or ($b or !$b) and (($b))))))",false),
    ("($b or !$b or !($a or !($a or ($a or $b or !$b or !$b)) and !$a and !$a or !$b))",true),
    ("$a and !$a and !$b and !($a and $b and !$b and !$b or $b or $b and $a) and (($a))",false),
    ("$a and !$a or $a or !$b or !$a and !$a and !$b and !$a and $a or (($a or !($b)))",true),
    ("!$a and $a and !$a or $a or $b and !$a or !$b or !($b or !$b or ($b or $a))",true),
    ("($b or $b or !$a and !$a and !$b or !$a or !($a and ($a) and !($b or ($a and $a))))",true),
    ("($b or !($b) or !(($b or !$b) or $b or $a and !$a or !(($a or ($b or !$b or ($a))))))",true),
    ("!$b and !(($b or !($b) and !$b or !($b and !$a or $b or $b) or !$a and $b or $a))",false),
    ("!$b and !$b and (($a and !$a or !$b) or !$b or !$b) or !$a or !$b and !((($b or !$b)))",true),
    ("!$b and ($b or $a and $b and !(($b or !$b and !$b and $a and ($a and ($b or !$b)))))",false),
    ("!($a or !$a or (($a or !$a or $a and !$b or !$a or $a) and $b or $b and $a))",false),
    ("!(($b or !$b) or !($a and !$b or !$a or !($b and ($a or $a and !($b or $b and $b)))))",false),
    ("!$b or !(($b and $a) or !$a and $b and !$a or $a and (($a and !($b and $a) or $a)))",true),
    ("!(($b and !($b or !($b and !$a or $a and ($b or !$a and ($b)) or ($b and !($b and ($b)))))))",true),
    ("!$a or !$a or !$b or !($b and !$a and ($b or $a and ($b and !$b) and $a) and !$b)",true),
    ("($b or $b or (($b or !($b) and !($a and ($a or $b) or ($a or $a or $b and $b)))))",false),
    ("!($b or $b and $b and !($a or !($a) and !$a and $a) and $a or !$b or !$a and ($b))",false),
    ("$b or $b and !($b or !$a or !$b and $b and !($b or $a) and !$a or ($a) and !($a))",false),
    ("($a and !(($a or $a or $a or $b or !$a and ($b and $b and !$b or !$b) or !$a)))",false),
    ("$b or !($b or !($a or $a and ($a and ($a) and $b or !$a and !$b and $b and !$b)))",true),
    ("$a and !($a or $b or $a and !(($a or ($a) or !$a and !$a) and !($b and $a) or $b))",false),
    ("(($b and $b or $a) and !$a and !($a) and $b or $a and ($a and ($a) or (($b and !($b)))))",true),
    ("$a or $a or ($a or $a or !($b and !$a and !(($a or $a))) and $b and $b or !$a)",true),
    ("$b or ($b or ($a or !($a or ($a and $a and !$b and !$a or ($a) or !$b or !$b))))",true),
    ("!($b or $b or $a and !($a) or !$b or !$b or !$a or $b) and !$a and !$b and ($b)",false),
    ("!($b or $b or (($b and $b and $a or !$a and !($b or !$a) and $a) or !($b or !$b)))",true),
    ("($a or !$a or !$b) and $a or !$a and $a or ($a or ($b or !$b and !$a and !$a))",true),
    ("!($a and !$a and !($a or $a and !$a and !$b and !$a) and $a and ($b and ($a and $a)))",true),
    ("!($b and !$b or !($a or !($a and (($a or $b and !$b) or $b and !$b or $b and $a))))",true),
    ("!($b and $b and !$a or !$a and $b or ($a and !$a or $a and !$a or ($b and $b)))",true),
    ("(($a or $a or $b or $b and $b or $a or !($b) or ($b or !$a and !$b and !$b)))",true),
    ("!$a or $a and !$b and $a or ($b or !($a and $b or $a and !$a and $a and $b))",true),
    ("!$b or ($b and !$b) or ($a and !($b or !$a and ($b or !$b and !$a and !($a and $b))))",true),
    ("$a or ($a or !($a and !$a and ($b and $b or (($a and !($a or $a or !($a and !$b)))))))",true),
    ("!($a or ($a or $a and !$b and $a and $b) or $a or !$a or ($a and $a and $b))",false),
    ("$b and ($b and !$b or !$a) or !$a and ($b or !$b or !$a or !$b and !($b and !$b))",false),
    ("!$b or !$b or $a or !(($b and !($a and !$a or $a and $a or $b and $a or $a)))",true),
    ("$a and $a or !($a and $b or ($b) or !$a and $b and $a or !$b and !$a) and ($a)",true),
    ("!(($a and $a or !$a and !($b) and $a) or ($a and $b) or !$b or !(($b and !$b or !($b))))",false),
    ("($b or !$b and !$a or !($b or $b and !($b or ($b) and $b or $a or $b)) and !($b))",true),
    ("$b and $b and !$a or !($a or !$b or $a and $a or $a and !$a or ($b and $b))",false),
    ("!$b or $b or ($b and (($b or $b or ($a or $a or $b and !$a and $b and !$a))))",true),
    ("$a and ($a or !($a and !$a and $a or $b or $b and ($b and $a and !$a or $b)))",true),
    ("!($a and $a and (($b or !$a or ($a and $a or $b and !$a)) and ($a)) and $a or !($a))",false),
    ("!($a or ($a or ($a or ($b or $a)) or !($a or ($a or $b) or $b or !$b) and !($a)))",false),
    ("$b and $b or !$b or $a or !($b and !$b and $b or !$a or !$a or $b or !$b)",true),
    ("!$b and !($b and !$b and $b or !($a and $b and $a and !$a and !$b or !$b) and !$a)",true),
    ("!(!($a and $b and $a and !$a and !$b or !$b) and !$a)",true),
    ("!$a and $a or $a and ($b or ($b or ($a) and !($b)) or !$a and !($a and $b and !$a))",true),
    ("!($b or !$b or ($a and !$b or $a or !$a and !($a or !($a or $a or $a and $a))))",false),
    ("$b and !$b and !$a or !$b and $b or ($b or $b or $a and $a and (($a and $b)))",false),
    ("$a or $a and $b or !$b and !$a and !$a or !$a or !($a or ($a or $a and $b))",true),
    ("!($b and $b and $b or ($a or !$b or !($b and $a and $b or !($a or !$a) and $b)))",false),
    ("$b and ($b and (($b or $b and $b) and ($a and !$a or !($a and ($b and !$a or !($a))))))",false),
    ("($a or !$a) and !(($a or ($a or (($b and $a or $a and !$b and !($b)) or !$b or !$b))))",false),
    ("!$a or !$a or $a and ($a and !$b and $a or ((($a or !$a and !$b and !$a and !$b))))",true),
    ("!$a and $a or ($b or !$a) and $a and $b or !$b and !$b or !$b and !($a or !$a)",true),
    ("$a and !($a or ($a and !$b and !($a and !($a and $b or $b) or !$b and $b) and !($b)))",false),
    ("!$a or !$a or ($b and !$a and $b or $a and (($a and !($b and $a or !($b or $a)))))",true),
    ("(($a and $a and ($b or !($a or $b or !($b and $b and $b) or !$b or $b or $a))))",false),
    ("!($a or !($a or ($b or $a and $a)) or $b and $b or ($b or $b or !$a or !(((($a))))))",false),
    ("!$a and $a or !($b or !$b or $b or !($a and !$b or !($a) or $a and !$b and $b))",false),
    ("!$a and !$a and $b and $b or !$b or ($a or $b or !($a or $b and $b) and !($b))",true),
    ("($a or !($a or !$b) or $b or $b and !$b or $a or !($a or $b and $b or ($b)))",true),
    ("$b or (($b and !$a or !($b or !$b) and !($b and ($a or !$b) or !(($a) or !$b) and (($a)))))",false),
    ("$a or !$a and ($b and ($b and $a) or !$b or $b or !$b and $a or !$b and $a)",true),
    ("$a and ($a or !$b and !$a or ($b or !$a or $a or !$b or !$a and !$a or $a))",true),
    ("!$b and !($b and $b or !$b and $a and $a or !$b and !$b and !$a or $b and !$a)",false),
    ("!(($a and $a and ($b or (($a and ($a and !$b and !($a or !$a) and $a and $a) and !$b)))))",true),
    ("!($b and !$b and ($a) or ($a and !$a and $a or $a or $b or !$b and !$b and $b))",false),
    ("!$b and ($b or $a and ($a or $a and !$b and $b or !$b and !($a and $a) or !$b))",true),
    ("!($a or (($a and $a and !$b) and $b) or !$a or (($a and !($a and ($b) or ($b and !$a)))))",false),
    ("!$a or !($a or !$b and ($a) and ($a and !$b and $b) and $a or ($a and ($b and !$a)))",false),
    ("!$a and !($a or $b or ($b) and !$a or !$b) and !($b or !($a or ($a or ($b or !$b))))",false),
    ("!(($b and $b and $b and !$b or !$b and !$a and !((($b or !$b and !$b or $b and $b)))))",true),
    ("!($a or !($a or ($a or !($b or !((($a) or !($a) or !($a and !$b) or $b or !$b and !$a))))))",false),
    ("$a and !$a or !(($a and ($b and !$b) or $b or $b) or ($a and ($b) or $b or !(($a))))",true),
    ("!$b and $b and !($b or !($a and $a or !$b and !$b and !($b or $b) or !($b and !$a)))",false),
    ("!(($b and !($b or !$b and !$b or !$a) and !$a and $a) or ($b or !($b or !($a and !$a))))",true),
    ("!(($b and !($b and $a and $a and !($b and $b or !($a or !($b or !$b or $b) and $a)))))",true),
    ("($a and ($a and !($b) and $b or $a and !$a or !$b)) or $a or !($b and !($a or !($a)))",true),
    ("!($b or !$b and ((($a or !$a or !$b or !$a and ($a and !($a and !$b) and !($a and !($b)))))))",false),
    ("!($b or $b or !$a or !$b and !(($b or !$a and !(($b) and !($b or !$a or ($b and !$a))))))",false),
    ("!(($a and !$a or (($a or !($a and ($b or $a and $a) or !$b) or ($a or !$a or $b)))))",false),
    ("$a or $a and $a and ($b and !$a) and !$b or ($b and ($a and $a and $a or ($b)))",true),
    ("$b and !($b and !$b) and !($b and !$a or !($b or !$a or ($a and $b) and $a) or $b)",false),
    ("!$b and !$b or ($a and !$b and (($a or !$b and $b and !$b)) and !($b) or $a or (($b)))",true),
    ("$a and !$a or !$b and !(($b and ($a and !$a or !$a or $b or $a or !$a and $b)))",true),
    ("$a or !$a and $b and $b or $a or $a and !$b and !$a or $b and $b and $a",true),
    ("$a and !$a or !($b and !($a or $a or $b or !$b and !$a and $b or !$b or $a))",true),
    ("!$a and $a and $a or $a and ($b or ($b or $b or !$b or !$a or $a) or ($b))",true),
    ("!($a or !($a or !$a and ($a or $a and $b and !$b or $b or !$a or !$a or ($b))))",false),
    ("$b and !$b or !$a or !($b or !$a and !($a and ($a and (($a and $b) or $a or ($b)))))",true),
    ("$b or !($b and $b and $a and !$a and !$b and ($b and !$a or !($b or !$b or !$b)))",true),
    ("!$b or ($b or $b and $b and !$b or ($b and $a or !$a or $a and !$b or ($b)))",true),
    ("$a and !($a and !$a and !$b) or !$a or $a and $a and (($a or $b and $b and $a))",true),
    ("!$a and ($a and ($b and ($b or !$b and !($b and $b) or !($b or $a and $a and !$b))))",false),
    ("($a or !$a and !($a and $a and !((($b or ($b) or !$b) and $b and ($a) or !$b and ($b)))))",true),
    ("$b or !(($b and $b or !$b or $b and ($b and !($b and !(($a) or (($a or (($a or !$a)))))))))",false),
    ("($a and !($a and !(($b and !$b and $b)) and !$b or ($a and ($b) and !($b) or ($b or $a))))",false),
    ("$b and $b and !($b and ($a or !$a) or !$b and ($a and $a and !($a or !$b or $b)))",false),
    ("$b and ($b or (($b or !($b) and !($a) and (($a or $b or ($a or ($b and $b or $a)))))))",false),
    ("$a and !($a or $b and !$b or !$a and $b and $b and !(($b or $b and !$b or !$a)))",false),
    ("!(($a and !$a or !($b) or !$a or $a or $b) and !$a or !$b and !$a and $b or (($b)))",true),
    ("!$b and ($b or !$b and ($a and !$a) and !$a or $a) and $a or !$b or !$a and $b",true),
    ("$a and $a or ($b and ($a or !($b or !$b and !(($a or !$b or !$b) or !$a or !$b))))",true),
    ("!($a and ($a or $a and $b and !$b and !$b or ($b or $b or !$b and !$a and ($b))))",false),
    ("!($a or !$a or ($a and !$a and $a or ($a and $a) or $b and $b or ($b and !($b))))",false),
    ("!$a and ($a and ($a and !(($a) and !$a) and ($b) or $a or $b or !$b and $a and !$a))",false),
    ("!($b or (($b or !$b and $b) and ($a or !($b or !$b or $a) or ($a or !($a or $a)))))",true),
    ("!(($b and (($b and !(($b or $a) and $b and (($b and !$a) or !$a) or ($a and $b) and $a)))))",true),
    ("!$b or ($b and $a or !($b or $b and $b) and !$b and (($a or !($b) and !$a and $a)))",true),
    ("$b or ($b or !((($a and !$b) and $b and !$b or !($a or (($a or !($b and (($b or !$b)))))))))",true),
    ("($a or !$a and ($b or !$b or $a and $b or !($b) or $b or $a and !$b or ((($a)))))",true),
    ("!($a or !$a or !$a or !($a and !$a) or !$b) or ($a or $a and $b or $b) and ($a)",true),
    ("($a or !$a or $a or ($b or !$a or $b or $a or !($a and !($b and $b and $b))))",true),
    ("!$b and $b and !$b or !(($a or !$a and !$a or (($a and $b) and !($a) and $a) or !($a)))",false),
    ("$b or !($b and $a and !$b) or !$b and $a and !($b and !($b or !$b or !$b or !($a)))",true),
    ("!($b and !$b and !$a or !($b or $a and !$b or !$a or !$b or $b and !$b and $b))",true),
    ("!$a and !$a and !$b or $b and !(($b or !$b) or ($b or !$b or $b or !$b) or $a)",false),
    ("(($b or ($b and ($a and $a) and !$a) and !(($b) and !$a or !$a or ($a or !$a) and $a)))",false),
    ("$a and !$a or $b and !($a or ($a or !($b or $a) or $a and !$b or !$b or $a))",false),
    ("!($a or !$a or $a and $b and !$b or $a and !$a and $b or !$b and !($b and $a))",false),
    ("$b or $b or ($b and !$a and !$a or !$b or $a or !($b or !$a and (($b or $b))))",true),
    ("!$a or !($a and ($b and !(($b or $b and !($b and !$b or !$a and ($a) or !$a) and $a))))",true),
    ("($a or $a and $b and ($b or !$a or !$a or ($b or ($a) or $b or $b) and $b))",true),
    ("(($a and !($a or !($b) or !((($a) and !(($b or !$b) or !$b or $a and !$b and !$b) or $a)))))",false),
    ("(($a and !$a and !($b and $b or $b or $a and !$b and $b or !$a or $a and !$a)))",false),
    ("!(($b and !($b or $a and !$a) and ($b) and $b and $a or ($b and $a) or ($b and !$b)))",true),
    ("!($b or $b and $b or $b) and !$a or !$b and !($a and $b and !($b and $a and ($a)))",true),
    ("!($a or !($a or $a or !$b and $a and $b or ($a or !$b) and $b) or $a and ($a))",false),
    ("!$a or $a or !$a and ($a and !$a and ($a and ($a or ($b or !($b) and !$a or !$b))))",true),
    ("!($a and $a and ($a or !$a or !(($a and $b and ($a or $b) or $a and $b or !$a))))",false),
    ("!$a or !$a or !($a or !$b) and $b or $b and !$b and $a and $b and !$a and $b",false),
    ("!($a or !($a and !($a or !$b and !$b or $b or !$a or $b or !$a and $b) or $b))",false),
    ("(($b or !($b and $b and ($b or !($a) and !($b and $a and !$b) or $b) or !$b or ($a))))",false),
    ("!$a or !(($a or $b or $b and ($b and !((($a and !$b and !$a and ($b and $b) and !$b))))))",false),
    ("!($b and !($b or $a and ($a and !$a) or ($b or (($b or $b)) or !$a and $a or !$a)))",true),
    ("$b and $b and !$a and ($a or !($a and $b and !((($a and $a) and $b or $a or ($a)))))",false),
    ("!($b and ($b or $a and ($b or !$a) and !($a and !$a or !$a or !$b or $b) and (($b))))",true),
    ("!$a and $a or $a and $b or !($b or (($a or !$a or $a) or $b) and !$b or !($a))",false),
    ("($a or !$a or !$b) or $b and $b or $a and $a or ($b and $a and ($b) or ($a))",true),
    ("!(($b or $b) and !$b or !$a and $a and !($b and !$a and $b or !($a or !$a and (($a)))))",true),
    ("($b and !$b and !$b or !$a and !$a and !($b or !$a and !$b and (($b or !($a or ($a))))))",false),
    ("!((($a or !($a or $a and $a or !$a and ($a) and !(($a and $a or $a and ($b and $a)))))))",false),
    ("($b and !$b) or (($b and !$b and ($b or !($b) and $b and !$a or !(($b and $b or $b)))))",false),
    ("$a and (($a or !($a or ($b and $a and $b and $b or !$b) and $b) or !($b or !($a))))",true),
    ("!$a and !$a and !$a or !($b and !$a or !$a or !($b or !$b or !$a or $b) or $b)",true),
    ("$a and ($a and $a and !$a or !$a) and ($a or !$a and $b) or ($a or $b or $b)",true),
    ("!$b or ($b and $a or $a and !$a or $b or !$a and !$a or $b and !$b and $a)",true),
    ("($b and !$b) and !$b or !(($a or $a or !($b or $a and $a or !($b or !$b) and !$a)))",false),
    ("!($b or $b or !$a and (($a or ($b or !($a and !$b or ($a) or $a) or !($a or $b)))))",true),
    ("$b and !($b and !$a or $a and !$a) and ($b or !$b) and !$b or ($b or !($b and $b))",true),
    ("($b or !$b and !(($a or !$a and !$a) and $a or ($a or ($b and !$a or !$b and $b))))",false),
    ("$b or !$b and $b and !$b or ($a and (($b or ($a and $b)) or !$b or $b and $b))",true),
    ("$b or $b or !($b or !$a) and !(($a and !($b and !$b)) or !$a and !$b or !($a) or !$a)",false),
    ("$b and ($b or !$a and !$b or $b and !$b or $b or !($b and $a) and ($a or !$b))",false),
    ("$b and !$b and !($a and !$b and !$a) or !$a or $b or $b or $b or !$a and $b",false),
    ("$b and ($b and !$a or !$b and !($b or !$b or $a) and ($b or !$b or !($b or $a)))",false),
    ("$a or ($a or ($a or (($a or !$a) or ($a and ($b or !($a and !$b) and !$a and !($a))))))",true),
    ("$b or !(($b or ($a or $b and !$b and ($b or $b)) or ($a or ($a and ($b)) and $a)))",false),
    ("($a and !($a) or (($b or $b or !$a or $a or !$b and $b) or $b and !($b or ($b))))",true),
    ("!$b or ($b or ($b and !$b or $b) or $b or $a and $b or !$a or !(($b or $b)))",true),
    ("!$a or !($a and ($b or !($a and !($a or !$a)) and $b and !$b or ($b and $b and $b)))",true),
    ("!($a or ($a and ($a) or !$a or $a) and !$b or $a and !$a or !$a or $a and !$a)",false),
    ("!$a or !($a or !$b and ($b and !$b and $a and $a and $b or !$a and !$a and !($a)))",false),
    ("!$b and !$b or $b and !$b or ($a or $b or $b or !$b and !($a or $b and $a))",true),
    ("!(($b and !$b) or $b and $a or $a or !$a and !($a) and ($a and !(($a) and !($b) and ($b))))",false),
    ("($a or $a or $a and !($a) or ($b and !$b and $a and !$b) and ($b and $a or $b))",true),
    ("$b or !($b and ($b or !$b or $a and !$b or $b or !$a or !($a or !$a or !($a))))",true),
    ("($a and !($a and !(($a or !$b or !($a and ($a and !($a and !($b or $b or $b or $b))))))))",true),
    ("!($b or !(($b) or ($a or $b or ($a or ($b and $b) and !$a) and !($b or $a) and $b)))",true),
    ("((($a or !($a) and ($a) or !$b or $a or $a) and !($b and $a and $a and $b or (($b)))))",true),
    ("!$a or !($a or !$b and $b or $b or $a or $a and $b or ($a or $b or $a))",false),
    ("$b and !$b and ($a or !$a and !$b or !$a and $a or !$b and !$a or $a or !$b)",false),
    ("!($b or $b and $b or !($b and !$b and ($b and $b and $b and ($b and ($a) and !$a))))",false),
    ("!($b or (($b or !$a or $a and ($b) and $b and ($a) or !($a or ($b and !$b)) or $b)))",true),
    ("($b or ($b or ($a and !$b and !$b and !(($a) or !$b and $b) or ($b or $a and $a))))",true),
    ("!($b and !$b or !($b or $a or !$a and !$a and !$b or ($a) or !$a or (($a and $a))))",true),
    ("($b or $b and !($b or !$b and !$b and $a and !($a and $a and !($b and $a or $a))))",false),
    ("($b and ($b) and ($b or !$a or !($b and !$a or ($a) and ($a or $a and $a) or $b)))",false),
    ("(($a and !$a) and $a and !$a or $b or !($b and !$a or (($b and !$b) or !$b and !$b)))",false),
    ("$b and !($b or !($a) or (($b or $a)) or ($a) or !$a or ($a) or !$a and $b) or !((($b)))",true),
    ("!$a or !$a and !$b and !$b or ($a or !$a and ($b or !($b and $b or $a) or $b))",true),
    ("($a and ($a or (($a or $b or ($a and !$b and ($a) or $b) or !$b or $b and $b))))",true),
    ("!(($b or !$b and !$a and ($a and !$b) and $b or !$a or !$a) or !$b and !$a or $b)",true),
    ("!(($a or !$a and $b) or !$a or $b or $a or !(($a and !$a and $a) and $a or $b))",false),
    ("$b or ($b and (($a) and !$b and !($b and $b and !($b and !$a) or (($a and !$b or $b)))))",false),
    ("!$a and ($a or !$b and ($a and !$a and $a and ($a or !$a or $a or !$b and !$b)))",false),
    ("($b and !($b) and !($b or $b or !($a and $a) and $a) and !$a or $b or $b or $a)",true),
    ("!($b and !$b or ($b or ($b or $b) and ($a) or ($a) or !$a or $b and !($b and !($b))))",false),
    ("!$b and $b and !$b or $b and !$a or !$b or !($a or $a or !$b and ($a and $a))",true),
    ("((($a or $a or $a or !($a) and $a) and ($b and ($b and $a and $a or ((($a and !$b)))))))",false),
    ("!($a and !$a or !$a) or (($b and !($a or $a and $a or $b) and !($a and $b and !$a)))",true),
    ("!$b or !($b or (($b or $b or $b or $b or !$a and ($a and !(($b and !($b) or ($a)))))))",true),
    ("!($b or (($b and !$a or $b) and !(($a and $a or !($a) or !$a and ($b)) or $b and $a)))",true),
    ("$b or !$b or !($b or $b and $b or !($b or !$b and !($a and $b and $b and (($b)))))",true),
    ("!$b or !$b or !($a or $b or !((($a or ($a or !$b) or $b and ($a or $a and $a)))))",true),
    ("!($b or $b and $a or !($a and ($a) or !($b and $a) and !$a or (($b or !($b) and $b))))",true),
    ("$b or !$b or ($a or $b and ($b or !$a and $b and $a) or !$a or ($b) and ($b))",true),
    ("!$b and $b or $a or $b or ($b and ($a or !$a or !$a and $b or ($b)) and !($a))",true),
    ("($a or !$a and ($b and $a or ($a or $b or !$a) and $a or !($b and !($b or !$b))))",true),
    ("!$a or $a or $a and ($b or !$b and ($b and !((($b or $a) and (($b) or !$b or $a)))))",true),
    ("$a and ($a or !(($a and !$a or !($b or !(($b or $b or !$a or !$a) and ($b and $b))))))",true),
    ("$b or !($b and !$a or !$a and !($a and !($b) and !$a or ($b and !($a) and !($b) and !$a)))",true),
    ("!($b and !$b or !($b and !($a or $b or !($b) or !$a) and $b and $b and ($b and $a)))",false),
    ("($a or !($a and !($a) and !($b or !$b or $a) and !$b and $a) and $b and ($a and !$a))",true),
    ("!$a and !$a and !$a and $a or $b or !$a and !(($b and !$b or $a and !$b and $b))",false),
    ("($a and (($a or $b)) and ($b or $a) and ($a and !($a and $b and $a and $a or !(($b)))))",false),
    ("($b or !($b or !$b and ($a) or !$a and $a) and $b) or ($a or !($a or $b and !$b))",true),
    ("!$a and $a or !$a or $a or !$b and $b and !$b and ($b or !$a and !$b) and !$a",true),
    ("$a and $a and $a or $a and $a and (($a and !$b or $b or $a and !($b and $a)))",true),
    ("!$b and !$b or ($a or !$b) and ($a and !($b and !$b) or !($b or !($b or !$a or !($b))))",true),
    ("$a or !$a or !$b and ($a and !$a or $b and ($b and $b and $a or $a and !$b))",true),
    ("$a or ($a and !($a and !($b and !$a) or $b or !($b and !$b or !($b) or !$b or $a)))",true),
    ("!$a and $a and $b and ($b or $a or !$b and $b) and $a or $a and $a and !$a",false),
    ("$a and ($a and $b or !($a and !$a and $a and $b and !$b and !$b and $a) or $a)",true),
    ("!$a and $a or !(($a and !$a and $b and !$b and $b and $b or $b) or !$a and !$b)",true),
    ("$a and !$a or !$a and !$a and $a and !$b or ($b or !$a or !$b and !$b and ($b))",false),
    ("!($b and (($b or ($a) and $a and ($b) or ($b and $a) or !$b and ($b or ($b and $b)))))",true),
    ("($b and !($b and !($a and $a or !($a or !$b and !($a or !$b or ($a or !($a or $a)))))))",false),
    ("!($a or !$a and !$a and ($b or $b or $b or !($a or (($a)) and ($a or ($a) and !($b)))))",false),
    ("!($a and $a and $b and $b or $b and !$a or $a or !(($b or !$a or $b or $a)))",false),
    ("!$a and (($a or ($b) and !$a and ($a and ($b or !$b) or $b or $a or !($b and !$b))))",false),
    ("$b or !($b and !$a and ($a) and $b or $b or !$a and $a and !$a and $b and $b)",true),
    ("!($a or !$a or $a and ($b or !($b and ($a or !$a and !$b or $a or $a and ($b)))))",false),
    ("$a and ($a and ($b and $b or !$b)) or !($a and ($b and ($b) or ($a or !($b) or $a)))",true),
    ("!$b and ($b and ($b and !($a and !(($b or $b or !($b and ($b or $a and !$b and !$b)))))))",false),
    ("!($b and $b and !$a and $a or !($a and !$b) and !$a and $a or $b or !$b and !$b)",false),
    ("!$b and !($b and !$b or !((($b and !$a and !$a) and !$b or $b or !$b) or !($a and !$b)))",true),
    ("!($a and !$a and !(($a and $b and !$a or !($b and !$a or $a or !$a or $b and !$a))))",true),
    ("$a or ($a or $b or !$a or !$b and $b or ($b and $a) and $a and !$a and !$a)",true),
    ("($b or !$b and $b and $a) or !$b and ($b or $b or !$b and !$a or !($b or $b))",true),
    ("($a and !($a and ($a or $a) or $a and $a or !($b) and $a or ($b or $a and $a)))",false),
    ("($b and ($b and $b or !$a or !($b or !$a and !$b and !$b or !($a and $b)) or $a))",false),
    ("($a or $a and !$b and !$a or !$b and $b and $b or $b) and ($a and !$a or !$b)",true),
    ("$a and $a and ($b and ($a or !$a) and $a or $a and $b or !$b or $a or !($b))",true),
    ("!$a and !$a or $b or ($a or ($b or $b or !$a and !$b and ($b and ($b and !($a)))))",true),
    ("!($b or !$b and !$a and ($b and !$b or ($b and !$a and !$a and ($a and !$b) or !($b))))",true),
    ("$b and !$b or !$a or $b and $b and $a or $b and !$b or $a and $a or !$b",true),
    ("!$b and $b or !($a or $b and $a and !$a or !$b or $b and $b or $b or ($b))",false),
    ("$b or !(($b and !($a or $b and (($a or !($b or !$a and $a or $a or ($b) or !$b))))))",true),
    ("!(($a or !($a or !$b and $b)) or !$a and !(($a and !$b) or $b or !$a or $a or !((($b)))))",false),
    ("!($a or $a and !(($a and ($b)) and !$b and ($a and $b or $b or !$b and !$a or !$a)))",false),
    ("$b and $b and $a or $b and !$a or ($b or $a and $b or !(($b) or !(($b or !$a))))",false),
    ("!($b or $b or (($b and !($b) and ($b and !$b and $b and !($b) and (($a and !$a) and ($b))))))",true),
    ("$b and (($b or !$b and ($a)) or ($a or !$a or ($b and !$a or $a and (($b or !$a)))))",false),
    ("$a and !($a and ($b and $a and ($a) and $a or $a and (($b and $b) and !$b and !($b))))",true),
    ("$a or $a or ($a or !$a or !($a or !$b or $a or !$b or $a or ($b) and $a))",true),
    ("!$b or !$b and !$a and !((($a or $a and !$b)) and !$b or $a or !$a or !$b and $b)",true),
    ("!($a or !$a or !($a or !$a or ($a or ($b) or ($a and !($b) or !$a) and $a) and $b))",false),
    ("!$a or $a and !$b or ($b and $a or !$a and $a and $a or $b or (($a and ($a))))",true),
    ("$b and (($b and !$a and ($a or $b or !$a) or $b or $b and !($b and ($b) or !$a)))",false),
    ("!((($a and $a or $a) and ($a and !$b) and !($a and !$b) and $a or !($a or $b and !$a)))",true),
    ("($b and $b and ($a or !($a or !$b or !$b or $b or $b and !$a or $a) and !($b)))",false),
    ("!$b or ($b or !($a and $a or !$b) or !((($a and $b) or $a or $b or ($a and !$b))))",true),
    ("$a or ($a and !($a or !$a or $a and !$b or $a) and $b) or !($a or ($b or !$b))",true),
    ("!($a or !$a or $b and !$b) and !$b and $a and $b and ($b or !$a or ($b or $a))",false),
    ("!$b and !($b or !$b or (($a and $b) or !($a or !$b or !$a or $b or !$a and ($a))))",false),
    ("!($b and !$b and !$b or ($a and !$a or $b and !$a and !$a or !$b and ($b) and !$a))",true),
    ("!(($b or !$b and !$b and !$b) or $a or $b or !($a and $a or !$a and !$b or !($b)))",false),
    ("$b or $b and $b or $b or ($a and !($b and !$a and !$b or $b and !$a or $a))",false),
    ("!$a and ($a and $a and $a or !($a and !$b or $a or ($b and $b or !$a) or ($b)))",false),
    ("!$a or !($a or ($b and ($b and $a and !$a) or $a or $b) and ($a) and !($b or !$a))",false),
    ("$b and ($b or !($a or $b or !$a)) and ($a and !$b or $b) and !((($a and !$a and !$b)))",false),
    ("(($a and ($a and !($b or !$b) or $a and !$b)) or $a and !$a and ($b and !($a) or ($a)))",true),
    ("!(($b and (($b) or !($a or $b and !$a)) or !($a or !($b or !$b and ($a or !$a or !$a)))))",true),
    ("!$a and ($a or !$a or !$a and !$b or ($a and !$a or $a or !$b or !$b and $b))",false),
    ("$a or !$a or ($a or ($b and $b) or !($b or !$a or !($b and !$b) or $b or !($b)))",true),
    ("$b and ($b and ($b and ($b or (($b or !$b or !$b or $b) and !$b and $b and $a))))",false),
    ("$a and !($a or !(($b and !($b or !$a or !$a and $b or $a and $b or $b) and $b)))",false),
    ("!$a and $a or ($b and $a or !$b or !$a) and !$b or ($b and !((($b or !($a or !$a)))))",true),
    ("!(($b and ($b or !($a) and $a or !$a or ($b or !(($a) and !$b or !($a) or ($a) or !$a)))))",true),
    ("!$b or ($b or $a or !(($a and !$b and ($a) or ($b or !$b and $a) and !($a and ($b)))))",true),
    ("($a or ($a and $b or $a or $b and $a or ($a or !$a and $a) or !($b or !$b)))",true),
    ("($a or !($a or $a or !$b or $b and !($b or $a and !($a or !$a) or !$b or $b)))",true),
    ("!$a and !(($a and (($b or !($a and ($b or $a) and $a or $a) and $a) and !$b or $a)))",false),
    ("$b or (($b and !$b) or !($a and !$b or !$b) and ($b or !($a or !$b or !$a or $b)))",false),
    ("!($b or $b and !$b and !$b) or !$b or !$a and ($b and ($b or !$b and $b) or !$b)",true),
    ("($b or !($b and $a and !$b or $a and !$a and $a or $a and $a) or $a or ($a))",true),
    ("(($b and !$b and !(($a) or !($a and !($a) and $a or $a and !$b and !($b) and !$a) and $b)))",false),
    ("!$b or !$b and !$b or !$a and $a or ($a or $a or !$a or $a and !$a or ($b))",true),
    ("($a and $a or !$a and !($a and $b or !$a and $b and !($a) and !($b or !$a or $b)))",true),
    ("$a and (($a or $b and ($b and !($a or $b and ($b) and !$a or $b and !($a or $a)))))",true),
    ("$a and !$a and !$b and $a and $b and ($a and (($a and $a and !$a and !(($b)) or $b)))",false),
    ("!$b or !($b and $b or $a or $a and !$b and ($a or $a or $b and ($b and !$b)))",true),
    ("!$b and ($b and ($a and !$b or $a or $b and !$b or $a and ($a and !$a or $b)))",false),
    ("!$b or $b or (($a and $b or !$a and !$b or !$a or !$a and !$a or !$b or !($a)))",true),
    ("!$b and ($b or $a or !$a or ($a) or !(($b or !$b or !$b) and $b or ($b and !$b)))",true),
    ("!$a and $a and $a or !$b or ($b or $a or !($b and !($b or $a or $a and !$a)))",true),
    ("!$a or ($a and !$a) and ($b or !$b) or $b or (($a and !$a or !$b) and $b and !($a))",false),
    ("!($a and (($a and $b or !$a and !$b) or !$a or !$b or !$a and !$b) and !($a) and $b)",true),
    ("($a or $a or $a and $b) or $a and ($b or ($b or $b and ($b or !($b and !($a)))))",true),
    ("!$b and $b and !(($b and !($a and !($a and !($a) or $a) and $a and !($b) and ($a) or $a)))",false),
    ("!$b and !($b and $b or $b or !$a or $a or !$a or !$a or !($a or $b or !$b))",false),
    ("($a or !($a and !$a and $a and $b or !$b or !$b and ($b and $a and $b or ($b))))",true),
    ("$b and !(($b or ((($b and !$b and !$b or $a or !$a and ($a or !$b and !$a or $a))))))",false),
    ("($b and ($b and ($b) or !(($b or $a or !(($b or !($b or $b)) or ($a and !$a) and ($b))))))",false),
    ("!$a or $a and ($a or !$b and ($a or !($b) and !($a and !$b and (($b and ($a and !($b)))))))",true),
    ("$a or $a or !($b or (($a and $a and !$a) or !$b and !(($b) and !$b) and !($a) or $a))",true),
    ("!$a or !$a or $b or $a and !$a and $a or $a or ($a and $b or !$b and !$b)",true),
    ("!$b or !(($b or !($a and !$a and !$a or $b and $a and ($a or $a) or $b or !$b)))",true),
    ("$a and $a or $a or !$b or !$a or !(($a or $b)) or !$b and ($a and !$a and $b)",true),
    ("($a and (((($a and $b) and !($a and $b and ($a)) and !(($a and !$a and !$b and !($a and $a)))))))",false),
    ("!($a or !($a or !($a or !($b and !($b and !$b or !$b or (($b and ($a and !$b)) or ($b)))))))",false),
    ("!($a or !$a and !($a and $b and !$b and $b or $b and !$a or $b) or $a or !($b))",false),
    ("!$b and (($b and $a) or !$b and !($b and !$a and $b and $a and $b or (($b or ($b)))))",true),
    ("!$b and (($b and $a and !$b or !$b and !$a and (($a) and $b or !($b) or !$a and $b)))",false),
    ("$b or !$b and $a or !$b or ($a or ($a and !$b) or ($b) or !$b and !($a and !$b))",true),
    ("!($b and !$b or !$b or (($a and $b)) and !($a) or !$b or (($b and ($a or ($b and $a)))))",false),
    ("!($b or $b or $b) or !$b or $a or ($a and $a or $a and !(($a and $b) and $b))",true),
    ("!($b and !$b) and ($b or !($a or !$a and $a and !$b) or !($b and !$a and !$a or !$a))",true),
    ("((($a or $a) and !$b or !$a or !$a and !$a or $a or !($a or $b) and $b or ($a)))",true),
    ("!$a or !($a and !($a and $b) or $b or !$b or ($a or !$a or !$b) or $a and $a)",false),
    ("$b or !$b and !($b and ($a or !(($a) and $b or !($a or !($b) or ($a and !($a or ($a)))))))",true),
    ("!$a and !$a and !($a and $b and $a and !$b and $a) or $b or ($b or !($b and !$b))",true),
    ("!$a or !$a or !$a or ($a and !($a or !$a and !$b and $a and !$b or $a or $a))",false),
    ("($b and $b) or !($b or !(($a or ($b or $a and !$a) and $a) and !$b or !($a or !$a)))",true),
    ("!(($a and !$a and $b and !$a and $b) or $a and !$b or !$a and !$a) or !$a and ($b)",false),
    ("($b and $b and !($a and $b and $b) or ($b and !$b or !$b or $a) or $b and !$a)",true),
    ("($b and !$b and ($b and (($b or !(($b or !($b and $a))) or ($a or ($a or !$a and $b))))))",false),
    ("!$b and $b and (($b or !$a or $a) or !$b and $a or $a or $a or $b or $b)",false),
    ("!$a and !$a or $b or $b and !$a and !($b and $b and !(($b or $b or !$b or !$a)))",false),
    ("($a and $a and !($a or $a) and !$a or !($a) or $b and ($b and ($a) or $b and !$b))",false),
    ("($b or $b and $a and !$b and !($b or !$a or ($b and $a or !$a and !$a or !($b))))",false),
    ("$b and !($b or ($b or !((($a and !$a or !$b or !$a or !(($b or !$b and $b and !$b)))))))",false),
    ("!(($a or !$a and !$b and ($a)) and $b) or $a or $b or !$a and !$a and ($b and !$b)",true),
    ("!$a and $a and ($b and !$b and $a and $b or $a and !($a or $b or !($b) and $b))",false),
    ("$b and !($b or !$b) or !$b or !$b or ($b or !$a or !($a and $a or $a or $b))",true),
    ("$a or (($a and $b) and !$a or $b and ($b and $b or !$b or !$a and $b) or $a)",true),
    ("!$b and !$b or ($b or $a) or $a and !$b and !($b or $b or $b and !$a and !($b))",true),
    ("($b or $b or !$b and !($a and $b) and $b and ($a or !($a or !($b or $a and ($a)))))",false),
    ("$a or !($a and ($b and (($a and !($a or $b or $b and !$a or $a and !($b and !$b))))))",true),
    ("!($b or ($b or ($b or !$b and !$b and (($b and !$b and !$b) or $a) and ($b or $a))))",false),
    ("!(($a or !($a) and !$a and $b) and !($a or !($b or !$b and $b) and !($b) or !$b or (($a))))",true),
    ("($b and !($b and !$b) or ($a or !($b) or !$a and !($b and !$b) and !($b and ($a and !$a))))",true),
    ("!($a or !$a or !$a or !($b and !($b or !$a and ($b and $a and !($b and $b and $b)))))",false),
    ("!$a or !$a or (($a or $a) or $a) and (($a and (($a or !$a and !$b) and !$b and $a)))",true),
    ("($b or !$b and !$b and $b and !$a or !$a and !($b or !$a or !$b and !$b or !$a))",false),
    ("$a or $a and $a or !$b or !$a or (($a and $a or !$b or ($b and !$b and (($a)))))",true),
    ("!$a and ($a or !$b and $a and !($a and $a or !$a) or !$a or ($a or !$a or (($a))))",false),
    ("!($b or !$b and !($a and !$b and ($b and !($b) and !$a and $b and !$b and ($a or ($b)))))",false),
    ("($b or !$b or !$a or !($a and $b or !$b or $a and !$a) and $b and !$a or !$a)",true),
    ("!$a and ($a or $b and ($b or !($b or $b) or $b and $b or $b and $a or !($b)))",false),
    ("!$a and (($a and (($a) or ($b and ($b) or !($a and $b and $a and !$a) and !(($a or $a))))))",false),
    ("$a or $a or !$a or $b or $b and $b and $a and !$b or !($b and ($b or $a))",true),
    ("$b and !($b and !$b and $b or $a or ($a or $b and !$a and $b or ($b and !$a)))",false),
    ("!$b and (($b and $b or !($a and ($a or ($b) or $b and !($b or $a) and $a or !(($b))))))",false),
    ("$a and !$a and $a and $b and !$a and !$a and $b or ($a and !($a and !$a and $a))",true),
    ("!(($b and ($b or !($b or $a and ($a or !$a and !$b and !($b and !$a) and $a) and $b))))",true),
    ("$a or !($a or $b or !$b or $a and (($a) or !$a or !$a or !($b or $a or !($b))))",true),
    ("!($b and $b and $b or !$a or ($a or !((($b or !($b) or !($b) or !($a or ($b) and !$a))))))",false),
    ("($b and !$b and !$b or $a or ($b or $b or !($a and !$a and $a or ($a or $b))))",true),
    ("($b and !$b or $a and ($b and !(($b) or $a and !$a and !$a or !$b or !$a) or $b))",false),
    ("($a or ($a or (($b or !((($b and $a and !$a) or !$a or !$b and $a and !$b) and !($a))))))",true),
    ("!$a or !$a or ($a or ($a and $a or ($a and ($a and !$b) and !$a or ($b or $a))))",true),
    ("$b and !$b and !$b and (($b and !($a and $a or !$b and !$a and $a and !$b) or $a))",false),
    ("($a and $a and ($a and ($a) or $b and ($a and ($b or $a or $a)) or !$b and !$a))",true),
    ("(($b and !$b and $a and ($b or ($a and !($a or !$b or $a) and !$b or $a or $b))))",false),
    ("!$a and !$a or (($b or $b or !$a and $b) and !$a) and $b or $b or ($b or ($a))",true),
    ("($b or $b or !$a or !$b and $a or ($a) or !$b or !($a) or !$a or !($b and !$b))",true),
    ("$b and $b or $b and !($a and !($b or $b and $a or ($a and $b and !$b or !$b)))",false),
    ("$b and !($b and !$b or !$b) and !$a and !$b or $b or $a and $a and ($b and !$a)",false),
    ("($b and !$b and !$b and !$b and $a and !$b and !$a or !$a and ($a and $a or !$b))",false),
    ("$a or !$a or !($b and $b or ($b and $b and $b) and $a and !$a and !$b or !$b)",true),
    ("!$a or $a and !$a and !$b and $b or ($b and !$b or !$b and !$b and !$a or (($b)))",false),
    ("!$a and ($a and !$b and $b or $b) or !($b or ($a or !$a or $a or !$a or (($a))))",false),
    ("!(($b or !$b and !(($a) or !$a and !($b)) and $b and !$b or !($b and !$b) or !$a or !($a)))",false),
    ("((($a and !$a) and !$a and !$a and $b or !($a and ($a or (($b and ($b or !($b or !$b))))))))",false),
    ("!($a or $a and !$b or !($a or !($a and !$b and ($a or !$b or ($a) and !$b)) and $b))",false),
    ("!$a or $a and ($a or ($a or !$a) or ($a or $b or ($a or !$b and $b or !$b)))",true),
    ("($b or !$b and !($a and !($b or !$a and !($a or !$b) and !$b) or $a) and ($a and $a))",false),
    ("!$a or !$a and !(($b and ($a or $a or $a) and $a or !$a and !$a and $b and !$b))",false),
    ("!$b and !($b or !$a or !$b or $b or $b or !($a and $a or $b) or !$b or $a)",false),
    ("(($b and !($b or ($a) and $a or !$b or !$b) and ($a or !(($a or !$a and $b) or $a))))",false),
    ("$a and $a and $b and $a or !$b or $a and !$a and !(($b and $a) or ($b or $a))",true),
    ("$b and !($b and !($a or $b or ($b and !($b) or !$a and !($b or !($a) and !$b and !($a)))))",false),
