Reasoning-Fce-Quorum-Intersection

The model receives the prompt (and optional system message). The run uses scorer rubric_json_metrics with the JSON configuration below. Pass/fail and partial credit are determined entirely by that scorer against the model output; no human grading.

Return JSON only with keys answer, evidence, constraints. A design claims any two write quorums intersect in a 5-node cluster when quorum size is 2. Provide a counterexample and the corrected quorum condition.

{
  "metrics": {
    "accuracy": {
      "checks": [
        {
          "contains": [
            "counterexample"
          ]
        },
        {
          "contains": [
            "disjoint"
          ]
        },
        {
          "contains": [
            "quorum size 2"
          ]
        }
      ]
    },
    "evidence": {
      "checks": [
        {
          "contains": [
            "5-node cluster"
          ]
        },
        {
          "contains": [
            "write quorums"
          ]
        },
        {
          "contains": [
            "intersection"
          ]
        }
      ]
    },
    "constraint": {
      "checks": [
        {
          "contains": [
            "majority"
          ]
        },
        {
          "contains": [
            "3"
          ]
        },
        {
          "contains": [
            "condition"
          ]
        }
      ]
    }
  }
}