The OP’s question has nothing to do with the pope or the Catholic Church or her theology.
It is a question about whether anything can be known as a certain truth, infallibly. The OP stated 1+1=2 can be known to be infallibly true, but anything that can not be demonstrated as true in that manner he wonders about.
The statement, “God exists”, or the question, “Does God exist”, has a yes or no answer. God can not both exist and not exist. The question is whether or not the correct answer can be infallibly known.
We can look to Aquinas and his proofs, or even Aristotle the philospher who proved the existance of God, but those proofs are a bit more complicated than 1+1=2 and some people may not be able to follow them.
If God exists can we know it for certain? Although Aristotle, Aquinas and Anselm proved it without relying on faith, there is still another way.
For God’s existance to be known God would have to reveal His existance. The question then becomes: “Has God revealed Himself to men”?
What is the evidence that says He has?
The Church holds that God’s existance is demonstrable, but that without revelation we can know nothing more about him other than He exists.
The discussion in the thread about scripture being useless unless it can be understood properly, began with the assumption that it can not be understood properly, based on the fact that there are so many conflicting interpretations. The fact there are many disagreements on its meaning does not demonstrate that infallible truth is not knowable through scripture. To do that it would have to be provable that ALL interpretations are false.
The fact that many people are confused does not prove all are confused.
Logic says all are false or one is true.
The problem of scripture not being able to lead us to infallible truth is ironically a Protestant problem. The group that holds sola scriptura can not agree on its meaning and therefore can not know truth infallibly through scripture. But, if God reveals Himself in the stories found in scripture then truth about God can be infallibly known through scripture, or its right understanding. If it can not be rightly understood and God revealed it why did God reveal it? It would be like throwing a life ring to someone you knew could not reach it.
Back to the OP’s question on what or what can not be known infallibly, even God’s existance, and the answer. IF God has revealed Himself it can be known that He exists, but this does not mean everyone will know God exists. It means everyone can know God exists.
Assume it can be known that colds are caused by virus. Some people know this to be true and others do not. I have never seen a virus, but believe they cause colds. They do or they don’t. Taking aspirin reduces a cold’s discomfort. It does or it does not. In the same way we can empirically apply the things to our lives God supposedly has revealed and see the results, especially in the lives of the saints. Or, we can not apply them and see the results in broken lives and a broken world around us. We can take the medicine or not and see the results. The results are a proof.
Beyond whether God exists can be infallibly known, if God revealed Himself through revealtion, we also know the things He says are true about Himself and us, through the means He gives us to know it. Those means are found in scripture which tells us He sent men to all the nations to teach His truths. We learn from them what God has revealed, by the testimony of those He appointed and sent. Scripture does not tell us we learn infallible truths from scripture, but from the men God chose and taught and commanded to teach the nations. These are the men who gave us scripture.
A whole body of truth is knowable then. Or the alternative is, nothing is knowable.