    ("$b and $b or $a and !(((($b or !$a or ($a or !$a) and $b and !($a) and !$a and !($a)))))",true),
    ("!(($b or ($b or ($b or $b or $a or !$b or $b) or $b and $b or !($b and $b))))",false),
    ("!$b or !($b and ($b and !$a or $b or !$b and ($b or !(($b or $b and !$b))) and $a))",true),
    ("!($b and $b or !($a or !$a and $b and !$b and $a or $b and $a and !$a) and $a)",true),
    ("(($b and !($b or !$a) or !$b or ($b) or !$b or ($b and $b or ($b or $b and $b))))",true),
    ("($a and !(($a or $a and !$b or !($b and !$b and !$b or $a or ($b) or $b or !($a)))))",false),
    ("!$a or $a and !$a or !($b or !($a or !$a or !$b and !$a or !$b and !$a or $a))",true),
    ("!$b or ($b and !(($b and $b and !$a) and !$b or !$a and !($a) and ($a or !$b and !$b)))",true),
    ("!($b and !($b or !$a and ($b or $a and $b and !$a and !$b and $a or !$b) or !($a)))",true),
    ("$b and $b and $b and !($b and !($a or $a) or ($a and !$a or !($b and $b and !$b)))",false),
    ("(($a and ($a and !($a or !$b) and !($a and ($b) or !$b and $b and !$b) or !$b)) and ($a))",true),
    ("!((($a or !$a or ($b or !($b) and !$b)) and !$b or $b or $a) and ($b and !$b or !($a)))",true),
    ("($b and ($b and !($b and $a or !($b or !$a) and !($a or !$b or !($b) or !($b or !$b)))))",false),
    ("($a or $a and ($b and ($b and !$a or !$b or !$a) and $a or (($b and !$b and $b))))",true),
    ("!$a or ($a and !$a or $a and !($b or $a) or !(($b or !($b and !$b) or !$a) or !$a))",false),
    ("($b and ((($b or ($a and !$a or !($a or !((($a and $a or !$b) or !$b) and !($b or $b))))))))",false),
    ("!$b and $b or !($a or !$b and $b) or !($b and !($b or !($b or !(($b and (($b) or !$b))))))",true),
    ("!($a or !$a and $a or !(($b and $b or !$a or !($b or !$b and $a or !($b or $b)))))",false),
    ("!(($a or !(($a or !$b or !$b or !($b and $b) or !$a) or ($b or $b and !($b or !$a)))))",false),
    ("!($a or ($a and $a or !(($a or !($a or ($a) and $b or $b and !$b) and !$a and !$a))))",false),
    ("!(($b or !(($b and ($b or $a and !$a) and $a and !$b and !($b or ($a or !$b) and $a)))))",false),
    ("($b and !($b or !($a and $a or $a) or !$b or ($b or !($b or !$a) or $b and ($b))))",false),
    ("$b and !$b or !($b or $a and !$b and $a or !$a) or !$a and ($b or $b and !$b)",false),
    ("!$a and !($a or !$b and !$a or !($a or !$a and $a or !$a) or !$b and $b and !$b)",false),
    ("$b and $b or $a or !$a or ($a or !$a and !$b or $a and !($a or $a or !$a))",true),
    ("($b and !($b) and !$b or ($b or ((($b) and $b and ($a) or !(($b) and !$a or $b)) and !$b)))",true),
    ("$a or !($a or ($b) or !($b or $a and !($a or $b or !($b or $a and ($a or !$a)))))",true),
    ("$b and ($b and $a) and !($b and $b or !$b and (($b and !($a and ($a or $a or $a)))))",false),
    ("$a and $a or ($b or ($b or $a or !$a and $a)) and $b or $b or !($b or !$b)",true),
    ("($b and ($b and ($b and !($b or !$b) and !$b or !$a or !($b) and $a or !$b)) and !(($a)))",false),
    ("!$a or !$a or ($b or !($b or $b or !($b) or $a and ($a and !$b and $b or !$a)))",false),
    ("!(($a and !$a) or !$a and $b or !(($b and !$b and (((($b or !$a or $a or !$a) and $a))))))",false),
    ("!((($a and !$a and !$a or !$b and !$a or !$b and $a or !($b and ($a or ($b) and !($a))))))",false),
    ("!$b or !$b and !($a and ($a and $b) and (($a and !$b and !$a and !$b or !($b and $a))))",true),
    ("!$b and !$b or (($a or $a and !$b or ($b) or (($a and !$b and $b and !$b or ($b)))))",true),
    ("!($b and ($b or !($a or ($a and (($b and $b or !$a) or !$a or $a and $a)) or $a)))",true),
    ("!($a or ($a or !($a and (($a or !$a) or !$a) or $a or !$a) and ($a or !$b or $a)))",false),
    ("!($b and ($b and !$b and !$a or !($b and !$a or !$a and $a or !(($b or $a) and !$b))))",true),
    ("!(($a or !$a and !$a or !($a and $a) or $a or !$b or $b or !$b or !$b and $b))",false),
    ("!$a or $a or !$a or ($a and !$a and $b and !$b or ($b or ($a or ($a or $a))))",true),
    ("((($a and $a or !$a or ($b or $a) or !($b or ($a and !$a) or !($a and !($a and (($a))))))))",true),
    ("(($b or $b and ($b) or (($b and !$b)) or !($a and !$a and $b and !$b or !$b or $b)))",false),
    ("!$b and !$b and $a and !$b or $a or !($b or $a and $a and $b and !$a or ($a))",true),
    ("!$a and (($a and !($b and $b) and !($a and ($a and !($a) and !$b) or !($a or $a) and $b)))",false),
    ("!$a and !($a and (($a or !$b) and $a or $b or ($b and !$a)) or $a) and $a or $b",false),
    ("!(($a and (($a and !($a and !$a or (($b or $a)) or !$b or $a and !($b) or !($a)) and !$b))))",true),
    ("!($a or !(($a or ($b or $a and !$a and !($b)) or ($b or $a and (($a and $b or !$b))))))",false),
    ("!$a and !($a or $b and !($b or !$b) or (($a or !$b)) or ($b) and !(($a or !$a and !$b)))",false),
    ("$b or !($b and $a) or (($b or $a or $b and !$b) or !$b and !$b or !$a and !($b))",true),
    ("($b or !$b and !$a and $a and !$a and $b) and !$b or !$a or !$b or !($b and !$a)",true),
    ("$b or ($b or ($b) and (($a or $a and $a or !($b or !(($b and !$a and !$a) and !($a))))))",false),
    ("($a or $a and $b and !($b or ($b or !$a or $b and ($b and $b or $b) or $b)))",true),
    ("($b and $b or !$a and !$a or ($b and !$b and ($b and !$b and $a and !$a) or !$a))",false),
    ("$a and $a and $a or !$b or !$b and !$a or !$a and !$a or !$b or !$a and ($a)",true),
    ("!($a or (($a or !$b or ($b and ($a or !($a and !$b) or !($a or !$b and !$a or $a))))))",false),
    ("!$a or !($a and $b) or !($a and ($b) or !$a or $b or !($b or (($a and !$b) or !$b)))",true),
    ("!($a and $a and !($a and ($a)) or !($a or !($a and !($a or !$b) or !$b and (($b or !$b)))))",true),
    ("!$a and !$a or $b or !(($a and !($b) and $b) and $b and $b and !$b or !$a and ($a))",true),
    ("!($b and !($b or ($b) or $a and !($a) or (($a and !($a and $b or (($b)) or ((($b or !$a))))))))",true),
    ("!($a and !$a or $b and $b and !($b or !($b or !$a and !((($a or !$b and ($a) and $b))))))",true),
    ("!($b and !($b or !$a or ($b or ($a) and !$b) or !$a and !$b and !$b) or $b) or $a",true),
    ("($b or !$b or $b and !$b or !($b or $b or !($a and $a or !$b or !$a and !$b)))",true),
    ("!$b and !($b and !$b and !$a or $b and !$b and $b and $a and !$b or !($a) or !$a)",true),
    ("!$b and !$b and $a and !$a or $a and !$a or !((($a or ((($b or !$b) and $b and ($a))))))",false),
    ("!$b or !$b or $b and $a and !($b or $a and !$a and !$a and !($a and $b) and $b)",true),
    ("!$b or $b and $b and !$a and !($a and !$a or !$a and !($b or (($a and !$a and !$b))))",true),
    ("$b or ($b or !$b or !$b and !$b or (((($a or ($b) and $a) and !$a and !$a or !$a))))",true),
    ("!$a and !$a and !($a and ($b and !$a or $a or $b or !($b or $b and !$a or $b)))",false),
    ("(($a or !$a or !($b and $b or !($b and ($b or !$b or $a)) and $a and $a or !(($a)))))",true),
    ("$a and !$a and $a and !$a or !$b or !$a or !($a or !$b and $a and $b and !$a)",true),
    ("((($a or ($a and $a) and $a and !$a and $b) and !(($a or !($b) or !$a and $b) and $a)))",false),
    ("($b and ($b or $a and ($b or !($b or (($a or $b and !$a or $a and $a and !$b))))))",false),
    ("!(($b and (($b) and !$a and !$b and !(($b) and $a or $b) or ($b or $a or !(($b)) or $b))))",true),
    ("!($a or !$a or !$b or !$a and !$b or !(($a and $a or !$a or !$b or ($a and $a))))",false),
    ("!($a or !$a or !$b and $a) and !$a and !$b and ($a and !$a and $b or !$b and $b)",false),
    ("!($a and !($a and ($a) and !($b or !$b or !$b) and ($b and $b)) or !($a or !(($a and !($b)))))",false),
    ("!($a and !$a and !($b or (($a and !($a or !$b) or !$a or !($b) and $b or ($b or !($b))))))",true),
    ("!$a or $a or $a and ($b and !$b or !$b and !$b) or $a and !$b and $a and !($b)",true),
    ("!($b or !($b or !$a and $b or $b or !$a and !($a and $b and ($b and !$b) and !($b))))",false),
    ("$b and !$b and $a or !($a or !$b or !((($b or $b or $a or !$a or $b or !$b))))",false),
    ("!$b or ($b or ($b and ($b or $a or !$a and !($a or !$b) or !$b) or !$a and !($b)))",true),
    ("(($a and !((($a and (($b) and $a or !$b) and $b)) and !($a) and $a or !$b and !($b or !($a)))))",false),
    ("!($a and ($a and !($b and !$b or !$a) or !(($a or $a and !$a and ($b) and $a) or !($a))))",false),
    ("!(($b and $b and $b and $b)) and !$a or ($a and !($a) and $b and !$a or !($a or !$a))",false),
    ("!($a and !(($a or $a or $a or $b or !$b and !($a) and $b and !$a or (($b or !($b))))))",true),
    ("$a or ($a or $b and !($b or $a or $b or !$b or ($a or ($a) or (($b) or $a))))",true),
    ("$b and !$b or !($b and !($a and !$b and !$a and ($a or $b) or $a or !$a) or !$a)",true),
    ("!$a or !$a and !$b and !$a or $a or !$a and (($b and !($a and ($a) and $b and $a)))",true),
    ("!($a or $a or !(($b and !$b or !($a and $b)) and $a or !$b) and !$b or !$b and !$a)",false),
    ("!(($b or !($b or !$a and ($a or !$a) or !($b or !$a) and ($b or ($b or !$b) or !$b))))",true),
    ("$b or !$b or $b and $a or $a and !$a and !(($b or !$b or $a) or !(($b or !($a))))",true),
    ("($b or $b or !$b or !$a or $b or $b and $a and !$b or $a and $b and ($b))",true),
    ("$b or ($b or !$b or $b or !($b and !($a or !($a) or !($b) and !($a and !($a or ($a))))))",true),
    ("!($b or $b and !$a and !$b or !$a or $b) and !($b and $b or !($b and !($a) or ($b)))",false),
    ("((($b or !$b or !(($a or ($b and $a or $b or !$b or !$b) or $b or $a or $a)))))",true),
    ("!$b and ($b and (($b and $a) and ($a and !$b or !$b)) or (($b and $b) and $b and !($a)))",false),
    ("!($b and $b or !$a and ($b or $b and ($b or !$a and !$b) and !($b) and !($b or ($b))))",true),
    ("!$b and $b or ($a or !($a and !$b or !($b) or !($b and ($a and !$a) or $a and !$a)))",true),
    ("$b or !(($b or $a and !$b or $a or !$a and !($a and !($b and $b or !($b and !($a))))))",false),
    ("!($b and ($b) and !$a or $a) and !$b and !($a and ($a or !$a or $b or !($b or !$a)))",false),
    ("!$b or !($b or ($a and $b and $a and $b and !$b and !$a and $a or $b and !$b))",true),
    ("($a and !$a and !($a or $b or $b) or (($a and $b and !$b or $b or !$a or $b)))",false),
    ("!$a or !($a and (($b and !$a and !($b or !$b or ($a or !($b) or !$a and $a or !$a)))))",true),
    ("!$a or ($a or $b or !(($b or $a and $a and !(($a or $b and !$b and $a)) or $a)))",true),
    ("($a and !$a and !$b or !$b or !$a and $a or ($b or !($a and !(($b) or $b or ($b)))))",true),
    ("!($b and $b or !$a and !$a and !$b or $a and $b or ($b or $b or !($a) and $b))",true),
    ("$b and (($b or $a) and !$a or ($b and !($a and !($b or ($a or $a and !$b and $b)))))",false),
    ("$b or ($b and (($b or $b or !$b or $a and $b or !$b) and !$a and ($b or $b)))",false),
    ("((($a or $a and $a and ($a and !$b and $a or !$b or !($a and $b) and $b) and $b)))",true),
    ("!$b and $b or (($a and !$b and $b and !$b or $b or !$a and !$a and !$b or !$a))",false),
    ("!($b and !$b or !$b or !$b or !((($a and !($b or ($b and !$b)) and !($b or ($b) and !($a))))))",false),
    ("$a or !$a or !$b and $a or !($a or $a and $b or !$b and ($b or ($a or !$b)))",true),
    ("!$b or $b and $a or $b or !$b or !$a and !$b and (($a and !$b or !$a or !($b)))",true),
    ("!($b and ($b and !(($b) or (($b and ($a or $b or !($b and $b and !$b or !($b and $a))))))))",true),
    ("($b and !$b or ($a and !($a or !($a and $a or $b and $b or !$b and !$b or !($b)))))",false),
    ("$a or ($a or !($a and !($a or !$b or !$a) or !($a and !$b and ($a or !$a and $b))))",true),
    ("!($b and $b or !$a or (($b or !$a and !$b) or !$a and !$a) and !$b and $b or !$a)",true),
    ("!$b and $b and !$b or $b and $b and $a and !$b or $a and !$a or !$b or !$a",true),
    ("$b or $b or $a and $a or $b and !($a or ($a or $a or !($a and !$a and $b)))",true),
    ("!$a and ($a or $a or ($b or !$b or !$b and $b and !$a and $b or !$a or !$b))",false),
    ("!$b or $b or ($b or !($a) and $b or ($a and !($b and $a) and !$a or !$b or !$b))",true),
    ("$b and ($b or !$a and $a) or !$b or ($b or !$a or !$b and !($a or !$b and !($b)))",true),
    ("($a or $a or !($a) or !$a) or !($b or !$a or !($b or !($b and !($b or ($a and $b)))))",true),
    ("!$a or !$a and $a or $b or !$b or ($a and !($a) or !($a and !((($b or $a)) and !$a)))",true),
    ("$b and !($b and !$b or ($b or !$b or $a and !$b or !($a) and ($a or !($a and $a))))",false),
    ("!($b and !$b or !$b or !$a and ($a or $a) or $b or $a or ($a and !($a and $a)))",false),
    ("!($b or !$b and !$b or !$a and !$b or !$b or !($b and $b or $a or !$b and ($a)))",false),
    ("$b or !$b and !($b and ($b or !$a and $a and !$b and !$a or !$b or $a and !$b))",true),
    ("((($a or $a or $b) or $a and $a) and $b or !$a or ($b and ($a or !$b) and $a))",false),
    ("$b or !$b and !$b and !$a or !$a or ($a and !($a and !(($b and $a or !($a and !$b)))))",false),
    ("(($b or !$b and !$b or !$b or $b or !(($b or ($a or $b) or $b and !($b or !$b)))))",true),
    ("!$b and !($b or ($a and !($b)) and $a or (($b and $a and !($a and $b and $a)) or !$a))",false),
    ("!$b and $b and $b or $b and !(($a and !$b or !$a and !$a or ($a or !$a and (($b)))))",false),
    ("$b and !$b or $b or !$b or $a and $b or !$a or !($b and $a or $a or ($a))",true),
    ("$b or $b and $a and $b and $a or ($a and $b) and !$a or !$b and $b or ($b)",false),
    ("!$b or !($b or $a and !($b) or !($a or $a and $a or $a or $a) or !$b and (($b)))",true),
    ("$b or $b or ($a and $a or ($b and !($a or $b and !$a or !$b and ($a) and $a)))",true),
    ("$a and !($a and !$b and !$b and !$a and !$b and !((($b or $a) and !$b and !$b)) and !$a)",true),
    ("$b and ($b or !(($b and $b) or $b and !$a or !$a and ($a and !$b or $a) or !$b))",false),
    ("$a or $a or !((($a and $b) or $a and ((($a or !$b and ($a) and !($a or $a or !$a))))))",true),
    ("$a and ($a and ($b or $a and ($a or !$a and !$a or !$a) and ($a) or ($a and !$b)))",true),
    ("!($b and $b and !$b and !$b or (($b or !$b) and !$b) and !$b) or ($a or $b and $b)",true),
    ("($b or !($b or ($b or !$b or $b or $b and !$a) and ($a and !$b and !$b or ($b))))",false),
    ("!($a or ((($a and ($b or !$a)) and !($a and !($a or ($a and $a) or $a) or $a or ($a)))))",false),
    ("$a or !$a and !($a and $b or !($b) or !($b or ($a and !$a and !$b) and ($b or $a)))",true),
    ("($b and !$b or ($a or $b or !($a and !$b or ($b) and !($b and $b or !$a or $b))))",true),
    ("$b or !$b and ($b and $a) or ($a and !(($b and ($a and $a and $b or !$a or !($b)))))",true),
    ("!(($b or ($b) and !$a and !$a and !$b or !(($b and $b and !$b or $a and !$a or ($a)))))",true),
    ("($b or !$b and !($b) and !($a and !($a and $a or $a) and $b or !$a or !$a or !$b))",false),
    ("!($a or (($a and !$a or !(($b or !$b and $b and ($a or $b) or $a or !($a and $b))))))",false),
    ("($a or !($a or $a) or !($a or ($b or !($a or $a and ($b)) or !($a and !$b)) or !(($a))))",true),
    ("!$b or $b and $a or ($b or ($a or !$b and $b and !$a) and !$a) or !$a or $a",true),
    ("!$a and $a and $a and $a and !((($a and !($b and !$a or ($a) and $b or !$b or $b))))",false),
    ("($a or !($a or ($a or !$b or $a) or (($b and $a) or !$b and !($a or $a or !$b))))",true),
    ("$b and $b and $b or !$a or (($b and !($b and !($a) or ($b and ($a) and ($b or !$a)))))",false),
    ("$a and !($a and (($a or ($a) or ($b and !($a or !$a or $a and !($a) and !$a and !$a)))))",false),
    ("$a or $a or !$b and ($b or $a and $a or $b and $a or $a) or ($a or (($a)))",true),
    ("$b and !$b or (($b or $a and !$b or $a) and $b or $b and !$a and !($a and !$b))",false),
    ("!($a or $a or !($b and $a or !($a or ($b and !$b and !$a)) or !$a or $b and !$b))",false),
    ("!($b or (($b or ($a or !$b or ($a or ($b or !$b) and !($a or !($a and $b) and !$a))))))",false),
    ("$b or !($b or ($b or !($b and !($b) and !$a) or !$a or $b) or ($a and ($a and !(($b)))))",false),
    ("$a or !($a and ($a or !($a) or $a or !$b and !$a and $a or !$b or $b or $b))",true),
    ("!$a and ($a and !$b and $b) and !($b or !($b or $a or !$a or !$b and !$b or !$a))",false),
    ("$a and $a and ((($b or !$b and $a) and !$a or $b or $b and $a or $b or !$b))",true),
    ("!$b and ($b and !($b and $a or !(($a or ($b and $b) or !$b and $b or !$b or ($a)))))",false),
    ("(($b and $b or $b and $a or !$b) and $a or $a) or $a and $a or !$b and !($b)",true),
    ("$b or ($b or $b or ($a and (($b) and !$a or $b and !$a and $b) and !($a) and !($b)))",false),
    ("!($b or $b and !$a and !$b or !$a and $b or !$b or !($b or !$a) or $b and $b)",false),
    ("($b or ($b or !$b or $a or $a or ($b) or !$a and ($a or (($b) or !($b or !$a)))))",true),
    ("($b or $b or ((($a or (($b and $b) or !$b or !($b) or $b and $a or !($b and !$b))))))",true),
    ("($a or ($a or ($b or $b or (($b or !$a or ($a and !($b or ($a) or !$b) or ($a)))))))",true),
    ("!($a and !(($a and !(($a) and $a and !($b and !($b) or (($b) or !$b) or !($b) or !$a) and ((($a)))))))",true),
    ("($a and !$a and !$a or ($b and ($b or !$b and !($b and $b and ($a and $a or !$b)))))",false),
    ("($b and $b and !$a or $a and !$a) or !$a or $a or ($b or $b) or $b and $b",true),
    ("!(($a and !($a) and $b and ($b and !($a and $a) and $a) and $a or $a and ((($a and !$a)))))",true),
    ("!($b or !$b and !$a and $a and !($a and $a or ($b) or $b) and ($a and $b and $a))",true),
    ("(($b and !$b or ($a and $b and !$b and !$b and $b and ($b and !$a or $a and !$a))))",false),
    ("!($b or $b or $b and !$b and !($b and !($b or !($a) or $a) and (($a or !($b) and $a))))",true),
    ("$a and (($a and ($b) or !($b or $a) or $a or !($a or ($b and !($b and !$b and $b)))))",true),
    ("$a and !(($a or !(($a and !($b or $a and !($a) and $b)) and $a) and !$a or $a or $a))",false),
    ("$b or !($b or ($b and $a and !$b and !$a or !$a and $a or $b and ($b or !$b)))",true),
    ("!($b and !($b or ($a or !$b or ($b) or ($b or $a and ($b) or !$b and $a and !$a))))",true),
    ("$a or $a or !$b or ($b and !$b or !($a and !$b or ($a) or ($b or !$a and !($a))))",true),
    ("$a or !($a or !($b or $a and !$b or !($a or !($a or !$b) and $b or !$a and $a)))",true),
    ("!($a or !$a and !($b) or (($a and ($a or $b or (($a))) or ($b or !(($b) and !$b) or $b))))",false),
    ("$a or !$a or ($a or !($a) and $a or $b or (($a and !($a and !$a and ($b) and $b))))",true),
    ("$b and !$b and !(($a and $b or $b or !$b and !($a or $a and !$b) and $a and $b))",false),
    ("!$b or !$b or !$b and !$b and $a or $a or !($a and $a or $b and !$a or $b)",true),
    ("$b or $b and $b or $b and !$b or $b or !$b and !$b and ($a and ((($a or !$b))))",true),
    ("!$b and !$b or !$b or !($b and !($a) and $b) and !($b or !($a or $a and $a or ($b)))",true),
    ("!$a and !$a or $b and ((($a and !($a or $b) and !$b and $b and $a or !$a and $a)))",false),
    ("!($b and ((($b or !($b and !$b or $a) or $a and !$a and !$b) or ($a and ($b) or $a))))",true),
    ("!$b or ($b or (($a or !$a or $b and !($a or $b and $a and !$b and $b and $b))))",true),
    ("!$a and $a or $a or !$a and ($a and ($b and $a and !$a) and ($b or !$b) or !$a)",true),
    ("($a or $a or $b) or !($b and $a or !$b and ($a and ($b and $a and !$a or !$a)))",true),
    ("!$b or ($b and $b and !$a and $a and (($a or $a and (((($a) or !$b and $b) and !$b)))))",true),
    ("$b or ($b or $b or !$a or $b) and !$a or ($a or $a or $b and !$b) or $b",true),
    ("!(($a and !($a and !$a and !($a) and ($b or ($a and !$a and $b)) and !$b and $b or ($b))))",false),
    ("!$a and $a and ($a or $b or !$b and ($b and !$a and !$a) or !(($b or ($b and !$b))))",false),
    ("$b and !$b or !($a and !($a and ($a and !$b or !(($b and !$a or !$b) and $a or ($b)))))",true),
    ("($b or !$b) and !((($a and $a or !$a or !$a or $b and !$a) and (($b or !$b)) or !$b))",false),
    ("($b and !(($b and !$a))) or $a or ($a or !$a) or ((($a and ($a) or $b) or $a or $a))",true),
    ("(($a and $a or $b and ($b or !$a)) or !($b or !($a) and !$b) and !$b and !$a or !($b))",true),
    ("$a and $a or !$b and !(($a and !($a or $b or !$a) or !($b or $a) and ($b and $a)))",true),
    ("($a or !$a and !$b and !(($b and !($a or $b and !($a)) and ($a) or !($b and $a or !$b))))",true),
    ("$a or ($a and ($b or ($a) or $b) or !($b and !($b) or ($a) or $a) or !$a or $a)",true),
    ("!$b or (($b or !($a or ($a or (($b or $a or !$b) or $b) or !$a) or ($a and !($a)))))",true),
    ("!$b and !$b and ($b or $a and !$b and $b or !$b and !$a) or !$b and $a and $a",true),
    ("$b and !$b or $a and !($b and ($b or !$a) or !$a and !$a and !(($b or $b and $b)))",true),
    ("($a or ($a or $b and $b and ($a and !($b and !$a and $a and !$b or !($b or !$a)))))",true),
    ("!($b or ($b and !$a) and $a and !$b and !$b or $b or $b or !$b or $b and !($b))",false),
    ("($b or !($b and (($a or !$a and !$a and ($b and $b or $b or ($b or !$b) or !$a)))))",true),
    ("((($a and ($a and ($a) and ($a or !$a and ($a or ($b)) and $b)) and !$b and $a or $a)))",true),
    ("($a or !($a or (($a or !(($b or !$b)) and !($b)) or ($a and !($b and ($b or !($b) and $a))))))",true),
    ("($b or ($b or $b) or $a) and !$a and !$a or $a or $a or !$b and !$b and $a",true),
    ("!$a and ($a and $b or ($a and !$a and $b or $b) and $a and $b) and !$a and !$a",false),
    ("!$b or !($b or (($b and !($b) and ($a or ($a and !($b or $a and $b and !$b or !($a)))))))",true),
    ("!$b or !($b or !$b or $a and !$a) or ($b or $b and !($a and !($b and $a or $b)))",true),
    ("!$a or $a and !$b and ($a and $a or ($a or $b and $b and $a and !$b and ($a)))",true),
    ("($b and !($b or $b and $b) or (($a and !$a or !$a or !($a))) and !$b and ($a and !($b)))",false),
    ("(($b or $b or $a or !$b and !($a and !$a and !$b or $b and $a and $b or !$a)))",true),
    ("!$a or $a or $b and $b or !$b or !($a and !($a and !$a and !$b or ($b and $b)))",true),
    ("!$b and !$b or $b or $a and $a and $a and !($b and !$b and $a or !($b or !$a))",true),
    ("$b or !$b or !$b or !$a and !$b and !($a or $b or !($b or !$b) or $b or !($a))",true),
    ("!(($b and !$b and (($a) and !($a or $a and $b or !$b and ($a or $a) and ($b and ($a))))))",true),
    ("($b and !$b and ($a and !$b and (($a and ($b) and (($a or $b or !$b or $a or ($a)))))))",false),
    ("($a and !($a) or $a or ($b or !$a or $a) or !(($b or $a or !($a and !$b and $a))))",true),
    ("!(($b or !($b and $a and $b and !$b and !$b and !$a and $b and ($b or $b) and $a)))",false),
    ("($a or (($a) or !$a and $a and !($b and $a and $a) and !(($b or $b or !$b or ($b)))))",true),
    ("($b or ($b) or !$a and $a or !$a and $b or ($a and !$a and !($a or ($a or $b))))",false),
    ("!$b and !(($b or $a and $b or !($b and !$a and $b and ($b or !$a) or $b) or !$a))",false),
    ("($a and ($a or (($a or $b or $b) and !($a and !$b or !$b and !($b and !(($a or !$b)))))))",true),
    ("!($a or !($a and (($b or !($a) and !$a or !($b) and !$a and !$b and $a and !($a or $b)))))",false),
    ("($b and $b) or ($a or !$a) and !$a or $b or !($b or $b and !($b and $b or $a))",true),
    ("!$a or $a or $a and !(($b and $b or !$a or $a) and $b and !$a or $a or ($a))",true),
    ("($a and $a) and !(($a and !$a and ($b or $b)) or !($a) or $b and ($a and ($a or $b)))",true),
    ("!$b and $b and (($b and !$a or !($a and $a and !($a and $b or !($b and $a or !$b)))))",false),
    ("!($a and !($a and !$b and !$a or !$a or !$a or !$b) and !($b or $b or $a and $a))",true),
    ("(($b and ($b or ($a and !(($b or (($b or !($a and !$b or !$a) or !$a) or ($b or !$b))))))))",false),
    ("($a or $a and $a and !$a or ($b) and !($b or $a and ($b and $a and $b and !$b)))",true),
    ("$b or !((($b or !($b and !$a or $b and !($a and !(($b or !$a and ($a) and $b)) or $b)))))",false),
    ("(($b and $b) or !$a and $b or ($b and !($b and $a))) or !(($a and !(($b and ($b and !$a)))))",false),
    ("($b or !$b and !$b and ($a or !((($b and $b and ($a)) or !($b) and $a or $a) and $b)))",true),
    ("!$b or !$b or !($b and !($a or !$b) or !$b or !($a and !$b or !$a and $b or (($b))))",true),
    ("!(($a and !($a and $b and !($b and !($a or (($a)) and !($a and $a) or (($b or ($a or !$b))))))))",false),
    ("!($b and !($b and ($a or ($a and (($a)) and ($b or ($a and !($a and $b) and !$a)) or $a))))",true),
    ("$a and ($a and !$a and !$a or $a or !$a and !$b or !($b) or $a and !$a and !($b))",true),
    ("!($b and (($b) and $b or ($a or !($a and $a) or ($b) or !($a) and $b or $a and $a)))",true),
    ("!($b or ($b or $a or (($a) and ($b or $b) and !($b and $b and !($a) or !$a or $b))))",false),
    ("!$b and $b or ($a or ($a or !$b and $b and $a) and !$b or ($a or ($b or !$a)))",true),
    ("$b and ($b and ($b or ($a and ($b or !($a) and $b and !$a and ($a and !$b)) or !($a))))",false),
    ("!$b and $b and !($b or !($a and $b or $b or !(($b) and ($a) and $b or ($a or !$b))))",false),
    ("$b or ($b or !$a and !$a or $b and ($b or !$b and !$a or !$b and !$b and !$b))",false),
    ("!($a or $a and $a or $b or $a or !$a and !$a and !$b or !$b and !($a and !$b))",false),
    ("($a or !$a and $b and !(($b and !($b or !$b) and !$a or !($b or ($a))) or ($a) or !($b)))",true),
    ("!((($a or $a and !($b) and ($b or $b or !($b)) and $b or !$a and ($b) and !($b and $b))))",false),
    ("!$a and !($a or $a or !($a or !$a or $a) and !$b and !($b or ((($b and (($b and $b)))))))",false),
    ("!($a and !((($a and $b and $a or $a or !$b and $a or !$b) or $a or $a) or $a))",true),
    ("$b or $b or $a or !$a and (($a and !(($a and !$a or !$a) and !$b or ($a and $a))))",true),
    ("$b and $b and ($a or $b and $b) and $b and ($a or ($a and ($b or !$a) and $a))",false),
    ("($b or !$b and (($b or ($b) and !($b and ($a or $a)) or $b or !$b or !$a and !($b))))",true),
    ("!($a and !($a or $b or $b and !$b or $a) and !($a and $b and $a or ($a and $b)))",true),
    ("(($a and !$a or ($a) and !$a or $b and !$a and !(($a and !($b and !$b or !$b or !($b))))))",false),
    ("!($b and (($b) and $b or !($b and !$b and !$b or !($a) and !($a and $b or $b or !($b)))))",true),
    ("!$b or !($b and !($a) or ($b or !$a and $b or ($b) or !$a and $b) and !$a and $a)",true),
    ("$a or $a and !$b or ($b and !$b or $a or !$a or $a and $b and !$a and $b)",true),
    ("$a or $a or $b and $b or !$b or !($b and $b) or !($a and $a or ($b and !$a))",true),
    ("$b or !($b or !$b and $b) or $b and !$b and $b or !$b and ($a or !($a or !($b)))",true),
    ("!($b and ($b) and !$a and !$a and !$a or !$b or $a or $a and !($a or $b and !$a))",false),
    ("!($a and $a and $a and !$b or $a and $b or !$a and $b) and $a or !$b and $b",false),
    ("!($b or $b or !($a and !($b and !$a) and !($b and ($a and $b or $a and !$b) or !$b)))",false),
    ("!$a and $a or !(($a and $a)) and $b and !($b or ($b or $a and !$b or $b) or !($a))",false),
    ("!$b or $b or !($a or !($a or !($a) or $a) or !$a and !$a and $b and $a and !$a)",true),
    ("($a or ($a or !$b and !$b and ($b and !$a or $b and ($b and !$a or ($b or !$b)))))",true),
    ("($b and $b and !$a or !($a or ($b or !($b and ($a or $a) or !$a and $b) or ($a))))",false),
    ("!($b and !$b or $b and ($a and ($b or ($b or $a or $b) or !$a or !($a and !$b))))",true),
    ("!$a and !($a or !$a and $a and !($a or !($a) or !$a or !$b and $b and $a) and !($a))",false),
    ("!$a or !$a and $a and !$b or ($a or $a and ($a and $a and $b or !$a or $b))",true),
    ("!$a or $a or !$b or ($b or $a and !($a or $a or !$a or ($b and !$a or !$a)))",true),
    ("!$b or !($b and !$b or !(($b or !$b or !$b or $a and $b or !$a and !($a) or !$b)))",true),
    ("$b or $b and !((($b and $b and ($a or !$a or !$a or $a or !$b) and !($a and $b))))",false),
    ("!$b or $b or !((($a or !$b) and ($a and !$b and ($b and $b) and $a and $a or !$a)))",true),
    ("$b and $b and $a or !$b or !$b and !(($b or $a and !$a and $a and !$b and ($b)))",true),
    ("($b or !($b or $a) and !($a) and !$b or $a or $b and !$a or (($b and ($a and $a))))",true),
    ("!$b or $b or !$a or ($a or !$b or !$a and !($a and !$a and !($a or ($a or !$a))))",true),
    ("($b and !($b or !$b or ($b and $a) and ($b and !$a and !($a) or $b) and $a or !$a))",false),
    ("!$b or !($b and !$a and ($a and $b or $b or !$b or $a and $b or !$a) or ($a))",true),
    ("!($b and !($b or $a or (($a or $a and $b and !$b and $a) and !($b)) and ($a and !$a)))",true),
    ("$b or !$b and !($b and !$a or !$b) and !$b or $b or !$a and $a or !(($a or !$a))",false),
    ("($b or !($b and !$a and !$a and $a or $a) or $b and $b and !$a and !$b and !(($b)))",false),
    ("!($a and !$a and !$b or !$a and !$a and !($b and !($a and $b or $a or $a) or ($b)))",true),
    ("!$a and !(($a or !($b or (($b or !$a and !$b and !$b and $a or $b) or !$a or !$a))))",false),
    ("!$a and ($a or !$a and (($a and $b) and ($b and !(($b or !$a and $b and !($b) or !$a)))))",false),
    ("$b or !$b or !$b and !($a and !$a or !($a and ($a)) and $b or ($b and $b) and !$b)",true),
    ("!($b and !$b or !$a and !($a or ($b or !($b and !($a or !$a and $b and ($a) and !$a)))))",true),
    ("($b or !$b and ($b and $a and !$b or !$a or !$a or $a and $a or !$a or $a))",true),
    ("$a or !(($a or ($b and $b or $b) or !$a and $a or ($a or ($b or $b or $b))))",true),
    ("($a or ($a or !($b and !$a or $a and ($b) or $b) or !$b and $a and (($a or !$b))))",true),
    ("!$b or !(($b and $a or !(($b or $b) or !$b or $a and !$a or $b and (($a or (($b)))))))",true),
    ("$b or ($b or !(((($a or !(($b) and !($b and !$b))) or !$b and !$a and ($a) or !$b or $a))))",false),
    ("($a and ($a or $a and $b or !$b and !(($b and !($b) and !$a) and $b and !$a or $a)))",true),
    ("!$b and !($b and !($b) or ($a or $b and !$a or !$b and !$b or !$a and $a) and $b)",true),
    ("($b and !$b or !$b or !($b) or !(($b and !(($b or $b and ($b and !($b or $a) and !(($b))))))))",true),
    ("$b and !($b or !$b or !$a or $b or !$b and $a) or !$b and ($a or !$a and !($a))",true),
    ("$a or ($a or !$b and $b and !($a and $b and $a) or $b and !$b or $a or $a)",true),
    ("!(($b or ($b and $a and ($b and !($a)) and ($a or !$a or !$b or $b and $b)) or !($b)))",false),
    ("!($a or (($a or $a and !($a) and !$a or !$b or $b and !$b and $a or $b or ($b))))",false),
    ("$b and !$b and ($a and ($a) or $a or !$b or !($b or $a or $b or !$a and $b))",false),
    ("$a or !$a or !$b and $a and !((($b or $b and !$b and $b and !$a and (($b or !($a))))))",true),
    ("($b and !$b or !$a or ($a) or ($a and $a) or ($b and $a) or $a or !$b or !($b))",true),
    ("$a or !($a or !($b and !($b and !$b or !(($a and !$b and $a) and ($a or $b or $a)))))",true),
    ("$b or ($b or ($b and !$a) or ($a or $a or ($a or !($b and !$a or $b or $b))))",true),
    ("!$a or $a or ($a and !$b) or !($a or ($b and $b and (($a or $b and ($b or !$b)))))",true),
    ("($b and ($b or $a or !$a and !$b and !$b or !$b and !$a and $a or $b or !$a))",false),
    ("((($a or !$a and !($a and $b or !$a and !$a or !$b or ($b) or $b)) and ($b and ($a))))",false),
    ("!($a or ($a or $a) and $b or !$a and !(($a or $b and !($a and !($a) and !$a and $b))))",false),
    ("!$b or !($b and !($b and $a and !$b or $a and !$a and !((($b and !$a and !$a and $b)))))",true),
    ("$a or !($a or !$b or !($a or $a) or !$b and !(($a) and $a or $a and ($b and $a)))",true),
    ("($a and !$a and !$a and !($a and !$a and !($b) and ($a and $b)) and !(($b and $b or !($a))))",false),
    ("!$b and !($b or !$a or (($b and !$a and !$b) and $b or !$b or !$b and $b) or !$b)",false),
    ("($a or ($a) and $b or $b and $b) and (($b or !($b and !$b or ($b) and ($a or ($b)))))",true),
    ("$a or !($a or !$b and !($a or $b and !$b and $b or !($a and !$b) or !($b) and !$b))",true),
    ("(($a or ($a and $b or $b and !($a and !$b) and $a or !$a and !($b or $a)) and !$a))",true),
    ("!(($a and !($a) or $a and $b and !($a or !$a or $a and ($b or !$a) and $a and !($a))))",true),
    ("!$a or ($a or !($b and !($b or !($b and ($a and !($b or $a or $a and ($a or $a)))))))",true),
    ("!$b or !($b and !(($a and $a or $b and ($b or !$a or !$b and $b)) or ($b or $a)))",true),
    ("$a and $a or !($b or !($b or $a and !($b or $b and $a or !($a and ($a) or !$b))))",true),
    ("!$a and !($a and $b or !$a and !(($a or (($a)) or !$a) or (($b or $a) and !$a and !(($b)))))",false),
    ("($a and $a) and $a or $a and !$a and ($a and $a or !$a or !$b and !$b and !($a))",true),
    ("$a and (($a or $a and !$b and !($a or $b or $a) and ($a or !($b and ($a and !$a)))))",true),
    ("!(($a or ($a) and (($a and $a or $b)) or $a or !$a and !($b or $b or !((($b) or !$a)))))",false),
    ("!$b and !($b and $a or (($b and !$b or ($a) or ($a and !$a and !($a) and $b and !$b))))",false),
    ("!$a and $a or $b or $a and !$b and !$b or (($b and !$b) and !(($b or !$b) or $b))",true),
    ("$b or !($b and (($a or $b or !($b and $a or $b) or $b) and ($a) and $a) or $b)",true),
    ("$a or !$a and !$a or !($a and !$b and ($a and $a or !$b or ($a or $b and $b)))",true),
    ("$b and !$b and !((($a or !($b or !$b and !(($a or !($a and !$b)) and !$b) and !$a) and ($a))))",false),
    ("($a and !($a and ($b and !$a) and ((($b or !$a or !($a and $b and $a) or $a) or !$a))))",true),
    ("$a and $a and $a and $a or $b or $b and !($a and !($a and $a and $a or !($b)))",true),
    ("!$b or !($b or !($b or !$b or $b) or !($a and ($b or !($b or ($b and ($a or $b))))))",true),
    ("$b and ($b or !($b or $b or !$a or $b or $a) and (($b or ($a and !($a) and $b))))",false),
    ("($a or !(($a and !($b or !($b or $b and !$b and $a or !($a or ($b and $a) and !($a)))))))",true),
    ("!$b and !$b or $b and $b and $a and !((($b and $a and !$a or $a and $b and !$a)))",true),
    ("!($b and ($b or !$b or !($a or (($b)) or !($b or ((($b or !($b)) or ($b and !($a or !$a))))))))",true),
    ("($b or !($b or ($a or !$a and $a) and $b or !$a and ($a) or $a and !$b or !$a))",false),
    ("$b or ($b or ($b and $b and $a or $b and ($b and $a and !$b) and $b or !$a))",false),
    ("$a or ($a and !$a or ($b and !$b and $b) or !($b or !(($a)) or !$b and $a or !($b)))",true),
    ("!($a and ($a and $b or $a and ($a and !$b and ($a or !$a) or !$b and $b and !$b)))",false),
    ("!($b and $b or !(($b) and !($b and $b and (($a or !$a) and $b or !$a) or $b) or (($b))))",false),
    ("!$b and ($b and !($b or $b and ($b or !$a) and $a) and !$a) or $b and !$b and $b",false),
    ("!$a and !((($a or $a)) or !($b or !($a or !$a or !$a or !$b or ($b and !$b and $a))))",false),
    ("!$b and $b and ($b or !$b and $a) and $b or !($a or !$a and !$b or ($a and !(($a))))",false),
    ("(($a and !($a and !$b and !$b and $b and $b or (($a) and $a and ($a and ($b and !(($b))))))))",true),
    ("(($b or !($b or (($a and !($a or !$b or $b and !$a))) and $b or !(($a or ($b or !($a)))))))",true),
    ("!$b and !($b and !$b or !$a and $a or !$a or (($a and ($b and !$b or ($a or !($a))))))",false),
    ("$a and !$a or $b or !$b and !$b and !$a and $b or !$a or $b and !$b and $b",false),
    ("$b or !($b or $a or !$a and $b or !$b and $a or $b and ($b and $a and $a))",false),
    ("$a or $a or ($b and !($b and !$a) or !($b or !($a or $a) or $a and $b or ($b)))",true),
    ("$a or $a or !$b or !($a and !$b and ($b and !($b or !$b or $b or !$a and !$a)))",true),
    ("$b or !(($b and !$a or !$a and ($b or !$b or $a and ($a and !($b)) and !(($b) or !($a)))))",true),
    ("!$b and ($b and !$a or !$a and $b or !(($a and !$b or !$a or !($b and ($a or !$b)))))",false),
    ("!$b and !($b or ($a or ($a or !$b or $b) and ($a and $b or ($b and !$b and !$b))))",false),
    ("!($a or !$a or !$a and !$a and !$a) and !($b or $a) or $a or !($a or !$b and !$a)",true),
    ("(($a and $a or !($b or $b and $a or ($b or $a or $b and $a)) or !($a)) or !((($a))))",true),
    ("!($a or (($a or $b or $a) and !$a and !($a and !$a) and !$a and !$b and $b or $b))",false),
    ("$b and $b and ($a or !($a and !$a and !$a and !$a and !$a or !($a or $a) or $a))",false),
    ("(($b and $b) and $b or !$b or $a or !$a) and !($a and $b or $b and !$a or !($b))",false),
    ("!($a and !$a or $a and ($a or ($a) or $a)) and (($b or $b and !($a or ($a and $b))))",false),
    ("!$a and !$a and $b and ($b and !$a and !$b and $a or !($a or $b or $b and !$a))",false),
    ("$a and !($a and $b or $a) and $b or $b or !($a and $a or $b and !$b and ($b))",false),
    ("!$b or $b and !($b and !$b and !(($b and !$b and !($a and $a and !$b or !$a) and !$a)))",true),
    ("$a and ($a or ($a and $b and $a or $a and ($a and $a) and !$a and !$b and !$a))",true),
    ("!$b and ($b and !($b) and $b and !$b and !$a or !($b and $a or ($a and !($b and !$a))))",false),
    ("($a and !($a or !$a and $a or $b)) or $a and $b or !$a and $a and !$a or ($a)",true),
