Could you be more explicit about the intention of the question?
Omega’s surgery doesn’t introduce contradictions in your code: it doesn’t (say) make Pi(10000) evaluate to 7, it just replaces Pi(10000) in the code with 7, which gives perfectly good code, just different from the original.
What does Omega do if your algorithm contains “if ⊥ is provable, then give $100”?
Could you be more explicit about the intention of the question?
Omega’s surgery doesn’t introduce contradictions in your code: it doesn’t (say) make Pi(10000) evaluate to 7, it just replaces Pi(10000) in the code with 7, which gives perfectly good code, just different from the original.