Theorem 1: Stuart Armstrong cannot prove this sentence is true. (G-SA)
Proof (by contradiction): Suppose not-G-SA is true, that is, Stuart Armstrong can prove G-SA. Then by G-SA, we would have a contradiction. So not-G-SA is false (or our logic contains a contradiction, in which case the principle of explosion applies).
Theorem 2: Cyan cannot prove this sentence is true. (G-Cyan)
Theorem 1: Stuart Armstrong cannot prove this sentence is true. (G-SA)
Proof (by contradiction): Suppose not-G-SA is true, that is, Stuart Armstrong can prove G-SA. Then by G-SA, we would have a contradiction. So not-G-SA is false (or our logic contains a contradiction, in which case the principle of explosion applies).
Theorem 2: Cyan cannot prove this sentence is true. (G-Cyan)
Proof left as an exercise for the reader.