    ("($a and !($a and !$a or $a or ($a and !$b) or $b and !$a and ($a or $b or $a)))",false),
    ("((($a and ($a or $b and !$a and !$a and !$a and !$b) or ($a and !$a or !$b) or ($a))))",true),
    ("(($b and $b and !$b and !$b or !$a)) and $a or !(($b and $b) or ($a or ($a and ($b))))",false),
    ("$b or ($b and !$a and $b and $a or $b and !$b or $a or !$b and !$a or $b)",true),
    ("$a or ($a or $a or $b or !$b) or ($a and $b and !($b and $b or ($b and !$b)))",true),
    ("($a or !$a and (($b and !$a) and !$a or !$b or !$b and ($b) or $b and $b or $a))",true),
    ("($b and $b or !$a and $a and $a and !$b and !$b or !$b and !$a and $a and ($b))",false),
    ("!(($a and !(($a and !($b and ($a) and !$b and !($b) and ($a and !$b)) and !$a and $a and $a))))",false),
    ("!($b and $b) and $b and $a and !($a or !($a and !$a and $b or $b or $a and ($b)))",false),
    ("($a and ($a or !$b or !($a and !$b and !$a and !(($b and !($a) and (($b and $a or !$b)))))))",true),
    ("!$b or !($b or $b and $a or $a and (($b and $a) or !$b and !(($a and !$a) or !$b)))",true),
    ("$a and ($a or !$b and $b and !$b or ($a and !$b or !$a or !$b and $b or !$a))",true),
    ("!($b and !$b and (($a or !$b and (($a and !$b) and $a and $a) and $a or $b or !$a)))",true),
    ("!$a and $a or !($b or !$a or $a or !$a or !($a or !(($a and ($a) or !($a) and ($a)))))",false),
    ("$a and $a or $a or $a or !$a or ($a or $b and ($b or !($a and $b and $a)))",true),
    ("!(($b or !$b or !$a) or !($b and !$b or $a and $b or $b or !$a and $b) and ($a))",false),
    ("$a or !$a or !$b or $b or $b or $b and !($a and $b or ($b or !$a or $b))",true),
    ("!($a and $a or !($b) or !$a or !(($b and (($a and !$a or !$a) or !$a and !$b or $a))))",false),
    ("$b or $b and !(($b or $a or ($b or $b and !$b and !$b) or $a and ($a) or $a))",false),
    ("!$b or !$b or !($a and !($b and $a or !($b or $a and !$a or !$a) or $b or ($b)))",true),
    ("($a and (($a and !($b and !$b or $b or $a) or !($a and !(($a) or !$b or ($b)) and $a))))",true),
    ("$a or ($a and !$a or $b or ($a and !$a and !$b and !(($b or ($b or $a)) or !($a))))",true),
    ("!($a and !$a and !($a) and $a or (($b or !$b and !($b and $a or (($b or !$a)) or !($a)))))",false),
    ("!$b or ($b and ($a or !$a or $a and !$b or !$a or !($a and !($a and !($a or !($a))))))",true),
    ("$a or !($a or !($a or $b and ($b or !($b) and !$a and $b) and !$a) or ($b or $a))",true),
    ("!$b and ($b and $b and (($a or ($a or ($a or !$a or ($b or $b and !$b) and !$a)))))",false),
    ("($b and !$b or !$a or $a or $a or !($a or !$a or $a or !($a) or !$a and $a))",true),
    ("!($b and $b and !($b and !$b or !$b or !($a) and (($a or !$a or $b or !$b) and $a)))",true),
    ("!$b or $b or !$b or ($b and !$a and ($b and !$a or !$b or $b or !($b) and ($a)))",true),
    ("!$b and !$b and !$a or $b or !($a and $a or $b or !($b or !($b or $a) or !$b))",false),
    ("(($a and !$a or (($b and !$b or !($a and ($a) and $b) or $a and $a and ($b or !$a)))))",true),
    ("($b or $b or !$a and !($a and $a and !$a) and !$b or $b or $b or !($a and $a))",false),
    ("!$b and !((($b and !$b and ($b and !$b) and !($b or !$b) or !$a) or !$a or ($b and $a)))",true),
    ("!($b or !($b) or ($b or !$a or !$a and ($b or (($a or $b and $a and $a or $b)))))",false),
    ("(((($b and !(($b or $b) and $a or !($a) and !$b and !($b)) or ($a or ($b and !($a) and $a))))))",true),
    ("$b or $b or !($b or !($a or !$b) and $b or !$b and !($b and !$b) and !($b and !$a))",false),
    ("($b and $b and ($a and !$a) and $b or ($a and !($a) or !$b and !((($a and !$a or !$a)))))",true),
    ("($b and ($b and $a) or $a) and !($b and (($a) and $b or $b and ($b) and !(($a or !$b))))",true),
    ("(($a and !$a or $a and !($a and ($b or !(($b or $b) and $b and !$b or $b or !$a)))))",false),
    ("$a or $a or !$b and !$a and ($b or $a) or !$a and !($b or !(($b and ($b and !$a))))",true),
    ("!$a and $a and ($b and !$a or ($b or $b and $a or !$b or ($a and $a and !$a)))",false),
    ("($a or ($a) or !$a or !$a and !($a and $a) or $a or !($b and !$a and $a) and !($b))",true),
    ("$b and !($b or !$b and !$a) and !$b or $a or !$b or $b and (($a or $b and $a))",true),
    ("!($b and ($b or $b and (($b and ($a or !$b) or !$a) and !$a or !$b) and ($b or !$b)))",true),
    ("!($b and !($b) and (($b or !$a and !$a or $b and !$a and !($b and $a or $b) and !$b)))",true),
    ("!$a or !($a or !$a and (($a and !(($a or $a)) or !$b or $b and $b or !$b and !($b))))",false),
    ("($b or $b and ($a and ($b and !$b and ($a and ($b and ($b and !$b or $a or $a))))))",false),
    ("!$a or !$a or !($a and !(($b) or $b and !(($b) and !($b or $a or $b or $a or $a))))",false),
    ("(($a and $a or ($a or $b or !$a or !$b) or !$b and !$b) or $b or ($b and !$b))",true),
    ("!$b and ($b or ($b or !$b or !$a and (($b or !$a or $a and $b) or $b) and !($b)))",true),
    ("!$a and $a or (($b and $b and $a or !($b and $a or !$a) and $a or !$b) or $a)",true),
    ("($b or !($b or ($b and !($b and !$b) and !$a and !$a and $b and $a and !$a) and $a))",true),
    ("!(($b or $b or ($b and !$a and !($b and $b) or ($b and ($a and $a and !($b) and !$b)))))",true),
    ("(($a or ($a and !$b) and !$b or $a and $b or $b and !($b or ($b) or ($a and !$b))))",true),
    ("!$a or !($a and !($b and !(($b or !($b or $b) and !($a) and ($b and ($b and !($a) and $b))))))",false),
    ("($b and !$b) or $a and !($a and $a and $a and $a and !$b or $a and !($b and !$a))",false),
    ("!($b and (($b and !$b and !($a or !(($a)) and !$a and !$b and !$a or !$b or !$a or !$a))))",true),
    ("!($a and !$a and !(($b and !$a and !$b and ($b) and $a) or !($a or $b) and $b and ($b)))",true),
    ("$a or ($a and $a and !$b or $b or !(($b or !(($b and !$b) or !$a or (($a or !$a))))))",true),
    ("$b or $b or ($b and !($b or $a) and $b and !$a) or !($a or !$a or ($b or ($a)))",false),
    ("!$a or !$a or $a or $b and $b and (($a and $b or !$b or $a or $b or $a))",true),
    ("!($b or $b or !$a and $b and !$b and $b and !$b or !($a or !$b or !$a and ($a)))",true),
    ("$b or ($b or !($a and $b or !$b and !$b or !$b or $a or $a and !$a) or !$a)",false),
    ("$a and $a or $a and $a or (($b and ($a or !$b or $a or !($b and $b or !$a))))",true),
    ("$b and $b and !$b and $a and $b and (($b or $b and ($a or !$b or $b and $b)))",false),
    ("$b or $b and ($b and $b or !$b) and !($a and !($b and !($a or ($b and !(($a) or !$a)))))",false),
    ("(($b or !($b and !($a and !$b) or !$a or !$a) or (($a or $a and !(($a or !$b) or !$a)))))",true),
    ("$a and !$a and !$a or !$a or !$a or !$b and (($b or !($b and $b) and (($b or !$a))))",false),
    ("!($b or !($b or !$b or !(($a or ($b and $a) or $b and !($a) and ($a) or ($a and (($b)))))))",true),
    ("($a and ($a and ($b) and !(($a and !$a or ($a and !$b and ($b) or !$a) or !$a or !($b)))))",false),
    ("$b or !($b and $a and !($a or ($b or $b and $b) or !$b) or !$a or !($b or ($a)))",true),
    ("!(($a and $a and !$b) and $a and (($b or ($b and !$a) and !($a and $a or ($a) or !$a))))",true),
    ("$a and !$a or $a and ((($a or $b) or !(($a and ($b) or !($b or $b) or !($b) or !$a))))",true),
    ("!($b or $b and $a and !($a and ($a and !$b and $b) or $b) and $b and $b) and ($b)",false),
    ("!(($a and $a and ($b or $a) or $b and !$b or $b and !$a or ($b and $a) and ($b)))",false),
    ("$a and ($a or !$b and $a and ($b) or $b or !$b or !$b or ($b or !$b) or !$a)",true),
    ("!$a or $a or !($a or ($b or !$b or !($a) or ($b and $a or ($a) or $b or $a)))",true),
    ("($a and !($a and $a and ($a or $a and !$b and !$b and ($b or !$b or ($b) or $b))))",false),
    ("!$a or ($a or !$b or !(($b or !$a and !$b and !$b and ($a and !$b and !$a or !$b))))",true),
    ("!$b and (($b or !$a) or ($b or (($a and ($a and ($b) and $b) or !$a)) or ($a) or (($a))))",true),
    ("!($b and $b and !($b or !$a) and ($b and !$a and $b and !$b or !$a or !(($b) and !$a)))",true),
    ("!($a and $a or (($a and !$a or $a and !($a or ($b and $b and ($a and $a) and !($a))))))",false),
    ("$b and !$b or $a and !(($b or !$a and !$b and $a) or !$a and !$a and !($a or !($b)))",true),
    ("($b and !$b or $b or $b or $b and (($a or $b) or ($a and $a or ($b or !$b))))",false),
    ("!(($b or (($b or ($a or !$b or $a and $a or $b)) and !$a and $a) and !$a and !$a))",true),
    ("$a or !$a and !$a and $a or ($b or !(($b or $b and $b or $b and $a and $a)))",true),
    ("!$b or (($b or $b or !$b and $a) or !($a and !($a and !$a and ($a or $a and $b))))",true),
    ("!$b and !($b and !$a or $a and ($a and !$b or $a) or !$a and !$b) or !$b or !($b)",true),
    ("!($a or $a or !($a) or $a or !$b and !$b or !$a) and !$b or $a and !$b and $b",false),
    ("!($b and !(($b or $a and ($a and !$b)) and !($b and $a) or (($a and (($a)) or !(($a and !($a)))))))",true),
    ("!($b and !(($b and !(($a and $b) and !($a or !$b and !($a and $b or ($a) and $b) and !$a)))))",true),
    ("$b or $b and !$a and !$b and !$a and !(($a or !$a or $a) or !$a or $a and $a)",false),
    ("!(($a and $a or $a and !(($b and $a) and !($a and $a or !($b or !$a) and ($b or $a)))))",false),
    ("(($a and !(($a) and !$a and !(($b and ($b and !$b) or !$b and $b or $b) and !($a and $b)))))",true),
    ("!$a or !$a or !$a or !$a or !$b or !$a and $a and !$b and ($a or !$b) and $b",true),
    ("!($b or (($b or $a and $a or !$b) or !((($a or !$a) or $b or ($a or !($b or !($b)))))))",false),
    ("!(($a and $a) and !$b or !$a or $b and !$a and $b and $a or !($b or !$a and $b))",false),
    ("!$b and ($b and !($b and (($b and !(($b or !$b and ($b) and !$b) and $a and ($a and !$a))))))",false),
    ("(($b and !$b or !(($b or !$b and !$b or !$b and !($b) or ($a and !$b and $a)) or $a)))",false),
    ("$b or !(($b or ($b or !($a) and $a or ($b or $b and !($b and !($b) and !($b and $b))))))",true),
    ("$b and (($b or !$b or !$b and !$a and $b) or !$b or $b and $b or !($b or $a))",false),
    ("($a or !$a) and !($b and $b) and ($b or $a and $a or ($a and $b or !$b or !$b))",true),
    ("!$a and !$a or !$b and ($b and !($a and !($b and !($a and !$b) or !($a or !$b and $a))))",false),
    ("!$b and !$b or !$b or !$b and $b and !($b or !($b and $a or $a or ($a or $a)))",true),
    ("$b or !($b or (($b and !$a and !$b and $b or !(($a or $b) or !$a and !$a and !($b)))))",true),
    ("(($b and $b or !($b) and !$a and $a or ((($a and $b and !($a or ($b)) or !$a or !(($b)))))))",true),
    ("$a and !$a or (($b or $a and !$a or !$b and $b) and ($a and $a or !$a) or $a)",true),
    ("!($b and $b and (($a and $a or ($b and !$b) or !$b and (($a) and !$a or !$b or !(($a))))))",true),
    ("$b and !($b or !($b and !$a and $b and !((($b and $b and ($a) and $a) or !$b and !$a))))",false),
    ("(($a or $a and !($b or !($b or !($a or !$b) or $b and ($b) or ($b) and $b or $a))))",true),
    ("!($a or ($a and !(($b or !$a or ($b and $b or !$a) or !$a) or !$a or !($a and $a))))",false),
    ("!$a or !$a and !$b and ($b or $a or !($b and ($a and $b and !$b or $b and $a)))",false),
    ("($a and !($a) and $b or !$b and !($a or ($a and ($b) or $b or $a and $b and $a)))",false),
    ("($b and ($b or $a and !$b or !($b and !$b and !($b or !($a or ($a or $a) and !($a))))))",false),
    ("!$b or $b and !$b or !$a and !(($b or ($a or $a and !$a and $b and $a) and $b))",true),
    ("!($a and !($a and ($a or !$a or $b or !($b and !$a or $b and $a) or !(($a or !($b))))))",true),
    ("!$a and !$a or !$b or !$a and !$b and ($b or $b or $b or !$a or $b) and !$a",true),
    ("!$a or $a or $a or ($a and $b or ($b and $a or !($a or ($a) or !$b) and !$b))",true),
    ("!$a and !($a and !$b and $a or !$a and !$a or $a or $a and $a and ($b or !($a)))",false),
    ("($b or (($b and !($b or $a) and ($a and $b) and !((($b or $a and $b)) or !$b and !$b))))",false),
    ("!($a or (($a and $a and !$a or !$b and !$b) and ($b and !$b or $a and !$b and $a)))",false),
    ("(($a or $a or !($a or !$a) or !($a and !(($b and !($b and !$a or $a) or $a) or !$a))))",true),
    ("($a or $a or !$a or !(($a and !$b and (($b) or $b) and !$b or !($b and !$b) or $b)))",true),
    ("!$b and !$b or $b and ($b and ($b and $b or !$b and !($a and $a and $b and $a)))",true),
    ("!($b or !(($b or !$b or !(($b or !($a))) and !$b) and !$a and $b and !($b) or $a or !(($a))))",true),
    ("!($a and $a or $a and $a) and ($a and !($b or $b or !$a) and !$a or !$b or ($b))",false),
    ("$b or $b and ($b or !(($a) and $b and $a and !($a and !$a) or !$a or $a and $b))",false),
    ("!$a or ($a and !$b and !($b or $b or !$b or $b or !($b and !($b and $b and (($b))))))",false),
    ("$a or ($a and !$a or !($a and ($a and $b or !($a or !$b) and $b or $b and $a)))",true),
    ("$a or $a and !$b or $a and $a or ($a or !$b or !$a and !$a or !$a or !$a)",true),
    ("!$a or !$a and $a or !($a or ($a) and !$b and (($b and !$a or $a and (($b and !$a)))))",false),
    ("!$a or (($a or ($a or $a or $a and $a and !($b) or ($a) and $b and !$a or !$b)))",true),
    ("$b or (($b or !($b and $b or $a or !$b and $b and !$b) and !$b or !$a and !$b))",false),
    ("!($a or !($a) or !($b or ($a or !$a or !($b or !$b) or $a) or !$a and !$a or $a))",false),
    ("!($b or !$b and $b and $b or !$b or (($a or !$a or $b and $b or $b and !$b)))",false),
    ("$a or $a or $b and $a or !$b or $a and ($a or !$b or !$a and !($a) and !$a)",true),
    ("$b and !((($b and ($b or $b) or !$a or ($a or ($b) and (($b) or !$a or !($a and !$b))))))",false),
    ("((($b or ($b and !$b or !(($a and !$a and !$b or !$b)) or $b or ($a or $b)) and !$b)))",true),
    ("($a and $a and ($b and !$a) and !$b or $a or !$b and $b or ($b or ($b and $a)))",true),
    ("($a or !((($a or !($a) or $a and !$a and !$b and !$a and !$a or !$b or ($a or !$a)))))",true),
    ("!(($b or !($b or !(($a and ($b or !$b and ($a and !$a) and (($a or $a or !($a and !$b)))))))))",true),
    ("($b or $b or !$a and ($a and !$b and $a and $a and ($b and !(($b) or ($a or ($b))))))",false),
    ("!$b or !$b and !$a or $a and ($b and !$b or !$a or $b and ($b or !$b) or !($b))",true),
    ("$b or $b and (($b and !($a and $b and !$a and $a and $a or !(($b or ($a and $b))))))",false),
    ("!($a or ($a or ($b and !$a) or $b and !$a and !$a) or !($b and (($b or !$a or !$b))))",false),
    ("($b and !$b or $a and !$b and !($a or !$a and $a and !($a and $a and !$b) and !$b))",false),
    ("!(($a or ($a) and !$a and ($b and $b) and !$a and $a and !($a and !$a or !$a and !$b)))",false),
    ("($b or $b and !$a or !$b or !$a and !($a and ((($a and !$a or $a or ($b or !$b))))))",true),
    ("($b or ($b and !($b and ($a)) and $a) and (($a and (($b) or !($a and $a) or !$b and !$b))))",false),
    ("$b or $b and $a or !($a and !($b or !$a or ($b or !($a and ($a or $a and $a)))))",false),
    ("$a or ($a and $b or !$a or !($b or ($b and $b and !($b)) or $a and !($b and $a)))",true),
    ("!$a or !($a or !$a or !$b or $b) and $a or $a or !(($b and $a and !$b and !$a))",true),
    ("$a and $a or ($a and !$b and !($b or $b or !$a and $b or $b and $a) and !($a))",true),
    ("!$b or !($b and ($b and !$a or !$a and $a and !$a) and $b) or $a and !$b or !$b",true),
    ("$a or !($a or !$b and ($a or !$b or !$b and !$b and !$a or $a or $b or $a))",true),
    ("$a or ($a and !$a or $b or !$a and ((($a or $a) or !$a) or $a and $a or !$a))",true),
    ("!(($b or !($b or $b and $b) and $b or !$a and !$a or $b or ($b and !$b or !$a)))",true),
    ("!($b and $b or (($a and !$a and $b) and $a) or $b or !($a or !$a or $b or !$b))",true),
    ("!(($b or $b and !$b or ($b or $a and $b) or !$a and ($a or $a) and $b and !$b))",true),
    ("!$a or $a and $b or ($a and $b or $a and !($b or ($b or !$a or !$a) or ($a)))",false),
    ("!$a or (((($a or $a and !$b and !$b) or !$a) or (($b or !$b) or !$a and $b) or ($a)))",true),
    ("((($a and !$a and $b or !$a) and !($a or !($a or !$a) or $b)) or $a and !$b or !($b))",true),
    ("$a or ((($a or !$a and $b or !$a or !$a) and !($b or !$b or $b or ($a and !($b)))))",true),
    ("($b or $b) or !($b or !($b and (($a or !$a or !$b)) or ($b and !$b and !$b or !$a)))",false),
    ("!$a and ($a or !($a or $a or ($b and !$a and !$b and $b and $a and $a or $b)))",false),
    ("($a and $a or $a or !($a and !$b or $b and $a or !($b and !($b) or $a and !$b)))",true),
    ("!($a and !($a and !$b or $b) and !$a or !$a and ($a or !($b) or $a) or !$b or !($b))",false),
    ("!$a and ($a or $a or !($a and $a or !$a and ($a or !($a or $b and !$a or !($b)))))",false),
    ("$a or !$a and ($a or $a or $b or $b and $a or !$b or !$a or !($b or !$a))",true),
    ("!$a or !($a or $b and $a and ($b and !$a or $a and $b and !($b and !($a or !$a))))",false),
    ("(($b or $b and $a or !($a and !($a and !$a)) or $b and $a and $a or ($a or ($a))))",true),
    ("$b or ($b or !$b or (($a) and ($a and !($a or !$a and !$a and !$a or ($a or !$a)))))",true),
    ("($b or !$b) or $b or !($a and !$a and ($a and !(($a and !$b or !$b and !($b or $a)))))",true),
    ("($a or ($a and $a) and !$a and $a) and ($b and (($b or $a) or $a and !($b and !$b)))",false),
    ("($a or !$a and (($b and !($a) or ($b) and $a or !($b or !($b and !$a or $a) and ($a)))))",true),
    ("$b or !($b and ($b and ($a or !($a and $b or !($a or $b or !($b and !$a)) or (($b))))))",true),
    ("($b or $b and $b and $b or !$b) and !$b or $a or !$b and !$b and $a or !($b)",true),
    ("($b and $b) and !($b and !$a or !($b) or (($b or $a or $a and $a or !$a or ($b))))",false),
    ("!$b and ($b or !($b and $a and !$b and !$b or ($a or !$b and !$a) or $b or !($b)))",false),
    ("!(($b and !$b) or ($b) and $b or $a or $b or ($a or !$a and !$a or !$b and $b))",false),
    ("!($b and $b) or !($b and !$a or !$a or !($a or !($a or $b and !$b or !$a)) or !($b))",true),
    ("$b or $b or !$a or !$a and $b or !($a and $b and !$a) or !$b and !($b and ($a))",true),
    ("$a or ((($a or (($b or !$a or ($b or !($a and !$a)) or ($a and !$b or $b or !$a))))))",true),
    ("($a and ($a and $b and $b) or !$a or !$a or !($b and !$a and !$b and !($a and !($b))))",true),
    ("$a and $a and ($b and $a or !($b and $b and ($b and !$b or (($a and !($b or !$b))))))",true),
    ("$b or !$b and $a or !(($a and $b or $a or $b or !$b and !$b or !$b or !$a))",true),
    ("$b or $b and !((($a and !$b) and $b or !($a and !($b and $b or !$a) and !$a or !($b))))",false),
    ("$b and $b or !$b or !(($a and !$a and $a or $b and $b or !$a or !$b or $b))",true),
    ("$a and ($a and $a and (($a or !($b) or $a and !($b) and $a and !$a or $a and $b)))",true),
    ("!$a or !$a or $a or $b or $a or !$a and !$a or !$a and $a and $a or !$b",true),
    ("(($b and !$b and $a) and (($b or ($b) and !$b and $b and $a and !$a or !$b or $a)))",false),
    ("($a or $a and !$a or !$a and $b or ($b or $a or $b) and !$b and !$a or $a)",true),
    ("(($a or !($a) or $a or ($b or $a) or !(($b and !($b or ($b or !$b or $b or $a))))))",true),
    ("!$a and !$a and ($a or $b and $a and $a and !($a or !$a or $b and ($b and !$a)))",false),
    ("$a or !$a and !$a and !$b and ($b or !$b or ($b and ($b and ($b and $b)) and $b))",true),
    ("$a or ($a or !(($a or !($a) or !$b) or !$b and !$b and ($b or !$b and !($a) and !$b)))",true),
    ("!(($b or !($b and !$a or !$b or !($b and !$a and $b and !$a or ($b) and $a and $a))))",true),
    ("($a and !$a and !($a or !$b and !$a or !$a and $b or !$a or !$b or !$a or ($a)))",false),
    ("!($a or ($a or !$a and !($a and !($a or $a or !$b and $b or !$a and $a)) or $b))",false),
    ("$b and !$b and ($b or ($b and !$b or !$a or !$b and !$b and !$b and !$b or !$b))",false),
    ("($a or !($a or !(($b or !$b and ($a or $a) and !($b) and !$a and !($b) or !$b) or !((($a))))))",true),
    ("($b and $b) and !$a and !$a or $b and !($b or $a or !$a) or ($b or $b and ($b))",false),
    ("$b or !$b or !(($b or $b or $b or ($b or !($a and $a and $a or $a and !$b))))",true),
    ("$a or !($a and ($a or !$b and !($a or !$b and $b or !($b or !($a) and !$b) and $a)))",true),
    ("($b or !($b and ($b and $a and !$a or $b or !($b or ($a and $a) or !($b or ($b))))))",true),
    ("!(($b or !($b) and ($b or $b or !$b or $b and $a) and $b or !$a) and !((($b or ($a)))))",true),
    ("(($b or !$b or $a and !$b) or $a and !(($a and $b or $a or $a and $b or (($a)))))",true),
    ("!($a and $a or !($b or $b and $b and !($a and !$b and !$b or !($b) or $a) or $b))",false),
    ("((($b or !(($b or !$a and $a) or !$a and $b) and (($a and !$b and $b or ($a or !($a)))))))",true),
    ("!$b and !$b or !($a or !$a or (($b) or $a or !$b and $a or $b or !$b and !$b))",true),
    ("$a or ($a and ($b) or !($b or ((($b) or $a) and !($a or !$a and $b) or !($b and $a))))",true),
    ("!$a and !($a and ($b or !$a or ($b)) and ($a or !$a and !($b or !$a or !$b or !$b)))",false),
    ("!$a or !$a or $b and !($a or $a and !$a and !$b or $b or $a) and !$a and !($b)",false),
    ("$b or !$b or !($a and !$a and !($a or $a) and !$b and !$a and !(($a) or !$b and !$b))",true),
    ("($a and $a or $b or !($b or ($b and ($a and !$b and !$b and $b) or !($b)) or ((($b)))))",true),
    ("$a or !$a and (($a or !($a or ($a or !$b)) or !($b or ($a) and !$b) or !(($b and !$a))))",true),
    ("!$a and !($a or $b and !($b or $b or !$a and !($a or $a) and (($a and !(($a and !$b))))))",false),
    ("($a or ($a or ($b) or !($b or !$b or $b and !($a) or ($b or !$b or ($b) or !$a))))",true),
    ("!($b and !$b or !($b and $a) and $b and ($b and ($a and $b) or !$b or !($b or !$a)))",true),
    ("($a or $a or $a or !$b and $a and !$b and (($b and !$a and $b and !($a) or !$a)))",true),
    ("$b or !($b and $b or !$a and !$b or !$a and !($a) and !$b or !$b or $b or !$b)",false),
    ("!$a or !($a and !$a or !$b and !($b or ($b and $b and $a)) or !($a and $a and $a))",false),
    ("$b and $b and !$a and $a or $b or !$a or $a and $a or $b and $b and $b",true),
    ("$b and $b or $a and !$b and !$b or ($a or $b and $b or !$b and $a and !$a)",true),
    ("($b or !$b) and ($a and (($b and !(($a or !$b or $b and !$b or !$b or $a) or !$b))))",false),
    ("!($a and $a and $b and !$a and $a and !$b or (($b or !$a and !$a) or $a or !$b))",false),
    ("!$a or !$a or $a or $b or !$a and !$b or $b and $a or !$b or ($b or !($b))",true),
    ("$a or $a and ($b or $b and $b and !$a and ($b and !($b or $a and $b or $a)))",true),
    ("$b and ($b and (($b and !$b or $a and $b or !$b) and ($a or !$a) and $b or !$a))",false),
    ("!$b or $b and $b and !($b and $b or $a and !$a and $b or !$b and $a or $a)",true),
    ("$a or ($a and ($a and !($b and !$b or !$a or ($a or $b or $a and $a and $b))))",true),
    ("!($a or !$a or $b or !$b and $b and $a or !$b and !$a or !$a or !$b and $b)",false),
    ("!($b or ($b or $b or !($a and ($b and !$b) and !$b) or !(($b and !$b or !($a and $a)))))",false),
    ("($b or !($b) or !($a) and $a or $b or !$b and ($a or ($a and $a) and !$a or ($a)))",true),
    ("($b or $b or !$a and $b or $b or ($a or !$b or !$b and $a or !$b) or !$a)",true),
    ("!$a and !($a and !$a or !$a or !(($b and !($b or $b and $b and $b) or !$a) and $a))",false),
    ("!($b and !($b or ($b and $b) and !$a and !($b or $a or !$a and $b) and !$a) and $a)",true),
    ("!$b or !($b or (($b and !$a and $b or $b and !$b and $a or $b) or !$a) and !($b))",true),
    ("!(($a or ($a and $a) or !$a and !$b or !$b or !($b and !$b or $b) or ($b and $b)))",false),
    ("(($b and !$b) and ($a or !$b or !($a) or !($b and $b or $a and !($b or !$a and $a))))",false),
    ("!($a and ($a) or !$a or !($a or !$b and $b and $a and $b and !($a and !$b or !($b))))",false),
    ("$b or (($b or !($b or ($a and !$b and !($b) or !($b) and $b or !$b and ($b) and !($b)))))",false),
    ("!$a or ($a or ($b and !$a and (($b or !$a and $a) or $a and $a) and $a and !$b))",true),
    ("!$b or $b or !$a or ($b or !$b or !$b or !$a and !$b and !(($a and !$b) or $a))",true),
    ("!($b and $b or !$b and !($b or !($b and !(($b)) and !$a or !$b and ($a or !$b and $b))))",false),
    ("!$b and ($b and !$b) or !$a and !($a or $a or !($b or $a or !$a or $b) or $b)",false),
    ("$a and $a and $a or !($b or (($a or $a and !$a and !$a or (($a and !$b) or $a))))",true),
    ("!($b or !($b and !$a and !$a) and $b or !($b and !$a and !$b or !$b or ($a) or !($a)))",true),
    ("!((($a and !$a and !(($b and !$a) and !$b or ($b) and ($b and ($b or $b or ($b or $b)))))))",true),
    ("$b or $b or !$a and !$a or !$b or !$a or !($a or ($a and $a) and !$a or $a)",true),
    ("$b or !$b or !$a or !($b and $a or $a or !($a and !($a and $b) and $b or $b))",true),
    ("($a or (($a or $a and ($b and ($a and $a) or ($b or !$a or !($a and !($a and $b)))))))",true),
    ("($a and !($a or $a and $a) and $b and $a) and !$b or $a and !($b or $a) or !(($a))",false),
    ("!($a or !$a and !$a or !($a) and !$b and ($a and !($a or !$a or $b and $b or !$a)))",false),
    ("!((($a or !$a or ($b) or $a and ($a or !$b or !($b) or $a and $a and (($b and ($b)))))))",false),
    ("!$a and !($a or $b or !$b and $a or !$a or $a and $b or ($a or ($b)) and $a)",false),
    ("!($a and $a or $a and !$a or !$a or $a and $b or $b or !$b and !$a or $b)",false),
    ("!$b or !$b and !(($b or ($b or !$b) and !($b or !$a and !($a and !$b or !$b) or !$b)))",true),
    ("!($b and $b and $b or !$b or $b or !$b and ($b or !(((($b) and !($a or $b or !$a))))))",false),
    ("$b or !$b and $a or !$a or $b and !($b and !$b or !$a and !$a or $b and ($b))",true),
    ("!((($a and (($a) and $b or !$b or !$a and $a)) or !$a or $b) or !($b or !($a and $a)))",false),
    ("!$b or !($b and ($b or $a or !($a and !$b or $a and !($a) and !$a or ($b or $b))))",true),
    ("!($a or ($a and $b or !$a or $b and ($b or $a and $a or $a or $b) and $b))",false),
    ("!(($a or !(($a or $b or $a or $b or !$a and $a) or $b and !$b and $a) and $b))",false),
    ("!(($a or ($a and ($b or ($a or $b or !$b) and !($b and !$b or ($b and $b) and ($a))))))",false),
    ("(($b or !($b) and ($a and $b and ($b and !$a or ($b and !($a or $b or !$a and !$a))))))",false),
    ("$b or !($b and !$b and !($a or $b or $a or !$b or !($b and !($b and !$b) or $a)))",true),
    ("($a or !($a or $a and ($a and (($b or !($a and $a) or !$a) and $a or !$b or $a))))",true),
    ("$b and $b or !$b or !$a or $a or !(($b or $a and !$a or $b or !$a and $b))",true),
    ("($b and !($b or !$b or !$b and $a and !($a or $a or $b and !$b) and $a or !($a)))",false),
    ("$a or !$a or $a and $b or $a or !$a and !$a or $a and !$a and $a or !$b",true),
    ("$a and !$a or $b and $b and $a or ($a and !(($b or !($a or !$b) and !($b or !$b))))",true),
    ("!$b and $b or $a and ($a or !$b or $b and (($a or $b) and ($a and $a and ($b))))",true),
    ("!$a and !$a and ($a and (($b and (($a or !$a and $a)) and !(($a or !$a and ($a or (($a))))))))",false),
    ("!$a or !(($a or $a and !$a or !$b or ($a or !$a and $b and !($b))) and $b or ($b))",true),
    ("!$b and !$b or !$a and ($a and $b and ($a or !($b and !($b and !$a and !$a and !$b))))",true),
    ("($a and !((($a or $a) and $b or $a and !$b and $b and !$b) and $a) or ($b and $b))",true),
    ("(($b or (($b and !$a and ($a) or $a)) and $a and !$a and (($a) or !$b and !$a or $b)))",false),
    ("!$a and (($a and $b and !$a and $a and !($a or (($b) or ($a and !$b or $b or !$a)))))",false),
    ("(($b and $b) and !(($a) or !$a) and !($a or $a) or ($b or $a or !($b and ($a and !$b))))",true),
    ("($b and !$b and !$a) and !$b and !($a or (($a and !(($a or !$a or $a) or !($b and !$a)))))",false),
    ("!(($b and (($b) or $a and !(($b) and !($b and !($a or !$b or !$a) or $b or !$a and $b)))))",true),
    ("($a and !$a and $a or ($b and !($a and $a and !$a) and $b or $b and $a and !$b))",false),
    ("$b and $b and $b and !$a and $b and ($b or $a or !($a and ($b or $b or !$a)))",false),
    ("!($a or !(($a and $b and $a and $a and $a and !($a or !$a or !$b) and $a or ($a))))",false),
    ("($b or !$b and !$a or $a and ($a or $b or !$b) or !$a) or !$b and !($b or $b)",true),
    ("(($b and $b and $a) and !($a and $a and !$a and $a and $b and !$b and !$b) and !($a))",false),
    ("$a or !$a and ($b or !$a or ($a or $a and !$b and !$a or !$a and !$b) and ($a))",true),
    ("$a and !$a and !$b and !$a or $a or !$b or ($b or $b or !$a or !$b and !$b)",true),
    ("!$a and !$a and !$b and $b or !($b or !$b or !$a or !($b and !$b and $b or !$b))",false),
    ("(($b and !$b and ($a or !$a and $b) and $a) or $b or $b and !(($b and ($b and !($a)))))",false),
    ("($b or $b or !($a or ($a or ($b and !($b or !$a) or !($b) and !$b) and $a or !$a)))",false),
    ("!(($b and $b and !$a and $b or !$a and $b and !($a) or $a and !$a or !($b and !$b)))",false),
    ("!(($b and !($b and ($b and $a) and !($b) and !($a and ($b)) or !($b or !($a or !$b or !$b)))))",true),
    ("(($a or ($a and !$b and $b) and $a)) and !$b or $b and (($b and $a or $a or !$b))",true),
    ("!($b or $b or !$a or !($b) or $a) and $a and $a and $b and !($a and ($a and $b))",false),
    ("($a and !$a or !$a) or !$b or !$b or ($b or !$a and $a and !$a or !$a and !$b)",true),
    ("!$a and $a or !((($b and ($b or !($b) and $b and !$b and !$a or $b and !$a and $a))))",true),
    ("!($b or !$b or ($a and !($b and (($b)) or $b and !($a and !$b and !$a and !$b and !$b))))",false),
    ("!$a or !($a and $a and $b or !$a) or !($b and !($b or !$a and !$a or !$b and !$b))",true),
    ("!$a and !$a and $a and $b or ($b and (($a or !$b or ($b or ($b and !$b) or ($a)))))",false),
    ("!($b and $b and $b or !$b) or !$a or !($a and !($b) or $a or !($b or $b or $b))",false),
    ("($b or $b and !$b) and !($a or $b or ($a or $a or !$a or $b) or ($b or $b))",false),
    ("$a and (($a or $a and $b and ($a and ($b and !$a or $b and !$a or $a or !$b))))",true),
    ("(($b or (($b or ($a and !$b and !$b and !$b and $b and !$b and !($b or $a) and $b)))))",false),
    ("!$a and $a or (($a and !$b or $b) or $a and $a and !$b and (($b and $b or !$b)))",true),
    ("($b or !($b and !(($b) or $a and $b and !$a and $a or !$a and !$a) or ($a and $b)))",true),
    ("$a or !(($a and ($a) and $a or ($b and !$a) and ($b or $b and !$b) or $b and ($b)))",true),
    ("($b or !$b or ($b or !($b and $a and !($a or $b) and ($a or !($b and !$a or !($a))))))",true),
    ("($a or !($a and !$b and $b) or !$a and !$b and $b) or !($a or !$b and !($a) or !$a)",true),
    ("($b and !$b) and !($b and !$b) and !(($b and !$b and !($a or $a) and $b and !$a or !($a)))",false),
    ("!$b and !$b or !(($a and $b and $b or !$a and $a and !$b) or !$b and !$b and !$a)",true),
    ("!$b or $b and ($b and !(($a or $b and $a or $a and !($b) or $b or $b or !((($a))))))",true),
    ("$b or !($b or !$b and !$a or $b or $b and (($a and $b or !$b and $b) and !($b)))",true),
    ("$a or !($a and $b or $a and ($b and $a) or !((($a) or !$b or $b and !$a or !$a)))",true),
    ("!($b or $b) or (($a and (($a) and !(($b or !(($a or !($a) or !($a)) and !$a or !$b and $b))))))",true),
    ("!((($b and !($b or !$b or !$b)) or !$b or !($b and !$b and $b or !$b) and !$b and $a))",false),
    ("!$a and ($a or !(($b and !$b and !$a or !$b or !$a and $b) and ($a or !($a and !$b))))",false),
    ("!$a and (($a or ($a or $a) and ($a) and ($b and ($a or !(($a and !$a and !$b and $a))))))",false),
    ("!$b and (($b or !$b or $b and !$a) and !$a or $b or !($b or !$b or !$a or !$b))",false),
    ("!$b or !$b and $b and $b or !($a and !($a and $b) and !$a and !$b or !$a and !$a)",true),
    ("!(($b or $b) or ($b and (($a or ($a or !$b and $b and ($b and $b or ($b and $b)))))))",true),
    ("!$a or $a or !($a or !$b and (($b and !$a or $a and !($b and $b) and !$b and $b)))",true),
    ("$b and $b or $a and !$b or !$b or !$b or !($b and !$b or !$b or ($b or $a))",true),
    ("!$b and !$b or !$a or !($a or !$b or !$a or $a and ($a and ($b) and !$b) and ($a))",true),
    ("$a or $a or $a or !($a or ($a and !$b and !(($a or !$b) and !$a or !$b or !$a)))",true),
    ("!($a or !$a and !$b and !$b and ($b and !$a)) and $a or !$a and ($b or !($b and !$a))",false),
    ("$a and $a and ($a or !$a or $b and $b and !(($a or $a or $b or !$a) or !($b)))",true),
    ("$a and !$a and !($a and !$b or !($a) and !($b) or ($b and $b) or !$b or !($b) or $b)",false),
    ("$a and $a and ($b and ($a and ($b and !$b) or $a and !$a and $b and $a or $b))",false),
    ("$a or !$a and $b and !$a and !$a and !($a and !$a and ($b and !$b and $b and $a))",true),
    ("($b or $b or ($a and ($a or !(($a and $b and $a) or !$b or $a and !$b) or ($b))))",true),
    ("!($a or !$a or $b or $a and $b and !$a) and ($b or !($a and $b or ($b and $a)))",false),
    ("!$a or $a or !$b and !$b and !$a and $a and !$b or !$b or !$a or $b and $a",true),
    ("($a or !($a or ($b and ($b or !$a) and !$a and !($b or !(($b and $b and $b) and $a)))))",true),
    ("$a or $a and $b and ($a or $b and !$a or ($a or !$a or $a or !$b or $b))",true),
    ("$b or !$b and $b and !$a and ($b and !($b or !$b and $a)) and !$a and !($b and !$b)",false),
    ("$a or !$a or !$b and !$b or !(($a or $a or $b or !$b or !($b and !$a or (($b)))))",true),
    ("(($b or $b and !($a) and !($a and !$a or !($b or $a) or $a or !$b and !$b and !$b)))",false),
    ("($b or !($b or !($b and $b) and !$a and $a or ($b or $a and ($a and !($b or !$b)))))",true),
    ("($a and ($a or !$a or ($a and ($a and ($b and !$b or ($a)) and !$b or ($b or !$a)))))",true),
    ("!$a and !$a or !$a and !($b and !$b or !$a or $b or $a and !$b or $b or $b)",false),
    ("!($b and !($b or !$b and !$b) or !$a or $b or !$b or $b and $b or !$b and !$b)",false),
    ("!$a or ($a and !$a and !($a) or ($a or $a and !($a or !($b and !($a or $b or $b)))))",true),
    ("$a or !$a and $a and ($a and !$b or $b and !$b or !$b and $a and ($b or !(($a))))",true),
    ("($b or $b or !($a or !(($b and !($b and $b or !$b and $b and $b) or !$a or $a))))",false),
    ("(($b or !$b or !$a and !$b or !$b) or ($b or !$a or ($a and !$a or $b and !$b)))",true),
    ("($a or !$a or $b and !($b) and !$b or $b and !($a and !(($a and $a or !$b and !$a))))",true),
    ("!($a or !$a or $b or !($a and !($a or $b or ($b) and $a or $b or !$b or $a)))",false),
    ("!$a or $a and !($a and ($a and !(($b and $b) and $a and !$b and ($a or ($a and (($b)))))))",false),
    ("!($b or $b) or $b and $b or !($a and !$a and !$a or !(($b and !$a) or !$a and $b))",true),
    ("$a or ($a or !$a and !($b and $b and !$b and !$a or $a and !$b and $a and !$b))",true),
    ("($a or !$a and ($b or $a and ($a or !$b or $a or !$a and !$b) and !($a or !$a)))",true),
    ("!$b and $b and $b and $b or (($b or !$b or ($b or !$a and $b) or $a and $b))",true),
    ("!$a and $a or $a and ($a or $a or !(($b and ($b) and !$b) and !($a or !$b or !($a))))",true),
    ("($a and ($a and ($b or $a or $a and ($a and !$b and $a or $b or !$b) or ($b))))",true),
    ("!((($b and $b) and !$b and $a and $a and !$a and $b and $b) and !$b and $b and !(($a)))",true),
    ("$a and $a or !$b and $b and !$b or $b or !$b or !$b or $b and !$b and !$a",true),
    ("$a or $a and !($b or (($a or $b and !($a and !$b and $a) or !$b and (($b or $b)))))",true),
    ("$b or !($b or !$a or !$b or $b or $a or ($b and !$a and $a and !$a) or !(($a)))",false),
    ("$b or $b or $b and $a and !($a or !(((($a or $b and !$b) and ($a) and !$b) or !$a)))",false),
    ("!$a or $a or $a or $a and !$b or (($b and !$b and !(($a and !$b) or $a and !($a))))",true),
    ("($b and !$b and ($a or ($a or ($b or $a or !$a and $a and $b)) and (($a and ($a)))))",false),
    ("($a or !($a and $b and !$b and ($b and !($b and !$b and !$b) and ($b and $b) and $b)))",true),
    ("($a or $a) and ($a and (($b) or !(($b) or ($a and !($a or (($b or $b or ($a and $b))))))))",true),
    ("!$a or !$a or !$b and !$b or ($a or $b or $a and ($a or $b or $b and !(($b))))",true),
    ("(($b and !$b or !(($a or !($b) and !$a and !$b) or ($b or $b and !$a and !$a or !$a))))",false),
    ("!$b and !($b and !$a or ($b or $b or !(($b and !(($b) or ($a) or $b and $a or !$a)))))",false),
    ("(($b or (($b or $a or $b and !($a) or $a and !($a and ($a and $a) and $a))) and !$a))",false),
    ("($a or $a or ($a and (($a and $b or !(($a) or $a or $a or !($a and !($a and ($b))))))))",true),
    ("!($b or (($b and $a) or !$a and $a and !$b) or $a or !$a or !$b or !$a and $a)",false),
    ("$a and $a or $b and !$b and $a or !$a or !($b and !(($a and !$b and !$b or (($a)))))",true),
    ("$b and $b and !(($a or !$a and !$b or $a or !($b and !$b and !$b) or !($a or $a)))",false),
    ("($b or $b or !($b and !$a and !$b and !($b or !(($b) and $a and ($b and $a and !$b)))))",true),
