It is obvious that belief, opinion, lie, fact, and truth are related in some way. Most in this forum confuse the difference. In 'fact', most dictionaries ignore a 'definitive' meaning and concentrate on opinions and wrong usage over time and evolved misuse. Even if the terms are reversed in usage now compared with previously, what they refer to is the subject of this forum, not the errors of interpretation and usage.
Truth transcends all facts. Any fact is a manifestation to a thinking physical being that there is a transcendental being that rules over all physical being. The physical being is the fact and the ruler is Truth. I capitalize Truth from now on to show it as an authority over all fact. Truth is prior and higher than fact. Fact is not determinate of Truth, but Truth is determinate of any and all facts. Facts are infinite and specific. Truth is universal and ruling. In that sense Truth is One, while facts are many and each positive fact, is matched with a negative.
The operator of Truth is that something is, not what something is. Fact tells when, where, how, and why. The reflection of 'is' is 'not'. 'Not' is the meaning of non-truth. Not true is as factual as true. Not Truth is impossible. Think; does anything that does not exist, exist somewhere in a physical world? The answer is not. But, in a hierarchy of all being, Truth is higher. Truth rules what is and what is not. Non-existence is not a truthful possibility, but is a ruling of Truth over all. No fact determines Truth, but only manifests that Truth is.
We cannot prove the negative because it means, in Truth, that something said is not. There is no such image of a square circle, or a round square. There is also no such value such that 2 plus 2 equals five. In a digital number system, 2 plus 2 is 4, not 3, 5, or any fraction. Math is about Truth, while figure is about fact. Mathematics is transcendent to all mathematical operators and values. Logic is to reasoning and expression in prose what mathematics is to number and physics. Statics also depends upon mathematics as do statistics.
All measurements carry a tolerance limit for practical usage. Truth has no tolerance limits. Truth is absolute and immutable, forever, everywhere, in all time and for every act intended or executed. For Truth, there is no choice. Each fact can be true or false, exist or not exist. Truth cannot not be. The double negative always produces true. One fact in one place can coexist with another fact in another time and place, but Truth applies to all time and space and even to proof of the negative for those things impossible.
A unicorn can be presumed not to exist, that is a fact. God, who is Truth, cannot be presumed not to be, unless God is reduced to a fact that could be true or false. As Truth, which cannot be false, God cannot be not. And God, who is Truth, can prove the negative as clearly as it can be manifest to a thinking being.