package engine

var (
	operands = OperandMap{"$a": true, "$b": false}
	// Key: condition Value: expected result according to operands
	conditionMap = map[string]bool{
		"$a":                           true,
		"$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,

		// size 10

		"!$a or !$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,

		// size 20

		"!($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,

		// size 30
		"($a and !$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,
	}
)