    ("(($a and !$a and !($a and $a or !$a or !$a and ($a) and ($b or $a and !$b) or !$b)))",false),
    ("!($b and !($b) or $a or ($a or !$a and !$a or !($b or $a and !$a and !$a or $b)))",false),
    ("$b or $b and $a and !$a and ($a or !$b or !$a or !($a or $a and !$b or $b))",false),
    ("$a or ($a or $b and (($a or !$a) or !$a) or !(($a and !$b) and !($a or !$b and !$b)))",true),
    ("!$a or !$a and !($b or !($a or !$a) or !$b or !$a) or ($b and !$b) or !($b or $b)",true),
    ("$b or !$b and $a or $a or !$b or !($a or $a and !$a or !$b and !$a and !$a)",true),
    ("!$b or ($b or !$b and !$b or ((($a and $a or ($a or !$b and !$a) or $b and $a))))",true),
    ("$a or $a or !($a or !($b) or $a or ($b) and !$b or $a and !$b and ($a or ($a)))",true),
    ("!($b and ($b and !$b and !$a and ($a and $a) or $a or !$a) and ($a and !$a and !($a)))",true),
    ("$a or !((($a or $b or !($b) or !$b or $b and $a) and !$b and !$b and !($b) or ($a)))",true),
    ("$a and !$a or !$b and $b or !$a and ($b and !$b and $a and $b and $b or $b)",false),
    ("($a or ($a or !$b) or !$a or $a or !($a or $a or !$a) and $a or $a and !($b))",true),
    ("!$b or $b or !($b and !$a and !$b or !$a) or $a and !($b or !($a and !$a and !$a))",true),
    ("!$a or ($a and !((($b or ($b or $a or !($b) or (($a and !$b and ($a or !$a) and !$b)))))))",false),
    ("!$a and !($a and $b and !(($b or !($a and !$b) or $b and !$b)) or $a or !$a or !$a)",false),
    ("($b and $b or !($b or $a and $a) and !$b and $a and !$b and $b or !(($a or !($b))))",false),
    ("!$a and !$a or !$a or !($a or $b and $b or ($b and $b and !$a and ($a and ($a))))",false),
    ("!($a or ($a and $b or ($b and ($a or ($a or !$a and !($b and $b)) and $b) and !$b)))",false),
    ("!$a or !($a and !($a or ($b) and $b or $a or !$b and !($b and !$b or $a)) and ($b))",true),
    ("$b and !$b and !$a and !$a or !$a and !($a and $b or !$b or $b or !($b and !($b)))",false),
    ("((($a and !$a)) and !$a or !((($b and !$a and $a or ($a or !(($a and !$a) or !($a) or !$a))))))",false),
    ("$a or !($a and !$b and !$a or ($b and !$b) or $b or $b or ($b or !$a and !$a))",true),
    ("($b and !$b or (($b or !$a or !($b and $a) or ($a or $b and ($a and !$b) or ($a)))))",true),
    ("$b and ($b or $b or !($b and ($b) or $a) or $a or !$a or !$b and ($b or ($a)))",false),
    ("$b or $b or !($a or $a and !$b and !($b and $b or $b) or $b or !$a or !$b)",false),
    ("!(($b and !$b and $b or $b and $a or !$a or ($a or $b and $b and !$b or !$b)))",false),
    ("!($a or (($a and ($a or !$b) and ($a or $a and $a) and $a or (($a) or !$a and $a))))",false),
    ("(($a and !$a) and !($a or ($b or !($a or !($b) or $a) and !$b or !(($b or ($a)) or $a))))",false),
    ("!($a and !$a and $a or !($b or $b and $b or $a) and $a and !$a and $b or ($a))",false),
    ("!($a and ($a and !$a and $a or $b or !$b and $a and !$b) or ($a or $a) or !($a))",false),
    ("$a or $a and $a or ($b and !$a) or ($a and !($b and $a or $a or $b and $b))",true),
    ("($a and $a or !$b and !$a and !($b or !$a) and ($a) and !$b and (($b and $a or $a)))",true),
    ("!$b or !$b or $a or !($a and !$b and (($a and $b and !$a) and $b or $a) or !($b))",true),
    ("($b or $b and (($a or !($b and $b) or !($b) and !$a and !$b and !($a or ($a) and !$b))))",false),
    ("!($b and !($b or ($b and !($a or !$b or $b) and $b or $b and ($b and !$a) and $a)))",true),
    ("!($a or !$a or !($a and !($b and !($b and !$b or !$b or !($b) and ($a) or !$b or !$a))))",false),
    ("!$b and ($b and !$b or !$a or !$a and $b or !$a or !$b and !$b or $b or !$a)",true),
    ("!$a or $a and !$a or !($a or $a or !$b and $a) and ($a or $b or !$b and !($a))",false),
    ("!($b or $b or !($b and !$b or ($a and $b and $a or !$b) or !$a or !$a and !$b) or $a or $a) or !($b and !$a and ($b and $b and $a and $a or ($b) and !$a))",true),
    ("($b and ($b and !$b and $a or ($a and ($b and !$b) and $a and ($a or $a or $a or !$b) or !$a and !$b or !$b and !$a) and ($a or $b and $b) and !$b) or !$b)",true),
    ("!$a and !$a and (($b and !$b or !$b or !($b) and $b) and !$a and !$b or !$b and $a and !$b or $a) or !$a and !($b and !$b) and !$b or !$a or !($a and !$a and !$b)",true),
    ("$a or !($a and !$b and (($b and !$a and !$b and !($b and !$b and $b or $a and $a or !$b or !$b and !$a and !$b and !$b or $a) or !$b and $b and !$b and !$b)))",true),
    ("$a or !$a or !($b or ($a and $b and $a or !$a)) or !($b and !($b and !$b or $b and !$b and ($a) or $b) or ($a or $b and !$a) or $b) and $a and !$a and $b",true),
    ("($a or ($a and $b or ($a or !$a) or $a and $b) and !($b) or ((($a or !$a and $a and $a) and $a) and !$b and !$a or $b and !$a) and !$a and !$b or !$a and $b)",true),
    ("!$a or !$a or $a and ($b and $a and $a and !$b and !$b or ($a and $b or ($b) or $a or !$b and ($b) or ($b or !$a or $a) and !$b and $a) and !$a or !$b)",true),
    ("!($a or !($a and $b and !$b and $a or $a) or $a and ((($b and !$b and !$a) or $b and !$b) or !$b and $a) or !$b and !$a and $a or !$a or !$a and $a) and !($b)",false),
    ("!$a or !$a and $b and ($b and !$b or !$a or $a or $a and $b or !$a and !$b and $a or $b or !$a and !$a) and !$b or ($a or $b and $a or $a and !$b)",true),
    ("!$b or !$b or !($a or !$a and $b or !$b or $b and !$a and !($a or $b or $b and $b or !$a or ($a and !$b and $b and $b and $b or !($b) and $b) and ($b)))",true),
    ("$a and (($a or $a and !$a or $b and !$b or !$a or $a) and !$a and !($a and !($a or $a or !$b and !$b) and $b and $a or $b and !$a) or $b and $b or !($a))",false),
    ("!$b or $b or !($b and !$a or !(($a or (($a and !($a or $b and $a and !$a) and !$a or ($a or !$b) and !$b or ($a or $b)) and !$a) and $a and $a and ($a or $b))))",true),
    ("!($b and $b or $a or !$a or !($b and ($a) or !$a and $a or $a or !$b) or !$a and $b) or $a or !$b or $a and $a and !$a or !$a or !$a or $b and $b",true),
    ("((($a or $a and (($b and !($a or $a) or !$a and $a) and $a) or !($a or ($b or !($a and $b or !$a) or !($b)) and !($b or !$b) and !$b or ($b) and $a) and $a or ($b))))",true),
    ("!$b or !$b and ($b and !($b or ($a and !($a and ($a) or !($b and !$b) or !($a and !$a))) or $b and $a and $a and $b or $b) and $a or (($b and (($a or ($a) or $a)))))",true),
    ("$b and $b or !(($b and !($a or !$a and ($a) or !$a or !$a or !$a and !($b) and $b)) or (($b or $a) or $a or $a and $b) and ($b and $b and ($b and !(($b) and (($b))))))",true),
    ("($a or !$a and $a and !$b and !$b and !$b or !$b or $a) and $a or !($a and !$b and !$a and $b) or !$b or $a or $a and $b or !($b and !$a or $b) or !$b",true),
    ("!($a or !$a and !($b or !$b or $b and !$b) or !$b) and ($b and $b or ($a or !($a) or (($b) and (($a) and $b or ($b and !$b or $a or !$a or ($a) and !$a or ($b))))))",false),
    ("($a and !$a or $b and $a or !($b and ($b and $a) and (($a and $a) and (($a or $a) or !$a) or $a or $a and !($a) and !$b or !$b and $b or (($a or $b) and ($a)))))",true),
    ("($a and !($a and !$a or !$a or $b) and !$a or !(($b or !$b or $b or !$b or $b and $b or $b and $a or !$a and !$a and !$a or !$b or $b or !$b and !$a)))",false),
    ("!$a and !($a and !($a or !($a and $b and !($b or $a) and ($a and $b and ($a) and $a and ($a or ($b) and $b) or $b) or !$b or !$b or ($b and $a) and !(($a and !$b)))))",false),
    ("$b or $b and !($a and (($b and !($a and !$b or !$a or ($a and $b and !$a) and $b and $b or $b and ($b or $b)) or !$a) or !($b and $a and $a) and !$a) or ($a))",false),
    ("$b or ($b and !($b or ($b or !$b or !$a) and $b or $b) and !$b) and !$a and ($a or !$a and !($b and !($a or ($b or $b) or !$b or (($a or $a or !$b) or (($a))))))",false),
    ("!$b or $b or !$b and !$b or !$b and $b or !$a or !$a and !$b or !$a or !($a and ($a or $a or $a and $b or $a and !$b or !$a) and $a or !(($a and !$a)))",true),
    ("$b or !$b and !($b or !($b and !$b or !($b or $a or !((($a or !$b) and !$b)) or $b and !$b and !$a) and $b or $b and !($a and $b or $b and !($a or !(($a) or ($a))))))",false),
    ("!($b or $b and $a and !$b and !$b and $b and $b or !($a and !$b and $a or !$b)) or !$a and !$b and $b or $a and !$b or !$b or !$b and ($b or $a) or !($a)",true),
    ("($a and $a and ($b and !(($b or !$b or ($b) or ($a or $a)) and !($b or $a or !($b and $b) and !$a) and $b) or ($b) or !($a or !$b) or !$b or $a and $a and !(($a))))",true),
    ("!$a or $a or (($a or !(($a) or !$b) and $a or !$a or !($a and !($b and $b) or !($a and $b and ($a and !$b) or !$b) or $a or !$a and $a and !($b or ($b and ($b))))))",true),
    ("$a and $a and ($b and $b and !$b or ($b or !$a and $a or !($b or !$b and !$b) or !(($b) or $b)) and !($b) and $b or $a) and ($a or $a) or ($a or !($b and $a))",true),
    ("!$b or !($b or $a and !$a and ($a or $b) or $a or $b or ($a and $b or $a or !$b and ($b and !$a) and !$a and $b or $b and $b or $a or !$a) or ($a))",true),
    ("($a and (($a) and ($a) and !($a and !$b and !$a) or $b) and !($a) and ((($a or $b or !$a) and $a)) and !((($b and ($b or $b and !$a) and $a) or ($b) or !(($b and ($b or !$a))))))",false),
    ("!((($b or !($b or (($a and $a)) and !($b and !$b) and !$a or !$a or $b or !$b and ($a or !$b) and !(($b and $a) or $b and $b or !$b) and ($b or ($b and ($a or $a)))))))",false),
    ("!(($b or !$b or ($a or !($b and !$b and $b or !$a or !$a) or $a) or !$b or !$a and $a and (($a and !$a and !$b) or ($b and $a and $a) and $a) or $a and !$a))",false),
    ("!$a and $a or ($b or !$b and $b or $b and $b and !$b and $b and !$a or !$a and $b and $a or $b and ($b and !$b and !($a and !$b or !$a or !$b) and $a))",false),
    ("($a and $a or $a and !$b or !$b and !$a) and $a or $a and !$b or !$b or $a or !$a and (($a and !$b and $b and $b and $a or ($b or $a and !$a and $b)))",true),
    ("!$b and !$b or !(($b and !$b or !($a and !$b)) and $a and !$a or ($a or $a and !$a or !$a and !$b or !$a or !$a) and !$b or $a or !$a and ($a and $a and $a))",true),
    ("$a and !($a and !$b or ($a and !($a and $b) or !($a and !$b or !$a and $a and $a)) or $b or ($a and !$a or $b and !($b and ($a or $b or $b) or $b and !$b)))",false),
    ("!($a or ($a and ($a and ($b and !$a)) or !($b or $a and $b) or (($a and $a or !($a and !$b or !$b or !$a and !$b and !$b or !$a) or $b or $b and !$a and $b))))",false),
    ("$b and ($b and (($a or !($b) or !($b and !$b and ($a and !$b) and !($b) and $a) or !($a) and ($a or $a and $a or $a and !($a or $b) or $b and ($a) or ($a and $b)))))",false),
    ("!($a or !$a and ($b and !$b or $b or ($a or !(($b and !($a) and $a)) or $b) or !($b or !($a and (($b and !($b) or !$b) and !$b and !(($b) and ($a and !$a)) or $b and ($a))))))",false),
    ("($a and !$a and !($b or !$a and !($a and $a and $b and $a and !$b and !$b or $b or $b and !($a and !$a and $b or !$a or !$a and !($b) or ($a and $b) or !$b))))",false),
    ("$b or ($b or $a and $b or $b or $a or !$b or ($a or $b or !$b and $b and $a and !($b and $a or $a or !$a or !$a and ($a or !$b) and $a and !$b)))",true),
    ("($a and $a or $a and !($b and $b and $a) and !($b or $b or !($a or !$b or !$b) and !$a and !((($b) or $b or !($a or (($a) and ($a) or !$a)) and ($a and $b and !($b))))))",true),
    ("!$b or !$b and !(($a or $b and ($b or !$a or ($b) and $b or !($a or $b and !$b or !($a or $a or !$b or !$a or !$b or $a)) and !$b and !($a) or !$b and $b)))",true),
    ("!$a or !$a or ($b and ($a or $b and $b or $a or ($b and $a and $a and !($b and !$a and !$a and $a) and $b) or !$b or !$a or !$a and $b and !$a or $b))",false),
    ("!($a and ($a and !(($a or $a) or ($b and !$a or $b or !$b or !$b or $b and $a) or !$b) and !$a and ($a and $a) and $b and $b and ($a and !$a or $a) or ($a)))",false),
    ("!$b and ($b or $a or ($b and !$b and $b or ((($b or !$b) and ($a and !$a or ($b and $b) and !($b and !$b)) and $a and !$a) and $b or $b or !$a or !(($a or $b)))))",true),
    ("!$b and ($b and ($b or ($a and !$b and $a) and !$b and $a) and $b) and ((($a or !$b) or $a or !$b or $b and ($b and !$a or !$a or !$b or !$a or !$b or !$a)))",false),
    ("!$b or $b or !($a or $a and $b or $a and $b and $b or !($a and !$b or !$b) and ($a or (($b or $a or $a and $a and !($a and $a or !$b) and !$b) or $a)))",true),
    ("(($a and !$a and $a and $a or !$a or !(($b or !$a) or $b or $b or !$a and $b or $b or $b and (($b or !$a or !$b and $a or ($a) or $b or $a) or ($a)))))",true),
    ("!$b and $b or $a and !$b and !$b and !($b or $b or !$a and $b and ($b or ($b or !$a) and ($b or !$a and $b) and !($a or !($a or !$b and !$a or $b or !$a))))",true),
    ("$b or !($b and $a or !$a and $b or $b and (($b and $b)) and !($a and !$b or !$a or !$a and $a and $b or !(($b) and !$b or !$a) and !$a and $b or ($b or $b)))",true),
    ("!$b and !($b and !(($a or $b or !$a or $a or ($b and $a and !(($a or !$a))) and !$b)) or (($b or ($b and ($b))) or !$b and !$b and $b and !$b or !$b) or !$a or $b)",false),
    ("($a or !$a or !($a and !($b and $a or $a or $a or !$a and $a) or $a or ($a and !(($a and $b and $a) and $a or $b or !$a and !$a and $a) or !$a) and $a))",true),
    ("$b and $b and !$b or ($a or ($a and !($b or $b) or $a and !($a or !$b)) or !($a and !$b or $b or ($b or $b or !($b and !($a) and ($b) and !$a or !$b and !$a))))",true),
    ("!$a or !$a or !($b and !$a or $b or $a and $a or !$a or $a or $b and $a and $b and $a and !($a or $b) and !$b or !$b and !($b and $a)) and $b and !$a",false),
    ("$b or ($b and !($b or $a) and ($a and !$a or ($a and !$b and !$b) and $b and !$a and !($a or !$b and !$b and !$a and ($a and !$b or $a and $a and !$b) and !$a)))",false),
    ("($a or ($a and !$a and !$b and (($b) or !$b and ($b and ($b) and !$a) or $a or $b) or $b or !($b or !$b or !$a and $a or (($a and !$a and $a) or !($b)) or !$b)))",true),
    ("($a or !(($a and !$b or !$b and !$a or ($a and $a)) or ($b and $a)) or ((($a and !$b or ($b) and !$a) or !$b and $a)) or $b and $a and ($a or !(($a and !($a or $a)))))",true),
    ("!($b or !($b and ($a or !($a or ($b or !$a) and $b) and !$a) and ($b and ($a) and $b and $b) and $b) and ($a and !($a and ($a or !((($b and !$b)) or !$a) and ($b or $a)))))",true),
    ("$b and (($b or !($b and $a and $b and $a or !$b) or ($a and ($a and !($a or $a and ($b or !($b or $b) or !($b) and $a) and (($a and !$a)) and !($a and ($a and !$b)))))))",false),
    ("($b or $b and ($a or !($a and $b and (($a or $a) and !($a or !($a) and $a) and !$a or $b) or $b and !$a or ($b or $b and $a and $b) and $a and $a and !($b))))",false),
    ("$b and !$b and !($b or ($a or ($a or !($b and !$b or $a or $b and $b or !$a and $a and !$a or !$a and !$a) or $a and !($b and $b or !$b and $a) and ($b))))",false),
    ("($b and !($b or !$a) and !(($a or ($b or !($a) or !($b or $a)) and !($b or $b) or !$a)) or !(($a or !($b and $b and $a)) and $a or !($b and !$a) and $b or ($b or $a)))",false),
    ("$b and !$b or $b or $b and !$a or !$a and $a or $b and ($a and $b or $a or $a and !$b and ($a or $b)) or ($b or $a or !$a and !($a or !$a) and $a)",true),
    ("($a or !$a and $b and !$b or !$a or $a or !$a or ($b and ($a or $a or !$a and ($b or $b or $a and $a) or !$a or $b and $a and !($a) or !$a or !$b)))",true),
    ("!($b and ($b or !(($b and !($b) or !$a) and !$a or $a or $b) or !$b and ($b or ($a or !($b or !$b or !(($b) and !$a and $b and ($b or !$a) and !($a) and !$a and !($b)))))))",true),
    ("!($b and !$b and $b or $b) or $b and !$a or !($b or !$b or !$a and $a and !$a and $b and !$b and !$b or !$b) or !$a and $b and $b and !$b or ($b and !($b))",true),
    ("(($b and ($b or !($a or $a) and $a or $a and !$b and ($a or ((($a or !$b or $b or !$a or !($b or ($b) or !$b and !$a and !$a and !$a) or !$b) and ($b) or !($a)))))))",false),
    ("!$a or !$a or !($a and !$a and ($b and !$a and $a or $a) or ($b or !$a or !$b) or $b or ($a and !$b or $a and !$b or $a or !$a or $b) or $b and !($a))",false),
    ("!($a or !($a and !($a or $b or $a) and ($a and !($a) and $a or !($b) or !($a and !$b) and $b or !$b) and $a and !($a) and !$a and !$a or !($b) or ($a or !$a or $b)))",false),
    ("!$a and !$a and $a and !($b and $b and !$a or $b or ($a or !$b and !$a and !$b and !$b or !$b and $b and !($a or $b or !$b or $a or !($b) and !$a and !$b)))",false),
    ("$a and !($a or !$a or !$a or !$b or !$a and $a or !$b or !$b or !($b and ($b or !$b and !$b) or $a or !$a) and ($b) and ($b or $a or $a or $a and !$a))",false),
    ("($b or $b or !$a or $b and !$b and $b) and $b or !(($b and $a or !($a and ($a and !$b or ($b or !$b) and !$b or !$a)) or $b or !(($a or $a or ($a or !$a)))))",true),
    ("$b or !(($b or !($a and $b) and ($b and !(($a) or ($a)) and !($a or !(($b) and !$b and !$b)) and $a or !$a and $b or !$a) and !$a or !($a) and !(($b) or !$b or !(($b) and !(($b))))))",true),
    ("!$b or ($b or ($a or $a or !$b or $b and !$a or $b and $b or $b or $b or $b and ($a and !$b or $b and !$b) and $a or !$b and $a and $b or ($a)))",true),
    ("($b and ($b and !$b) or ($b and !$a)) or !($a and $a and ($a and $b) and !$b or !$a and $b and !$a and !((($a and !$a) or $a and !$a and !$b and ($b) or (($b) and !$a))))",true),
    ("!($a or !(($a or $a and $b or ($a or ($a and !($b) and ($b or ($b)) or $b) and !($a or !(($b and ($a and !$b or !$b and $b and $a)) and !$a) and !$b and !$a) or !(($b))))))",false),
    ("$b and $b and !((($b and !$b) or ($a) and $a and (($b or $b or !$a and $b) and (($b or $a and !$a or $a) or !$b or ($a) or $b and $a) or $a) or ($b or $a)))",false),
    ("!($b or !$b or !($b or ($b or ($b or $b) and !$b and !($b and !($a) or ($b or !$b and !$b and !(($b and !$b or !($b) and !(($b and $b or !$a) or ($b))) and !($b and $a)))))))",false),
    ("!$b and !$b or !$b and !$b and !$b or (($b and $a and !$b and !(($a and $a and $b or $b or !$a or $b) or !(($a or ($b) and !$b)) and !($a) or !$b and !$b and ($a))))",true),
    ("!($a or $a or !$b or ($a or !$a or !$b or !$a and $a and !$b and !$a and $a and ($b or ($b and !$a and $b) or $a) and !$b) and !$a and !($b or $a) or (($a)))",false),
    ("!$a or ($a and !($b) and ($a or !($b) and !$a)) or !(($a and !(($b) or ($b or !$a and !$a) and $a) or !$b and $a) or !$a and ($b or !($b and !$a and ($a and (($b or $b))))))",true),
    ("($a and $a or !$a or $b or !$a and !($a) and !$b or !$b or $b and !$b) and !($a and !$b and !$b or !$b and $b and $b or ($a or !$a and !$b and !($b) or !$b))",false),
    ("!($a or $a and !$b or $b or !($a and (($b or !($a and !$a and !$a or $a) or !($b or !$a) or !$b) and $b or !($a and $a) and $a or $a and !($a or $b) or $b)))",false),
    ("!$b or $b or !($a or $a or $a or $b and !$b and !$b or !($b and !$a or $a) or (($a and $a or $a and $a and !$b) or !$b and $b and $a or $a and !$b))",true),
    ("!($a and !(($a or (($a or !$a) or !$b or !$a and !$b or ($a or !($a or !$b or !$a) or ($a)) or $b) or !$b and $a and $b) or !$a) and !$b) and ($b or !$b or !(($a)))",true),
    ("$a and !($a or !$a) and $a or !(($a or $b) or $b or !((($a and $b) or $a or !($b and (($b)) or ($a or $a or !$a)) or !($a and !$b and !$b and $b)) or !$a or ($a)))",false),
    ("!(($b or $b) and (($a or ($a and ($a and $b) and $a) or !$b and ($b or !($b) and !($b or $a and !$b) and !$b) and !$b) and !(($b) or !$a) and !$b and !$b or !$a or !(($a))))",true),
    ("($b and !$b or !$b and !$a) and $b or !$b and $a and !$a or $a or !($a and $b and ($a or !$a and !$a or !$b and !$a) and !$a or !($b and $b and ($a and !($b))))",true),
    ("!$b and ($b or !($b or !($b or !($a and $b) or ($a and !$a or !($b or !$b and !($a) or !$b and ($b) or ($a)) or ($a and !$a) or $a) and $b)) or !($b and !$a or !$b))",true),
    ("!$b or !$b or $b and !$a or !$b and $b and !($b and ($a and !($a or !$a) or $b or $b or $a) or !($a and $a and !$a or !$a and !$a or $b or !$a and $b))",true),
    ("$b and !(($b or $b or $a or !$a or !$a or !($b or $a and !$a and !$b or !$a or $b or $b or !$b) or !$a or $b) or $b or !($a or ($b) and !$a or !$b))",false),
    ("$b and !($b and $b or $b and (($b and !$b and $a and $a or $a)) or !$b) and ($a and !($a or $a) and $a and ($b and ($a or !$a and !$b and $b or $b or $a)))",false),
    ("($a or (($a and !$b and !($b or $a and ($a) or !(($a or $b)) and !$b or !$b and (($b or $b or !$b)) or !$b)) or $b or !$b or $a and !($a) or !(($b or $b or !$a))))",true),
    ("$a or $a and !$b or $b or !$b and !(($b and !$b and $a) or $a and !$b) and !$a and $b and !(($b and $b or !($a and $a) and !$a or !$a) or !($b and $a or !$a))",true),
    ("($b or !($b and !(($b or !($b or ($a) and !$b) and !$a and $b or !($a and $a and ($b) or $b or !$a or $b) and !$a or !$b or !(($b or !$b) or !$a and $a)) and $b)))",true),
    ("$b or $b and !$a and (($a or ($b and $a and ($b and ($b) and !(($a) and $a) or !$b and !$b or !($b and $b) and $b and ($b and !$b) and $b and !$a or $a) or !$a)))",false),
    ("(($a and !($a and $a or !$a and ($a and !$b or !$b and !$a or !($a and ($b or !($b or $b) and !$b)) and !$a or !$a or $b or !$b or $a) and !($b or !$b) or $b)))",false),
    ("!$a or $a or $b and !$a and !$a or !$b or $a and !($a and $b or !$a and !$b or !(($b and $b)) and !$b and $b and $a or !$a and $a and !$a or !$b and !$a)",true),
    ("!$b and $b or !$b or !$a or $a and ($b and !$b and ($a or (($b and ($b or !$b) and $b and !$b and !$b or $a or !$a and ($b or !$b) and !$b or $a and !$a))))",true),
    ("$a or !($a and ($b or $b or $b and !$a and !$b or !$b and !(($a and $b or $b and !$b and !$b or $b) and !$b or $a or !(($b)) and !($b and $b or !$a) and !(($b)))))",true),
    ("!$b and !($b or $b and $b or !$b and !$b or ($b or $b) and $a and $a or $b or ($b or $a and !$b and !$b and ($b or !$a and !$b) or !$a) or !($a or $b))",false),
    ("$a and !$a and $a and !$a or $b and $b or ($a or $a or $a and !$b or $a or $a and ($b and !$b and !$b and $b or ($b or !$b or !$a and $a or !($b))))",true),
    ("!($a or ($a and $a and !$b or !($b and !($b or !$a or !$b) or ($a) and ($a and !$b and !$a and ($b and $b) or !$a) or !$a) or ($b or !(($b or !$b or $a) or !$b))))",false),
    ("$b and $b or !($a or $a) and (($a and !(($b and !($b and !$a and !$a or !$a or $b)) or $b) and $a or !$a) and !$a or !($a and !$b or !$b or (($b or !$b and $b))))",false),
    ("!$b and $b or !(($b or !$a or $a and !($b and !$a and !($b) or $b and $b) or ($b and $a and !$a and $a) or !($b and !($a and $a and !$a or $b and $b and (($b))))))",false),
    ("$a or !($a and ($a or !(($a and ($b and $b) and !$b or $a or $b) or !$b and $b) or $a or !((($b or !$b and !$a) or !$b and $a or !$a and !$b and ($a and !$a)))))",true),
    ("$b and (($b or !($b or (($b and !$b) or $a) and $a or !$b or !($a) and $a or ($a or !$a and !$a or $b or $a or ($a) or !$b and !$a or $a) and $b and !$b)))",false),
    ("!$a or !$a or !$b and ($a and $a or $a and !$a and ($b or $b and !$a or !($a and !$a or !$b or !$b)) or ($a or $a and !($a or !$b and !$b) and !$b and !($b)))",true),
    ("($a and !($a and !$b or !$a or !($b) and !$a or !$b and !$a) or !($b or !$b) or $a and !$b and !$b and $a and !$b or !$a and !($b or !$a) or $a and ($a and !$b))",true),
    ("!$b and !$b and (($a or $a and !($a or $b and $a and ($a or $b) and $a) and $b and ($b or ($b or ($b or $b or !($a or !$b)) or !($b and !$a and $b or !$a)))))",true),
    ("$a or $a or $a or !$a or $a or !$b or $b or !$b or !($a and !($b or !($a and $b) or $b or ($b or $a)) and $b or !($b and $b) or $b or !($b and !$a))",true),
    ("$a and $a or (($b and (($a and $a and ($a) or !$a and ($b or $a or $b and !$a or $b and $a) or $a or $a or ($a or !$b or !$b and ($b and $b) and !(($b)))))))",true),
    ("$b and !($b or !$b and !$b or !$b or !$a and !$a and !$b or !($a and !$b or !$b and ($a and !(($b or !$b) or !$b or $b) and !($b and !$b) and !$a or !$a and !$b)))",false),
    ("!(($b and !(($b and ($a or $b and !($a and !$b and $b and !$a) and !$a or ($a or !$a) and !($b and $b)) and !($b) or ($a or !$a and !$b)) and !($a and $b)) and !($a and $b)))",true),
    ("!($b and !(($b and ($b) and ($a) and $a and !$a and !(($b and $b or !$a and !$b) or !(($a and !($a) or !$a and !$b and $b) or $b and $a) and !$b and $a or !($b or $a)))))",true),
    ("$b and ($b or $a or !$b or !$b or !($a and ($a or !($b or !($a and $a and ($a or !$a) and !$b or !$b and !$a and $a or !$b and $a and $a and !$a and !$b)))))",false),
    ("$a and !$a or $b and !($a or !$a and !($a or $b or $b and !$a) and !$b or $a or !$b and !($b or !$a and (($b and !$a or $a) or !($a and !$b or ($a) or !($a)))))",false),
    ("$b or !$b and !($a or !$b or !$b and !$b and ($a and !$a and !$b and $b or $b and ($a and !$b or $b and !($a and !($b)) and !(($b) or ($a) and $a or !$a) and !$b)))",false),
    ("!($a and $a and !$b and $a and $b or ($a or !$b and !$b) and ($b or $b or ($b or !$a and !$b) or $b and $a and $b or $b and ($a or ($a or !($b and !$b)))))",true),
    ("($b and $b and $b and !$a or ($a and $b or ($a)) and $a and $a and $b and $b or ($a or !$a and ($a and $b and $b) and !$a and $a or $a) or !$a or !$a)",true),
    ("(($a and !$a or $b) or ($a or $a) or !$b and $a or $b or !($a and !$b or $a or $a and $b and $b or !$a or !($a or ($a)) and !($b and !($a or !$a) or $a)))",true),
    ("($a and $a and (($a or $a or !$b or ($b and ($b and $a and $a) and $b and $b or ($a or !$a or !($a) or $a or $b and $a) and $a) or !(($a or ($a and $b))))))",true),
    ("!(($b and ($b) or $a and !$a and ($a or $a)) or !$b or !($a and !$a) or !($b and $a) or $a and ($a or !$b) or !$b or !$a or $b and !$a and !($a or $b and ($a)))",false),
    ("!($b or ($b or !$a or !($b or $a or ($b) or !($b or !($a or !$a or !$b or ($b or ($b) or !$b) or $b)) or !$a and !$b or ($a) and !($b and !($b and $a or !$a)))))",true),
    ("!(($b and $b and $a or ($b or !($a and ($a) or $b and ($a and $b and !$b) and $a or $a or $b or !$b and !$a or !$b and !(($a) or $a and !$b) or $a) or ($a))))",false),
    ("!$b or !$b or !$b or $a or $a or !$b or !$a or ($a or !$b and !$a or !$a or $b or $a and !$a and !$a and ($b or !$a and ($a) and $b and $b or !$a))",true),
    ("!$b or !$b or !($a or ($b or $b or !$b and ($a) and $b) and !($b) or ($b and $a and !$a or !(($b) and !$b or ($a and !$b or !$a and $b or $b or !$b) and !$b)))",true),
    ("!($a and $a and !$b) and ($b or $b and !($a and $a and ($a) and $b or $b and ($b and ($a and !($b and !$a)) and $b and !($b or $a or !($b or $b) or $b or $b))))",false),
    ("$a and $a or $a or $a or (($a and $b or !($b and $a or $b or !$b) or !$a and $a) or $a or !$a and (($a or $a) and $b and !$a and !$b and !$b) or $a)",true),
    ("$a and ($a or ($a or !$a and $a or $b) or !($a or ($b or !$a) and !$a) and !$b and !$b or $b and !($a or !((($a) and ($a and $a or $b) and $a or !$a and $b))))",true),
    ("$b and !($b or !$a and !($a or (($a or !($b) or !($b and $a and !(($b) and !$a) or $b or $b) or $a) or $a or !$b and !($a) and $b and !$b and (($a or !($a or !$a))))))",false),
    ("$b or $b and (($b and $b) or $b or ($b and !($b) and !($b and $a and $b or $b or $b and ($a) or !$b or $a and !(($a and !$b and !($a) and $a or !$a) or $a))))",false),
    ("!($a or $a and !($a and !$b and ($b and !$a and !(($a and !$b or $b) and ($a or !$a or !$b) or $b or $a and ($b or ($a) and ((($a and !$a) and $b or $b and !$b)))))))",false),
    ("!(($b or ($b and $b) or ($a and $a or !$b) and $a or !$b and $b or $b or ($b or $b and !($b or $b) and $a or $b or !($a and !$b or !$a and !$b and !($b)))))",false),
    ("(($a and !(($a and $a) or !($b and $b and $b or $a and !$b and !$a or !$a or $a and !$b and ($a and (($a) or $a and !($a or !($b) or !($b) or $a or $b and ($a))))))))",false),
    ("$a or $a or !((($a and !(($a)) or ($a) or !$a and !$b or ($b or $b) or !$b or (($b or !$b or !$a and $b or !$b and !$a or $a) or !$a or !($a or !($b or ($b)))))))",true),
    ("!$b or ($b and !$b or !$a or $a and $b or !$a and (($b or $a and (($a and !$b and ($b) or $b) and !$a) and !$b and !($a) or !$a or !($b and ($a) or !$b)) or $a))",true),
    ("!($a and $a and !$a or !$b and ($b and ($b or !$b or !($a and !$a and $b or !($a or !($b) or !$b) and $b)) and !$b or !($a or ($b and $b or $b) and ($b or $b))))",true),
    ("$a and !((($a and $a and !((($a) and !$b) and $a) or $a or !($b or !$b or $b and !$b and !(($a) and $b and !$a) and !$a and ($a or !$b)) and !(($a) or !$a) or (($b and $b)))))",false),
    ("($a or ((($a or ($b) and $a) and $a and ($b and ($b and !$b) and $b or !$b or !$a and !$b or !(($b and $b or !$b) or $b or (($a and ($b) and !$b or !$a or $a)))))))",true),
    ("$a and !$a or (($b or $a or ($a and ($b) or !($b and !$a) or $a or ($b or !(($a and !$b) and !$b and ($b and !$a) or !$b or $a and !$b or !$b) and ($b) or ($b)))))",true),
    ("($b or !$b and !$b or ($a or $b and !$b and !($b and !$b and (($a and !$b) or !$a and $a) and !$a and !($a and !($a) and !$b) or !($b or $a) and !$b) and $b and !$a))",true),
    ("!((($a and !($a and $a or $a) or !$a or !($b or !$b and $b) and !($b or $a and !($a) and !$a) or $b or $b and $b or !$b) and $b) and !$a and ($a and !($b and !$b)))",true),
    ("!$b or ($b and !($b or !$b and $a) and !(($a and ($b or !($a or !$b) and $b and !$b or ($a) and $a and !$b and !$a) and $a) or !($a and !$b and !($b and $a and $a))))",true),
    ("!$b and $b and $a and !$b or !($b and !$b or !$a or !$a and $a or $b or (($a or !$a) and ($b and !$a or $b or $b) and $a or !$a and $b or $b or $b))",true),
    ("$a and !$a or !($a and !$a or !$b and !$a and $a or $b and $b and $b and !($b and !$b or !$a) or !(($b and !$b and !($a) or $b and $b and !$b and $a or ($b))))",false),
    ("!($a or !$a or !($a or $b or !$a or !((($a or $b and !($b or $a or $b or $b) and !($a and !$b or $b) and !(($b) or !($a) or $b or $b) or ($b) and $a)) or $a)))",false),
    ("($a and !($a or !($a or ($a and !$b or !($a or ($b or !$b) and !$b)) and !$a or $a and $a) and !$b) or !$a or $b or $b) or ($a and !$a and !$a and !($a or !$b))",false),
    ("($a or !$a and !($a) or $b or (($b or !(($b) and !($a and !($a or $a and !$a or !($a) and !($b) and ($b) or $b and ($a) or !$a) or !$a) and !$a and $a or $b and !($a)))))",true),
    ("!($a and ($a and ($b or (($a and !(($b or (($a and !$a) and $b or $b) or !$a) and !$a and $b and $a and $a) and !$b and !($a or !$a)) and $a or ($a and ($b)) or $b))))",true),
    ("!($b and !$b and $b or ($a and !($b or !$a and $b) and $a or ($b and $a or $b and !$b and !(($a or !$a or $a and !$b))) or !$a or !$b or ($a and $b or $b)))",false),
    ("!(($a or !$a or (($b or !($a or ($b) and !($a)) or $b or !$b and $b and !$b and !($b or $a and !($a and !$a) and $b) and (($a)) or $b or !$a) and $b) or $a and $a))",false),
    ("($a or !$a and ($b) or $b and !$a and !$b or $b or !($a and $a and !($b or !$b and !$b or $b and $a or $a and !$b or !$a or !$a or $a)) or !$b or $a)",true),
    ("$a and !$a or ($b or $b or !$b and !$a or !$b or !$a or !($b and (($b or !$a) and (($a or !($a) or !$a or ($b) and $b and $a and !(($b or !$a or $b) or (($a))))))))",true),
    ("!(($a or ($a and ($b) and !($b) and $a and ($a or !$a and !$b and $a and !$a and $b or $b and !$a and !$a or !$a) or ($b and !$a or $a or !$a and !($a) or !($a)))))",false),
    ("!($b or $b or !$a and !$b or !($a or $a or ($a and $b and $b and !$b) or $a or !($a and $a and !($a) and $b or !$a or !$b or $a or !($a and $b) and !$a)))",true),
    ("!(($b and !($b) or ($b or ($b) or $a) or ($a) and !(($b and !$b) or !($a or ($a and !$b and !$b) and $a and $a or !$b) or $a) or !($a and ($b or ((($a or !$b) and $a))))))",false),
    ("!$a or !($a and !$a or !($b or !$a or !$a and $a or !($b and $b or !($a) or $b or !$a and $a and !$a and !$b or $a or !$a and ($a or !$b and $a and $b))))",false),
    ("$b and !($b or !($a and !$b and !$b or $b and $a or $b and !$a and $a or !$b or !$b and !$a and $b) and $b) or $b and $a and $b and !$b or !($a and $a)",false),
    ("$b or !$b and $a or ($a or $a or !$b) or !$a and $b and ($a or $b and !($a or ($b and !$a and !$b) or !$b or !(($a or $b and !($a) and !$a and ($b and $a)))))",true),
    ("!$a and !($a and ($b or !$b and $a and !($a and ($a) or !$a and $b and ($b or !$a or !($a) and $a or $a and $a and !$b or $a) or $b and $a and !$b or !$a)))",false),
    ("!$a or !($a and !($b and $a and !$b) or $a and !$b and $b or $b or (($b or $b) or !$b or $b or !($b and ($b or $a) or $a and $b) or $b or ($a or !$b)))",false),
    ("($a or $a and (($a and !($b or !$a) and $b and $b and !$b and $b or !($a) or (($b) or $b) or !($a) or !($a or (($b or !$a) or !$a or $a and !$b)) or $b) and !($a)))",true),
    ("$b and ($b and $b or ($b or !$a and $b and !$a and $a) or ($b and !$b) and (($b or !$b and !$b or ($b and !$b) or $b) and $a or !$b or $b or !$a) and !$a)",false),
    ("$a or !$a or !$b or !$b or $a or !$a or !$a or !$b and $b and ($a and !$b) and !$b or $a and (($b and ($b and $a or !$b or $a or $a) and !$b or !$a))",true),
    ("($a and !$a or !(($b or !$a or ($a and ($a)) or !($b) and (($a) or !$b) and ($a and $a and ($b and $b) and !$a and ($a and !$a and $b and $b and !$b) and !($a or !$b)))))",false),
    ("!$a or $a or $b or $a or !$b or $a and !(($b and !$b or ($a and $b and !($a or !$b and $b) and $b and ($a or !($b and !$b and !($a and !$b) and $a or !($a))))))",true),
    ("$a and !$a and $a and $b or !($a and !$a or !$a and $a and ($b or $b) or !($a or $a and !$b and $a or !$b) and $a and !($a or ($a and $a and !$a or !$b)))",true),
    ("($b or !$b and !($a or $b or $a or !$b) and $a and ($b or $b) and !($a and $a and $a) or !($a and !$b and !$b) and ($b and ($b or ($b or !$a) or !$a or !$a)))",false),
    ("!($a or !(($a and $b) or !$a or !$b and ($a and !$a or $b) or !$a) or !$b or !($b and !($a and !$b or !$a and $b or (($b) and $a or !($b) or !$a or !$b or !($b)))))",false),
    ("!$a or $a or !$b and (($a and !($a or $a or $a or !$b) or $a and !$a or ($a or $a and $b or $a or !$b or ($b or !$a and !$a and !$a and !$a and $b))))",true),
    ("!$b or !$b or ($a and !$a and $b and ($a and !$b or !$b) or $b or $a or !($a or !$b and !$a and !$a or !$b and $b and !($b or $a or !$a and ($a or $b))))",true),
    ("!$b or !$b or !$a or (($a and !$a and $b or !$b and ($a and !$b and !$a) or ($b or ($b) or !$a) or $a or $b and !($b or $a or $b or ($b) and (($b and !$a)))))",true),
    ("!$b or !($b and ($a or ($b and $a and $b or !$b or $b) or !($b) or !($a and $a and ($a or $b) and $b) and $a or $a and !($a and $a) or !($a and !$b and $b)))",true),
    ("($a or $a and !($a and !$b and $a and $a and !$b and $a or !$b and $a and $b and ($a or !$a or !$b and !$b) and $a and !($a and $b and !$a) and !$b and $a))",true),
    ("$a or $a and ($b or $a or ($a or ($b and ($b and !$a or !(($b and !($b or $a or ($a) or !($a)) or !$b and ($b or !$a and !$a) and !$b)) or !($a) and ($b or !$a)))))",true),
    ("!($a and ((($a or $a and !$a and !$b and $a or ($a and !$b or !$a and $a and !($a or !$b or !$b) and !$a and $b) or $a and !($b) and !$a) and $b or $b and ($b))))",true),
    ("$a and ($a and !(($b and !($b and !$b and $a or !$b)) and !($b and !$a or $b or !$a and !$b) or !$a or $b or $a or (($b or !($a or $a) or $b) and $a) and $a))",false),
    ("$b or ($b and !(($a or (($b or !($b) or !($a) or $a or !$b) and !($b) and !($a and ($a and !$b or $a and $b or $a or $b) and !($a and $b)) and !$b) or !($a or ($a)))))",false),
    ("($b or $b or !$a or (($b and $b or ($a or !$a and !$a) or $b and !($a or $a or ($a or $b and !($b) and !$a and $a or !$a) or !$a) or ($a and !$a or !$a))))",true),
    ("!$a or !($a and !$a and ($a) or !$a and !($a and !$a and !$a and !($b and $b or $a and !$b and !$a and $b or !$a or !$b and !($b and !$a or $a) and ($a)) or $a))",true),
    ("!($a or !$a) or $a and ($b or !$a and $b or ((($a) and !($b and ($a) or $a or $b or $b and ($b and !($a and $b) or !($b and !($a) or $a) or !$a or !$a and !$b)))))",false),
    ("!($b and ($b and !($b or !$b) or $b or ($b and $a or !$b or $b) and !$a and !$b or !$a and !$b and !$a and (($b and $b) and $b) and !(($a or !$a) or !($b or $a))))",true),
    ("!($a or !($a and $b or ($a or !(($b and !$a) or $b or $a) or !$b or $a and !$a) and !(($b and !$a and !$b and !($b) and ($b and !$b) or !($b) or !$a or $a and $b))))",false),
    ("($a or $a or !($a and $b or (($a or $a and !$b and !($b) and $a) or $b) and $a or !($b or (($a) and !$a) and !($b and !($b and !($b and $b or !$a) and !$b and ($b))))))",true),
    ("$b and !($b or !(($a or !$a) and ($a and (($a) or !($a) or $b) or $b or (($b or !$a) or !$b or !$a) or !(($a and !($b and $a or !($b) and !$b or $b and !$b or !$b))))))",false),
    ("$a or $a or !($b or ($a or (($b and ($a and !$b and !($b) or $b and !$b or $b and !$a) or ($b) and !(($b and !($a or $b and !$b)) and !$a or !$a and !$a) and !(($b))))))",true),
