These tautological games, even if flawlessly proven with logic symbols, have their problems.
It’s inconsistent with how we choose to describe the physical world. You can have the premise “if the ball is in my hand” and say it can’t not be in your hand at the same time. But look at the premise. The ball is arguably not “in” your hand. It’s “on” your hand. Furthermore, it’s technically NOT on your hand, it rests on some microscopic barrier of energy particles that may not technically be your hand.
What is a hand anyway? The dermis or the electron layer? Is it merely opinion when the hand starts? So in a sense the ball could be “in the hand” and “not in the hand” depending on how you choose the perceive these variables, let alone temporal is-was illusions, and we rarely talk like this or think like this, so our tautologies involving real world examples are rife with fallacies and unknowns. You might argue that depending on how we agree to arbitrariliy define our variables, once they are defined, it holds that it can’t be and not be true simultaneously. But when variables are so hapharzardly arrived at, what good is the efficacy of non-contradiction? What good is p or not p when we might not know precisely what any p is, p including objects, words, neuronal concepts, including non-contradiction itself. Which is why, while it is sexy, it’s relegated to the same bin as causality, time, space, and other fun tools that fall short of licking God’s face.