Here goes the proof....consider the following sentences:
1.) God exists
2.) None of the sentences in this pair is true.
Let us call sentence 1 and 2 as G and N respectively. Then we have the following conjunction of sentences as a pair, G & N.
Now G or N may be true or false, we do not know which is which.
Assume first that N is true. If so, then we have a contradiction because there is supposed to be no sentence in the pair that is true, and so the value of G is irrelevant. Whatever it is G & N is inconsistent.
Assume now that N is false. If so, then the negation of N means at least one of the pair is true. Since there are only two sentences, G and N and we know N is false, it must be G that is true.
Thus in order for statement G & N to make sense or for it to be consistent, G must be true.
Hence G is true or God exists.
This is my elaboration of Buridan's Proof of the existence of God.