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If the hog house has an internal ‘corridor’ (most have either an external ‘corridor’ or an internal one to deter predators, etc.) you could try reducing the height by putting a brick on the floor in that ‘corridor’. The hogs would be able to climb over but it makes it more difficult for the cat. If one doesn’t work you could try more to make the shallow area longer. If there is an extenal corridor you could try putting a heavy obstacle in that which would just give the hog space to get through but make it difficult for the cat.
Another thing you can try is to put a heavy obstacle at the side of the entrance to the box. Again if there is a ‘corridor’ in the box, cats usually go into them at an angle so that if the obstacle is in the way, it makes it more difficult. It’s more difficult if the box just has one chamber entered straight from the doorway. But, if the entrance is straight into the main chamber, you could try putting a heavy obstacle opposite the entrance (as well as at one side).
you could also try making the entrance to the hog house smaller. Hogs can squeeze through surprisingly small entrances.
Sorry for all the alternatives. It’s a bit difficult not knowing the design of the box! But hopefully, something there might work.