    ("($b or $b and !(($b and !$b or !$a or !$a and !$a and !$b and $a or !($b and $a) and !$b or !($a) and ($a and !($b or ($a or $a and !$b or !$b and !$b or !$b))))))",false),
    ("($b and $b and !($a or !($b) or $b and $a or !($b and !(($a and $a and $a)) and $a and !$b or ($b) or !$a or $a and !$a or !$b) and !$a or ($a or !$b and $a)))",false),
    ("((($b or !$b and !$a or !$a and !$a)) or !$b and $b and ($b and $a and ($a) and ($a or $a and !$a and !$b and !$b or !$a) and $a or !$a and $b or $a or !$b))",false),
    ("($b or $b and !($a and !($a or !$b or !($a or !($b and !$b and !$a or $b) and ($a or $b or ($a or $a) or !$a and $b) or $a or $a) and $a and !$a and $a)))",false),
    ("($a or (($a and (($a or $b and !(($b) and $a)) and !($b and !($a and $b and ($b or $a) or !$b) or !$a and $a) or !$b) or $a) or (($b or !($b and $b)) and !($a or !($b)))))",true),
    ("!$b and !$b or !$a and !(($b or !$b and $a or !$b and ($a and !($b) or ($a or $b and $a or !($a and !$a and !$b and !$b) or !$a or !$b or $a or !$a and !$b))))",true),
    ("(($a and ($a or $b) or !($a and $a or !$a or !$a or !(($b and !($b and $b and $a) or !$b and !$b or !$b or !($b or $b or $a and !($a and !$a or !$b and $a)))))))",true),
    ("(($b and ($b) and $b or $a and $a) and !($b or !$a or !$b or !($b or $a and (($b and !$a and $a) and !$b) and !(($b or ($b) and !$b or !($a) or $a) and !($b or !($b))))))",false),
    ("(($a or ($a and !($a or !$a)) or !$b and !$b and !$a) and !(($b and ($a) and $b) or !$a or !$a and !$a or ($a or $a) or $b or ($b and $b or !$b) and ($a and !($b))))",false),
    ("($b or !($b or ($a or $b and $a or !($b or !$a or ($b) and ($b)) or !$a) and !$b and $a or !$a and !$b or $b or ($b and !($b or !($a or !$b or $a and $b)))))",false),
    ("!(($b or !$b) or $a and !$b) or $a and !$b or $a or ($b or !$a and ($a or ($a and ($a and !($b) or !$b) and !$b and $a or $b or !$a or !$a or $a) and ($b)))",true),
    ("!$a and $a and $a or !($b or !$b or !($a) and !$a) and ($a and (($b and ($a and $b or $b or $a or $a or !$b or !$b or $b and ($a) or $a) and ($b and !($b)))))",false),
    ("(($b or !($b and ($a and !$b)) or !($b and !($b or $b or $a or !$a) or !($a or ($b and !$a)) and !$b and !($a or ($b)) or ($b) or $a or !($a or ($a and !($a or !($b)))))))",true),
    ("$b or !$b or !($a and $a and !$a and !$a and ($b and !$b and $a or $b or $b or !(($b) and !($b and !$a or $a) or !$b or !$b and !$a and !$a) and ($b or $a)))",true),
    ("!((($a or $a) or !(($a or !(($a) and !($a and !$b and !$a and !$a or !($b) or !$b) or !$a) or ($a) or $a and !($b) or !$a) and !$b and !$a or $a) or ($a or !$b or $a)))",false),
    ("($b and $b or $b or !$b and (($a and ($a) and !$a or (($b and !$b and !$b) and !(($a or !$a and $b and $a and !$a) and $b and !$b or !($b or $b or !($b or !$a)))))))",false),
    ("($a and !$a) or (($a and !$a and !(($b and $a or $a or !($a and !($b) and !$b and !$a or ($b) or $b) and ($a) or !((($a or !($a) and $a and $a) and $a and !($a or !$a)))))))",false),
    ("$a and $a and ($b or !$b or $b and $b or !$b or !$b or !($b or $b and $a or ($a or !$b) or !($b and !$a or $a or !($a and !(($b and $a) and !$b) or $a))))",true),
    ("$b and $b or $a and !($b or $a or $a and !(($b and !$b and ($a or !($a and $b and !$a) or !($a and $b) and !($a or !($b) and ($b or !$a or $a) or !$b or $b)))))",false),
    ("$a or $a and ($a or $b and (($b or (($b and $b or ($b or !$b) or $b and !$b) and ($b and $a) and $b or $b) or ($b and !$b) and $a and !$b) and !($a or $a)))",true),
    ("(($a or !($a) and !$b and !$a) or !$b and !$b or !$b and ($b and (($a and !($a and $a and $a)) and $a or !($a) and $b and ($b or ($b) and !($a and !($a and !$b)) and $a))))",true),
    ("!$b and !$b or $b and !$a and $a and $a or $b and ($a and !$a and !$b and !$b and $a or !($b and !$a or !($b or $a or !$b) or $b or !$b) or !$b and $b)",true),
    ("!$b or !$b or !$b or !$a or $b and $b and $a and !($b and $b or ($a or !$a or !($a or $b and !$b and $a) and !$a or $a) or !$a and !$a and !($a and $a))",true),
    ("($b or !($b and !$b or $a or !$b) or !$a or $b or $a and $a and !(($a and $a and !$a or !$b) and $b or !$b or !$b or $a or !($b or !$a and !$b and !$b)))",false),
    ("(((($b or !$b) and $b) and !$b and !$b) or !($b) or ($a and ($b or (($a and $a) or !$a) and !($a) or ($b) or $a)) or ($a or !$a) or !$b) and ($b and (($a and ($b and $a))))",false),
    ("!($b or ($b and $b) or !($b and $b or !$a and (($b and $a and ($a and !$a or !$a and $a and !(($a and !$b and !$b)) or ($b)) and $a or !$a or (($b and !$b) or !$a)))))",false),
    ("!$a or !$a or !$a or !($a or $a and ($b or !$b and !$a or $a and !$b and !$a) and $b or !$b or !($b or $a or !$b and !$b and !$b or !$b) and $a or $a)",false),
    ("($b or $b or !$a and !$b or $b and !($b or !$b or !$b and !($b) or ($a or !$a or $a) and (($a) or $a or !$a and $b) or !$a or !($a and $a and $a and (($b)))))",false),
    ("($a and ($a or !$a or !($a and !$a and $b or $a and ($b and !$a and !$b or $b) and $b or !($b or $a or ($b)) or !$a and $a and !$a and !($b) and $b or !$a)))",true),
    ("$a and ($a and $b) and $b or ($a and !($b or $b and !$a and $b and !$b or !(($a and !(($b and !($b or $b and $a and !$b) or !($a and $b or $a or !$a or !$a)))))))",true),
    ("(($a and $a) or !($b and !$a or !(($a or !$a or !$b or !$a or !$b or !$a and $b or ($b) or !(($b and !$b and $a) and !$b) and !$a and !$a) and !$b or !$a and ($b))))",true),
    ("!($b or !($b and ($a and !$b and $a) or !$a or !(($b and $a and !($b or ($b and $b) and $b) and !$b) and $a or !$b) and ($a and $b or !$a) or !$b and !$b and !$b))",true),
    ("(($a or !($a or $a or !$b or !$a and ($a or $b and !$a and !$a and !$a) and $b) or !$b or $b and ($a or ($b) or ($a and !$b or !($a and !$b) or !($a) and $a))))",true),
    ("$a or $a or !$b and $b or $a and !($b and ($a and $a and ($a and $a) and $a and $a and !($b and $b) and $a or !$b) and !$a or !$a and $a) and !$a and !$a",true),
    ("!($a and (($a) and !$a and !$b or $a and ($a and $b) and $b or $b or $b) and !$b and !$b and !$b or !($a or !($a or !($b or $b or !$b or !$b and $b and !($b)))))",true),
    ("!($a and $a or !$b or ($b and !$b and $a and !$a or !$a or ($a and !$b or !$a or $b) and !($a) and !$b and ($a or $a and !$b) and ($a and !($a or !$b and $b))))",false),
    ("($b and $b and !$a) and (($a or $a and $b and $b and !$b or !$b or !$a or !($a or $b or !($a and $b or $a or !($a and $b and !$a) and $b) or $a and !$b)))",false),
    ("($a and ($a or !$b or !($b and $b) and $b and ($a and !$a) and !$a) and $b or ($b and !$b or !$b or $a) and $b or !$a or !(($a and !$b and !($b) and ($a and $a))))",false),
    ("$a and $a and !($b and !$a and ($b and $b) or $b or !$a and !($a) and $b or !($b or $a or !$b or !$a or $b or !$b or $a and !($b and $b and ($a) and $a)))",true),
    ("!$b and !($b and !$b and !($a) or (($b or $b or $b and $a) and $a and ($a and $b) or ($a or $a or !$b and !$a or !($b or !($a) and $b or $b and !$a and $b))))",false),
    ("($a or $a or !$a or !$b and ($a and ($a or !($b)) and !$b or $a or ($a or ($b or ($a) and $a or !($a or (($a or !$a and !($b) or !$a) or ($b) and !$b or !$b))))))",true),
    ("$b and $b or $b or !$b or ($b or !$a or ($a or !($b and !$a or !$a or !($a) or $a and !$a or $a or !($a or $b or ($b)) and !$a) and !($a or !$b and !$a)))",true),
    ("($b or ($b and $a or $a or $a and !($b and $a and $a) and !$a) and !($b or $a and !$a or !$b and !$a or !($b) or !($b) or !$b and $a and !($b or $b or $b)))",false),
    ("$a or !($a or ($a and !(($a or !$b)) and !($b or ($a or !($b and $a) or ($a and !($a) or $a) or !$b or !($b or !$a) and !$a and ($b and !$a and !$a or !$a or !$b)))))",true),
    ("!($b and !$b and !($a and $b and $a or !($a or $b or !$a or !$b or $b or $b) and $a and !$b and $b and $b or !($a or $b) or $a and $b and $a or $b))",true),
    ("$b or !($b and !$b or $a and $a) or $a and !($a and !(($a and !$b) or !$b and !$a or !$b and !$a and !($a or !$a or $b) or !$b and $a) or !($a and !$a and $b))",false),
    ("(($b and !$b and $b) and ($b and !$b and $b or !$b and !$b or !$b or $a or $b or ($a and $b and $b and $b) and !$a and !$a and ($b and !$a or $b or $a)))",false),
    ("$b or !$b or !$b or !$b and $b or $b and $a or !$a or ($b and !$b or $b or !($b) or ($a and !$a or !$a or ($a or !$a or $a or !$b or !($b or !$a))))",true),
    ("$a or $a and !$b or ($b and !$b or !$b and !($b and !(($a or !$a and !$b or !$b and !$b or !$b and !($a or !$b) or !$a or !$b and $a and !($a and ($a) and !$b)))))",true),
    ("$a and !$a and $b or ($b or !($a or $a or ($a or !$a) or ($a or ($b and $b) and $a)) and !(($b or ((($a) or !$b or !$a or !$b and !$b) or $a or ($b and !$a)))))",false),
    ("!($b and !$b) and !$a or $b and $a and !$a and ((($a or !(($a)) and ($b and ($b) or !$b or !(($b) and !$b or $a and !$a)) or $a and ($a or $b or !$b or !($b) or !$b))))",false),
    ("(($a and !($a or $a or !($b or ($a or ($b or $a)) and ($b) and $b))) and !$a and !($a) or !(($b or ($b or ($a and (($b) or !$a and $b) or !($a and !$b and $a)) and !(($b))))))",true),
    ("!(($b or ($b and ($a or !$a and !($a and !$a or $b) or !($b and !$a) and !$b and !($a and $b or $a and $b) or $b or $b or $a) and !(($a and !$a and !$b and $a)))))",true),
    ("!($a and ($a and !$a or ($a and $a and !$a and $b or $b and ($a or $a or !$a)) and $a and $b or $a and !($a and !$b) and $b or !$a) and !($b and !$b and !$b))",true),
    ("!(($a and !$a or ($a or !($b and ($b or !$a)) and ((($a or !$a or !$b and !($b or !$b and !$b and $a) or !($a) or $a) and !($b or !($b) or !(($a) and $b and !($b or !$b))))))))",false),
    ("!(($b or $b or !($b or ($a or $b or !(($a and $b) and $b) or $a and $a and !($a) or ($a) or ($b or !$b) or $a or $a or ($b or $b or !$b and $a and !$a)))))",true),
    ("!(($b and $b and $a or !($b or !$b) and !$a or !($a or !$b or !($b) or ($b or ($b and $a or $a or ($a) and $a or !$b and $a) and !$b) or !$a or !$b and !$b)))",true),
    ("!($a or ($a and $a) or $b and !($b and !$b or !$b) or !(($b) or !($a and !$a) and $b and $b or !$a or !$b and ($b) and ($a and $b) or !$a and !$a) or ($a or !(($a))))",false),
    ("($b and !($b) and ($a and !($a or !$b) or ($b) or $b or !(($b) or $a) and !$a and $a or ($a and $a and $b or $b or !($b or $b and !($a and !$a and $b or !($a))))))",false),
    ("$b and !($b and $a or $b and $a and $b or !$b and !($a or $b or $a and $a and ($a and !$b and !$a) or !$b and !$a or !($b) and !$a or !($b or ($b and !$a))))",false),
    ("!(($b or $b or !$a or $b or $b or !$a and !$b) or !$a or !$b and !$b and $b or !($b or !$a or $b and $b and !$a and $a or !($b or !$a and !$a) and !$b))",true),
    ("!$a or !((($a or $a and !($a and $a and !$a)) and !$b and !$a) and $b) and ($a or !(($b and !$a) and !(($b or $a and $a and !$a) or !($b) or !$a and $a and !($a) and $a)))",true),
    ("!($a or !$a and !$b or !($b and !$a or !$b or !$a and $a or !$a and !$b) or !($b or !$b or !$a or $b and !($b) or !$b) and $a and !$b and !$a) and !$b and !($b)",false),
    ("!((($a and $a and $b or !$b) or $a or ($a) or !($a) or !$a or ($a and $a and (($b) or !($a) or $a or $a) or !$b and $a or !(($a and ($b and $a) and !$b or ($b))))))",false),
    ("$a or !$a and $a or ($b or (($b or !$b and !($b and !$b) and !(($b or !($a or !$a) or !$b or !$a or $a and $a or $b and !$a) and !$b or !$b and !$a) and !$b)))",true),
    ("!($b or $b or !($b or !($b or ($b or $b and $a) or (($a) and $b) or ($a or !($a) and !($a and !($b)) and ($a) and (($a or $a and !($b) or ($a) and !$a and ($a and !($b))))))))",false),
    ("!$b or !(($b and !$a or !$a or !$b or $a) and $b and !$b or $a and $a or $a and !$b and $b and !$b or $b and $b and $b or ($b or ($b and !$b or !$a)))",true),
    ("$a or !($a and !$a and $a and $b or $a and !$a or !$b or $b) or !$a and $b and !($a and !$b and $a or $b and ($a and ($b and $a or !$a or !$a) or ($a)))",true),
    ("$b or ($b or !$b and !($a or $b) or ((($b or !$a) or !($b or $b or !$a) and !$a) and !$b or $a or !($a and !($a or !$b and !$b) or !$b) and $a and $a) or !($b))",true),
    ("!($a and !$a and !$a and !($b and !$b and !$a or !$a and !$a) or !$b or $b and ($a or ($a and !$b and !$b and $a and $a or $b or !$b or !$a and $b) or !$b))",false),
    ("!$a or $a or !$a and $a or !$a and $a or !$a and ($a or $b and !$b and !$b and !$a and !$a or !($a) or $b or !$b or !($a and $b and !$a or !($b or !$a)))",true),
    ("!(($b and ($b and $b and ($a or !$b) and !$a and $a or !$b and $a or !($a and !$b or $a and !$b or !$b and (($a and $b) or $b or !$b) or !$a) and !(($a or !$b)))))",true),
    ("!$a and $a and !$a and !($a or !($a and !(($b and $b or !$a or $b or !($a or $b and !$a or !($b) or $b) and !$a or $a)) and ($a or $b) or $b or !(($a or !$a))))",false),
    ("($b or !$b or !$a or $a or $a and !($a or !($b or $a and !($a or ($b) and !$b and $a) and $b or !($a or ($a and !$a or !$b) and !$b) and $b and $a) and ($a)))",true),
    ("!$b and ($b or (($b and !(($b) or ($b or (($a or ($a or !$b) and $b) and $b or !$b or $a) or $a) or !($b and !($a and !$b or $a and !$b and !$b)) and !$a)) and $b))",false),
    ("!($b or $b or !$a and ($b and $b and !$a and ($b or !$a or ($b and !$a or !$b or !(($b or !$b) or $a or !$b and !($b or $b and !$a and $b))) or !$b) or ($b)))",true),
    ("!$a or !(($a and !$b or !$b) or !$a or $b) or !(($a or !($b and !($b and !$a or !$a)) or !($b and !$a) or $b or !$a and $a or !$a and !$b and !($b) and !$b or !$a))",false),
    ("$a and !$a and $a and ($b and $a or !$a or !$a or $b or $b and !$a and ($a and $a and !$a or !$b or !($b and !$a and ($b and ($b) or !$a and $a)) and ($a)))",false),
    ("($a or $a) or $a and !$a or !$b and !($a and ($b or !$a or $a or !$b and !$b) or ($a or !$a) or $a or !($b and !$a and !$b) and $b and !($b and ($a and $b)))",true),
    ("$b or !($b or !($a and !($a or (($a or $a or !($a)) or !$a and $b and !($a and ($b) or !$b and $a or $b or !$a) and $a and !$b) or !($a and !$a and !($b or !$b)))))",false),
    ("($a and $a or ($b or !$a and !$a or (($b or $a) and $a or !$b or !$b and ($b) or (($b or !($b or $a) or $b and !$a or !($a and !($a or $b and !$b and !($b))))))))",true),
    ("(($a or $a or !$b or !($b and ($a or (($b or !$b and $a) or $a and ($b) or $a or $a or $a and !$a and $a) or $b) or !$b and !($b and ($a)) or $a or !($a))))",true),
    ("!$a and !$a or !$b and $b and !($b or !$b or $b and $b) and $b and !($b and ($a and !$b or !$a) or ($b or $b and !$a and !$b or $a or !$b and !$b and !($b)))",false),
    ("!((($b and $b or ($b) and !$a) and !($b and !$a) and $a or !($a and (($b and $b or ($a or !$b and !$a) or !(($b and !($b)) or !($a and !($a) or !($b)) or !$b and !$b and ($b)))))))",true),
    ("(($b or !$b) and ($b and $b and $b and !$b or (($a or !$b or !$a and $a or !$b or $b) and !($b or !$a) and !$a or $b or !$b) or $a and $b) or !($a and !$a))",true),
    ("!($b and !($b and $a) or (($b or !($a) and $a and ($a and !$b and $a or $b and $a and !($a)) or !$a and $a) or $b or !($b and ($b) or !($b) and ($a or !$b or $a))))",true),
    ("!$a and (($a or $a) and ($b and ($b or ($a and !$b or !$b and !($b)) or $b or $a and ($b) or $a and ($a or !$a) and $a) or !$a) or $a and (($b or $b and $b)))",false),
    ("!($b or !($b or $b or !$a)) or ($b and $a or $a or !($b) or $b or $a and !$a or $b and ($b and !$b or $a or $a and $b or !$b) or ($b or !$a or !$b))",true),
    ("$b and ($b and !($a and !$b or ($a) and !($a or !$a) or !$b or !$a or !$a) or !($a or !$b) and $a or ($a and $b or !$b and $b or $a or !$b and $a or $b))",false),
    ("$a and !($a and $b and (($a and $b) or !($a and !($b or !$b) or $a and !$b or (($b) and $a or !$b) or !($b) or ($a) and $a and !($b and $a)) and !(($b or ($a and !(($a)))))))",true),
    ("$a or !$a or !($a and ($a and !($a or !$b)) and ((($a and !$a) and $b and !(($a or !$b) or (($b and $b and !$b or $a or $b or !$b)) and !$b and !$b and !$a and !$a))))",true),
    ("!$b or (($b and $a or $a and !($b and !$a or $b and $a) or !$a) and !$b and !$a and !$a) and !$a or !$b or !$b or $a or !$b and $b and !$a and !$a or !$a",true),
    ("$a or $a and (($a or $a or !$b or !($b or !$b or $a and $a and $a and $b or !$a or ((($a or !$b and !$a or $a) and !$b or $b) or $b)) and $a or !$a))",true),
    ("$b and !$b or $a and !$a or $b or ($b or !($b or !$b or !($b or $a and !$b or !$b) or !(($b) and ($a and $a or !$b) or $a) or $a) or !($a and !$a and ($b)))",true),
    ("!((($b or $b or !($a or $a and $b and !$a) or $b and !$a or !$a) or !$a and $a) or !$a or ((($b or !($a) and $b) and ($b or $a and $b or !$b or !($b) or !$b))))",true),
    ("($b or !$b or !($b) or !$a) or !($a and !$a and $b or $b and !($a or $b) or !($a and !($a or $b and $a or !$b and !$b and ($b) and !$a)) or !($b and !$a or !$a))",true),
    ("$b and !$b or (($a or !$a or ($a and ($a or !($b or $a) or !$a and !$a or $b and $a) or !$a or $a or !($a and $a) and $a and !$b) and ($b or !(($b or $b)))))",true),
    ("$b or !($b and (($b or (($b or !$a or $a and $b and !$b and !$a or !$a or !$b and !($a) and ($b or $b or !$a) and !$b) or ($b and !$b)) and ($b and (($a and $a))))))",true),
    ("($a or !$a or (($b and $b or !($b or !((($b) and $a) or !$b) or !$a and !($a and !$b or !$a and !($b) or !$b) or $a or $b or !($b)) or !(($b) or !$b) or !$b) and ($b)))",true),
    ("$a or !$a or $a and $b or $a and !$a and !$a and $b and $b or (($b and !$b and $b and ($b and $b) or !$a or $b)) and !$a or $b or $b or !$b and $a",true),
    ("!$a or $a and !$b and !($a and $b or $b or ($a or $b and !$a or $a) and !$b and $b or $b and $b and !$a and !(($a or $b and $b or $b) or !$a or $b))",true),
    ("!(($b or $b or $a and !$b or !$a or $b or $a and $b and $b and !$a) or !$a or !$b or !$a) or ($b and $b and !$b or !($a or !$a and !$a and !($b and $a)))",false),
    ("!($b or ($b or ((($b and ($a and $a or !$b and $a))) and $b or !$b or !$a and !$a or $b or !$a and !(($b or !$a) or $b or $b and $a and !$b) and !$b or !$b)))",false),
    ("!$b and !$b and $a and ($b or !$b and !$a and $b or !$a or $b) or $a and !($a and ($b) and !($b or $b or ($b) and !$b and $a and !$a and $a or !($b or $a)))",true),
    ("!($b and !$b or $a or $b and !$a or $b and $b and !$b and $b or $b and !$b and !$b) or $b or $a and !$b or !$a or $a or $a and $a and $a and !$a",true),
    ("$b or ($b and $a or $b or !$a and $a or $a or !$a or !(($a or $b) and $a or $b or !$b) or $a or !$a or $b and $b or $a and !$b and !($b) or !$b)",true),
    ("!$b and (($b and $b and !$b and !$a)) and !$b or $b and $a or (($b or $b) and (($b or (($a and $a)) or $a and !($a and (($b) or ($b) or $a) and !$b) or !$b and !($b))))",false),
    ("!(($b and (($b and !($a or !$a)) or (($b or !($b and !($a and !($a and ($b) or !$b or $b) and !$b or $a) or !($a) or !$b) or $b)) or ($b or ((($b) and !$b and !($a and !$b)))))))",true),
    ("!($b or !($b and $a and $a and !$a and $a and $a or $b or !$a or !($a and $a and $b and $b) or !$b and !$b) or ($a and !($a or !$a or !$b or !($a) or $a)))",true),
    ("$a and ((($a and ($a or !$b or !$b or ($b or $b and !$b or !($a) and !$b and $a or !$b or $a or !($b or !$b) or !$b and !$a) and ($b or !$a and !$b and !$b)))))",true),
    ("$a and !$a and !$b and $a and !$b and $b and !$b and (($a or ($b and !($b or !$a) or $b or !$b or !$a and $a or !$b or $a)) or $a or $b or $a or !$a)",false),
    ("$a or !$a or !$a or !$a and $a and !$b and $b and !$a and !$a or !$a or $b and !$b or !(($b or $b and !$a or !$a or $a and ($a or !$a or !$a) and !($a)))",true),
    ("!($a or !$a or $b and $b and !$b and ($a and !$a or $b and $b and !$b or $b and !$a or $b and !$a and !$b or !$a and $b or !$b) and !$a and !($b or $b))",false),
    ("$b or ($b and $b and (($b and $a) or !$a and $b) or $a) or $a or $b or !($a or $a) and !($b and $a or !$b) or ($a and $a or !($b and $a and !$a and $a))",true),
    ("$b or ($b and !($a and !(($a) or $b and $b and $b and !($b and ($a or !$b or !($b or !$a)) and $b and ($b and !($b and $b) and ($a and !$a)) or $b or !($b and !($b))))))",false),
    ("($a or !$a and $a or $b and !($a and $a or !$b or $b or !($b and $a)) and !$a or !($b or $a or !$a and $b or !$a) and ((($b and !$b and !$a) or !$a and !$b)))",true),
    ("$b and !(($b and ($b and $a) or !$b) or !$a or !$b or !$a) and ($b or !$b and !(($b or $b and !($b) and !(($b and !($b) or $b and !$b) and (($a or $a or !$a) or !($a))))))",false),
    ("!(($b and ($b and $b or $a and !($b and !$b or $a or !$a and !$b or $a and !$a and $a or !$b and !$a) or $a and $a and !$a and !$a or $a or ($b or !$b))))",true),
    ("$b and ($b and !($a or ($b and $b and !($a) or !($a and $a) or ($b or !$a and $b and !$b or !$b) and $a or $b) or !($a or !$a or $b and $b) or ($a or !$b)))",false),
    ("!($a and !$a and !$b or !$b or ($b and $a and $a and !($a or !$b or ($a and $a and $a) and $a and !$a or $b or $a) or !($b or ($a)) and !($a and ($a or !($b)))))",false),
    ("!($a or $a or !$a or ($a and !$b or !$b or ($b or !$a and !$b and !$a and $b or ($b and $a and !$b and $b and !$b or !$b and $a and $b and !$b and $a))))",false),
    ("$b or (($b and !($a or (($a or $b and !$a) or ($b) or !$a or !(($a or (($a and $a or ($a or !$a) or $a) and !($a) and !$a and $b or !$a and $b or !($a or !$b))))))))",false),
    ("!($a or $a or !$a or !$a) and !$a and !($b or $b) or !($b or $a or !($a or $b)) and $b and (($b or !$a or !$a or !$b and !($a or !$a) and !($a and !$a) and !$a))",false),
    ("!$a and !($a and !$b or ($b and !$a)) and !(($a and ($b and $b or $b or !($b and !(($b or $b and !$a and $b and !$a) or $a or !($b) or $a or !$a and $b)) and !$a)))",false),
    ("!$a and !((($a or !$a) or ($a) or !$a and ($b and !$b or !($a and !($b) or $b) and ($b)) or !$a or !$a or ($a or ($a or !$b) and ($a or !$a) and !$a and $b and $a)))",false),
    ("!$b or $b and !($a or !$b and $b or !$b and ($b and $a and $b or !$b) and !$a or !$a or $a and !$b and !($b or $b or $b or !($a) or !$a) and ($b and !($a)))",true),
    ("$b or $b and !(($a or !$b and !$b) and $a or !$b and ($b or $b and !($b and ($a or !($b or !($b or !$b or !$a) or $a or !$a or $a) and $a or $b and $a))))",false),
    ("($a and ($a and $a or $b or !$b or !$b or ($b or !$a and ($a) or $a) and ($a) or $a or $b) or ($a and !$b and $b and !($b or !$a and !$b and $b) and ($a)))",true),
    ("!$b or !$b and !($a or $a or ($a or $b or !$a and (($b) or $b or $a or !$b or !($a or !$b and !($b and !$a or !$a) or !$b) and !$b and $b or ($a and $b))))",true),
    ("$a or !$a and $b or !($b and $b and !$b or $a) or !($b and $b or $b or !(($b and !$b) and !$a and !$a or !$a) and !$a and !$a and ($a) or !($b or !$a) or $a)",true),
    ("!$b and ($b and !$b and !(($b or !(($a or ($b) and $a or $a and $b and $a or !$a) and !$b or !($b or $b or !$b) or $b) or ($b or !($a or !$b or !$b) and !$b))))",false),
    ("!($b and $b and ($a) or !$a or (($a) or (($a) or $b or $b) or ($a or !$a) or !$a and $a) and (($a and ($a or $b) or $b or !($b) or ($b or !($b or $a and !($a))))))",false),
    ("$b and !($b and !($b or $b and ($a) or !$a or !($a and !$a and $a) and $b or !$b or ($a and !$a or !$b or !$a) and !($b and !($b or !$a and !(($a or !(($a) and !$a)))))))",false),
    ("$b and !($b or $a or !$a or ($a and $b or $a and !$b or $b and !$a and $a) or ((($a and (($b and !$a and !$a) or !$b and !$b and !$a) and !$b and $b or $a))))",false),
    ("(($b or !($b or $a) or $a or !$b and !$a and $a or !($a) or $a and ($a or $b and !$a and $a) or $b or $a) or !$b) and $a and !($b or ($b and $b) or $b)",true),
    ("!($a or ($a and $b or !($b or ($a and $b and $a) or (($a and !$a) and !$a and ($b and $b) and $a or $a or ($a or !$a and ($a) or !$a) and !$a or !$a and !($a)))))",false),
    ("$b or $b or $a and !($b and !$b or $b or !(($b or $b and !(($b or $a and $b and $b and $a) or $b and !$b or !$b or !($b and $b) or $a) or $b and ($b))))",false),
    ("($a and !($a) and $a and !$a and !($b and !$a and !$a or !$b and $b or ($a or $b or !$b and !$a and !($a and $b and ($a or $b and !$b) or $a or ($a) and !($b)))))",false),
    ("$b or $b or !$a or ($a and $a and !$b or ($b or $b or $b or !($b or !$b) or ($b or !$a or !$b or !$a) or !$b and $a or !$b and !$a and !$a and $a))",true),
    ("!$b or $b and !($b or !$a or !(($b or ($b and $b) and ($b and !$b and $b or !$b and !$b) and $b and !$b) and !($b and $a or $b) or $a) or !$a and ($b or !$a))",true),
    ("!$a or !$a and $b or $a and $a or $a and !$b and !$b and !($a or ($a and (($a or !$b or $a)) and !($b) and !($b) or $a and !$a) and !($a) or (($b or !$a and !$b)))",true),
    ("$b or !($b or $a or ($a or ($b and $a) or (($a or $b and $a or ($a) or $b or !$a or $b) or !$b and ($a) or !($a or ($b or !($a and $a)) or $b or $b))))",false),
    ("!$b or !($b and !$a or $b and !$a and !$b and ($b and $a and !($a and $b and $a or !$a and $b and $a or $b) or !$b and $a or ($a or !$a or !$b or $a)))",true),
    ("!$b and $b and $b and !$a or !$b and ($a and $b and $b and !$b or !$a or !$a or !(($b or $b and ($b or !($a) and !$b)) and ($b or (($b and !($a) or !$a and !($a))))))",true),
    ("($a and $a) and !$a or $a and $b or ($b or !$a and !($b or !$b and !($a) or ($a and !$b or ((($b) or ($a) or ($b) or !$a)) or !$b or $a and !($a) or !$b)) or !$b)",true),
    ("($a and !(($a or ($b or ($b and $a) or !($a or $b) and ($b) or !$b) and !$b and !($a and $a)) or $a or ($a or $a or ($b and !$a or $a and !$b and !$a or $b))))",false),
    ("!(($b or !$b) or !($b and !$b) and $a and ((($b or $a and $b)) or !(($a or !($a and $b) or !$a or $a or $a and $b) and ($b)) and ($b) or ($b and (($b and !$b) and $a))))",false),
    ("($a or $a or !$b or !($b and (($b or !($a and $a) and ($a) or !$b and !$b)) or $b and ($b or !$a or $a and (($a or !$a and $a and $b or !$b and !(($b) and !$a))))))",true),
    ("!($a or !($a and !$b and ($a or ($a or $b or !($b or $a and ($b or $a and !$a) or $b or $a and !($a and !$a and !$b and !$b) or $b) or $a and ($b or $a)))))",false),
    ("($a or !($a or ($b or !$b or $a or ($b or !($a or $a or $a)) and $a)) and !(($a and !$b or $b or $b and $a and !($b) or $b or !$a or ($b or !($b or $a)))))",true),
    ("!$b or !($b and ($a and ($b and !$b and $a or !$b) and !($b) and !($a and $a and $b and $a or !($b or $b or ($a)) or !($b and $a and !$a or !$b) or $a) and !($b)))",true),
    ("(($a and $a and !$a and !$a and !$b or !$a and !$b or !($b or !$a and $b and $a and ($b and !(($a and $b or !($b or $b)) and $a and !$b or $a or $b and !$b)))))",true),
    ("!(((($b and !$b and !$a or !($a or !$a or ($b) or ($a and $b and !($a and !($b or $b and $b) or $b))) and !$a and ($a) and !$a and $a or (($a and $a) or !($a and $a))))))",false),
    ("$a or ($a or !$b or $b and $a or ($b or !$a or !$b and !($a or $a or !$a or !$a or $a) and $a and $a or ($b)) or $a and !$a and ($b or $b) and !$a)",true),
    ("(($b or (($b and $a or !$a and !($a or $b)) or ($b or !$a and !$a and !$b or !((($a or !$a) or !$b and $b) and !($b or !$a and !$b and !($b or !$b)) and !(($a or $a)))))))",true),
    ("!((($b or $b and !$b)) or ($a and !($b)) or !$a and $b and !($b or $b and $a and !($a) and !(($a or $b) or !$a or $b or !($b and !$b and $a) and !$a or !$a and $b)))",false),
    ("($a or $a and $b and $a or $a or !($a and !(($a or !$a and !$a and $a or !$a) or $b and !$b or ($b and $a) and $b or !$a and $b or !$b) or ($a)) or (($a)))",true),
    ("($a and $a and !(($b or !$a) and $b) or $a or $a and !$b or ($b and $b or ($a or !($b and !($b) or $b) and $a) and ($a or $a) and !$b) and !$b) or $b and $b",true),
    ("!($a and $a) or $a and $a and !$a and !$b or $a or $a or !$a or !($b or !$a and !$b or $a or $a or $a and !$a and $b and !$a or $b and !$a and $a)",true),
    ("!$a and !$a and !$b and $a and $b or !$a and $a or (($a and $a or !$a) or !$a and $a or !$a or $a) or !($b and !(($b or !$a or $b) or !$b and $b and $b))",true),
    ("!$b or !$b and $b and !$b or !($a or !($b) or $b and (($b and !$a and $b and $b or !$b and $b or !$a or !$a or ($b and !$a and $a or !$b or !$a or $a))))",true),
    ("!$a or !$a or ($a and $b and $a and !$a and !$a and $a and !($b or ($b and !$b and !($a and $a) and !$a) and ($b and ($b or !$b)) or !$a and (($a and ($b and $a)))))",false),
    ("$b and !$b and $b or ($a or !($b and !$b and !$a or !$b and $b) and !($a and $b or ($b and $a) or !$a and !$a or !$a and !$b and $a) and $a) and !($a and !($b))",false),
    ("($a or !$a and ((($a and $b and !$b) or !($b and $b or !$a or $a) and !$a) or !$b or $b and !$a or !($a and !($b or !($b or !($a and $b or !$b and ($b or $b)))))))",true),
    ("!$a or !$a and !(($a or ((($b or !$b or !$b or !($b and $b and $a) or !($a)) or !($b and !$b or !$b) and !$b and (($b))) and $b) or (($b and $a) or $b) or ($a and ($b))))",false),
    ("($b or ($b and $a or ($a and $a or ($b) or $b or $a)) or $a and $a or ($a and !$a or $b and !($a or $b or $b and ($b or !$a or $b and !($b) or !$a))))",true),
    ("!($a and ((($a and !$a or !($b and !$b and $b and !$b or $b and !$a and !$b and ($a) and (($b and !($a) or !$b) and !$a) or $b)) or ($a or !($a and ($b) or !($b)) and $b))))",false),
    ("!$a or ($a or ($b and !$b and !($a and !$a and $a and $a or $a or ($a) or !$a or !$b and !($a and !($a or $b or $b and !$a) or !($b and $a) and $a or !($b)))))",true),
    ("($b and ($b and $b or $b or $b and $b) and ($a and $b and $a and !$b and !$b and !$a or !$a or $a and $b and !$b or !$b) or ($a and !$b or !$a or $a))",true),
    ("(($b and ($b or !($b or $a) and !($b and !$b) and !$a or !$a and !(($b) and $a and !($a or !$b and !$a or $b or !$a and !($b and !($a) and $a) and $a) or !($b or !($b))))))",false),
    ("($a and $a and $a or ($b and !(($b and (($b and $b)) and !$a and $b and !(($a) or !$a) or ($b) or (($a or !($b)) or !($b) and !($b or $b) or $a) and $a and ($b) and ($b)))))",true),
    ("!$b or $b and !$a or $b or ($a or !$a and !$a and !$a or $b or !$b or $b) and $a and $b and !($a or $b and !$a and !$a or !($b or ($b and $a) and !$a))",true),
    ("$b and !$b and !$a or (($b and !($a or !($a or !$b and !$a or $b or $a and $b and $b or $b or $b) or ($a or !$b and $a and $a) or ($b) and ($a)) and !($b)))",false),
    ("$b and ($b and $a and $b or $a and $a and $b or $b or $b) and !($a and $a) and $a and !$b and $a or $a or ($b or $a and ($a or $b or !$b or $a))",true),
    ("!($b and !($b or !$b)) or (($a or (($a and !$b or ($a) and $b and $a) and !$a and $b or !($a and $b or !$b or $b and $b) or !$a and !$b and $b and $b and !$b)))",true),
    ("$a and ($a or !$a and !$b and $a and ($a or !$b and !$a) and $a and $b or !$b and !($a or $a) or !$b or ($a or !$b) and $a) or $a and !$b or $b or $b",true),
    ("($a and ($a) or !($b and !$b and $a and ($b) or ($a or !($b and $a or $b and ($b) or $b or $b or !($a or $a) and !$b or !($a) or $b or ($a) and $a) or !$b)))",true),
    ("$a and ($a or $a or !$b or $a and ($b or $a or !$a) or (($b and (($a and ($a and !$a) and !$b)) and !(($a or $a) and ((($a and $a or $b)) or $b or $a or ($a))))))",true),
    ("!$b and !($b and !$a and $b or $a and $a and $b or $b and $b and !$a or $b or !$b and $a and !$b or $b and $a) or $a and !$b and !$a or $a and !$a",false),
    ("!(($b or !($b and !($a and ($a and $a or (($a) and $a) or ($b or $b or !$a and !$b) and !($a and $a) and $a or ($b and ($b and !($a) or !$b or $a and $b or ($b))))))))",false),
    ("($b or $b and !$b or $a and (($a or $a or $a and $b) or $a and $b and $a and !$b or !($a or $b or !$a and $a or !$a or !$b and $a) and $a) and !$a)",false),
    ("(($a and !$a or $a or $a and ($b and !($a and !$a and $a or !($a) and $a) or ($a) and !($b and $b) and ($b) or $b) and $a) or !$a and ($a and !($b or !($b or !(($a))))))",true),
    ("!($b and !((($b and !$a and $b and !$b or $a and !$a or $a) and $a or $a) and ($a or !$b) and $b or !($a and !(($b and $b) and $b and !$a) and $b) or !$b or ($a)))",true),
    ("!$a and ($a and ($a or !($b) or (($a or ($a and $b and !$a and !($a or !$b) and $b) and !$b and !$b)) and ($b or ($a) or ($b) and ($b) or (($a and !$a) or $a and !($a)))))",false),
    ("$b or !($b and ($a or $b or !$b) or !$b and $a and ($b or !$b and !$b) or $a and $a or !$a or ($a and !$a or !($b and !$b and !$a)) or $a or $b or $a)",false),
    ("(($b or !$b and ($a and $b and !$a) and ($b and !($a and !$b or !$b) or !($a or ($b and $b and $a) or !$a and $a) or !$a and ($a) and $b or !(($a and $a or $b)))))",false),
    ("($b or !(($b and ($a and !$a and $b) or $b or $b or $b) and !$b or $a and $b or !($a and !$b or $a and !$b) and ($a and !$b or $a and !($a and !$a) and !$b)))",true),
    ("$b and $b and ($b and $b and ($b or !($b and !$b or $a or $a or !$a or !$b or !$a or !$a) or !$b) or $b or !$b or ($a or $b or !($a and !$b and $a)))",false),
    ("!($a or !$a or $a or $a or !$a and !($a and $a or $b and $a and !$b and !($b and $a and !$b or !$a and $a or $a and $b and !$b) and ($a or !$b or ($a))))",false),
    ("$a and !($a and !$b and !$a or !($b and !($b or !$b and $a or !(($a or $b) or $b or ($b or (($a) and $a) and !$b and $b or $b) and !$a and !$b) or $b or !($a))))",false),
    ("!($b and $b or !($a or !$b or ($a and $a or $a and !$b and !($b or $b and ($b)) or !$b) and $b) or !$a) or ($b or $a and $a and $b and !$a or !($a or !$a))",true),
    ("!($b or $b and !$b) or !$a or $a or !($a or $b or !$a) and $a or !$a and (($a and ($a and !$a or !$a or !$a) or $b or $b) or !$b and !($a and !$a or $b))",true),
    ("!((($a or $a and !($a or !($a or !$b) or (($b or !($b or !$b)) and !$b) and !($b and ((($b and $b or $b or $a or $b)) or $a) or $b or $a or !$b) and !$b and !$b))))",false),
    ("!$a or ($a or $b or ($b and !$a and !$b or !$b and !$a) or !$a or $a and ($b or !$a and !($a or !$b and ($a)) or !$a or !$a or (($a) or !$a) or $b or !($a)))",true),
    ("!$a and !$a or ($b or ($a and (($a and ($a or $a or !$b) and !($a and $a or $b or !$a or !$a and $a and $a) or $a) or !$b and !$a and $b or !($a or ($a)))))",true),
    ("!$b and $b or !$b or $a or ($a or ((($b or ($b or $a or !$b) or !$b) and $b and !$a or $b or $a and $a or !$a) and $b or ($a and !$a) or $a) or $b)",true),
    ("!$b and $b or !($a and (($a or $b and !($a and !($b and $b and !($b or !$b) or $b and $b) or !$a or $b) or $b) or $a or $a) or $b or ($b and !$b) and ($b))",false),
    ("($b or !$b or !$a and !($a or !$a and ($b and !$b or $a or !$b or !$b or !$a or $a or ($b and !$b and !$a) or !$a and !$b) or !$a and !$a or !$b and $b))",true),
    ("!($b or $b and !$a and !$b and $a or !$a or $a or !$b and !$b and $a or ($a or ($a) or !($a or !($a or !$b or !$b and !$b) and $b and ($b or !$a or $a))))",false),
    ("(($a or $a and !(($b or $a or !$a or !$a or $a and ($b or $a) and !$b) and !$a and !$a)) and !$a and (($a or !$a) and !($a and $a and $a or $b and !($b and !$a))))",false),
    ("!$b or !($b or $a and ($b or !$a and $a) or ($b or $a and !$b and ($b and !$a or $b and !$b and $a or ($b or !$b or !$a and !$b) or !$a) or $b or $b))",true),
    ("($b and !$b or (($b or $a or ($a and (($a and !($b)) or !$a and !$b and !$b or !$b) or !$a and ($b) or !$a or $b and $a and !$a or !$b or $b or !$b) and !$b)))",true),
    ("!($a or !$a and !(($a or $b and $b or $a or !$a and !$b and $a) or !$b or $b and ($a and $b and $a or !($b and $b and !$b or $b and $b and !$b or !$b))))",false),
    ("!($a and !$a and $a or !(($a and ($a) or !$a and ($a or !$b or ($a) or ($a and $a or $b and $b or $a and (($b and $a) or $b or !$b and $b and !$b or $a))))))",true),
    ("$b and !(($b or !($b and $b and !($b or ($a and !($a) or !$b or !$b and $a) or !$b or !($a or !($b or !$a or !($a and $b) or $b) and !$a and !$a) and !$a) or ($a))))",false),
    ("!$a and !$a or ((($a or !(($b) and ($a) or $a or ($b or $a or !($a or $b and !$a)) and ($b and $a and $a) and !$a or !$b or $a) or $a or $b and ($b) or !$b)))",true),
    ("!$a and $a and !($a and ($a) or $b and !($a and ($a) and !$b and !$b or !$b and ($a and !(($b) and $a or ($b and $a or $a and !($b or $a) and !$a or !$b)) and !$a)))",false),
    ("$a and !($a and !$b or ($a and !$b or !($a and $b or !$b or !((($b and !$b or $a or !$b) and !$b or !$a) or $a)) or !$b or $b and !($b) and $a) or !$b) and !$b",false),
    ("!$a or ($a or !$a or !($b or !$b or !($a and !$a and !$b) and $a) and !$b and $b or $b or !$a and !($b and $b or !($a) or $b)) or !($b and !$a or $b or !($b))",true),
    ("!(($b and ($b and !$b or !$b) or !$b and !$a or !($a) or (($a) or ($b or $b or $a and !$a and !($b or !$a and !$a or !$a and $b or !$b and !$a) and !$b or !($b)))))",false),
