theorem :: NUMBER15:52

for x, y, z, t being positive Nat st x <= y & y <= z & z <= t holds
( (((1 / x) + (1 / y)) + (1 / z)) + (1 / t) = 1 iff ( ( x = 2 & y = 3 & z = 7 & t = 42 ) or ( x = 2 & y = 3 & z = 8 & t = 24 ) or ( x = 2 & y = 3 & z = 9 & t = 18 ) or ( x = 2 & y = 3 & z = 10 & t = 15 ) or ( x = 2 & y = 3 & z = 12 & t = 12 ) or ( x = 2 & y = 4 & z = 5 & t = 20 ) or ( x = 2 & y = 4 & z = 6 & t = 12 ) or ( x = 2 & y = 4 & z = 8 & t = 8 ) or ( x = 2 & y = 5 & z = 5 & t = 10 ) or ( x = 2 & y = 6 & z = 6 & t = 6 ) or ( x = 3 & y = 3 & z = 4 & t = 12 ) or ( x = 3 & y = 3 & z = 6 & t = 6 ) or ( x = 3 & y = 4 & z = 4 & t = 6 ) or ( x = 4 & y = 4 & z = 4 & t = 4 ) ) )