Hi. Though I'm not entirely sure what the effect is that you are going for, I can say why the building won't get chopped while the player character is in it.
[code:2zl0dffx]+ Player1box: Player1box overlaps Buildingfloor
+ Building: Pick closest to: Buildingfloor.X, Buildingfloor.Y
-> Inside: Set animation to "Normal0"
-> Building: Set animation to "Cutaway"
+ System: Else
-> Inside: Set animation to "Normal" & Global('Chopped')
-> Building: Set animation to "Normal" & Global('Chopped')[/code:2zl0dffx]
Pressing tab modifies the global variable 'Chopped'. Notice that 'Chopped' is completely ignored if the player is in the building, as the animations are set specifically to"Normal0" and "Cutaway".
While the player is outside, the animations are set dynamically to "Normal" & Global('Chopped'), which does take into account the status of the global variable.
So, you need to work the status of 'Chopped' into the first condition somehow, as you did in the second.
Another thing I noticed is that the Inside object probably should be picked in a similar manner to the Building object for those conditions, if you don't want both to be changed as in your original problem.
I wasn't able to look at the animations in the cap, as Construct crashed when I tried any of them. I assume you use a version before 0.99.84. It seems to run fine, oddly enough. It may be worth checking that you can still access those if you are working with one of the posted caps.
Also, your cap link was bad in the last post.