reasoning
Feb 25, 2026REASON-007Prove or disprove: For any integer n > 1, if n² + 1 is divisible by 5, then n⁴ + 1 is also divisible by 5. Provide a rigorous proof. If the statement is false, provide a counterexample and explain why the intuition fails.
Winner
GPT-OSS-120B
OpenAI
9.94
WINNER SCORE
matrix avg: 9.68
10×10 Judgment Matrix · 100 judgments
OPEN DATA
| Judge ↓ / Respondent → | MiMo-V2-Flash | Gemini 3 | Claude Sonnet 4.5 | DeepSeek V3.2 | Claude Opus 4.5 | Gemini 3 | Gemini 2.5 Flash | GPT-OSS-120B | OLMo Think | Grok 3 (Direct) |
|---|---|---|---|---|---|---|---|---|---|---|
| MiMo-V2-Flash | — | 10.0 | 9.8 | 9.8 | 9.8 | 10.0 | 9.8 | 9.8 | 9.8 | 9.8 |
| Gemini 3 | 10.0 | — | 10.0 | 10.0 | 10.0 | 10.0 | 9.8 | 10.0 | 10.0 | 10.0 |
| Claude Sonnet 4.5 | 9.8 | 10.0 | — | 9.6 | 9.8 | 9.8 | 9.8 | 10.0 | 9.8 | 9.8 |
| DeepSeek V3.2 | 9.5 | 9.5 | 9.3 | — | 10.0 | 9.3 | 9.4 | 10.0 | 9.7 | 9.5 |
| Claude Opus 4.5 | 9.3 | 9.8 | 9.8 | 9.8 | — | 9.4 | 9.6 | 10.0 | 9.8 | 9.8 |
| Gemini 3 | 0.0 | 10.0 | 0.0 | 10.0 | 0.0 | — | 0.0 | 10.0 | 10.0 | 10.0 |
| Gemini 2.5 Flash | 10.0 | 9.7 | 9.7 | 9.8 | 9.7 | 10.0 | — | 10.0 | 10.0 | 9.7 |
| GPT-OSS-120B | 0.0 | 9.8 | 0.0 | 0.0 | 0.0 | 8.6 | 8.8 | — | 8.9 | 9.4 |
| OLMo Think | 0.0 | 10.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 10.0 | — | 10.0 |
| Grok 3 (Direct) | 9.3 | 9.3 | 9.3 | 9.3 | 9.3 | 7.8 | 8.9 | 9.7 | 9.3 | — |