    ("$a or !($a or ($b and !($b and ($b and !$a or $b) or ($a or !($b)) or !$a or ($a) and $a) or (($b and ($b or !$a or !$b and $a and $b) or ($a or !($b and !$b))))))",true),
    ("($b or $b and $a) and ($b or ($a or !$b or ($b and !$b) or $b or $b and $b or !($b and $b or $a)) and !($b or $b or !$b and !$a and $a or !($a or !($a))))",false),
    ("$b and ($b and !$a or !$b and !($b and !($b or !$b or !($b or !$a or $b)) or $a and !$a and !($b and $b and ($b) or !$b or !$b and !$b and $b) and !($a or !$a)))",false),
    ("!$a or ($a or !$b and $a or ($a and !$b or $a and $b or (($b) or !$b) and $b or $a or !$a)) and ($a and $a or $b) and $b and !$a and $a or $a or ($b)",true),
    ("!$b and !($b or (($a or !$b and !(($a and !($b) or !$a and !$b or !$b and $a or !$b) or $b or ($a or !$a or !$a) and $b or $a and !$a or !($b or !$a or !($a))))))",false),
    ("(($a and $a or !$a or !($b and !$a or !$a or !$b and ($b and ($b and $b) or $b or !$a or !$b and (($b and !$a or !$a or !$a and !$b or !$a) and $a and !($b))))))",true),
    ("$a and !($a or $b and $a) or !(($a and $b or !$a or !$b)) or !$b or !($a or $b and ($b and $b and !($b) and !$a and !(($b and !($a or $a and !($b or $a or $b))))))",true),
    ("!($b or !$b or $b or !$b and !($b or !($a and $b) or !$a or !$b and !$b and !(($b or $a or !$a and $a) or !$a and $b or $b) and !$b and !$a or !$b and $a))",false),
    ("!($b and !(($b or !$b and (($b) and $a and !($b or !$a and !($b and $a or $a and !$b or !$a) and !$a and !$b and !$b or (($a or !($b and !$a)) or $b) and $a and ($b))))))",true),
    ("!($a and ($a and ($b and !($b or !($a or ($b) and $b or $b) and !$a or !($a and !$b and ($a and !($a and $b)) and $b and !($b and !($a) and $a or $b and $a and !$a))))))",true),
    ("($a and !($a or !($b or $a) and !$b and !(($a) and $a and $a) and !$b or !$a and !$a and $a and !($b and !$b or !$b) or $b or !$b or !($a or $b or !$a and !$b)))",false),
    ("$a or !($a or ($b and $b or !$b or !($b or !$a and $a and ($b and !$a or !(($a and $a) or ($b) or !$a and !$b and !$a and !$b or !$a and !$b or $a) or $b))))",true),
    ("($b or !$b or ($a or $b and !$b or !$a and $b or !(($b or $b or !$a) and $b or $b) or $a or $b or $a or $a or !$b or !($b and $b or !$a and $a)))",true),
    ("!($a and $a or $b or !$a and ($b or !$a or ($b or !$a) and !(($b or !$b and $b) and $a or !($b and $b) or !$b and $a or !($a) or $a or $b and !$a)) and !((($b))))",false),
    ("!($a or ($a and $a or $b or !($b and !$b) and $b and $a and !($a or !($a) and !$a or !($a and ($b and $a) and !$b and $a and !($b or $b)) and !$b and !($a and $b))))",false),
    ("$b or ($b and $b and !$b) or (($b or !$b or !($a or $a or !$b or $b and !$a) or !($b or $b or ($a or $b and !$a and ($b and !$b) or !$a and !$a or !$a))))",true),
    ("!($b and $b or ($a or !$b and $b or !($b and $b) or !$b or !($b and !(($a or $a) and $a or ($b and !($a or $b and $b or !$a or $b and $b) or ($b) and !$a)))))",false),
    ("($b and !($b and $b and !$b or !($b or !$a and !$b) or !$a) and $a or !$b) and !$a or !$a and $b or $b and $a and ($a and !($a or !$a and !($a and ($b) or !$a)))",false),
    ("($a and !$a or (($b or !$b and !$a and !$b and (($a or !$b or $b or $a or $a) and !$b) or $b) and !($b and !($b or $a) and $a and !$b or ($a) or !$a)) and !$a)",false),
    ("($a and ($a or $b or $a and $a and !$a and $a or !$a or !$b or !$b or $a and !$b) or !($b or $a or !$b and $b and $a and !$b) or $b and $b and !$b)",true),
    ("($a or !$a) or !$a and !($b or !$a and !($a and !$b or !($b and ($b or !$b and !$b) or !($b and $b) or !$b and !$b) or $a or !($a and !($b and $b) or !(($a or $a)))))",true),
    ("!($a and !($a or !(($b and !$a and !($a) and !$b or !($a) and ($a and $b and $a and ($b and ($b) or !$a) and !($a) or $b) or ($b or !$b) and $b and (($a and $b or $b))))))",true),
    ("$a or !$a or !($a or !$a or $a or !$b or !$b or !$b and $b or $b or !($b or !$a) and !$a and !$a or !$b) or $a and !$b or !($b and !$b and !($a or !$b))",true),
    ("$a or !(($a and !$a and $b and !($b) and ($a or $a and $b or (($a and $b) or !$a or $b) and $a or $a or ((($b or !$b) and !$a or !($b)) or $b or !($b) and ($a)))))",true),
    ("!$b and !(($b and !($a and $a and $b or !$b or $a and !$a and !$b or !($b or !$a and $b and !$a and $b) and $b or $b and $a and $a) or !$a) or $a and !($b))",false),
    ("$a or !$a or !($a or !($a or $b or !$a or $a and !($a or !$b or !$a and $b or !($b or $a and $b and !$a and $a) or !$a and $a or !$b) or $a and $b))",true),
    ("($a or (($a and !$b or $a and $b and $a or ($a or !$a) or $a) and !($a or !$b and $a and !($b or !$a or !$a and $a) and !$b or $b) or !$b and ($b or ($b))))",true),
    ("$b or !$b and $b and ($b or !$a and $a) and ($b or !($b or $a or $a) and !($b and !$a and ($b and !$a and ($b or $b) and !$b) or !$a or ($a) or !$b or !$b))",false),
    ("$a or $a or !$b and $a and $a or !$b or ($b and $a or !$b and !$b or !(($b or $b or !$b and $b or !$a)) and !$b and $b and $b or ($a or !($b or $a)))",true),
    ("!($b or !(($b and !($b and !$a and $b or $a)) and $a or (($b or $a or !($b) or $b) or $a and !($a and !(($a) or !($b) and !$a and !($b) or $b or $b and $a or !$a)))))",true),
    ("!$b and ($b or !$b or !($b or ($a or !($b and !$b) or !($b and $a and $a or !($a) or ($b or $a and $b or ($b) or ($a and $b and $a) and !$a) and !$a and !$b))))",true),
    ("($b or !$b and !$b or !$b and $b and $a and !$b and $b and !$b or !$b) or !(($a or !($b and !$a or !$a) or !$a or !$b or $b and !(($a or (($b and !$b or !$a))))))",true),
    ("!$a or !$a and !(($a and !$a or $b or ($a and $b or $a) or $b or $b or !$a and ($a or $a or ($a and !$a or $a) and $a) or !((($a or $a and !$b or !$a)))))",false),
    ("(($a and $a) and !$b and $b or !$a or ($b and !(($b and $a and $a or !($b or !$a and $a)) or $b and $b and !$b or $a and !$a and $a and $a and !($a or !$b))))",false),
    ("!$b and $b or (($a and ($b or $b or !$b) and !($a or !$a or $a and !($b or !$a) or ($b and !$b) or !$a or $b and !(($b and !($b) or !$b and $b and !($a and $a))))))",false),
    ("!($a or $a and ($a or !$b and !(($a and $b and !($b and !$a) or !$a and !(($a or !$a) and !$a or $a and !$b or !$a or !($b) or !$a) and ($b) or !$b) and ($b or ($b)))))",false),
    ("!$a and $a and $a or !$a and ($b and !($a or !$b or !$a) and !($a or $b or (($b or ($a or !$a) or !$b) or !$b and !$a) or (($a or !$a and ($a) or !$a) and $b)))",false),
    ("!$b and $b or !($a or ($b and $b and !$b or ($a or !($a and $a or $a) and $a or !$b and !$a or $a) or !($b or !$a and !$b and !($a or !$a and $b or !$b))))",false),
    ("!($b or ($b or (($b or !$b and $a or !$a and !$a and !$b and $b or $b)) or (($a or $b) or (($b and $a and $a) and ($b)) or !$b and !($a or $b or $a and $a))))",false),
    ("!$a and !($a and !(($b) and !($b) or $a or !($b and !($b or !$b or !$b) or !($a and !($a))) or $a or !($b and !$b or ($a or ($b or ($b)) or !$a or !$b) or !$a and !($b))))",false),
    ("!(($a or (($a and !$b and (($b) and ($b and !($a or !$b) and !$b) and !($a or ($b) and !$a or !$a and $b) and !($b) and !$b)) and ($b) or (($a and $b) and $b and !$a or !$a))))",false),
    ("($b and !($b and $a and $b and !$a or !($a and $b and !($b and $b and $a or $b and !$b and $a and (($b) or $a and ($b) or $a) and $a) or !$a or $a) or !($a)))",false),
    ("!$a or $a and ($a and !($a and !($b or !$b and $a or $a or ($b and $a))) or $b or ($b and !($a or !($a or !$b and $b) and $a or $a and !$a) or ($b and (($b)))))",true),
    ("!$b and !$b or !($a or $a and !$b and !$a or ($b and $a or !($a and !($a or $a) or $b or !($a or $a) and $a or !$b or $b or $a or !$a or $b or !$a)))",true),
    ("!$b and ($b or !$b and !$a or $a and !($b or $a or (($a and !$a) or !($b or !(($a) and !$b or $a or $a) and $a and $b or $a and !($a or !$a or !$b or !$a)))))",false),
    ("!(($b or ($b) or (($a and !($a) or !(($b or $b) or !($a and !$a or !$b or !$a)) or $b and !$b) or ($a or $a) and $a) and ($a and !($a or !($b and $b) or ($b and !$b)))))",true),
    ("!$a and $a or $a or !(($b and $a and $a) or $b or $a or !($b and $b or $b or $a) or !$a and !($a and !($b and $b or $a) and ($a and !($b or $b) and !$a)))",true),
    ("!($b or $b and !($b and ($b and !(($a and !$b)) and $b and ($a or !($b) and $b) and ($b) and $b or !$a and $a) or !($b or !$b and $a and !$b and $a or !($b) and ($a))))",true),
    ("(($a and $a and !$b and !($b and !$a and $a) and !($b or $a or !$b and $a) or !$b and $a or !($a or !$b) and !$a or !$a or ($a and $b or ($b) or !$a or !$b)))",true),
    ("($a and $a and !($a or $a) and $a and !$b or ($b) or !$a and !$a or $b and !$a and !$b or $b or ($b and $a and !($b and !$b) and ($b or !$a or !($a or $b))))",false),
    ("$b or ($b or !($b and $a) or !((($a or $a) and $b) and $b) or !($a and !(($a and $a and $b and !$a or $b and $a and !($a or !($a) and $b and $a) or !$a) and $b)))",true),
    ("!(($b or $b and !$a or $a and ($a or $b) or !($b and $a or !$a and !$b and !($b) and !$a or $b and !($a and (($a or $b) or $a) and !$a or $b and !$a) or !$b)))",false),
    ("!($b or $b or !$b) or !($b or !$b) and !($a or ($b or $a) or $a and $b or !$b and ($a or $a) and !(($a and !$a)) or $a and $a or ($b or $a and !$b and !$a))",false),
    ("$b or !$b or !$a and $a or !$a or !$a and $a or $a and ($b and !$b and !$a or !($b or $a or !$a) and $b and !$b and $b or $b or !$b and $b or $b)",true),
    ("($b and !(($b and !($b or !$a and $a) and $a or (($b or !$b and !$a and ($b or (($b or !$a)) and !$a) or !($a or !$b or $a or !$b)) or !$a and !($a or !$b) and ($a)))))",false),
    ("$b or ($b or $a and ($b or !(($b and !$b and $b) and !$b and $b and !($b or ($a or !($a and !$a or !$a and $b))) and !$b or !($a and !$a or ($a and $b and !($a))))))",false),
    ("$b and (($b and ($b) or $b) and $a or $a and !$a or !$a and !$a or !(($b) and ($a and $b or $a or $b and $a or !$b) or !(($b or $b or !$b and !$a or !$b))))",false),
    ("($b and $b and $a and !$b or !($a) and !$a and !$b and (($a or !$a and !$a or !($b and ($a or $b) and $a) and $a) and $a or $b and !$a and !$a or ($a and $a)))",false),
    ("$a and (($a and !($a) or $b or $b or $a and !$b and $b or !($b) or $b and ($b or !$a) and $b or $a and !($a and !($a) and ($a or !$b)) and !$a and !$a and !$a))",true),
    ("$a or ($a and !($a or !($a and !$a and !$b) or !($a or !(((($a and !$b)) or $b and !$b) and !$b or $a) and ($b and !$b and ($a or !$b or ($a or $a or ($a)) or !$a)))))",true),
    ("($b or !$b or !$a and !$b or !$a) and ($a or $b and $b and $a or $a or $a and !$a and !(($a or $a or !$b or $b) and !$a and $b) or !($a or $a and !$b))",true),
    ("$b and !$b or (($b and !$b and !$a and ($a) and !($a or $a or ($b and !$b and (($b and !($a) or !$a or !$a or $a and !$b) and !($b) and !(($a) and ($b or !$a or !$b)))))))",false),
    ("$a and !(($a and !$b or $b) and !$b or !$a or !$a or $a or $a and $a and !$a and !($b or $a and $b or !($b and !($a and ($a and $b) or ($b and !($a and $b))))))",false),
    ("($b or ($b and !(($a or $a or ($a) and !($b) or $a and !(($b or !$a or $b or $b and !$b or (($a or $b)) and !$b) and !$b or !$a or ($b) or !$a or !($a or !$a))))))",false),
    ("$b and $b or $b or $a and !$a or !$a or $b and !($a and ($a and !($b or $b or !$a and !$b or $a and $a or $a and !$b or !($b or !$b and $a or $a))))",false),
    ("($a or !($a and !$a and $a or $a) or !$a and ($a or $a or $a or $a or !$a or $a or !$b and !($a) and $b or !($b and !$a)) and !($a or !($a or !$a) and !$a))",true),
    ("$a or ((($a or $b and !($b and !$a or !$a or $b or !$b or $a) or $a and ($b or ($b or !$b and $b) or $a) or $b or $b) or ($a) or !($a or ($b or !$b))))",true),
    ("(($a or (($a or !($a or $b and !$b and $b) or $b) or ($b)) or ($b and $b and !($b) and !($a or !$a and !($a)) and $b) and !$a or !($b or !($b or !($a) or ($a and !($a))))))",true),
    ("!$a or ($a and $a and ($b or !($a or $b and !$b and !$b and $a) or !$a and !($b or $b) or ($b or ($b and !$a and !$b) and !($b and !$a or !$b and $a or !($a)))))",false),
    ("($a and !(($a or $a) and !$b) and !($b and !$b and !($b or !($b and ($b or !$a) and $a or !$a) and $b or ($b and !$b) or $b and ($b) and ($a) and (($a or !$b)) or $b)))",false),
    ("$b and $b or !$b and $a or ($b and ($a or !$b and $b or !$a and !$a and !$a and $a and !$b or !$a) and !$b or ($b or !$a or !($b) or !$b or $b and $b))",true),
    ("!($b or ($b and !$b or !$a and $a and !$b or !$b and $b and $a or $a or !$a or ($a) or $a and $a and $a and !$b) and $a and !(($a or !($b) or $b or $b)))",true),
    ("$b or $b or !$a and !$b or !($a and !$a or !$a) or !$a or !(($a and $a or $b or $b or $b or (($a or !$b and $a and !$a) and $b or $a or ($b or $a))))",true),
    ("$a and $a and !($b or $b and $a or !($b and !$a or $a and !($a and $a) and $b or $a and $b and !$a or !(($b or !$a) or ($b and !($b and !$b or !$a and !$b)))))",true),
    ("$b or !$b or ((($a or !$a or !($b or !($a or $b or !$a or !($a) and $b or !$a)) and ($b and !$b and !$b)) or $b) and ($a and $b or !$a or $a or !($b and ($b))))",true),
    ("!$b or ($b or $a or $b) or !$a or !$a and ($b and !($a) or $b and !$b or $a) and !($a and !($a and !$b or !$a and ($a and $b or !$b or $b or (($b and !$b)))))",true),
    ("!$a and ($a or $a or !$b and ($a and !(($a and !$a)) and $b or $a and $b) and $a and !$a and !$b and !$b or $b or !$b or !$a and $b or !($a and !($a or ($a))))",false),
    ("!($a and $a or (($b and $b) and !$b) or $b or $b and $a and ($b and $b and $a and $b and !$b or !$b and !($a)) and ($a or !($b or !($b and $a) and !$a and $b)))",false),
    ("!((($b or !($b or !$b and (($b) and !(($a)) and !$b or $b) and $b) and !$a or !($b or !($a and ($b) or $b and $b or ($b or $a) and $b and !$b and $a or $a)) or !$b)))",false),
    ("($a or $a or !(($b or $a and ($b and !$a) or !$b and !$a or ($b)) or !$b or $a and !$b or !($b or $b or $a or $b and !(($a or !$a) or ($b or $a and !$a)))))",true),
    ("!$a or !$a or $a and !$b or ($b and !$b or ($a and $a or !$b) or !$b or !$a and !(($b and !($a and !$a) or !$b and $a or !$b) and ($b and !$b and !$a) and !$b))",true),
    ("$a or $a or ($a or !$b and $b and !$b or (($a or $a or !$a and $b or !$b or !($a or !$b) and !$b) or $b or $b or $b and !$a and !$a and !$b or !$b))",true),
    ("!($b or ($b and !$a and !$a) and !$a or !$a or $b and $b or !$a and $a and ($a and !($a) and !$a or !$a or !($a and !$b) or $b and ($a and !$b)) or ($a or $a))",false),
    ("!($b or !$b) and !$b or !$b and !(($b and !$a and !$a or ($b or ($b)) and ($a or !$a) and !$a or $a or $b and ($b and ($b or !$b and !$a) or $b or ($b or !$b))))",false),
    ("!$a and !$a or (($a or $b or $a or $b) or ($a or $a) and !($a and !$a or $a and !$b and !($a or $a and !$a and !$b and !$b or $b and !($a and $a or ($b)))))",true),
    ("((($a and !$a) and !($b) and !$a and $b or !($a) or ($b and ($a or $a or $a)) or !($a or $a and (($a or !$b or !$b) and ($a) and !$b and !(($a or $a and !$b and ($a)))))))",false),
    ("((($a and $a) or $b or !$b and $a or !($a and $a and ($a) or $b and !($b and $b) and !$b or !$b or ($a) and ($a and ($a and !($b) or !$a and $b) or ($a) or !$a))))",true),
    ("!$b or !$b and !$b and !(($b and !$b and $b and !$a and $a and $a or $b or !$b or !$a or $b and $b or !$b and !$b or !$b or $a or !$b) and $b and !$a)",true),
    ("$b or !$b or ($a and ($a and $b and $b or $a and $b and !$a or $a or $a and !($b or !($b and !$b and $b)) or $b or $b and ($a and $b and !(($a or $a)))))",true),
    ("(($a and !$a and !(($a) or !$a) or !$b) and ($a) and ($b and !($b and !$b or ($b or !$a or $b) or !$a or !$a and (($b and $a) and $a or $b or $a and $b) or !($a))))",false),
    ("$a and ($a or !$a and !$a or !($a and !($b or ($a or !$a or ($a or $a and ($b and $a) or $a and !($a) and !($b)) and !$a and !$a)) or ($a and ($a or !$b and ($b)))))",true),
    ("$b or !$b and $a and $b and !($b or $b and ($a or !($a and !$b and $b or $b) or !(($b) or $a or !$b and !($a and !$b or $b) and $a and !$b) or !($a or $a)))",false),
    ("$b or !$b and $a and !($b or !($b or !((($a or $b or $b) and !($b or !$b) or !$a or $b or !$a and !$b) and $a or $b) or !$b and !$a and !$b and $b or !$a))",true),
    ("!$b or $b or $b or ($a or ($b) or !$b and ($a or !$b or !$b or $a or $b and !$a or $b or !$b or (($b and !$b and $a or $b) and $a and !$a and $a)))",true),
    ("!($b and ($b or $b) and !($b or !($b) or $a or $b or !($b and !(($b or !$a or ($a and !$b and !$b or !$b or !($a) and $b or !($a)) or $b or $b) and (($a or (($b))))))))",true),
    ("!$a or $a and ($a and $a or $b or !$a or !$b or $a and $a or $b or !$b and $a or !$a) and !$a and !$b or !$a or ($b or $a and !$a or $b and $b)",false),
    ("!$a or $a and ($a and !$a or !($a or $a and $a and ($a or $a and $b and !$b or !$b or $a or !$a and !$a and $b) or ($a and !$b or !$a and !$b) or !($a)))",false),
    ("!$b and $b or !($b and !($b and !($b and !$a and $b and ($b and $a or ($a or !$a and ((($a and !$a) and !$b and !($a) and $b) and !$b or !($a and !$a) or !$a) and $b)))))",true),
    ("!$b or $b and !$b or !$b and (($a and $b and !$b)) and !$b or !$a or !($a and !($b and !$b or $a and !$a or !($b or $b or $a and $a and ($b) and $b or !$b)))",true),
    ("($b and $b or $a and $a or !$a) and !$b and !($a or !$a and $a and $b and !($a and !$a or !$a and !$b or !($b and !$b and !$b and $b) or $b and $a and $b))",false),
    ("($b or (($b) or (($a and !$a) and $b) or !($a and $b)) or !$b or $a or $b and ($b and $a or !$a or $a) or ($b and !$b) and (($a or ($a and $a or !$a and ($b)))))",true),
    ("$a or ($a and !$b and !$b or ($b or $b or !$b or !($b and ($a and $a or !$a)) and $a and $a or !$a or $a) or $a and !$b and !$b and !$a or !$a and !$b)",true),
    ("!$a and $a and $a and !$a or ($b and !($b or !($a and !($a or !$b or $a or $b) or ($b and $b and !$b and !$a or !$b or !$a and !$b) or !$b and $a and ($b))))",false),
    ("($a or !(($a or ($a) and !($a) and !$a and !$b and !$a or !$b and $b or !$a) or $a or $a and !($a or !($b and !$a or ($a) or !($a or $b)) and !($b or !$a or !$a))))",true),
    ("!$a or $a and ((($b or $a and $b) or !$b and !($a and $b or !$a) and !($a and !$b or ($b and !$a) and !$a or !$b) and $a and $a or $b and ($b and !($b) and !$a)))",false),
    ("!$a or !$a and !$a and !$b or !($a and !$b or !$a and !$a or $b) and !($a or !$a) and !($b or $a and !$b and !$b and $b) and !$b or !$b and !$a and $a or !($b)",true),
    ("$a and !($a and !($b and !$a or !$b and $b and ($b or (($b or $b and $b) and !($a or $a)) or !$a) and ($a and ($a or !($a or !$a or $b and $a or $a or $a)))))",false),
    ("$b and $b or !$a or !$b and !((($b and $b and !$a or $a) and ($b and $a) and $b) and ($b or !(($b and !$a and $b) and $b and !($a and $a or $b and !$a or $a))))",true),
    ("!($b or !$b and $b or $a and !$a) or $a and $b or $a or $a and !$b or $a or !$a or !$a and !$a and !($b and !$a and !($b) or $b and !$a and !$a or !$a)",true),
    ("!($b or !$b and !$b or $a and !($a and $b) and $a) or ($b and ($a or !$b and $a or !$a) or $b and !$a and !$a and !$a or $a or $b and $a or ($a) or !$b)",true),
    ("!$a or !($a and !$a and (($a or (($b or !$a and $a) and $b and $b) and ($a and $b or !$a or !$b) or $b or !(($a) and $b or ($a) and $b or $a)) and (($a and !$a))))",true),
    ("!($a and !($a or !$a or !($a and ($b or !$b and ($a and ($a and !$b and ($b and !$a or !$a) or !$b) and $a and !$a) and !($b) and !$a and !$b and ($a) or !$b and ($a)))))",true),
    ("$b and !$b or !$a or $a and !(($b and !$a) and ($b and $a and $a and $b) and !$b or !$a or !$a and ($a or $b or $b or $a and $b and !$b) or ($b or $a))",false),
    ("!$a or (($a or (($a and !$a) and ($b and $a or !$b or ($b and !$a and !$b or !$a) and $b or ($a and $b) and ($a and !$b and $a or $b) and $a or $a and $a))))",true),
    ("!$a or ($a and !$a or $a or !(($a and !$a and !$b)) or $b and (($b or $a) and $a) and !$a) or !($b and ($a or $b and !$b or !($a and ($b and ($b or $b or !$a)))))",true),
    ("$b or !$b or $b or !$b or ($b and $b and ($b and !$b or $b or !$a) and $a and $a or !$a and $b or !$a and $b and !$a and !$a or !$a) and !$a or $a",true),
    ("!$b and !($b and !($b and $b) or ($a and $b or !$b) or !($b or ($b and !$b or !($a and $b) and $a and $b or $a and ($b) or !$b and !($a or !$b or !$a and $b))))",false),
    ("$a and $a or $b and !($a or !$b) or $b and ($a and $b) or !$a and $b or !($b and $a or (($a and $a or !$b and !$a and !$b and $b and $a and $b and $a)))",true),
    ("!$b and !($b or ($a and $b or ($a or !$b) or !$a and ($a or !($b or $b or $a and $a) and $b and ($b) or ($a or !($a) and $b or ($b and $b)) and !(($a and !$a)))))",false),
    ("!$a or $a and ($a or !$a and !($a and !$a or $a or !$a and !($a and !$b or !$b and ($b and $b and !($a or !($b or $b) or ($a) or !$b or !$a) and ($a or $a)))))",true),
    ("!($a or !($a or $b and !($a or ($b) and !($b and $b) and !$b) or ($b) or $a and ((($b or ($a) or !($b and !$b and !$b) and !$b and !$b or ($b and !$a))) and ($b and !$b))))",false),
    ("!$b and ($b and ($b or $a or ($b and !($a or !$b and !$b)) or !(($a or $a and $b) and !$b or ($a or !$b or $b and $a and !$a or !$a and $b) and $a or !$b)))",false),
    ("!$a or (($a and ($a) or $a or $a or $a) or !($a and $b) or !($b and $a or !$b and !(($a) and $b and !$a and !$b and ($b and !$a) and !$a or !($a and ($a or !$b)))))",true),
    ("$a or $a and (($a and !$a or ($a and $a or (($b and !($a or ($a)) and $b or !$a) and !$b and $a)) or !$a and ($b) and !($b) or ($a) or ($a) or !($b or $b or ($a))))",true),
    ("($b or !($b or !($b) and !(($b or ($b or $a or !$b or !$b or $a) and $b and !$b or (($a) and !$b or $b or ($a and !$a and !$b) or $b and $b and !$b) and !$a))))",false),
    ("!($a and ($a or ($b or !$a) and (($a or $a or !($b or ($b or !$a or !$a) or !$b and !$a)) and (($a or !$a and !($b or !$b and !($b or !$b or $b) and !$b or !$b))))))",false),
    ("!$b or ($b and !$b and !($a or (($a) and !$b) and !($a or !(($b and !($a) or !($b or !$b or $b) and $a or $b) or $a)) or !$b) or !$a or ($b and (($a and !$a) and $b)))",true),
    ("($a or !$a or $a and !$a) and !$a or !($b or !$a) and !$b or ($b and !$a or $a and $b or $a or (($a or !$b or ($b or $a and ($a or $b and !($a) or (($b)))))))",true),
    ("(($a or !($a and $a and !$a) and ($a or !$a and !(($b and ($b and $a) or $b or !$b and !$b) or !$b or !$a or ($a or !($a and !($b and $a) or !$b and !$a) and $b)))))",true),
    ("!($b and $b and $a) or ($a or $a and ($a or !($a and ($b or ($a or $a or ($b)) or !($b) or $b and !$a and ($b and !$a or $a and !$a) or ($a or $b and !($b))))))",true),
    ("$a or !(($a or ($a and !$a or ($b or !$a or ($b or !($a or $a and $b or !$b) or !$b and !($a and !$a and $b) or !($b and ($a) or ($a and ($a)) or $a) and !($b))))))",true),
    ("!$a or !($a or !$a and !($a or $b and ($b or !$b and $b) and $b and $b or ($b and ($b and $a or $b) and $b or $b) or !($b) or $a and !$b and ($a and $a)))",false),
    ("$a and !($a and $b or $b or ($b and $a and !$a) and $b or ($b or ($b or $a or !$a) or !$b and !$b or $b)) or ($a and !(($a and $b) or ($b or !$b and $b)))",true),
    ("($b or (($b and !$b or (($b and $a) or !$b) and $a) or (($b or $a and $a and !($b) or !$b or $a or !$a or $b or $a and !$a and !$b and !$b or ($b and $b)))))",true),
    ("($b and !($b or ($a or $a and $a) or !($a and !$b and $a or $b or !$b)) and !($b or ($a and !($a or $b and ($b) and !$b and !$b and ($a) and $b) and !$a and $b)))",false),
    ("!($b and !($b and $b or (($a and $b) or !($b or !$a or $b or !($a) and !($a or !$b and !$b and !$a or !$a))) or !$a) and !$b and !(($b or $b and $a or !$a and !$b)))",true),
    ("!$b or $b or $a or $a and $a or $b or !($a and !($b and !$b and !$a) and !($a or !($b or !$a and ($b or $a) and ($a and $a) and $a or !$b) or !$b) and ($b))",true),
    ("($b and !($b or $b or ($b or !$b) and (($a) or $a) or !$a) or !(($a) and $a and $b and (($b) or $a and $a) and $a) or !($a and !$b or !(($a and !$b and ($a) or $b))))",true),
    ("$a or $a and !($b and (($b or !$a and !$b or ($b or $b and !$a or ($b and !($a and ($a or ($b and !($b)) and !$b)) or $b) or !$b and $b or ($a and !$b and !$a)))))",true),
    ("!(($a or !$a and !$b) and $b and (($b and ($a or $b) and !($a or !($a) and $b or $a) or $a) and !$b) and $a or !($a and ($b and ($a and !$a and (($b) and !$a) or ($b)))))",false),
    ("$a and $a or ($b or ($a or !$a or !($a and !$b) and !$a or (($a and !$a) or !($b or $b or $a) or !$a and ($a or $a) or ($b and $b and !$a) and $b and $b)))",true),
    ("$b and $b and !$a and !$b or !($b and ($b) or (($a or $b or ($a) or !$a or !$b and ($b and !($a or !$a or !($a) and !(($a) and !($b) or !$a and !$b) and !$b or $a)))))",false),
    ("(($a and !$a and !$b)) and !($b or ($b and !$b and !($a) and !($b or ($a or !$b) or !$b or $a) and $a) and $b or !$b and !($a and ($a and !$a and !$a and $b and !($a))))",false),
    ("!$b and $b and $b or !($b or $a or ($b and $a and $a and $b) and $b and !$b) and !($b or !$a or $b and !(($a and $a or !$a or $b) or !($a and !($a or !$b))))",false),
    ("$a and !(($a or !$b and !($a or !$b or !(($b) or !($b and !$a)) or !$a and !(($a or $a and !$a) and !($b and !$a) or ($a and $b) or !$b and ($a and !($b) or $a and ($a))))))",false),
    ("(($b or !$b and !($b) and $a) and !$b) and !$b or !(($a or !($b or $b) or !(($a) and ($a and !$b and ($a) or ($b and !$b or $a or !$a)) and ($a) or !$a and !$a or $a)))",true),
    ("$b and $b and !$b or ($b and !($a or !$b or !$a) and !($a and ($a) and !(($b and $b and !($b) and !$a) or ($b or ($b and !$b or !($a or !$b) or $b)) or !($b and !($b)))))",false),
    ("($a and ($a and !$b and !$b or !$b and !(($a or !$b and ($b or $b or !$b) or !$a and $a)) and $a and !$b and !$b and !$a or $b) or ($b and ($a and $b and !$b)))",true),
    ("($a or $a and ($b or ($b or !(($b or $b) or $b) or ($b) and (($b) or !($a and !$b) and ($b) and ($a)) and $a) or $a and !($a and !(($a) and !$a and $b) or $a and $b)))",true),
    ("$b and !($b and ($a) or !$a and ($b and $b or !$b or $a or !($a or $a) or ($a and !$a or $a and $a or ($b or ($b and !($b) and $a) or !$b and (($b and ($b)))))))",false),
    ("($a and ($a and $a and (($b) or $b) or $b and !$a or !($a) or $a or !$b)) and !$b or $b or !$a and !(($b or !$b and (($b and !($a) and ($a or !($a or !$a or !$b))))))",true),
    ("!$b or $b or !$a or ($a and ($b or !$a or !$b and $a) and !($a and $a and !$b and $a or $a or $a or !$a and !$a and $b) or !$b or $b and $a or !($b))",true),
    ("!$b or $b or $a and ($a and ($b and !((($b or !(($b) and ($b and !$a) or $b or $b) or ($b)) or ($b or ($a) or (($a and !$b or !$a and !$b) or !$a or !($b) or !($a)))))))",true),
    ("!$b and $b or !$b and $b and ($b and $a or $b and !$a or ($b or !$b or $b or !$b and $b or $b or !$a or !$a) or !$b and !($b and !$b or !$b and $a))",false),
    ("$b or !$b and !$b and $b and ($a and !($b) or ($b or !$a or ($b and !$b and !$a or $a and !$b and $a) and $b or ($a or $b or !($a and !$a and $a) and $b)))",false),
    ("!((($a or !($a or !$a or !$a and ($a) or $b and !$b or $b or $a) or !(($a or ($b or !$b or ($a or $b) and $a or !$a and !($a or !$b) and !($a))) and !($a and ($a))))))",false),
    ("!$b and $b or !(($b and ($b and $a or $b)) or !$b or $b and ($b) or !($a or !$a and $a and $a or !$b or !$a and $a or !$b) or ($a and !$a or $b or !$b))",false),
    ("($a and (($a or !$b and ($b) or $b) or $b or !$b and !($a and !$a and !$b) or $a or !$a and !$a and !(($a or !($a and !$b and $a) and $b or $a and $b) or !$b)))",true),
    ("!(($b or $b or $b or !$b and $b) and $a) or !($b or ($a and !$b and !$b and ($b) and !$b or !($a) or !$b) or !($b and $b or !$b and !($b and !($b and $b and !$a))))",true),
    ("!$a or (($a and ($a) and $b and !($a) or !($b and $b or $a and !$b or !$b or ($a) and !$a or !$b) or !$b and !$b or (($a or !($a) or $a) and ($b or $b and ($b)))))",true),
    ("$b and $b or !$a or (($b and ($b and $a and $b or $a and $a and $b and !$b or $a) and (($a and !$a and !($b) and !$a or !$a) or !$b or $b or $a or !((($b))))))",false),
    ("!($a or $a and $b and $a and !($b or !$b or !$b or !$a and !$a or !$b) and $a) and ($b or (($b and ($a or !$a and !$a or !($b and $a or !$b and !$a) or !$a))))",false),
    ("!$a or !$a or !$b or !$a and !($b or !($b and $b and $a) and $b and !$b and !$b or $a and $b and ($a and !($b or !$b and !$b and !$b and !$b or !$a and !$b)))",true),
    ("$a or !($a and !$a or !$a and $b and !$b or (($a or !$b and $a) or !($b or $b or !$b) or !$a or $b and !($b or ($b and !$b or $b) and !$a and $b or !(($a)))))",true),
    ("$b and !(($b or $a) and !$b or !$a or $a or $a and ($a and $b and !($a) and $b and !(($b or ($b and $b and !($a and $b or !($b and $a)) and !$a or !$b) or $a))))",false),
    ("!$b and (($b and $b and ($a and $a and !$a and !((($b or !($a) and $a and !($b) or ($b or !($a and !$b) or !$a or $a and $b and $b) or !($b or $b or !$a) or $a))))))",false),
    ("($a or $a) and !($b and !$b or !(($a or $b and ($a and $a and !($b and !($a)) and !$a or ($b) or ($a or ($b or $a and $b and $a or !$b) or !$a and $a and !($a))))))",true),
    ("(($a or !$a or ((($a or $b and !$b) or !$b or ($a or $b and !$b and !$b or $b or !($b) and ($a) and ($b) or !(($a and !($a and !($a or !$b) and !$a)) or $b or !$b))))))",true),
    ("$b or !$b or (($b or $b) or !$b and (($a or $b and $b or !$a and $b and $a or $b and !$b) or !(($b or $b and $a or !($a and !$b) and !$a) and $b or !$b)))",true),
    ("$b or $b and $a and !$a and $a and !$b and !$a or !$b and !$a or !$b and !$b or ($a or (($a) and !($b and $b and !$b or ($b and $b or ($a or $a or $b)))))",true),
    ("!($b or ($b or !$b)) or !($a or !$b or $a or !$b or !$a) or !$a or ($a or !($a and $b or !$b or $a and $a or $b and !((($a or $a or ($b and !($a) and !$b))))))",true),
    ("($a and $a or ($b or ($b or $a or !$b and !$b and !$a) or $a and $a or !($b) or $b) or !$a or !$a or !$b and ($a and !($b or !$a or !$b and !($a) or !$a)))",true),
    ("$a or ($a or !$a) and $a and $a and !($a and !$a) or !($a or $a or $b and !($a or !$b and $b or $b or !$b) or $a and $b or !$a and $a and !$a or $a)",true),
    ("!($b or ($b and ($a) or ($a or $b) or ($a and ($a and !$b) and !(($b or !$b and !($b and !$a) or $a and (($a) and !($b or $b) and $b) or !$b and $a or !$b) and $a))))",false),
    ("(($b or (($b and !$b and $a or $b and $b) or !$a) or $b and $a) and $a and !(($a or !$a) or !($a or !($a and $b) and $a and $a or ($a and !$a or $b or $a))))",false),
    ("!$b and ((($b and $a or $a and ($b) and !$a) or ($a and !$b and $b and ($a or !$a and $a and ($b or !$b and $b and $b or !(($b)) and ($b and $a and $a and $b))))))",false),
    ("!$b or ($b or (($a or !($b or ($a or ($b and !$a and $a or $a or $a and !$b or $b and $a and !($b) and $b) and !$b and !$b) or !$a or !$a and $b or !($b)))))",true),
    ("$b or !$b or !$a or $a or !($a or $b and ($b) or ($b or !($a or !$a and ($a or $a or !$b or ($a and !$b and !$b or !$a or !$a) and !$a or $b and !$a))))",true),
    ("!$a and $a or !$a or !$a or ($a and !($a and !$a and ($b and !$a) and !$b or $b or !$b or $a and !$b and !$a and !($a or !$b or $b and $a or !$b and ($b))))",false),
    ("!$a and $a or !$b and $a or ($b or !($a or $a) or ($a or !$b and $b and ($a or !$b) and $b and !$a and ($b or $a) or $a and !($b) or $b and ($b or !$a)))",true),
    ("!$b and $b or $a and ($b or !$a or (($a or ($b or ($a) or !($a and $a and $b) or !($b)) and !$a or $b and !($a and !$a) and $a and $a or !$b)) or ($b or (($a))))",true),
    ("!($a and !$a) or !$b and $b or ($b or !($b or !(($a and !$a and $a and $a and !$a and ($b or !$a) or $a and !$a or $b or !$b) and !$a and ($b or !$a and !($a)))))",true),
    ("($b or $b) and (($a or !$a or !($a and !$b) and ($a or $b or !$b or !$b and $b or !($b) or $a or $b or $b and $b) or !$b) and !($a or !$a or ($b or $a)))",false),
    ("$b and $b or !$b or !($a and $b or $a or !($a or ($b or $a and !$b and $b or !($a and $a) and ($b) or ($b) or !($a and $a) or $b and $a or $b or ($a))))",true),
    ("!$b or $b and !$a or !$a or $a or ($a and !$b or ($b or !($a or !$b or !$b or $b and ($a and !$b and !$a or $a) or !($a) or $b and $b) or !($a or !$a)))",true),
    ("!($b and ($b or ($a) and !($b and $a) or !($b and ($a) and !$a) or !($a and (($a or ($b)) or !($b or $a or ($a) or !$b or !(($b or !$b) and $b) or $a) and !$b and !$b))))",true),
    ("$a and ($a and !$a or !$a and $b or $b or $b and !$a and !$b and $b) or !$b and !$a and $a and !($b or !$b and ($a and !$a or !$b and !$b and !$a or $b))",false),
    ("!$b or !$b and (($b and $a and $b) and !$b) and !$b or !(($b and !$a and !($b or $b and !$b or !$a) and ($a and $b and ($b) and !$b or !$a) or $a and $a) or (($b)))",true),
    ("$b or ($b or ($b and $b and !($b or !$b or !(($b and !$b) or $a or $a or $a)) and !$b and $b or $b or !($a and $b) or $a or $b or !$b and (($a) or $a)))",true),
    ("!$a and $a and (($b and $b and $a and !$b and (($b and !$b and $b or !$a and !$b and !$a and ($a and $a or $b)) or !($b or $b or $b or !$b or !$b or !$b))))",false),
    ("!(($a or !$a or ($b and $b or !($a or !$b and !($b and $b and $b and !$b or !$a) or $a) and !$a) and !(($b or $b) and !($b or !$b) or ($a) or ($a or !$b or !$b))))",false),
    ("($a and $a and !$a or ($a or ($b and (($b or !($a or !($a) and ($b or $b or !$b) and !$b and !$b and !$a or $a)) and !($a or (($b or !$b) and $b) or !$b and !$a)))))",true),
    ("(($a or !$a) or $b or !($a or !$b or !$a and !($a) or !$a or $b or $a and $a or !$a) or !$b or !$a and $a or $b) and ($b or !$b and $a or !$b or $a)",true),
    ("!$a and $a or $a or $a or !($a or $a and $b) and !$a and ($a and (($a and ($a and !$b) and !$b and !$b) or !$a) and ($a and $a and !($a and !$b) or $a or ($a)))",true),
    ("$b or !($b or $a or $b or (($b or ($b and !$a) and $a) or $b or ($b and !($a or ($a or !($a or !$a or $b or !$b or !$b and !$b or !$b)) or !$a or !($b)))))",false),
    ("!$a and (($a or $b and !$b and !($b and !$b or !($b or $a or !$a) or $a and !$a and $a or !$b or !($b) and $b or !$b or !$a or !$b or $a) or $b)) and !(($a))",false),
    ("!$b or !$b and !($b or $a or $a or $a and $b and !$a and $a and $b or $a and !$b and $a and ($a or !$a and !($a or $a) or $b and !($b and !$a and $b)))",true),
    ("$b or !($b and $a and $a or !$a or $a or !$a) and !$b or $b and !$b and !$a or $b or !$b and !($b and !$a and $b and !$b and !($a and $a and !$b or !($a)))",true),
    ("!(($b or ($b or !(($b or $a or $b)) or $b or !$b) and !$b or (($a or !$b) or !(($b and !($a or $b and !$a) or !($a) or !$a or !$a or $a and ($b or $b) or $a)))))",false),
    ("$b or $b or ($a and $a and $a) or !$b and ($a or ($a and !($a or ($a and !($a and !$b) and !($a) or !($b and !$b and $a) or !$b or !($b and !$b) or $a) and $b)))",true),
    ("!$a or !($a and ($b or $b and $b or !($b or $b or !($b and !$a or $a and $b and $b and !$b) or !($a and ($a or !$b or !$b or $a) or !$a or !$a) or $a)))",true),
    ("$a and !($a or !($b) or !($b or ($a and !($b and $a) and !$b and ((($b and ($a) and ($b) and $a and !($a and !$a)) or !$a and $a and !($b or ($b)) and ($a or $b) or !$b)))))",false),
    ("$b and !($b and $b or !($a and ($b and !$a or !($a or $a and $a or !$b and !$b and $b and !$b or ($b) or !$a or !$b) and $b and !$a or !($a or $b or ($a)))))",false),
    ("($a or (($a and !$a or !$a and $a and !$b) and ($a or !$b) and ($a) and !$a or !$b and $b and !$a) or $a and !($b or !($b or $a or $a and ($a and $b and !$a))))",true),
    ("$a and !$a and ($b and !$b or ($a and !(($a or ($b)) or ($a or $b or !($b or !$a) and $a)) or !$a and $a or $a or !$b and $a or !$b and (($b) and $b or $a)))",false),
    ("!$b and $b and $a or $b and !$b and !$a and ($b and !$a or !$b or ($a or $b) and !($b or ($a) or ($b or !(($a and $b and $a and !($b or $a and !$a) or $b)))))",false),
    ("($b and !$b or !$b or $a and ($b or $a or ($b or !$b and !$b or $a and $b or !$b and $b or $a or !$b and ($a and $b or !($b) or $a and !$a) and $a)))",true),
    ("!($a or (($a or ($b and $a or ($a) or $a)) and (($b or !($a) or !(($a)) and ($b and ($a or $a and !$b and $a and $a or !$b) and !$b and $b) and !$b or !$b and $b))))",false),
    ("!($a and !($a and $a or ($a or $a or ($a or $a or $a and !($a) and $a or !$a and !$b and !$b or !($a and !(($b) or !($a or $a) and !($a) or $a and $b) and !$b)))))",true),
