You agreed with:

Forcibly impregnating someone is also called rape.

Also agreed with:

It’s not rape if it’s your dog

And clarified:

However, my dog is my property, and someone can only artificially inseminate my property with my permission.

With these, we can derive your proposition: “Forcibly impregnating a dog that is your property is not rape”.

I then made the first question:

If I own a human slave, me artificially inseminating them without consent isn’t rape?

Which is directly related, I just substituted “dog” with “human slave”. No mention of “dog” or “livestock” in the above question, so there’s no comparison nor equating as you said “Animal livestock are not comparable to human slaves”. (If you disagree, please explicitly point out what is being compared and bring quotes).

Then I posed another question:

If I DNA test the slave from earlier and discover they aren’t human, inseminating them without consent wouldn’t be rape? Which is still completely relevant to your proposition, I just added a qualifier to the being that’s being artificially inseminated.

If your logic worked in real life […] then prove it by sticking to reality. You are commiting a modal fallacy by saying “real life” and “sticking to reality”, as if had posed a physical hypothetical, which would mean “possible in this world”.

I am posing you a logical hypothetical, which means “true in a possible world”. If your proposition holds up to logic and reason (i.e. is a resonable proposition), you should be able to answer my logical hypotheticals and stop avoiding them like they’d hurt you.