Make a wff false (Applied logic)

[CJPowell27]

Hey guys, I've been trying to study for my midterm that is next Tuesday by doing a bunch of problems in the book and I've come across one that is completely stumping me. Basically I'm supposed to find integers that make the given wff false. I was wondering if someone could just give a hint or some method to solve this because I've tried about 50 combinations of numbers with no luck.

The given wff is: {True} if x < y then y := y - x {y > 0} over the domain of integers 

I've basically tried to use logic to narrow it down, because the precondition does not help narrow the integers down at all; so I decided that the integers cannot be the same number because that would not satisfy the operation. I've tried using the assignment axiom to make it {y - x > 0} if x < y then y := y - x {y>0} but that didn't seem to help at all.

[unkn0wn1]

it looks like you check if y is larger than x and if so subtract x from y and set it equal to y.

 

so try to make x larger than y?

[CJPowell27]

4 minutes ago, unkn0wn1 said:

it looks like you check if y is larger than x and if so subtract x from y and set it equal to y.

 

so try to make x larger than y?

Wow I was way over thinking that then lol

[straight_stewie]

6 hours ago, CJPowell27 said:

Wow I was way over thinking that then lol

Just as an aside, and because you've already figured it out, the output of this function can also be defined as y = y - (n - k) where n < y, and k is the i^th term in the set, minus one.
This means that there is a closed form solution to get the i^th item in the set. Can you derive it?
Additionally, the goal of the original problem is to find the set that makes the function false. There is also a closed form solution to get the i^th term not in the set. Can you derive this function?