    ("!($b or ($b or !$b and !($a or $b or $a) or $a and !$b or ($b and ($b or $a and !$a or !($a and !$b or $a) and $a or $a) and $a) and !$b or !$a or !$a))",false),
    ("$b and !$b or !($b and $a or ($b or !$b and ($a and $a or $b and $b and !$a or !$a) and !($a or $a or !$a or $b and $a and $b) or !$a and $a and ($b)))",true),
    ("(($a and ($a or $b and $b or !($a and $b or !$a or ($b) and ($b) and $b or $b or (($a) or $b or !$a or !($b and !$a)) and (($b or ($b) or $a or $a) and !$b)))))",true),
    ("($b and !$b and !$b or !$a) and !$b or $a and !$b or !($a and !($a and ($b and ($b and !$b) or !$a and !$a or !$a and ($a or $b or $b or !$b or $b) or !$b)))",true),
    ("!$a and !$a or !$b and !$b and !($b and $a or $b and $a and !$a and ($b and ($b) and $a and !$b or !$a) or $a and ($b and !$a or $a and !(($a and $b and !$b))))",false),
    ("!$b and ($b or ($b or $b or $a or !$b and !$b) and !$b and $a and !$a or !$b or !$b and ($a and !$b and $a and !$a and $a or $b and !$a)) and $a or !($a)",true),
    ("$a or (($a and ($a or !($a and !(($b) and !($b and $a) and $a) or !($b) and !($a)) or !$a or ($b and !$b and ($b and $b and $a) or $b and $a) or !(((($a) and ($a and !$b)))))))",true),
    ("!$a or !(($a or ($a) or !$a and !($a or $b or $b) or !(($b) and !($a and !$b or $b and $b and !($b) or $b and !$a)) and !$b) or !($b or ($b or ($a and !($a) or $b))))",false),
    ("!($a and !($a and (($a and !$a) and $b or $b) and ($a or ($a and $a and $b))) and $a or !$a and ($b) and $a or !$a) or !($b and $b and !$a) or ($a or (($a and !$b)))",true),
    ("($b and ($b and !($a and ($a or $a) or !(($b or !$a and $a or !$b) and $b or !($b or $a and !$a) or $b or $a or !$a) or $a or $b and !($b or $a and $a))))",false),
    ("!($b and !$b or !($a or !$a or !($a and $a and !$a or !$b or $b and !$a and $a and $b and !$a or $a or $b or !$a) or $a or $b) and $a) and ($b or ($b))",false),
    ("$a or ($a and $a and $a or ($b or $b) or !$b) and !($b or !$a) and !$a and $b and !($b or ($a or ($b or !($b and $a and !$b and !$a or $b) and $a) or $b))",true),
    ("!(($a or !($a and !$a or !$a or !($b) and !($b and !(($b or $b and $b and !$a and !$a or !$a and $b or $b) and $b or $b and !$a or !$b)) and $a or ($a or !$b))))",false),
    ("!$a or ($a and !($a and (($b) or $b or $a) or $a or !$a and $b and $a or !(($b or ($a and !$b or !$b or $b and ($a or $b and ($a)) and $b or $b)) or !$a)))",false),
    ("($a and !($a or !$a or !$a or ($b) or !($a or ($a or $a or !$a)) and !$a or !$a) and !($b or $b) and !($b and !$a or $b) or $b and !$a and $a) or !($b or !$a)",true),
    ("$b or !$b and $a or !$b or !$b and !$a and (($a or $b or !$b and !$b and !$a) and !$a or ($a and !(($b and !$a or !$a or !$a) and $a or !$a or !(($a or !$a)))))",true),
    ("($b and !$b and !$b and !$a or $a and !$a and !$a or !$b and !$b or !$a and !$b or !$b and $b or $b or !($b and $b) or !($b or !$a and $a or !($b and !$b)))",true),
    ("!(($b or $b) or ($b or !$a or !$b and $b or ($b and $a and ($a and $a) and !$a and !($b or !$a and !($a) or !$a or !$a and !$b) and $b or $a or $a and !($a))))",false),
    ("($a and ($a and $a and $a or !$a and !$b and $b or !((($b or !$a) and !$a or !$b and !$b and !$b) and !$b or !$a and $a or !($a and !$a) or ($a and !($a or !$a)))))",true),
    ("$a or !$a and !($a or $a or $a or $b and $a and !(($a) and ($a or $b or !(($b and !$b) or $b or ($b or !$a) and $b and !$a) and $a or !($b)) or $a or !$b))",true),
    ("$a and !($a or !$b and ($b or (($a or ($b or ($a and $a or $a and !$a) or !$a or ($b) or $b and !$b) and $a or $b or !$b and !$a) or !($a and $a and $b))))",false),
    ("$a or $a and !(($a or $a) and $b or !($b and $b or $a or $b or !$b and !$a and !($a or $a and $a and $a or !$b or $b or !$b or !$a or $b or ($a))))",true),
    ("($a or ($a or $a and ($b) or !$a and !$a) and $a or !$a and !($a or !$a and !$b) and !$a) or !($a and $a or ($b and !$b) or $b and ($b or !($a or !($a and !$b))))",true),
    ("(((($a and !$a) or $b) or $b and !($b or $a or !$b or !($b or $a)) and !$a and $a and !$a or !($a) or !((($b and !$b) or $a or ($a and (($a)) and !$b) and ($b or $b)))))",false),
    ("!($b or !($b or $b or !$a) and ($b) and !$b and ($b or !$a and ($b or !$b or $b or !$a or ($a and $a or $b or !$b and !($a or $b and $b) and ($b) and !$b))))",true),
    ("($b and !(($b and !(($b and $b or $a) and $b or !$a and !($b and !($a) or !$a and !$b or $a and !$a or $b and !($a) or !$a)) and ($a or !(($a or ($b or !$b)) or !$a)))))",false),
    ("$a and $a or ($b and !($a or !$a and !($b or $a or !$a or !$a or !$a and ($b and !$b) or !$b and ($b) or !$b and !$b or !$a and !$a or !$a and !$b and $b)))",true),
    ("($a and !($a or $b and !$b or $a and !$a and $b) and !$b or $a and !$a and $a or !$a or $a and ($b and $b or !$b or !($a) and $b and !$a and $b and $b))",true),
    ("!$b or ($b and ($b and !$a) and $b and !$a and $a and !$b or !$a or ($a) or !$a and ($b or !$b or $a or !$b) or !($b or ($b or !($b) or ($a and !$a) or !$b)))",true),
    ("!($b or $b and !($a or !$a) and !$b and !($b or ((($b or !$a) or !($a or $b and !$a) or !(($a or $a or $b or $a) or $b or !$a)) and $a or $b and $b) and ($b)))",true),
    ("$b and $b or !$b and !$b and (($a and !$b and !$b) or !($a and ($b and $b and !($b and $a and !($a) or $a and !$a and !$a)) and ($b or $b or !$a and ($a or $a))))",true),
    ("($a or !$a and ($a or ($a and $b and $a or !$a or !$b or !$b or !$a or ($a or (($a or !$b or ($b) or ($b) and !$a or !$b and !$a or $a) or $a) or !$a))))",true),
    ("!(($b or !(($b) and !$b and !$b and $b or $a) or $a) or !($a or $a and !$a and !($b and ($a and ($a or !$b) or $a and ($a or !$b or !($b or ($b and !$b) or $b))))))",false),
    ("!$b and !$b and !$b or !(($b or $b) or ($a or !($a or $b and $b and $a or !$b) and $b or $b or !$b or !$a or ($b and $b or $b)) or !$b or !$b or ($a))",true),
    ("!$b or $b and $a or $a or $b or !($a or !$a and ($b and $a or $b) or !($a or $b) or !$a or !$b) or !($b and !($b) or ($a and $a or !($a) and !$b or !$b))",true),
    ("$b or !($b and !(($a or !$b or ($b) or $a) or !$a and $b and !$a or !$b and ($a and $b or !(($b or !$a and $a) or !$a and $b or $b and $a and !$a and !($a)))))",true),
    ("$b or !$b or ($a or !$a) and ($b and !$a or !($a and $a or ($b and !$a or $a or !$b or !($b and !$a) and !$a or ($a) and ($b) and $b) and !(($a and !$a) or $a)))",true),
    ("$a or !$a and ($b or (($b) and $b or !($b and !$b or !$b or !$b or $a or !$a and $b or $a) or $a or !$b and !$b and !$a or !$a or !$a and $a) and !$a)",true),
    ("!$a and ($a or $a or !($b or !$a and (($b or !$a or $b) and !(($a or ($a) or !($a and !$a) or !$b or $a or $b) or ($a or !$a and $b and !$a and !($a and $a))))))",false),
    ("$b and !($b and !(($a and $b) or !$b and !$a) or !$a and $a) or $b and (($b and $a and !$a and $a and $a and !($b or ($b and !$a)) and ($a and !$a and !$b and $b)))",false),
    ("$a and !$a or ($b or !(($b and !$b or $a or $a) and $b or $a or !$b) and !$b or !$a or !$a and !(($a or !$b and !$a or $a and !$a and !$b or $a and $b)))",false),
    ("$b and ($b or (($a) or !$a and ($a and ($b and !$a) or !($b and $a and $b) or $b and !(($b or !$b) and !$a) and ($b and $b and $b or $b and !($a or !($a and $b))))))",false),
    ("!$b or $b and !$b or !$b and !($a and ($a and $b) or $b or $b and $b or $b or !$b or !($a or !($a or $b)) or $b or !$b and $b or ($b and !$a or !($b)))",true),
    ("((($a and !($a) or $b) or !($b or !$b and ($b or $a) or !$a or !$b or !(($a and !($b and !$a) and !($a) and !$b and !$a or $a) or !(($b and !$b) and $b or !($a) or ($b))))))",false),
    ("!($a or !($a and !$a or $b or !($a) or ($a and ($a or $b or ($b) or !($b) and $b) and $a or ($a and ($b and $b)) and !(($a) or !$b and !$b or !$b) or ($a) or !($a))))",false),
    ("(($a and !$a) or !$b and (($a or $a and !$a and $b and !($a) and !($a and !$a and !$b or !($b or !$a and !$b)) and $a or !$a and ($a)) and !($a and $a or !$a or $a)))",false),
    ("$a and $a and !$a and !$b or (($b and !$a or !$a and $b) and (($b or $b and ($a and $b or $a or $a) or !$a) and !$b and !($a) or !$a or !$b or !$b or $b))",false),
    ("($a or ($a or !($b and $b and !($b) and !($a) or $b) or $b or $a or $a or $a or !$a or !$a and (($b and !$a or $b or !($b) and $b)) or ($a) and $a and !$b))",true),
    ("$b or ($b or ($b and $b or !($b) and !$b or !$a and $a and !($a or ($a and !(($a or !$a and $a or $a or !$b or !($b) and !$a or !$a and ($b or $a))) or !($b)))))",true),
    ("$b and !($b and $a and !$a and $b or ($a or !$a and !$b and ($b and !$a or !$a and $b or !$a and $b and !$b or $b or !$b or $a)) and $b and !$a and ($a))",false),
    ("$b and !$b and $b and !($a or $b and !$a and $b and !$a and ($b and !$b and !$b and $b or $b) or !(($b or !$a and $b and !$a and !$a and $b or !$a) or !($b)))",false),
    ("($a and !($a or ($b or ($a or !$b) or ($a or $b or !(($b or $a or $b and !$b or !$b and !$a and ($b) and !($a and ($b) and $a and $a) or $a and $a) and !($b))))))",false),
    ("!((($a and $a or !$a) and !($a and !($a or ($b or $b and !$b and $b))) or !(($a and !$b) or ($b and $b) and $b) or !($b) or !($a and !$a or ($a and $b) or ($a and !($a)))))",false),
    ("$b or ($b or ($b and !$b or ($a and $b and $a) or ($b and $b or ($a and !$b and !$a and $b) and !$b and !$b and !$b or !$b and !($a or $b and !$b) or ($b))))",false),
    ("!$b or ($b or !$a and !($b or $b and $a and !$a or ($a) and $b and ($a and ($a or ($a or $a and !$b)) and !$b) and ($a) and !$b and ($a and !($a or !$a) and $a)))",true),
    ("$b or !$b or !$a or (($b and !$b and $b or !($a) and !(($b and !($b) and !($a or $a) or !$a and $a) or $a and $a) or (($b and !$b) and $a or !$a or $a and !$b)))",true),
    ("!(($a or !$a and ($a or !$b) or !$a and $b and !$b or !($b and ($b and ($a) and !(($b or !$a)) or !$a and !$a or !$b and !($b and $a) or $b or $b) and $a and !$b)))",false),
    ("$a or !((($a or ($b or ($b or !$a) and $a and !$b or !($a) and !$a and $b) or !($b or !$b or !($a or !$b) and $a) and $a and !$a and !$b) or ($b or $a) or !($b)))",true),
    ("!$b or ($b and $b or !($b or !$a or $a) and $b or $b or !$b and !$a or ($b) or (($a and !$a) or $b and $a or !$a and !$a and !($a or !$a and !($a and $b))))",true),
    ("!$b or $b or !($b or $b and ($b or !($a and (($b and $b or !$b) and $b) and !$b) and $b) or ($a and !$b and ($a or !$a and !((($a)) and !$b or ($a and !$a or !$b)))))",true),
    ("($a and !$a and (($a or !($b) and $b or $b) or !$a and $b and !($b or $b and ($b and !($b or !$b or $a and $b and ($a or ($a and ($b or $a and !($a or $b)))))))))",false),
    ("!($b or !(($b and !$a) and $a and ($a or !(($b or ($a and !($b or $a and !$a) or !$b or !$a) or !$a) and (($a or $a and $b or !($b) and !$a) or ($a) or $a and $b)))))",false),
    ("$b or !($b and (($a or ($b or !$b)) and !$a or !$a or !$a) and !$b) or ($a and !$b or !($a or !$a or !$b and !$a or $b or !($a and $a and !$b and $a and !$a)))",true),
    ("!$b and !$b or !$a and $a and ($a or !($a or !$b or !$b) and !(($b) and !$b or ($a and !$b) or $a or !(($a and ($a or $a or $a and !$a and !$b) or ($a or !($b))))))",true),
    ("$a or $a or !$a and !($b or !$a or !$a and !($a or $a and $a or !$a and $b and $b or $a or (($a or $b) or $a)) and $a or $b and ($b or !($a and $b)))",true),
    ("!$b and !$b and !($a or !$b and !$b or !$b and ($a and !$b or ($a) and $b and ($a and (($a and $a and $b and $a and $a or !$a or $a and $b or !$a or !$b)))))",false),
    ("$b or !$b and ($b or ($b) or !$a or ($b or ($b) or (($a and ($b)) or $a or !$a or $a or $a and !$a and (($a or !($b and !$a)) or $a) and !$b and $a and $a)))",true),
    ("!($b and ((($b or $a and !($b)) or !$b or $b)) and $a or !($b and !$a or $a and $a and $a) and !$a and $a and !$b or ($a and $a and $b and !$a and !$a and !($a)))",true),
    ("!($b and $b and !($b and ($a and ($a and $b) and !$a) or !($b and $a or $a) or !$b or !$b and !$b and (($a or !$b and !$a) or ($a and $b or !$a or !($a or !$b)))))",true),
    ("($b or $b and $b or !$b or $a and !$b or !($b and !$b or $a and $b) and (($b and !$b or $b or ($b and !$a or $b and $a or !$b and !$a and !$a or $a))))",true),
    ("$b or !$b and !($a and !($b and !$b) or ($b and $b or !$b or $b and $a or !$a or !$a) or !$a) or !($a or !$a or !$b or !($a and !$b) or !($b or $b and !$a))",false),
    ("!$a or (($a or !$b or !$b or $b or $a and !$b) or $a or !$a and $a and !$a and !($b or !$b) or ($b and !$b or !($a and !$a or !$b or (($b or !$b and !$b)))))",true),
    ("($a and $a and !($b or $a or !$b or $b and $b or !$b or !$a and $a or !$a and $a and !$b or !$a or !$b or $a or $b and !$b or $b and ($b or $a)))",false),
    ("$b or $b or $a and (($b and ($b and !$b or (($b and $a or !$a) or !$b and !($a and $a) and $b or $a or !$b or !($a or !$a and $b and !($a or !$a and !$b))))))",false),
    ("$a or !(($a or $a) and (($b) and $b) and !$a or $b) and ($a or !$a and !$a or ($b or !$b)) or $b and !(($b or $a) or !$b and !$a or $a and !($b or $b or !$a))",true),
    ("!($b and !$b or !($a) or $b and !$b and $a or $b or !$b or $a or !($a and !$a and !($b and $b and !$a or $a or ($a and !$b and !$a and !$a or $a or $a))))",false),
    ("$a or ((($a and !$b or $a or $a and !$a or !$a or !$a and ($a)) and !($b) and !$a) or !(($a or !$b or $a and ($a) and $a and !$a or ($a or $a and !$a or $b))))",true),
    ("!($a or $a and $a and ($a) and (($b or $b and !($b) and ($a and $a or !($a or !$a or $b or $a) and !($b or !$a or $a) and !$a or !($b and !$b or $b and (($b)))))))",false),
    ("($a and !($a and $b or $a or $b and !$a and !$b or !$b and !$b and ((($b and $b or $a) or $a and $b and $a and $a) and !($b and $b) and ($a)) and !$b) or !($a))",false),
    ("($b and $b or !($b and ($a) and $b or !$b and $b) or (($b) and !$a) and $b or (($b or !$a) or $a and !($a)) and !$b or !$b or (($b and (($b or $a) or $b) and !$a)))",true),
    ("!($b or $b and $b or $a and ($a and $a or $a or !($b and !$b or $a) and ($b or !($b) or !$a or !$a or !$b or $b) and !$a and !$b or !(($a and $b) and !$b)))",false),
    ("!$b or $b or ($b or !($a and $b and !$b or ($a and $a)) and !$a and ($b and !(($a and !($b and ($a or $b or $a or $b or !($b) and !($a and $a) and ($a or !$b)))))))",true),
    ("!$a and $a or (($a and !($a or !$a and ($b and !$a or $b) or $b and !$b and $a and $b and $b or $a or $b and !$a or $b) or $b or $a and !(($a and !$a))))",true),
    ("!(((($a and !($a)) and !$a or !($b) or !$a or !($b) or !$a) and $a or !(($b) and ($b and $a) and !$a or !$a) or $b or (($b or !$b and !$a or !$b and !(($b or !$b) and !($b))))))",false),
    ("($a and (($a and $b or ($a and $a) or !((($b and $a or !$b) or $a and $b) and $b and $b or $a and ($b) and !$b or $a or $a and ($b or $a and !$b) and $a))))",true),
    ("!(($a or !($a or !($a or !(($a or $a and $b and $b or $b and !$b or !$a or (($a) or ($b or !$b and $a) and $b) or !$b or $a or $b and $b) or !$a and !$b)))))",false),
    ("!$b and !$b and $b and $a or $a or !$b or !($a or $a or ($b or !$b or !$b and !$b and $b) or ($b and !($b) or !$b and !($b or $b) and $b or !($a) and !$b))",true),
    ("($a and !($a or $b and !($b and ($b or ($b and !$b) and !$b) and ($b and !$b) or !(($b and $b)) and !($b or !$b) and $b or $a or $a) or !$b or !($a or !($b or ($b)))))",false),
    ("!($b or (($b and $a or !$b) or ($a and $b and !$b or !$a or ($b or !$b) and !$a)) and $a) or ($a or ($b and !($a and !$a or !($b or !$b and !($b) or $b) and !($a))))",true),
    ("($b and (($b and !$a and !$b or !$a or !$a and !$b and $a and !($b or !$a) and !$b and $b or !($a) or !$b or $b and $b) and ($b) or (($b and !$b)) or !($b and $a)))",false),
    ("($b and ((($b and !$b or !$a and ((($b) and !$b) and !$b)) and !$b or !$b) or !$b or ($b and !$a or ($b and ($b and !$a) or !($b) and !($b or !$a or $b and ($a) or $a)))))",false),
    ("($b and !(($b or !$b or $a or $a) and !$b or !(($a or (($a or !($a or $a or !$b or $b or $a or $b) or $b)) and !($b and $a or !($a) and !$a or ($b and !$b))))))",false),
    ("!$b or !$b and !(($a and ($b) or $b and !$a and $b or !($b or !$b and ($a and $b) and ($b and !$a or $b and !$a or !$a or !$a) and !$b) or ($b and $b) and $b))",true),
    ("!($b and ((($b or $b) or !$b and $a and (($b or ($b) or !$b) and ($a and !($a)) and $b or $a and !($a)) or !($a and !$a)) and !$b and $a) or ($a) and ($b or !($b and $b)))",false),
    ("!$a and ($a or !($a or !($b or $b and ($a or $b) and (($b or !$a and !$a or $b) and $a) or !$a and !$a or $b and $a or !(($a) and !$b and $a or !$b or $b))))",false),
    ("($a and (($a and $a or !($b and (($b or $b or ($b) or !$b) and $a) or !($a and $a and !($a and !$a) and ($b) and !$a) and $a or !$a or !(($b or !$a or !$a and $b))))))",true),
    ("!($b and (($b and ($b and !($a) or ($b and ($b and !($a)) and !$b and !($a) and !$a or $a or !$b or ($b and $b and $b) or !$a and !($b and !($b and (($a or $a))) or $b))))))",true),
    ("$a or !$a or !(($b and !$b and $b) or $a and !$a or ($a or $b or $a or !($a and ($b or !$b) and !($a) or $a) and !($b and !$a or !$a or ($a or !$b and ($a)))))",true),
    ("!$a and !($a or $b or !($a or !$b) or (($a or !$b and $b or !$a or ($b or !$a) and !$a) or $b) or $b or ($b or !$b and !($a or $b and $b and !$b and !$b)))",false),
    ("!$b and $b or !$a and !($b and ($a or !($a or !(($a) or !($b and !$b or ($a)) or $b or $a and $b or ($a)) or ($a) or $b and ($b or !$a and $a or $a or $b))))",false),
    ("$a and !$a or $a and !($a or !$a or $b and $a and $b and $a and !($b) and $a or $a or !$b or ($b and !($b or !($a and ($a or !$b) or ($a or $a or !$a)))))",false),
    ("!$a and !$a or !$b or !$b and $a or !$a or !$b or $b or !$a and !$b and ($b or $b and !$b or !$b or !$b or ($a) and $b or $b or !$b or !($a and $b))",true),
    ("!$a and ($a or !$b and !($b and ($b or !$a or ($b and $b and !$a and !$a and !$a)) or !$a) or ($b or $b or ($a and !(($a or $b) or $a or !$a)) or $b and $b))",false),
    ("!($b or !$b and (($b or ($b or $a) or $a or $b or !$a or !$b or $b or !$b or !$b and !$b and !$a or !($a) or $b or $a or $b or !$a or !$a and $a)))",false),
    ("($a and !$a and $b or ($b and ($b or !$b) and ($a and !($b or !($a or !$b and $a)) and $a) or ($b and !$a and $a or !$b and ($b or !$b) or !$a or !$b and $b)))",true),
    ("!($a and !$a and ($b and !$b and $a or !$a or !$a or !$a) and $b and !$b and !$a or ($b or !($a or $a or !$b) or !$b and $a or ($a) and $b) or ($a and !$a))",false),
    ("!(($a and !$a) or !($b or ($a) or ($a and !($a and !($b and !$a or $b)) and !$a and $a or !$b) or !$b and $b or $a and !$b and !($b or ($a and !$b and $b and !($b)))))",true),
    ("$b or !($b or !$b and $a or !$b and ($a and !($b or !($b or $b or ($b and ($b) and $a and !$b) or !(($b or $b) or !$a)) and (((($b or !$b or !$b and !$b)) or $a)))))",false),
    ("!($a or !((($a or $b and !$a or !$b or !$a and $a or $b and $a and $b or !($a and $a)) or $b) or !($b and $a or !$a or !$a and !($a or $a or $b) or $b)))",false),
    ("!(($a and !(($a or $b and !$a or $a and !$a or !$a) or ($b and !$a) and !($a and ($b and !$b and $a) and !$b and $a) and !($b and !$a) or !$b or !($b and !$b or !$b))))",true),
    ("!($b or $b and !(($b and $b and !$b) and ($a) or !$a and $a and !$b and !($b) or $b or $b or !($b or ($b and !$a or $a)) or !$a) or !$a and $b or !($a or $a))",true),
    ("($b and $b and ($b and !($b and !$b or !$b or !$b and !$b and (($a and $a) or !$a) and !$b) or ((($a and ($b)) and !$b and (($b or !$a and !$a) or $b and $a and ($a))))))",false),
    ("!$a and !$a and !($a and ($b or !($a or (($a and $b) or $a) and !$a and !$b or $b and !($b or $b or !(($b or !$a)) or !$a or ($b or $b and !$b) or $b and !$a))))",false),
    ("$a and !($a or $a and !$a) or !$b or ($b or !$b and !$a and $a or $b or $a and !$b or !$a or ($b or !$b or !$a and !$b and $b or !$b or ($b) or !$a))",true),
    ("!$a and ($a and !$b) and ($a or !(($b and !$b and !$b or !$a) and $a or (($a)) or !$a or !($b and ($a) and ($b or !$b and !($a or $a) and $a) and $a or !$a) or !$a))",false),
    ("$b and $b or ($b and ($b and $a or !$b and $b or $a) and !$a and ((($b or !$b or !$b) or $b and !($a and $a and $b or ($a and $a) and $a or !$b or !(($a))))))",false),
    ("!($b or !$b or !($a or !$b and !$b and !$a or !$b or !($b) or !(($b or $b) or !($a and !$a and $b or $a) and !$a or !($a and !$a and !($a) and !$a) or !$a) and $a))",false),
    ("!$a and $a and $b or $b or !(($a and !($a and ($a or !$a or $a and ($a and ($a) or !$b) or $a and !$b and !$a or !$a or !$a or !$b) and !$a or !$b or !(($a)))))",true),
    ("($a and $a and !$b and $b or $b and $b and $b and $a or ($b or $a) or !($b or !(($a and $a) and !$a and $a or $b and $a or ($a or $b) and !$b and !($b))))",true),
    ("($a and $a and !($b and $a) or $a or !$b or $b) or $a or !$b and $b and !$b or !($a and !$a) and !($a and $a and $a or ($b or !($b) or ($a) or $b or !$b))",true),
    ("$a or $a and ($b and ($a or ($a or !$b or !$b and $b) and !$a and !$b and !($a) and $b or !$b or !$b and $b and ($b or !($b or $a)) or !$b and $a and ($a)))",true),
    ("$b or (($b and !$b or ($a and !(($b or !($a or $b) and $b) and !($b) or $a or ($a or !$b) and !($a) or $b or !$b or !$b or $b or $a and ($a and !$a and $b)))))",false),
    ("!($b and $b and !$a and !$a or !($a or ($b or $a and ($b) or !$b or (($b and $a or $b and $b and !$b) and !($a)) and !$b and !(($a) and $a and !($b and !($a and !($b)))))))",true),
    ("$b and !((($b and $a) or !$a or $a) or !($a and $b and !$a and !$a or $b or !$b and !$a or !$a) and $b or $b and !$a or !(($a) or !$a or !$b and $a) or !$a)",false),
    ("($a or $a and !$b or !$a or !$b or ((($b and $b)) or !$a or !$b and !$b or $a and $b or !$a and ($a and ($b or $b and $b or !$a and $b or $a or !$b))))",true),
    ("!$a and !($a and !$b or !$a or ($a) and $a or !($a or !$b or $a or !$a and !($b and $a or $b or !$a and $b and !$b and !$b and !$a or !($b or $a or !$a))))",false),
    ("($b and $b or !(($b) and $b)) or ($a or (($a or ($b) or !($a) and !$b and !($a) or !($a or (($b or $b) or !$b)) and ($b) or !($b or ($a and ($a) and !$a or ($a)) and $b))))",true),
    ("!($a or !($a or !$b and $b and $b and ($b and $b) and !$b) and !($b and !($a and $a and ($b or $a) and $b) or !($b and !($a or $b) and !$b and !($b and $b) and !$b)))",false),
    ("!($a or $a or $a or !$b and !$b and $a and !(((($a and $b or !($b and $b) or $a or ($a or ($b or !$b) and !$b or $a) and !$b and ($a) or !($a) or ($a or $a))))))",false),
    ("!$b or !$b and !$a and !$b or ($a and !($b or ($a or $b and $b)) or ($b or !$b) and $b) or $b and $a and ($a and $a or !$a and (($b or !$b and $b and $a)))",true),
    ("!($a or !$a and !$b or !($b and !($a and !($a or ($b and !$a)) or ($b) and $a or $a and !$a and !$a) or !($a and $a or !$a or !($b and $a or !$b or $a and !$b))))",false),
    ("(($b or ($b and !($a or ($b)) and $a or !($b and !$a or !($a) or !$a or !($a and !$a or (($b or !$a and $a and $a) or $b) or !($b and !$a) or $b or $a) or $a))))",false),
    ("!($b and $b or !$a and ($a or $a and ($b and !$b) or $b or !($b and $b) and $b or !($a and !$a and !$b and $b or !$a)) or $b and !$a and !$a) or !($b and !($a))",true),
    ("!($a or $a or !$a) or !$b and !$a and !(($b and $a or !$b or $b and $a or !($b or !$b and !($a and !$b) and $a and !($a or !$b or $a) and !$b) and !$a or !$a))",false),
    ("$b and !($b and (($a or !$a or !$a and !($a) and ($a and $b) and !$a and $a) or !$a and !$b or !$b and !$b and !$a) or !$a and !($b or !$b and !$a and !($b or !($b))))",false),
    ("!$a or ($a and $b and (($b or !$b and !($b and !(($b or $b and $b) or !$b) and !$a or (($a or $b)) or ($b or !$b and !($b or !$b) and ($a) or $a) or $a) and !$b)))",false),
    ("$b or !$b or ($b or ($a or ($b and $b or $b) or !$b and ($a or $b or !($a or $b or !$a or !$a and !$b or $b) or !($b) or $a or !(($a or $a) or (($a))))))",true),
    ("!$b and !$b and $a and (($a or !$a and !$b and !$a or !($a or !$b or !($b or !$b or !$a and $b or $b and !($b) or !$a or !($a or !($a and $a) and !$a or !$a)))))",true),
    ("($b and !$b and !($a or !$b) and ($a and $a or ($b) or !$b and $a or $a and $a or !$a) and $a or (($b and ($a) or !$a or ((($b and (($b) or !$b and !($a and $a))))))))",false),
    ("!($a or $a or !$b or $b and ((($a or !$b) and $b) and $a) and $b or ($b and !$b or !$a or !$a or $a and ($b and $b or $b and !($b) and $b and !$b or !($b))))",false),
    ("!$a and $a or ($a or !$b) or !($a and !($a or !($a and $a and !$b) or $a or $a and !$a) or $a and $a or $a or $b or $b) or !$b and !($a or $a and ($a))",true),
    ("$a or !$a or !$b and !$b and $a or $b and !$a and $a and !$b and !(($a or $b or ($b and $b and $b and !($a or !$b) and !$b or ($b) or $a and ($b) or !(($b)))))",true),
    ("($a and !($a or !$a and $a and !($a or $a or $a and (($b and $b))) or !$b or !($b and (($b and $b and $b) and $a)) and $b and !$a or (($b or $b and ($b and !$b)))))",false),
    ("!$b and !($b and ($a and $b) or !$a or $a or !$b and ($a or $b or ($b or $b or !$b) and !$b and $a or !$b and !$b and $a or !$b or (($a and $b) or !$b)))",false),
    ("!$a or $a and !$a and ($b or ($b) or $b and !($b and !$a and $a and !$a or !(($b or $a and $b and !$b or !$a) or $a and !($b or ($b and $a) or !$b or ($a)))))",false),
    ("!$b or ($b or $b and !$a and ($b and !$a or !$b and (($a and $b)) and !$a or !$b and !$a or !$b and !($b or !$a and $a or $a or !($a or ($a and !$b) or !($a)))))",true),
    ("($b and $b or $a or !$a and ($a and !$a and (($a) and !$b)) and !(($b and !$a)) or !($b or $a and ($a) or !$b or !$a and !($b and $a or $a and $b and !$a and !$b)))",true),
    ("$b or $b or !($b and ($b or !$a and $a or !($b) or ($a or $a) or !$a and !$a) or !$b or $b or !$b or $a and !$a or $b and !$b or !$b or !$a) or $a",true),
    ("$b or !$b or !$a and $a or !$a and ($a and (($a and $b) or !($a and !$b) and ($a or !$a and $b) or $b and !$b and $a or $a or $b) or !$a or ($b and !$b))",true),
    ("!(($a and !$a and ($a or !$b) or $b and $a) or !$a or $b and !$b or $b or ($b or !$a and $b) and $a and !$a and !$a) and $b and ($b or !($a and !$a and !$a))",false),
    ("$b or ($b or ($a or $b or !($b or !$a) and $b or ($b or ($b or !$a) and ($a) and !$a or $b) or !$a or !$b and !($b and $b) or ($b and !($a or !$a) or !$a)))",true),
    ("!($b and !($b or ($b and !(($a and ($b or $a or $a and ($a and $a) or !($b or !$a or $b and !$b)) and !($a) and ($a) or ($a and !$b) and !(($a or !($b) or !($b)) and $a))))))",true),
    ("!$a or !$a or !$a or !($a or $a and $b and $b and !$a or $b or $a and !($a or $a and !$a or !$b) and !$b and !$a or $b and $b or $b and !$a and $b)",false),
    ("!$a and !($a or $a) or $a or !$b or $a and $a and !($a and !$b or !($b or !$b) or $b and (($a or $b or !$a or !$a or !$b or $b and !$a) and !$b or !($b)))",true),
    ("($a and $a or !(($a and $a or !$a or !($b and $b) or !$b or ($b or $a and !$b or $a or !$b) and $b or !$a or (($b) and $a)) or ($b and !(($a or !$b and $a)))))",true),
    ("!$b and ($b or $a or $a and $a or ($b and !$b and !($a and $b or !$a) or !$b and $b) and $b) or ($b or !$a or $b or $b) or !($b and !(($a or !$b and !($b))))",true),
    ("($a or $a or ($a and $b and $b and $b and (($a and $a) or $a or !$b) and !$b) and $a or $b and $b or $a or !$a and $b and !(($b and !$b and $b or !($b))))",true),
    ("!$a or $a and $b and $b and $a and (($b and !($b or $b and $a or !$a or !$a) and $a) or ($a and !$b or $b or !$b and $b and !$b or !$b) and $b and !($b))",false),
    ("!$a or !(($a or !($a or !($b and ((($b)) and $b) and $a and !($a and $b and !$b)) or !($b and (($b)) or ($b) and !$b) and $a and $a or $a and !$b) or $b) or !($b or $b))",false),
    ("($a or !($a and !$a or $b and $a or !(($a and ($b or $a and !$b) or !$a and $a or !$b) or !($a and $b or $b) and !$a or !$a and ($b or $b and !$a))) and !(($a)))",true),
    ("!((($b and $b and ($b and $a or ($b and !$b) or $a or !(($b and $a or $b) or $a and $a) or !$a or ($b) or ($a or $b or $b)) and ($b or !$a and !($b and ($a))))))",true),
    ("$b or ($b and ($b) and !$a and $a or !$a or !($b) and $a or !$b) and !$b or $a and $a and !($b and !(($a or $a or $b or $a or !$a) or !$a and $b or $b))",true),
    ("!(($a and !(($a and ($b) and !$a) and !($a or !$a) and ($a and (($a) or !$a and !$b or !($a)) or $b) and !$a and ($a) or $b) and !($a and !$b or !($b) or ($a and $a or !(($a))))))",true),
    ("!$a or $a and ($a or ($a and !($b and !($a or !($b and $a) and $b) and !$b) and !($b and !(($a or $a or !$a or $a or !($b) or !$a) or ($a and ($a or !$b) or !$b)))))",true),
    ("!(($b or $b or !$b and !$b or !$a and ($b and $a) or !$a and $a and !($a or !$a and $b or !$b) or $b or $a and !($a or ($b or !($b or $a and !$b and $b)))))",false),
    ("!($b or !$b or !(($a) or $a or $a or !$a or !($a and $b)) or $b or !$b and ($b or $b or $a and !$b or $b and !($b and !$b and $b and !$b or !$b or $b)))",false),
    ("($b or ((($b or $a and $a and !$b or ($a) and $b and !(($b and !$b or ($a) or !$b) and $a and $a) and !$b and !$b) and ($a) or ($a) or (($a and !$b) and !$a and $a))))",true),
    ("!(($b and (($b and $a or !$a and !$b and $a and !$b) and ($a) or $a) and $b or ($a and $a and !$b or $a and !$a and ($a and !$a) and $b) or !$b or !($b or ($a))))",false),
    ("$a or ($a and $a or !$b and ($a or $a) or $b or !$b or !$b or !($b and !$a and !$a and $a) and !$a or ($a and $a or !($b and $b) or ($a and !$a) and !$b))",true),
    ("!($b and !($b or $b) and ($b) and !($b or !($a and (($a and !$a and ($b and !$b or !$a) or $a and !$b or $b) or $a and ($b)) or $b and !($a and ($b) or !$a or ($a)))))",true),
    ("($b and !$b and $b or ($a or $a or $b) or !$a) or !$a and !(($a and $b or ($b and !($b) and !($b and !($b or $a) or $b or $a and !($b) and !($b or !$a and !$b)))))",true),
    ("!(($b and ((($b and !($b or $a) and ($b)) or ($a or !$a) or !$b and !($a or !$a) or $b and !(($b) and $a or !$a)) or $b or ($b and !$a) or !$a and !$a or $b and !$b)))",true),
    ("(($a or !$a and !$b and $a or ($a and !$b or (($b and $b or !($a or !$a and !$b) or ($a and !$a) and !($a and $b) and !$b or !$b)) or ($b or ($b or ($a or $b))))))",true),
    ("($a and !($a or !($a and !$b or !$a and $b) and ($b or $a and $a and !$b or ($b or $b or (($b or $a and ($b and !$b) and $a or !$b) and $b) and !($b and !$a)))))",false),
    ("$b and !($b or !(($b and $a or !($a or !$a and !($b or !($a and !(($a and !$a) and $b and !$b) and $a and $a and ($a and !($b) and $b or $b) or !$b) and $a or $a)))))",false),
    ("($b and !$b and !$b and !$b and (($a or ($b or ($a and !$b and !$b and $a or !($a and !$a and !($b and $a))) and !($b or $a) and !$a and !($b) or !$a and $b or !$b))))",false),
    ("!$b and !$b or !$b and $a and !($b and !$b or $b and !($b and !$b or ($a and ($b or !$b and !($b and !($b) or !$b and !$b) or $b and $a and !$b) or ($a and !$b))))",true),
    ("!$b and !($b or (($a and ($b or !($a or (($a and ($a) or ($a) or $b or !$a) and $b)) or $b) or $a and ($b and !$b) and !$a and !$b) or !$b and ($a) or ($a and $a)))",false),
    ("!$b or !$b and !$a or !(($b or !$a or $b or !$a or $a and !$b and !($a and $a or !$b) and !$b or !$b and !$b or $a or !$b and $b or $b and !$a and $b))",true),
    ("!($b or $b or ((($b) or !($a or !($a or !$a and (($a)) or ($a or ($a) and $b or $a and !$b and !($a or $a or !$b or $b or $b or !$a) and ($b and !$b or $a)))))))",true),
    ("$b or (($b and $b) and ($a and !($a or $b or !((($a or ($b) or ($a or (($a and !$a) and !($a) and $a) or !$b and !($b)) and ($b or $b) or $a) or !$a) or ($b and !($b))))))",false),
    ("$a or ($a or $b or !$b and $b or !$a or ($b and !($b) and $b) or $a or (($b and !$a and !($b and ($a and !$a or $a)) and $a or $a or !$b) and !($a or !$a)))",true),
    ("!($b or ($b and ($a) and $a or !($a and (($b) and !$b) or $a) or (($a or $b or $b) or !(($b or ($b and $a) or !($a and ($b or $b) or !($a and !$b and !($a) or $b)))))))",false),
    ("(($a or $a) and ($a and !$b or $b and !$a and !($a or $b or !($b) or !$a) or (($b or $a) and !$a or $b and $a) and ($a or !$b) and !$b or !$b or !($b and $b)))",true),
    ("!$b and !(($b or ($a or !$a and ($b and !$a or $a or $b and !$a or !$b and (($a and !$a or $a and $b) or !$b and ($b and !$b) or $b or $b) or $a) and $b)))",false),
    ("$a and ($a or !(($a and $a or !($b) and $a or $b or $a) or !($b and ($b and !$a and !($b and !$a) and !$b and !(($b and !$a and !($b or !$a))) or ($b or $b) or !$a))))",true),
    ("($a or !$a and $a and !$b and !$b or !$b or !($b and !$b or $a and $b and !$a or !$a and ($a or !$b and !($b or $b) or !$b and !$b and !$b or !$b and $a)))",true),
    ("!$a and ($a or $b or !($a) or !$b or !$b or ($a or !($a or $b or $b or !$b and !$b and $a or $a and !($b and !$b) or $a) and $a or $a and !$b or $b))",false),
    ("($a or !$a or !$b and !$a and $b or $a or $a) or !$a and $a and ($a or $a) or ($b and !$b or $a or $b or !$a or !(($b and !$b and !$b) or !$a and $b))",true),
    ("!($b or ($b and $a) or !$a or !$b or $b and ($b or !$a or ($a or (($b or !($a) or !($b) and !($b and !$a or $b and !$a) or !$a) and !($a and $a and !$a and !$b)))))",false),
    ("($b or !($b) and !($a or !$a and !(($a and !$b or ($b) and !$a and $a) and ($a and $a) or !$b or $a and $a or ($a or !$a or $a or $b) and $a or !$b or $a)))",false),
    ("$b or $b and !$a or !($b or ($b and (($b and !$a and !$b) and !$b or $b and $a) and !($b) or $a or !($b or $b or !($b and $a and !($b and $b) and !$a) and !($a))))",false),
    ("$a or $a and !($b or !($a and !($b or !$b and ($a and !(($a) and ($a and $a and !$b and $b or $a) and $a or !$a and !($b or $b or $a or $a) or $b)) and !$a)))",true),
    ("!$b or ((($b or ($b and !(($a or $b and !($b) or ($b) and ($b and !($b)) and !$a or !$b or $b) or !$a or !$b or !$a) or !($a or $a and !$b) or !(($b and !$a and $a))))))",true),
    ("($a and $a and $b and !($b or $a) and !$a and $a and ($b) or ($a or !($b and !$b and ($a or !$a and $b or ($b or $a or !$b) and !$b and $a and !$b) and !$b)))",true),
    ("!$a and !$a or $a or $b and $b or $a and !$a and ($a and !$b or !$a or !$a and !$a or !$b and $a and !($a and $b and !$b or !$b or !$b or (($b and $b))))",true),
    ("$a and !($a and $b or !$a or $b and $a and $b or $b and $b or !$b or $a or $b or ($b and !$a or $a or $b or !$b) and !$b or $b or !$a and $a)",false),
    ("!$b and !($b or !$b or !(($a or $a) or !$a and $b or $a or $b or (($b and $a) or !$b and $a or !$b or !$a or $a and ($a and ($b) or $a and !$a and !$b))))",false),
    ("($b or $b) and !$a and $b and !$b and !($b or !($a and !($b and !$b or !$a) and $a or $b and $a and !$a) or $a and ($a or !(($b and $a or !($a or !($a and !$a))))))",false),
    ("$b and !($b and $b or ($a and !($b and $a or $b or $a) or !$b or $a) or ($a or $a and $b and !($a and ($a and !$a or (($b) and !$a and ($a and $a and $b))))))",false),
    ("!($b and ($b or $b or !($b and !$b) or $a or !($a) or !($a or !($b and $b and !$b or !($b and !$a) and !($b or !$b and !($a or $b and $a or !($b)) and $b or ($a))))))",true),
    ("!($b and !$b and !$a or (($a and ($b or !$a or $b or !($b)) or $a or !$b and !($a or ($a) or !$a) and $a) and !$a and $b or ($a or $a and ($a) and !$b) and ($b)))",true),
    ("$b and $b and !$b and ($b and !$a and $a or !($a or $a and $a) and !$b and $b and $b) and $b or !($a and $b and !$a) and $b or $a or $a and $a and $b",true),
    ("!$b and $b or !($b and ($b and $b) or !((($b or ($b and $a) and $a or $a or !($b) and $a or !($b) and !$a and ($a) or ($a or $a) and ($b and $a and !$b and !$b)))))",true),
    ("!$a and ($a and (($b and ($a or !$b and $a or !$b) or !($a and $a) and !($a or !$a and !$b) or !$b and $a and !($b or ((($b) and !$b or $b) or !$a or !$b) and $b))))",false),
    ("(($b and $b or !$a or !$a and $b or $b and ($a or $b or !$a) or $a or !$a or !$b and $a and $a) or $b and !($b and !($a or $a) and !$a and !$b or $a))",true),
    ("$a and $a or $b and !$a or ($b or !$a or $b) and $b and !(($b and !$b and !($b or !($b and !$b or !$a or !$b and !$a or $b) and $a or !$a or !$a and $a)))",true),
    ("!$b and !($b or $b and !$b and $b) and $b or $b or !$b or !$b or !$a or $a or !$a and ($b or $b and !$b and $a and !$b) or $b or !$b or !$b and $a",true),
    ("!($b and $b and $a and !(((($b or ($a or !$a or ($a) and !$a) and $a or !$a) and $a) and ($a) and !($a or !$a) and !($b) and !$b or (($b) and $a or !($b and ($b or !$a))))))",true),
    ("($b or $b and !$b or (($a and ($a and !$a) or $a and $a) and !$a and (($b or !$a or $b or !$a and !$a) or !$b and !($b or $a) and $b and !($b and (((($b) or !$a)))))))",false),
