[
  {
    "id": "a01",
    "description": "Single positive atom P",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
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    },
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    "mode": "consistency",
    "atom_count": 1
  },
  {
    "id": "a02",
    "description": "Single negative atom \u00acP",
    "rendered_cnf": {
      "clauses": [
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          {
            "predicate": "P",
            "args": [],
            "negated": true
          }
        ]
      ]
    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 1
  },
  {
    "id": "a03",
    "description": "Direct contradiction P \u2227 \u00acP",
    "rendered_cnf": {
      "clauses": [
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          {
            "predicate": "P",
            "args": [],
            "negated": false
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          {
            "predicate": "P",
            "args": [],
            "negated": true
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 1
  },
  {
    "id": "a04",
    "description": "Disjunction P \u2228 Q",
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      "clauses": [
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          {
            "predicate": "P",
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            "negated": false
          },
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            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ]
      ]
    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "a05",
    "description": "Force false: \u00acP \u2227 \u00acQ \u2227 (P \u2228 Q)",
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      "clauses": [
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          {
            "predicate": "P",
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            "negated": true
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        [
          {
            "predicate": "Q",
            "args": [],
            "negated": true
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        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "a06",
    "description": "Conjunction P \u2227 Q",
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      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ]
      ]
    },
    "label": "consistent",
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    "atom_count": 2
  },
  {
    "id": "a07",
    "description": "Both true but at-most-one: P \u2227 Q \u2227 (\u00acP \u2228 \u00acQ)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "a08",
    "description": "XOR plus equivalence: 4-clause UNSAT",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "b01",
    "description": "Modus ponens premise: (\u00acP \u2228 Q) \u2227 P",
    "rendered_cnf": {
      "clauses": [
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          {
            "predicate": "P",
            "args": [],
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          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
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        ]
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    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "b02",
    "description": "Modus ponens contradiction: above \u2227 \u00acQ",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ]
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    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "b03",
    "description": "Two-step MP chain: (\u00acP \u2228 Q) \u2227 (\u00acQ \u2228 R) \u2227 P",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          },
          {
            "predicate": "R",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          }
        ]
      ]
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    "label": "consistent",
    "mode": "consistency",
    "atom_count": 3
  },
  {
    "id": "b04",
    "description": "Two-step MP contradiction: above \u2227 \u00acR",
    "rendered_cnf": {
      "clauses": [
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          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          },
          {
            "predicate": "R",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "R",
            "args": [],
            "negated": true
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 3
  },
  {
    "id": "b05",
    "description": "Modus tollens setup: (\u00acP \u2228 Q) \u2227 \u00acQ (forces \u00acP)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ]
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    },
    "label": "consistent",
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    "atom_count": 2
  },
  {
    "id": "b06",
    "description": "Modus tollens contradiction: above \u2227 P",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "c01",
    "description": "Three-step chain SAT: (\u00acA\u2228B)\u2227(\u00acB\u2228C)\u2227(\u00acC\u2228D)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "A",
            "args": [],
            "negated": true
          },
          {
            "predicate": "B",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "B",
            "args": [],
            "negated": true
          },
          {
            "predicate": "C",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "C",
            "args": [],
            "negated": true
          },
          {
            "predicate": "D",
            "args": [],
            "negated": false
          }
        ]
      ]
    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 4
  },
  {
    "id": "c02",
    "description": "Three-step chain UNSAT: above \u2227 A \u2227 \u00acD",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "A",
            "args": [],
            "negated": true
          },
          {
            "predicate": "B",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "B",
            "args": [],
            "negated": true
          },
          {
            "predicate": "C",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "C",
            "args": [],
            "negated": true
          },
          {
            "predicate": "D",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "A",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "D",
            "args": [],
            "negated": true
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 4
  },
  {
    "id": "c03",
    "description": "Redundant transitivity: (\u00acA\u2228B)\u2227(\u00acB\u2228C)\u2227(\u00acA\u2228C)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "A",
            "args": [],
            "negated": true
          },
          {
            "predicate": "B",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "B",
            "args": [],
            "negated": true
          },
          {
            "predicate": "C",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "A",
            "args": [],
            "negated": true
          },
          {
            "predicate": "C",
            "args": [],
            "negated": false
          }
        ]
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    "mode": "consistency",
    "atom_count": 3
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  {
