{
  "name": "The Controlled Tactic Table",
  "description": "A controlled experiment over Lean tactics. 27 arithmetic goals over Nat and Int, each put to ten tactics, with the axiom set recorded for every cell. Holding the goal fixed and varying only the tactic separates a classical dependence introduced by the proof from one required by the statement.",
  "version": "2026-08-12",
  "sha256": "8d8d79cabf5b458e1c10c3e629c16d9013c6e7b60b5356c82cee29adbc4ea5e5",
  "url": "https://f-keys.com/gonzalgo/controlled-tactics/",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "producedBy": {
    "software": "gonzalgo",
    "url": "https://pypi.org/project/gonzalgo/",
    "paper": "https://doi.org/10.5281/zenodo.21853489"
  },
  "measured": {
    "Lean 4": "4.32.1 with Mathlib v4.32.1",
    "design": "9 families x 3 goals x 10 tactics, fully crossed"
  },
  "fields": [
    "family",
    "goal_index",
    "goal",
    "shape",
    "tactic",
    "closed",
    "classical",
    "axioms"
  ],
  "displayed": [
    {
      "key": "goal",
      "label": "goal"
    },
    {
      "key": "shape",
      "label": "shape"
    },
    {
      "key": "tactic",
      "label": "tactic"
    },
    {
      "key": "closed",
      "label": "closed"
    },
    {
      "key": "classical",
      "label": "classical"
    },
    {
      "key": "axioms",
      "label": "axioms"
    }
  ],
  "rows": [
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
      "tactic": "aesop",
      "closed": true,
      "classical": false,
      "axioms": "propext Quot.sound"
    },
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
      "tactic": "decide",
      "closed": true,
      "classical": false,
      "axioms": "propext"
    },
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
      "tactic": "grind",
      "closed": true,
      "classical": true,
      "axioms": "propext Classical.choice Quot.sound"
    },
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
      "tactic": "linarith",
      "closed": false,
      "classical": false,
      "axioms": "sorryAx"
    },
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
      "tactic": "norm_num",
      "closed": true,
      "classical": false,
      "axioms": "propext"
    },
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
      "tactic": "omega",
      "closed": true,
      "classical": false,
      "axioms": "propext Quot.sound"
    },
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
      "tactic": "positivity",
      "closed": false,
      "classical": false,
      "axioms": "sorryAx"
    },
    {
      "family": "dvd_nat",
      "goal_index": 0,
      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
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      "closed": false,
      "classical": false,
      "axioms": "sorryAx"
    },
    {
      "family": "dvd_nat",
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      "goal": "(3 : Nat) ∣ 12",
      "shape": "equality/divisibility",
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      "axioms": "propext Quot.sound"
    },
    {
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      "tactic": "trivial",
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      "classical": false,
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    },
    {
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      "tactic": "aesop",
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      "classical": false,
      "axioms": "propext Quot.sound"
    },
    {
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      "goal": "(5 : Nat) ∣ 40",
      "shape": "equality/divisibility",
      "tactic": "decide",
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    {
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      "axioms": "propext Classical.choice Quot.sound"
    },
    {
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    },
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    },
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      "shape": "equality/divisibility",
      "tactic": "omega",
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      "classical": false,
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    },
    {
      "family": "dvd_nat",
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      "shape": "equality/divisibility",
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      "axioms": "propext Quot.sound"
    },
    {
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    },
    {
      "family": "dvd_nat",
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      "goal": "(1 : Nat) ∣ 7",
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    },
    {
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    },
    {
      "family": "dvd_nat",
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      "tactic": "grind",
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      "axioms": "propext Classical.choice Quot.sound"
    },
    {
      "family": "dvd_nat",
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      "axioms": "sorryAx"
    },
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      "family": "dvd_nat",
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    },
    {
      "family": "dvd_nat",
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      "goal": "(1 : Nat) ∣ 7",
      "shape": "equality/divisibility",
      "tactic": "omega",
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      "classical": false,
      "axioms": "propext Quot.sound"
    },
    {
      "family": "dvd_nat",
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      "goal": "(1 : Nat) ∣ 7",
      "shape": "equality/divisibility",
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    {
      "family": "dvd_nat",
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      "goal": "(1 : Nat) ∣ 7",
      "shape": "equality/divisibility",
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      "classical": false,
      "axioms": "sorryAx"
    },
    {
      "family": "dvd_nat",
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      "goal": "(1 : Nat) ∣ 7",
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    },
    {
      "family": "dvd_nat",
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      "goal": "(1 : Nat) ∣ 7",
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      "axioms": "propext"
    },
    {
      "family": "eq_int",
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      "goal": "(2 : Int) + 3 = 5",
      "shape": "equality/divisibility",
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    },
    {
      "family": "eq_int",
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      "goal": "(2 : Int) + 3 = 5",
      "shape": "equality/divisibility",
      "tactic": "decide",
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      "axioms": "(none)"
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    {
      "family": "eq_int",
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    },
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      "family": "eq_int",
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    },
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      "family": "eq_int",
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}