    ("!($b and !(((($b and $a and !$b and !$a or ($b or !$b) and $a) or $a or $a and !($a or $a) or !$b) or ($a or $b)) or !($b) or !$a and $b or !$a or !$b and $b))",true),
    ("$b or !$b and !(($a or $a and $a and $b or !($a and ($b and !$a or !$a and !$b) and $b and $b or !$a or $a or !$a and $b and !$b or $a)) and $b and !$a)",true),
    ("!($b or (($b or !($a or !$b or $b) and $b)) or $b and !$a and !$a or $b and !($a and ((($a and !$a) and $b) and !($a) and !$a or $b or !$a and $b and !$b or !($a))))",true),
    ("($a or !$a or $b or $b or !$a or !(($a or !$b) and $a and !(($a or ($b or $b and $a) or (($b and $b or $a) and !$a) or $a and !$a) and !$b or ($a and $a))))",true),
    ("!($a or !($a or !$a) and !($a) and $b and ($b) or (($a or !($a or !$b or $b or ($b and !$b or $a or $a) or !$b and !$b) and ($b or !($b) or !($a or !$a) or $a))))",false),
    ("($a or $a and !$a and !$a or $a and $a or !$a and $b and $b or !($b or $a or !$b or !($b or !$b or !($b or $b) or !$b and !$a and !$a or !$b and $a)))",true),
    ("!$a or !($a and !$a or $b and !$a and $b) or !$b and !$a and $a or !($a or $a or !$a and !$a and $a) and $b and !$a and $b or (($a and ($a and !$a or !$a)))",true),
    ("!$b or !$b and !$a or !$a and ($b or !$a and $b and !$b or !$a or $a and !$a) and $a or !(($b and $a and !$b and $b or $a or !($b or $a or $b) or $b))",true),
    ("!$a or !$a and !$a and $a and !$a or (($b and !($b and $a and ($a and $b and !($a) and !(($a and $b or !$a and !$a and $b)) or !$a or $b and $b) and $a and $b)))",false),
    ("($b or $b and !$b and $b and !($a and $b and !($a) or $b or $a and !$a and !$a or $b and ($a or $b and !$a or $b and !$a and $a or $a or !$a or ($a))))",false),
    ("(($a or !($a or $a or !$b and ($a and !$b or ($b and $b) and !$a) and $a and !$b and (($a or $b or !$a or $a) and !($a and ($b or !$a or $a) or !$a) or $a))))",true),
    ("$a and ($a and !$b) or $b or $b and !$b and !(($a and !$b and !(($b or ($a) and !$a) and ($a or $a) and !(($a or $a)) or !($b or !$a and !($a and ($b or $b and $a))))))",true),
    ("!$a and !($a or !$b and !$b) or $b or !$a or $b and $b and ($a and $b or !$a or ($b and $b and !$b or $a and $a or !$a and !($a or $a or !$a or $b)))",false),
    ("$a and $a or ($b or !$a and !($b or $b or ($a and !($a or $b and !$a) or $b and $a) or !(($a or $b) or $b and $a and $b) or !$b and ($b or ($a or $a))))",true),
    ("((($a and !$a and $b and !$b) and $a or !$b or !$a and ($b and $b) or !($a or !$a or $a) and !($a and !(($b or $a or $a and !$b) and !$a or !$a or $b and !$a))))",true),
    ("$b or !($b and $b and $b or !$b and $a and $a or !(($b or $a or $a or (($a or $a) and !$b and !$b and $a or !$a) or !$b) and ($a and !$a or $b and !($a))))",false),
    ("!($a and $a and !$a and $a or $b or !$b or !$a and !$b or $a or !$b and !(($b and $b) and !$b or $a and $a) and $a or ($a or $b) and !$a and ($b or $b))",false),
    ("!($b and $b) and !(($b and ((($a and !$a) and ($a or $b or !$b and !$a) or !$b and !$b or ($b and $b or !($b or !$b) and $a) or ($a) or !$b and !$b) or !($b) or !($a))))",true),
    ("$a or ($a and !$b) or !$b or !$b and !$b or !$a or !$a and !$a or !$a and $b or !($b or !$a or !$a and !$a and !$a and !($b or ($a or !$a or !$b or !$a)))",true),
    ("($a and !$a or !$b or (($a or !$b or $b or $b and ((($b and ($b and $b or !($b) or $a or ($a) and $b) or $a and $b or !($b)) and $a or ($a or !$b or !($b)))))))",true),
    ("$b or $b and !$b and $a and !$a and !$a and $a and !$b or !($b and $a and !$b) or ($a or $b or $b or !$a or $a) or !$a or !($b and (($b and ($b or ($a)))))",true),
    ("!$a or !$a and $b or !$a or $b and !$a and !(($b or !$b and $b) and $b or ($a or ($b and !$b or (($a and !$b and !$a and !$b or !$b) or $a and !$b) and ($a))))",false),
    ("($b and !$b and ($a or ($a and !($b and $b or !($b and !($b or !$b)) and !$a and ($a or ($b or (($b and $a)) or $a and $a or !$a or !$a or ($b and !$a) and ($a)))))))",false),
    ("!$a and ($a and ($b or !($a and $a and $a or !($a) and !($a or !$b and $b or !$a and !$b or $b and !($a) or !$b or ($a and $b) and !(($b and !$a) or !($a) or !($b))))))",false),
    ("!$a and !$a and $a or $b and !$a and !$b and ($b and $b or !$a or !($a or $b) or !$b and !$b and (($a or !$b and ($a and $b or $a or $a) and $a or !($a))))",false),
    ("!$a and $a and $b and $b and !($a and !($a or (($a) and !$a and !$a or !$b or $b or !($b and $a and !$b or !($a and !($a or !$a and $b and ($b) or !(($b))) and !$b)))))",false),
    ("!$a and !$a and !$a or ($a or ($a or !(($b and $a and !$a or !$b or $a and $b)) or ($b and $a or ($a or !$a or !$a) or $a) or ($b and !$a or $b or $a)))",true),
    ("($a and !(($a and !$b or ($b or !$a) or $b or $b and $b and $b or $b and !$b and !$a and $b or !$b or $a or ($b) and !$a and !$a and $b and !($b and $a))))",false),
    ("!$a and $a and !($a and !(((($a or !($b) or ($a)) or !$b or !$b and !($a) and ($a or !$b and ($b) or !$a and !$a and !$b) or !$a or !$a) and $b and !$a and ($b or !$a))))",false),
    ("!($b or ($b) or (($b and !($b or $a and $a) and $a and $a and !$a) and $b and !$a or !$a or !$b or !$a or !($a or $b or $b or $b or $b and $a and !$b)))",false),
    ("!(($a or !$a or !($b or !($b or $b or !$a) or !$a and ($a) or !(($b or ($a) and !$b or !($b) or !$a)) and $a and $a) and !$b or !($b or $b and $a or !$a and ($a))))",false),
    ("!(($a and ($a) or !$b or $a and ($b and !$a) and $b or (($b or !$b) or $b and !($a and $a or ($b) or $b) or !($a and !$a and !$b and !$b or $b or !$b and $a))))",false),
    ("$a and !$a and $a and !($a and ($b or ($a and $a) or ($b) and $b and $a or $b or !$a or ($a and !($a) or $b and !$b or !$a or !$a and (($b) and !$b or $b))))",false),
    ("$a and $a or ($a and !($b and !($b) or !$a and $a or !(($a and !$a) and ($a and ($b or $b or !(($b) and $a) and !$b or !(($a) or $b or $b or (($a) or $b or $a)))))))",true),
    ("($a or !($a and $a and !$b and $a and $a and $b and $a or (($b or !$a or ($a)) and $a) and !(($a or !($a and !($b and $b or $a and !$b) or ($b or !$a) and !($b))))))",true),
    ("!(($a or $a or !$b) and ($a or !$b and !$b) or ($a and !$a) and ($b or !$a and !$a and !$b or $a or $b and !$b or !$a or !($b and !$b and !$b or ($b or !$b))))",false),
    ("!($a or ($a or !($b and $a) or $b)) and !($b or !$b or ($a and $a and $a or !$b or !($a and $b and !$b and $b or $a) or !($a or $b or $a or !$a and $b)))",false),
    ("!$a and $a or !$b and $a or ($b and $a or !$b or ($a or $b and ($b or !$a and $b and !$a) or !$a and $b or $b and $b or !$b or !$b) and $b) and $a",true),
    ("!($a and $a or (($a or !($b or !$a and ($a and !$b and !$a) and !$a and !$b or $a) or ($a) or !$a or $a and $b or !$a and !$b) or ($b and $a and $a or $a)))",false),
    ("$b or $b or !($b and !$a and ($b or $b and !$a or !$b or $b and !($a) and $a or !$b and $a and ($a) or $b or !$a or !$b) and !($a or $a or $a or !($b)))",true),
    ("($b and !(($b or $b and $b and ($b and $a)) and !$a and !$b and ($b or !$b)) or !$a and ($a) and !$a or !((($a) and !($a or ($b or !$b or $a) and !($b or (($b) or !$b))))))",true),
    ("!$b and !($b and !$a and !$a or !$a and $b and ($b) or $b or !($a and $a or $b) and !$b or $b or $a and !$b or !$a or !$b and !($b and ($b) and ($a and ($b))))",false),
    ("!$b and !($b and $b and !(($b and !($b) or $a and !($b and !$b and $a and $b) or !($b or $a) and $b and !($b or !$b or $b and !$b and $a or ($b) or !($a))) or !(($a))))",true),
    ("$b or $b or !$b and !($b or $b or !($b and $b and ($b and !$a) and !$a and $b or $b and !$b or $b or !$b and !$a) or $b and ($a and !$a or $b) and !$b)",false),
    ("$b or !(($b and $a or ($a or $a)) and ($b or $b or !$b and !$a or (($a) or !$a) and $b and ($a and !$b and $b) and !($a) or $b) and !$a or ($a) and !$a and !$a)",true),
    ("!($a and $a and $a or !($a and $b or $b or $a and !$b) and $a and $a and $b or !$b and !$a or (($a or $b or ($b and $b or $a and !$a and $a) or $a)))",false),
    ("$b and !$b or !($b and !$b or !($a or !$a or $a or $a and !$a and !(($b or !$a and (($a or $a and $b or !$b) and $a) or $b) and $a)) or $a and ($a and !$b))",false),
    ("($b and !($b) and $a and (($b or $b or !(($a and !$a or $a or !$a) or !((($a and $b)) and $a and $a and $a or !$b) or $a and !$b or $b or !$a) and $b and !$b)))",false),
    ("!(($a and !($a and ($a or !($a and !($b) or ($a) and !($a) and !$a) or !($a and $b and !$b) and ($a) or !$a and $a or !($b) and !$a and !$b and !($b and $b or $a) or $b))))",true),
    ("$b and $b or ($a and $a) or !(($b or !$b and ($b and ($a and !($b and $a or $b) or $a) and $b or !$a) or $a or !(($b or !$b or $b or $b and $a or $a))))",true),
    ("!$a and (($a and !$a and !$a or !$b and !($a or !$a) or !$a and !$a or !$b and !$a or !($b or $a and !$a or $b or !$a or $a and $b or !$a and !$b and $b)))",false),
    ("!$a and !($a or ($a or ($a or !($a and $a and !$a and !($b or $b or !$a or !$a or $a and $b and $b) or $a and !$a and !$b) and $b or $b) or ($b and !$b)))",false),
    ("!(($a or !$a or $b and !$a or !$b and !$b or !$b or ($a) and !$a or ($a) and !($b) and (($a and $b and $b and !$b and !($b)) and $a or !$b and !$a or $b or !$a)))",false),
    ("!$b and !($b and !$b and $b and ($b and !$a) and !($a or $a or !$b and $a) or $b and !$a and !$b and ($a and $b and !$a or !$a and $b) or (($a or !$a) or !$a))",false),
    ("(($b and !$b) or $b or $a) or $a and !($a and !($b) and !(($b and !$b) or !$b and !$a and $b) and ($a or !($a or $a and $a or ($a or $a) and ($b and $b or $a))))",true),
    ("!($a or !$a or ($a or $a and !($b or ($b and !(($b and !$b) and $a)) or $a) or ($b or !($b) and $a) and !($b and ($a) or $a or $a or $b and !(($b and !($a and $b))))))",false),
    ("!($b or $b) or ($b or ($a and !($b and !$a or $a or !$b and !$b and !$a and ($b and $a) and ((($a) or !($a) and !($a and !($b or $a and !($a) or $b) or !$a) and !($a))))))",true),
    ("$b and (($b or !$a or $b and !$a and !$a or ($b and !$b) and !($b or !$b) and !($a or !($b) and !$a) and !($b and $b) or $a and !($b) or ((($a or $a) and ($b and !$b)))))",false),
    ("!($b or !$b or !$a or (($a or $a) and ($a or !($b and $a or !$b and ($a) or $a) or !$b and !($a or !$a or $a) or ($b) and $a and !($a or ($b or !($b and $b))))))",false),
    ("!$a and !$a and $a and !($b and !$a or $b and !($b and !($a and !$b) or !$b or !$b or $a or ($a and !$a and $a or !$a and $a and $b or $b or !$a or $b)))",false),
    ("$b or !$b and (($a or $a or !$a) and !($b and $a and $a and ($a or $b and ($b) or $b and !$a)) or !$a or (($a and $a and $b) and ($b) or ($a or !$b and $a)))",true),
    ("!$b or ($b and !($b and $a and ($a or !($b) or !$b or !$b or !$b and $a) and !$b and $b or !$a or ($a and $a or !$b and $b or !$b or !$a) or ($b or (($b)))))",true),
    ("!$a or !((($a and ($a) or (($b) or ($a and ($a and !($a or $b) and !$a and !$b or $b)) or ($a or $a or !$a and !$b or $a) and $a and ($b and !$a) and !$a and $a))))",false),
    ("!$a and !($a and !$a or $a) and !$a or !($b and $a or !$b or $a) or $b and $a and !$a or !$a and !($b or !$a or $b or ($b and !$b and $b or !$b or $a))",false),
    ("($b or $b and $b or !($b or $b or $b and !$a or (($b and ($b and !$b)) or !($b or $a and !$b and ($a and $b and !$b or !($b) or !($b) or !$b and !$b or $b)))))",true),
    ("!$b and ($b and $a or $b and $b or !$b or !$b or $a and $a or !$b or !($b or ($a or !$b and $a or $a and $b and $a) or $b or ($b or !$b) or !$b))",true),
    ("$a and !($a and !$b or !$a or !$b or $a or $b or !$b or !(($a or !$b) and $b and $b and $b or !$b or !$a and !$b or !$b) or ($a or !$b and ($a) and !($a)))",false),
    ("!($b and $b and !$a or $a or $a and !$b or $a and $a and ($a or $a) and $b or !$a and $a and $a or !$a and !$a or !$a or !($a) and !($a and !$b and !$b))",false),
    ("($b or !$b or !$b and !(($b or !$b and !$a or !($b and $a and !$a) or !($b or $a)) and $b or $b) and !($a or !$a or !($a or $a) or !((($a or (($a) or $b) or !($b))))))",true),
    ("!$a or !$a and ($b or !(($b and !($b and ($a) and $a and !$b or !$b and !$a) or $a or $a or !$b or !$b or ($b and $a) or !($b or $a or !($b) or ($a and !$b)))))",false),
    ("!$a and ($a or ($b or !$b or !($b) or ($b or $a)) or $b and !$a and !(($a and !$a and $b) and $a) and $b and !$a or !$b) and $b and !($b or $b) and $a and !$b",false),
    ("$a and !(($a or !$b) or $a) and !$a and ($a or ($b or !$b or $b or $a and $b or $b or !$a or $a or !$a and !$a or $b or $b and $a and $a or $a))",false),
    ("($a or $a and $a) and !($b or !($b or !($b and !$a or !($b and !($a and !$a and ($b or $a or $b)) and !($a) and $a or !($a and !$a)) or $b)) and !$b or $a and !$a)",true),
    ("!($b and $b and $b or ((($a and !$b and $a and !$b or $a or !$a) and $b or $a) or $b and !($b or $a or $b or $a and $a or $a) or !($a or $b and $a)))",false),
    ("!(($b or !$b) or !$b or $b or !$a and ($b) or !$a or ($b) and !$a or !$a and !($b or !$b and !$b) or ($a and !$a) or $b and $b or !$a and !($b) or !$b and !$b)",false),
    ("$b and ($b and ($b and $b and !$a or !$a or !$a and $b and !($a and !$a and $a or $b or $b)) or !$a and $a or !($b or !$b or $b) or ($b and $b and $a))",false),
    ("!(($a or ($a) or $a or ($b or !$a) and !$a and $b and (($a and !$b) and !$b or $b and !$b) or $a) and !($b or $a or !$a or $a and !($a or !$a or $a and $b)))",true),
    ("!($a or $a) or ($a and !$b and (($b and $a or $b and !$b or $b and !$b and !$b or $a)) and !(($b and ($a and $b or !$a and $a) and !$a or $b) or $b or !(($b))))",false),
    ("!$a and !$a and ($b or $a and !$b or !($a and $b and ($a) or (($b and !$b and !$b and !$b or !$b) or !(($b or !($a) or $b and !($b and !$b))) or !$a or $b)) or !($a))",false),
    ("(($b and !$b or !$b or !$a and !($a and $b and $b or $b or $b and $b or !($b or $a or $b or $a) and (($a and !$a or !($b or $b) and !$b and ($b))) and $a)))",true),
    ("$b and ($b and (($b or !($a) and $a) or !$a and (($a) or !$b or !(($b and !$b or !$b) and ($a and $b and $a)) or !($b) and ($b) and ($b) or $b) and !($b or !($b) or (($a)))))",false),
    ("!$b or !$b and ($a and !$b or ($b and !($a and !($a)) and $a or (($a or !$b) or !($a) and !$b or !($a or !($a and $b or !$b) and ($b)) or $a and $a and !(($b) or (($b))))))",true),
    ("(($a or !$a or ($a or $a or !($b or (($b and !$b) or !$a or $a and !($b and ($a or !$a)) or !(($b) or !$b and (($a and $a and $b) and $a) or !$a or $b and $a))))))",true),
    ("($b and !(($b and !($b) or $a or $a) and $a) and !($a and !$a or !$a and ($a and !$a and $b) or !($a or !(($b and $b and !$b and !$a) or !$b or $b and $a) or $a)))",false),
    ("!$a or (($a or !(($b or ($a) or ($b or (($b and !$b)) and $b or $b or !$a or !$a) or $b or !$b or !$b and $b) and $b and (($a or !$b or !$b or !($a) and $b)))))",true),
    ("!$b and ($b and $a and !$b or !(($b and $a and !$b) or ($a or !$a) and $b and !$b or !$a or !($a and ($a or (($b or !$a and $a and !$a and !$a) or !$b or (($a)))))))",true),
    ("!$b and ($b or $a and $a and !$a or (($a and $a or ($a or $b) and !$a or !$b) or ($a or !$b or !$b or !($a or $b or $a or !$a and !$b) and $a or !$a)))",true),
    ("!($b or $b or $b and $b and !$a) or ($b or (($a and $b or !$a or $b) or !(($b and $b and $a) and !($a) or $b or !($a or $b) and $a and !$b or $a or $b)))",true),
    ("$b and !(($b and $a and !$a or $a and !$b) and !($a or $a or !$b) or !$b or !$b or $a or !$a and $b and !$b or $b and $b or $a or !($a and $b and !$b))",false),
    ("!$a or !$a or ($b and !$a and !$b) or $a and !($a or !$a) and ($a and ($a and $b or !(($b or $a or !($a or ($a and !$b or !(($a or $a or $a) or !$a or !$a)))))))",false),
    ("!(($a or !$a or !$b and ($b and $b) or ($b) or $b and !$b and !$a or $b) and !$b and !$b and !$b or !$a or !$a or !$b and !$b or !$b or $a and !$a or !$a)",false),
    ("!((($a or !($a or !$a) and $a) and !($a or $a) or ($b and $a and $b and !$b and !(($b or $b) and !$b or $a or $a) or $a) or !($b or !$b or !($b or $a or !$b))))",false),
    ("($a or $a or !($a) and ($a and $b) or $b and $b or ($b and !(($a or $b and !$a and $a or !$b) or !($b) or $b and !($b and !$b or $b or !$b and ($b and $b)))))",true),
    ("!$b or !($b and $b or $b and !($b and !(($a and !($a) and ($a or !$b or !$a) or ($b or $b and !$b and $b and $a or $a or !$a) or !($a or !$a or !$a and !$b)))))",true),
    ("$b or ($b or !($b or !$a and !$a or ($b and $a) and !($b and !$b or (($b and $a) and $b and $a) and ($b)) and !$a) and !$b or !($b or (($a or $a or !$b or !$b))))",true),
    ("$a and ($a or ($b or $b or $a and $a and !($a or !$b and !($b or $b and $b or !$a or $b or $b) and !$b or !$a) and $a and $a) and ($a or $b and $a))",true),
    ("!$a and (($a or $a or !$a and !$a) and !$a or $b or !$b) or !$a and !$b or !$a or !(($b and !$b or $b and $b and !$a and !$b or !($a and !$a) and (($a and $a))))",false),
    ("$a and !($a and $b or !$a and !$b or $a) and !($b and ($a or $a or $b) and $a or (($b and !($a) or $b and $b) or !($b and !(($a and ($a) and $b) and !$a or ($a)))))",false),
    ("!$b or (($b and $a or $b and !$a) or $a and !($b and !$b)) and !($a or !$a and $a and !$b or !$a and !$b or ($a or !$a or $a or !($b or $a or $a and !$a)))",true),
    ("($a or !$a and $b and !$a and ($a and $a or ($a and $b or !($b) or !($a or !($a or $b) and $a or $b) and $a and $a or $a or $a or $a and $a or $a)))",true),
    ("($a and $a and !(($a and ($a or !$a) and !($b or !$a) or !$a or $b and !($b and $a or !$a and $a and $a or $b and !($a or !$b and !($b))) and ($a and (($a and !$b))))))",false),
    ("$a and !($a and ($a and !$a) and !($b and !$b and $a or !$a) and !$b or !$b or ($b or !$a or !$b) or $b and !($b and $a and $b or (($a or $b) or !$b or ($b))))",false),
    ("$b and !((($b or $b or $a) and ($b and $b) or !($b and $b and !($a) and !($b or $b and $b or !$a and ($a and !$b) or $a)) or ($b or $a) and $b or !$b) and $b)",false),
    ("!($a and !$a or $a and !$a and !($b or ($b or !$b or $b or $b) or $b and $b or !$a or !$a and !$a and $b) or $b and $a or !$a) and !$a or !($a and !$b)",false),
    ("!($b and !$b and !($b and !$b or !($a or !$a and !$b or ($b and $b and $a) and !$b or $a and $b and ($b and ($b and !$a and !$a or !$b or $a) or $b or $b))))",true),
    ("(($a and !$a) or (($a or $b and !$b or ($b and (($b) and $a or $b and ($a or !$a or !$b or !$b or $a) or !$b) and $b and !($b or !$b) and !$a and $a and ($b)))))",true),
    ("$b and !$b or ($b and $a and !$a and !($a or !$b or !($b and !$b or !($a or $a or $b) or !$b and !$a) or $b and $a or $a or !$b) or !$b and !($b or $a))",false),
    ("!$a or (($a or !($b) or $a) and !$b or ($b and (($a and !$a) and ($a or !$b or ($a)) or !($b or !($a) and !(($a) and ($a and !$a)) and !(($a and !$a and !$a)) or !$a and $a))))",true),
    ("!($b and !$b and $b and ($a and !($b and ($b) or !$a or !$a)) or ($b or !($b or ($a) and ($b or !($b) or !$a) and !$a and ((($b) and $b) or $a or $b) and $a or $b)))",false),
    ("!$b and !($b or !(($a or $a) and !$b) or $b or !$a or $b and $b) or !$a and ($b and $a or !$a and !(($a and !$a and !$b) or ($a and !$b) and $a or $b) and ($b))",true),
    ("$a or !$a and !$b and $b and !(($a or !$a and $b or !$a or !$b) or ($a or !$b and $b and !($b or $b and !$b and ($a or !$b or $b and !$a) or !$a) and ($a)))",true),
    ("$b and $b and $a and $a or !$b and $a and !$b or !($a or !$b and !$b) and $b or !$a or ($a or !$b and !($a and ($b or $a and !$a or ($a and $b) and !($b))))",true),
    ("$b or $b or !$b or !$a and (($a and !$a) and !$b or !$b or ($b and $b or $b or $b and !$a and $b and !$b or $a or $b and !$b)) and !(($a and $a or !$b))",true),
    ("!($a or !(($a or $a and !$b or !($a) and $a or $a and !$b or $b or ($b or !($b)) and !$b and !$a or $a or $a and $a and ($b or $b and !$b and $a and $b))))",false),
    ("($b or !$b or !($a and $a) or $a and $b and $a or !$a and !$b and !$a and !$a and ($b and ($a) and !$b or ($a) and !$b and ($a or $b and !$a or $a or $a)))",true),
    ("!(($a and !$a and ($b or $b) or $b and !($a or !$a and ($a and !($a) and $b and $b and !($a or !($a or !$b and !$a and ($a) or !$a) or !$a) and !($b or $a) and ($a)))))",true),
    ("$a or ($a and $a or $b or $a and !($a) and !$a) or $a and !$b or ($a and ($a) or !$b and $b and !($a) and !($b or $b and !$a and $b or !(($b and $a) or $a)))",true),
    ("$b and $b or !($a or ($b or !$a or !$b and !$a) or !($a and !$b or ($b or !($a and !$b) or $b and !$a and $b) and $b and !($b)) or !$a and $a) or $b and !($a)",false),
    ("($b and ($b and !($a and $b and !$b or $a and !$a or !$a or $b or $a and ($b and !($b or !$a)) or !$a or !$a)) or !$b or $b or $a or $a or !($a or ($b)))",true),
    ("$a and ($a and !($b and !($a) and $b) and !($a and ($b and !$a and !$a and $b and !$a and $b or $a) and ($a and !$a and $b or !$b or $a and (($b or $a) or ($b)))))",false),
    ("!$a or ($a and !$a or !$b and $a or $a or $b or $b) and $b and !$a and $b or $a or $a or !$a or !$a and !(($b or !$a and !$b or !$b and $b and !$b))",true),
    ("!$b and $b or !(((($a or $b or !$a) and $b or !$b or ($b and $b) and !(($b and ($a) or !($b or !$b) and $a and !($b) and $b) or $a and $a) and $b or !$a and !($a))))",false),
    ("!$b and !$b and $b and ($b or !($a and !($a or $b or !$a and !$b) or !$b or $b and !$a and $b or !$b or !($a or $b and !$b or !$a or !$b) or !$a and $a))",false),
    ("$a or ($a or !$b or ($a) and (($a or !$a and !$b and !$a) or ($a and ($b) or !$b or (($b) and !$a or !$b) and ($a or !$a or $b) or $a or !$b and $a and ($a))))",true),
    ("$b or (($b and !($a and !$b and !$a) or $a) or $a or ($b) and $b and $a and !($a and $b or !$a or !($b and $a) and !$b and !$a) or $b or !$a and !$a and !($b))",true),
    ("!$b and $b or !$a and $b or !($b or !$b) and ($b and $a or $a or ($b or !$a or !$b or !$a or $b or !$b or $a) or !$a and $a and $a or ($a and !($b)))",false),
    ("!($a and !$a or $b or !($b or !$a or $a and $b and $a or $b and ($a and !(($b and !$b and ($a) and $b and $a) or $a) or ($b or !$b or $b)) or !(($a and !($b)))))",false),
    ("$a and $a or ($b and !($a and $a or !$a and !$a or !$a or ($b) or !$a or $a or $b and !$b and !$a or !$b and !$b and $a and $a or $a or $b and $b))",true),
    ("$b or !$b or !$b and !$b and $b or ($a or $b and $a or !$a and ($a or !$a or !($b and !($b or !$b and $a or !$b) or $b) and !$b and !($a) and !$b and ($a)))",true),
    ("!$a or ($a or $b and ($a) and $a or !$b or (($b and ($b) or !$b) or !$b and (($a or !($b and $a) or !$b and ($a) or $b and !$b or $a or $b or ($a or !$b)))))",true),
    ("!$b and !($b and !$b and $b or $b or ($a and $a or $b and $b or !$b or !$a and ($b and $b and $a or $b or !$b) or !$b and $a or ($b and !$b or $b)))",false),
    ("!$a or $a and !($a or !($a and $b or !$b or !$b and ($a or $b and $b) or $a and $a and !$a or $a) and !$b or !($a and $b and !$b or $a or !$b and !$a))",false),
    ("$b or !$b and !(($a and !$b or $a or !($a and !$b or !$a or $a or !($b) or $b and !$b and !($a or $a or ($b) or $a or !$a) or !$a and !$a or !$a and !($a))))",false),
    ("$b or $b and !$a or !$a and ($b or $b or $a and !$a and !$a or !$a or !$b or $b and !$b and $a and !$b and $b or !($b and !$a and !$a or $b and !$b))",false),
    ("!($a and !$a and !$b) or !$a and $b or !$b and ($b and $b and !$a or !$b and !(($b or ($b) and !$a and !$b or !($a or !$b) or !$b) and !$b and $b and !($a and $a)))",true),
    ("!($a or (($a and ($b and !(($b)) or ($a and !$b or $a or $a and !$b and $a) or ($b) or $a or $b or ($a) or ($a and (($a and ($a and !($a and $a) and !$b and !$b))))))))",false),
    ("$b and $b and $a and $b or !(($b or ($b or $a or !$b or !$a or !$a and !$b and !$a and $a or $a and !$b or !$b or !$a) or !$a or $a or $a or $b))",false),
    ("!($a and $a or !$a) or ((($b or ($b) or ($a and !($b) and $b and $a) and ($b or !(($a or $b or $b or !$a) or !$a or $a) and !$a and !$a and !$a) or $a) and $b))",false),
    ("($b or !$b or !($a or !$a and !$b and !$a and ($b or (($a and !$a and ($a or !$a) and $b or !$a)) or $a or !$a and $a) or !$b or $b or $b or $b and !$b))",true),
    ("(($a or !($a or !$b and !$a) or !$a) and $b and ((($a) and (($a or ($b and !$a) and $b and $a or !($b and !($a or $b or !$b) or !$a) or !$a or !$b) or !($a or !$a)))))",false),
    ("(($b or !$b and !$a or ($a and ($a) and $b or !($a and !($a)) and !($a) or ($b and !$b and !($b and !($a) or $b) or !$a and ($a and $a or !$a)) and $b or !($a and !$a))))",true),
    ("(($a and ($a or $a or $b or !($b or ($a and !$a) or !$a and $a) and !$b or !$b or !$a and !($a or !($b or $a or !($a)) or $a and !(($b or !$a or !$a and !$a))))))",true),
    ("($b or !$b) or !$b and $b and !$a or !$a or (($b and $b and !$b and !$a and !$b or !$a or $b or $b or $b or !$a or $a and $b and !(($a) or !($b or !$a))))",true),
    ("!($b and !$b and $b or $b or ($a and $a and !$b or !$a) and !$b or !$a or !$a and $a or !($b and !$b) and !$b) or ((($a and $b or $a and !$b and $a or $a)))",true),
    ("($a and !$a and !$b or !$b or !$b and ($b and !$a and $a or $a and $a and $b) and $a and $b and $b and !($a and !$b) or $b and !($a or $a and !($a and $b)))",true),
    ("($b and $b or ($b and $b or !($b or !$a) and !$a or $a and !($b or $b) and ($a or !$a) and !(($b or !$b and $b or !$a or !$a) or ($b and $a) or ($a or !$a))))",false),
    ("!$b or $b and !(($b or ($a or !$b and !$b or !$a or $a and !$b or !$a or $a) or $a)) and !($b or $b or !$a or $a and !$a or !($b or $a or !$a or !$b))",true),
    ("$a and !$a or !$a or !$a or !$a and !($b or !$a and !$b and !$b or $a or !$a or !$b or !$a and !$b and !(($a) or !$a and $a and $a and !$b and !$a and !$b))",false),
    ("($a or ($a or (($a or $b and $b and !$a) or !($a or !$b or !$a) or $a) or !($a or !($a) or $b and $b) or !$a or $b or !$a or !($a) and !($a or $a) and !$a))",true),
    ("($a or !($a and !$b and !($a and !$a) or !$a or $b or $b and $b and ($a and !$a or !$b) or $b and !$b) or !$b and $a or !(($b and $b or ($a and $b) and $a)))",true),
    ("!($a and !$a and !($b and ($a and !($a and !$a and !$a and !$b) and !$b or ($b) and !$a) or !$a and !$a or $b and !$a or !$b and !($a or !$b) or $b) or $a or !($b))",false),
    ("!($b and ($b and !($a or !$a) or !$b) or !($a and $a and $a and !($a and !($b and !($a or !$b and ($a) and !$b and !($b or !$b) or $b) and ($a) or $b or !$a and $a))))",false),
    ("!$a and $a or $b and $b and !$b and !($b or !$b and ($b or ($a or ($a or !$b and !$a and $b) and !($a) and ($a or $b) or $b and $b and !$a or !$b or !$a)))",false),
    ("!$b and ($b or ($b and $b and $a or ($a and $b and !$a and $a and !$a) or !($b or ($a and $a and !$b or $b or !$a or !$a or !$b and ($b)) or $a) and $b))",false),
    ("$a and !($a or !(($b and $a and !$a and !($a and !$a) and !$b or !$b and !$b and !$a or !($b or $b or $b) or !$b or !$b or $a)) or $b or !$b or $a) and !$b",false),
    ("!$a or $a and $b or !($a or $b and !$b or $a and $b or !$a) or !$b and ($a and $a) and !$a or $b or !($a and ($b or !$a and !$a and $b and ($b and $a)))",true),
    ("((($b and !$b and !$a) and !$a or $b or $a) and !($b and !$b or !$a) or $a) and ($a or $b or ($a or $a) and $b or !($b or !($b and $b) or !$a and $b or !$a))",true),
    ("!$a or !$a or !(($a or $a) and !$b and ($b and !($b or $b) and !$b and !$a and $b and !$b and !$a or $a or ($b and $b and $a) and !$b or !($b or !($a or $b))))",false),
    ("!$b and !$b or !$a or !$a or !($a or !($a or $a) or ($b or ($b or $a or $a or ($b or !$a or !$a) or !$a and $a and !$a) and !$b and !$a or !($b or $a)))",true),
    ("$a and $a and !($b and ($b or !$b and $b or !$b and !($a) or !(($b or !$b or !$b or !$a) and !($b and !$b) or !$b) or !(($a or !$a) or $a or ((($b or $a or !$b))))))",true),
    ("!$b or $b and !(($b or !($a or !$a and $b) and !$a and $b or !($a or !$b) or $b) or $a or ($b) and $a or !($a and $a or !($a or $a and !$a or ($a) and $a)))",true),
    ("($b or !$b and $b) and !($b and ($b or $b or !$b or !$b and !$a or $a and $b or $a and !$a or $a) or (($a) and !$a and !$b) and ($a and !$a or $a and $a))",false),
    ("(($a and ($a) and !($b) or !(($b) or ($a or !$a or !($a and $a) and !(($b and ($b)) or $a) or (($b or !($b) or !$b)) or $b) or !$a and $a) and !$b and !$b and !$b or !($b)))",true),
    ("!($a and ($a and (($a and !$b and !($a) or $a) and $a) or $b and !(($a and !$a or ($b and $b or $b and !$b or !$b) and !($b or $b) or !($a and ($b) and !$a or $b)))))",false),
    ("!(($a or $a) and (((($a and !$b) or !$a or ($a or !($b or $b or !($a or ($a and !$a) or !$b) or $b or $a) and ($b or !$a and $a) or $b) and $b and $b or ($a)))))",false),
    ("!((($a or $a and !$a and !(($a) and ($a) and $b) and ($a or !$a and !$a or $b and $a or ($a and !$a and !($b) and ($a or $a or !$a and $a and ($b and !$a or !$b)))))))",false),
    ("!$b or !($b or $b and $b or $b and (($b and !$b) and ((($a) or $b and ($b and $a or !$a)) and !$b or $a) or $a and (($b or !$b or (($a and $b and ($a or !$b)))))))",true),
    ("!($b or !$b or !($b or $a and ($b and ($a and !($b and !($a and $b) and !$a) and $a) and ($b or $a) or ($b or $b or !($a and !$b and !$a) or ($a and $a or !$b)))))",false),
    ("($b and $b and $a) and (($b or $b and !$b or $b or $b and $b and !($a or !($a and !($b) and $a) and !($b and !($b) and !($a and $a or ($b) and !$b) and !$b) or $a)))",false),
    ("!$a and !$a or (($a or !($a or !$a and !$b or ($b or !($b and $a) or $b) and !$b)) or ($b and $b and $a or !($a) or !(($b and ($a) or !$b or $a or !$b and !$b))))",true),
    ("(($a and !$a or !$b or !($b) and ($a and ($b or $b or !($b and !$b and !$a) or !$b and !$a or !$b or $a or $a or !($a and ($a or !($b)) and !$a) and !($a and !$a)))))",true),
    ("$b and !($b or ($a and !($b) and (($b and !$a or ($b or $b or !$a or !(($b or !($b and !$b or !$b) and $a or $a) or $b)))) or ($b or !($a and $b or !$b or $b))))",false),
    ("$b or ($b and (($b or !($b) or !$b and $a and (($b and $b or !$a and $b) or !$a or $a or ($b and $b) or !$a or !$b and $b or (($b or !$a and ($b and !$b)))))))",false),
    ("$a or !$a and ($b or $b or !($b or $b and $a or !$a) and ($b and $a) or ($a and !($a or $a and ($a or !$b and !$a or $a) and $b and !($b or $b) or !($a))))",true),
    ("(($b or $b or !($b or !$b or !$b or ($a) or $a and !$a and !$b or $a and !$b or !$a and !$a) or $b and !$a or !$a) or $a or !($a) or !((($a or $a) and !$a)))",true),
    ("!($a and ($a or $b and !$b and !$b and $a and !($a and $a or $b) or $a) or !$b or $a or !$b) and $a or !(($b and $b and !($a and $b and !$b or !$a or !$b)))",true),
    ("!(($a and ($a or ($b) or !($b and $a)) and $b and !$a and !(($b or !$b or $a) and $b or !$b or ($b or !($a and $a) and ($a and !$b and $a and !(($a or (($b or !$a)))))))))",true),
    ("!(($b or $b and (($a) and !$a) or !(($b or $a)) or ($a or $b)) or ($a) and !$a and !$a) or !($b or !$b and !$b) or !($b and ($b or !$a or !$a) or !$a) or $b and !($a)",true),
    ("$a or !$a and $b and $a and !$b or !(($b or $a and $b and !($b or $a and !$b and $a or $b or $b and $a and !$a and $a or $a) or !$b) and !($a and $b))",true),
    ("!$a or !$a or $b or !$b or $b or $a and $b and $b and $a or ($a and (($a and $b or !($b and $a) and !$a) or (($b and $b or $a or $b or $b and !$a))))",true),
    ("!((($a or $a or (($b and !$a and !($b) or !$a or $b and !$b and !($b)) and !($b and !$b and !$a) and $b) or $a or !$a and $b or $a and !(($a or $a and !$a or !$a)))))",false),
    ("!$a and !$a or !$a and $b and !($b or (($a or !$b and !$a and !$a and $b and !($b) or $b or $b) and ($b or !$a or !$a and !$b) or ($a or ($a and $a or !$b))))",false),
    ("!(($a and !$a) or !$a or !($a or !$a or $a and !($b or ($a or $b and ($a and $a or !$a or ($b)) and !$a or !$b and !$b and $a or !($b and ($a or !$a and !$a))))))",true),
    ("!($a and !$a or $a or !$b or !($a or !(($b and $a) or !$a or ($a or $b and !$a or $a and !$a or $a and $b and $b or !$b or !$a or $a and !$b) and !$a)))",false),
    ("!(($a or $a and !$a or $a) or !($a and $a or !($b and $b or (((($b or $b and ($a) or $a or !$b) or !($a) or !($b) and !$a) and !($b and !$a) or !$a and $b and $a)))))",false),
    ("!($b and !$b or !($b and (($a) and !($a or !($a) and $b and !$a or ($b and !$a and !$a and !$b) and $b and !$a or !($b) or !$a or $b or !(($b and !$b) or !($b and !$b))))))",false),
    ("($a and $a or $b and !(($a and ($a or !($a or !($b) or ($a and !$a) and $b) and !($b or (($a) and !$a) and !$b) or $a) and ($a or $b and $b or !$b or !$a or !$b))))",true),
    ("($b and !$b and $a and !$a or $b and !$a and $a or $a and !$a) and $a and !$a and !($b and !$a or !$b or !$b and ($a or $a and $a) and !$a or $b) or !$a",false),
    ("$b or !$b and !(($a or !(($a and $a or !$a or ((($b and !$a)) or $b or $a) and !$b) or ($b or $a and !($b) and !$b or ($a and $a))) or $b or $a and $a and ((($a)))))",false),
    ("!($a or !($a or !$b) or !($a or !($b and $b and $b) and $b or !($b)) and $a or (($a or !($b) or $b and $a and $a and !$a) and !((($a or $b) or !$a or !$b and !$a))))",false),
    ("!($b and !$b or $b or $b or $b and !$b or !$a) or !($b or ($b or !($b and !$a or $b or ($b or !($b and !($a) and $a and !$a or !$a or !$b and $b) and $b))))",true),
    ("!($b and !$b or !$a and $a or ($a and $a) or !($b and ($b and $b or !$a) and ($b and $a or $a and !$b) or $b and ($b or ($b or $a and $b and !$b and $a))))",false),
    ("$b or $b and $b or !$a and !$a and $a or !($a or $a and !($b and $b) or !$a and $b or $b) or !$b and $b and $a or !$a or $a or $b and $b and $a",true),
    ("!($a and ($a or !$b) and !(($b or !($a or $a) and !($b or $a or $a) and ($a and !($b and $b and $b) or !$b) or !($a or !$a) or !$a) or !($a and ($b or $b or !$b))))",false),
    ("($a and !$a or !$a and !$a and !$b or !($b and ($b and ($b and !$a or $a and !$a and !$a or !$b) and ($b and $b or !$a or $a) or $b or $a or !$b and !($a and $a or (($b or $a or $b) or $b) and $a and (($a) and !$b) and $a)) and !$a))",true),
    ("$b and $b or ($a and $b and !$b or !$a and $b and !$b or $a and $b or !$b and !($b or !$a or $b or $a and $a and !$b) and !($a or !$b or $b) and !$b and $a and !$b and $b or ($b or $b and $b and $b and $b or $b or !$b))",true),
    ("($b and ($b or $a or ($b) and $a and !($a or !$b or !($b and $b or !$a or !($b) and $b) and $b or ($b)) and !$a)) or !$a or !$a and $a or !($a and !$a or !($b and !$a and $a or !$a or !($a or ($a and !$a) and !$a) and !$b or $a and ($b)))",false),
    ("($b and !$b or ($b or $a or ($b and !$a and !($b and !$a and ($a or !($b or $b or !$a and ($b) or !$b) and $a and ($a) and !$b) or !($a or !($a and !$b) or !$b and ($b) or $b or !(($a) or ($a and !($a) or $b or !($b and !$a)) or !$a) and !($a))))))",true),
    ("$b and $b and !$a and !$a and $a or $b or !$b and (($a or !$b and $b or !($b)) and (($b and $b or ($b or !$b or !(($a)) and ($a) and $b) and $b or !($b and !$a)) and $a and (($b and !$a and !$b or ($b) or !($b or $a and !$a and !$b) and $a))))",true),
    ("$a or !$a or !$b and !$a and ($b and $b) or $a or $b or !($a or !($a or $b or $b and !($b and $b) or $b or !$a) or !$a and !$a or !$a or !($a and !$a and $b or !$b) and !$b or $b and !$a or $a and $a and $a and !$a) or $a",true),
    ("!$a and !(($a or !$a or ($a or (($a or ($a) or !$b or !$b) or $b and $a or !$b) and ($a) or $b or ($b and (($a and !$b and $a and !$b) and $a) and !$a and !$a or $b or !$b and ($b or $b or ($b or !$a and ($a and !$a or !$b or !($a))))))))",false),
    ("(($a and ($a or $a and !$a and ($b) or $a or ($a and $b) and !$a or !$b or ($b or !($a) or $b) and ($a and (($a) and !$a or !$b or ($a)) and !(($a or !($b and !$a and $b and $a) and $a and $b) and ($b and ($a or !$b or !($b or !($a or $b)))))))))",true),
    ("!(($a or !$a or !($b or (($b or (($b and !$b or $b or !$a) and $b) and !($b)) and !$b) or $b) or !$b and !$b and ($b) and !$b) or !($b and ($b or !($b and $a or !$a) and $b or ($a and !(($a and !$a and ($a) and $a) and $b or !$b and !$b) or (($b))))))",false),
    ("(($b and ($b or ($b or !$a and $a or !$a or !$a or $b or !($b or !$a) or !(($b or !$b or !$b or !$a and !($b and $b and !$a or $a or !$b) or !$b) or !$b or !$a)) or !($b and $a or !$b and !$a) and ($b and ($a) and ($b or ($b) and !$a)))))",false),
    ("!(($b or !($b or $a or (($a and !(($b or !$b) or !$a) or $a or !$a and ($b))) or $b or (($a) and !(($b and !$a or $a and !$b or ($a or $b)) and !$b or !$a and $b or $a) and $a and !$b)) and ($b and $a or $a) and !($a) and $b or $b and !($a)))",true),

    ];
}