    "id": "c04",
    "description": "Transitive trigger: (\u00acA\u2228B)\u2227(\u00acB\u2228C)\u2227A",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "A",
            "args": [],
            "negated": true
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          {
            "predicate": "B",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "B",
            "args": [],
            "negated": true
          },
          {
            "predicate": "C",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "A",
            "args": [],
            "negated": false
          }
        ]
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    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 3
  },
  {
    "id": "c05",
    "description": "Transitive contradiction: above \u2227 \u00acC",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "A",
            "args": [],
            "negated": true
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          {
            "predicate": "B",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "B",
            "args": [],
            "negated": true
          },
          {
            "predicate": "C",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "A",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "C",
            "args": [],
            "negated": true
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 3
  },
  {
    "id": "c06",
    "description": "Cyclic implications: (\u00acA\u2228B)\u2227(\u00acB\u2228A)\u2227A",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "A",
            "args": [],
            "negated": true
          },
          {
            "predicate": "B",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "B",
            "args": [],
            "negated": true
          },
          {
            "predicate": "A",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "A",
            "args": [],
            "negated": false
          }
        ]
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    "label": "consistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "d01",
    "description": "Resolves Q: (P\u2228Q) \u2227 (\u00acP\u2228Q)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
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        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
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    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "d02",
    "description": "Resolution UNSAT: above \u2227 \u00acQ",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ]
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    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "d03",
    "description": "Resolves P: (P\u2228Q) \u2227 (P\u2228\u00acQ)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
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        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
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    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "d04",
    "description": "Resolution UNSAT: above \u2227 \u00acP",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          }
        ]
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    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "d05",
    "description": "Three-clause resolution SAT",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ]
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    },
    "label": "consistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "d06",
    "description": "Four-corner UNSAT (full XOR contradiction)",
    "rendered_cnf": {
      "clauses": [
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          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": false
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        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
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          {
            "predicate": "Q",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ]
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    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "e01",
    "description": "2-pigeon-1-hole UNSAT (each pigeon needs a hole, but only one hole)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P1H1",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P2H1",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P1H1",
            "args": [],
            "negated": true
          },
          {
            "predicate": "P2H1",
            "args": [],
            "negated": true
          }
        ]
      ]
    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 2
  },
  {
    "id": "e02",
    "description": "2-pigeon-2-hole SAT (place pigeons in distinct holes)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P1H1",
            "args": [],
            "negated": false
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          {
            "predicate": "P1H2",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P2H1",
            "args": [],
            "negated": false
          },
          {
            "predicate": "P2H2",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P1H1",
            "args": [],
            "negated": true
          },
          {
            "predicate": "P2H1",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P1H2",
            "args": [],
            "negated": true
          },
          {
            "predicate": "P2H2",
            "args": [],
            "negated": true
          }
        ]
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    "label": "consistent",
    "mode": "consistency",
    "atom_count": 4
  },
  {
    "id": "e03",
    "description": "3-pigeon-2-hole UNSAT (classic pigeonhole)",
    "rendered_cnf": {
      "clauses": [
        [
          {
            "predicate": "P1H1",
            "args": [],
            "negated": false
          },
          {
            "predicate": "P1H2",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P2H1",
            "args": [],
            "negated": false
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          {
            "predicate": "P2H2",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P3H1",
            "args": [],
            "negated": false
          },
          {
            "predicate": "P3H2",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P1H1",
            "args": [],
            "negated": true
          },
          {
            "predicate": "P2H1",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P1H1",
            "args": [],
            "negated": true
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            "negated": false
          },
          {
            "predicate": "Q",
            "args": [],
            "negated": true
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "R",
            "args": [],
            "negated": false
          }
        ],
        [
          {
            "predicate": "P",
            "args": [],
            "negated": true
          },
          {
            "predicate": "R",
            "args": [],
            "negated": true
          }
        ]
      ]
    },
    "label": "inconsistent",
    "mode": "consistency",
    "atom_count": 3
  }
]