The Path to The Equation of Functional Infinity

Is there a equation with enough complexity that it could be put into the machine of sufficient size/processing required to contain TREE(G64) (et. al.) in numerical form that it could not be proven to be or not to be zero? This is functionally similar to asking if an equation could have an unknown result that may be zero indefinitely, regardless of the processing used to resolve said equation, and the time spent doing it, but it is not precisely the same question. By placing a currently unfathomable but finite number as an upper limit the solution moves away from the purely conceptual form of infinity into something more tangible, and allows for an equation provided as a solution to overloading the system that is conceivable, but is known not to be in any possible time by power frame. 

Once this equation is found and can be represented, the form of it would be ¤ as most fully as I can fathom it, because, while technically real, its value is neither known or can be known, most importantly as zero or non-zero (because it is unknown if it "adds" anything or not). This solution would shed light on the shape of "the other," the void (deep, waters) in same same form, if observed from God's perspective. If agreed upon, the gates to nothing would remain unassailable and ever known. What is even more hopeful about this is that presumably another equation could satisfy the requirements (essentially of system overload), but still take on a distinctly different form than the first, allowing more to blossom from this method (with relatively ease, if the machine can be left operational or close to).