lean-eval Aristotle (Harmonic) submission for exists_nonisotopic_knots

Challenge.lean

import ChallengeDeps

open LeanEval.KnotTheory

theorem exists_nonisotopic_knots : ∃ K₁ K₂ : Knot, ¬ K₁.Isotopic K₂ := by
  sorry

config.json

{
  "challenge_module": "Challenge",
  "solution_module": "Solution",
  "theorem_names": [
    "exists_nonisotopic_knots"
  ],
  "permitted_axioms": [
    "propext",
    "Quot.sound",
    "Classical.choice"
  ],
  "enable_nanoda": false
}

Helpers.lean

namespace Submission.Helpers

end Submission.Helpers

lakefile.toml

name = "exists_nonisotopic_knots"
testDriver = "workspace_test"
defaultTargets = ["Challenge", "Solution", "Submission"]

[leanOptions]
autoImplicit = false

[[require]]
name = "mathlib"
git = "https://github.com/leanprover-community/mathlib4.git"
rev = "5450b53e5ddc"

[[lean_lib]]
name = "ChallengeDeps"

[[lean_lib]]
name = "Challenge"

[[lean_lib]]
name = "Solution"

[[lean_lib]]
name = "Submission"

[[lean_exe]]
name = "workspace_test"
root = "WorkspaceTest"

lean-toolchain

leanprover/lean4:v4.30.0-rc2

Solution.lean

import ChallengeDeps
import Submission

open LeanEval.KnotTheory

theorem exists_nonisotopic_knots : ∃ K₁ K₂ : Knot, ¬ K₁.Isotopic K₂ := by
  exact Submission.exists_nonisotopic_knots

Submission.lean

import ChallengeDeps

open LeanEval.KnotTheory

namespace Submission

/-- The standard unknot diagram: one arc, no crossings (fox3Count = 3). -/
private def unknot : Knot := ⟨1, []⟩

/-- The standard trefoil diagram: three arcs with three crossings.
    The Fox 3-coloring constraints all reduce to `x₀ + x₁ + x₂ ≡ 0 (mod 3)`,
    giving fox3Count = 9. -/
private def trefoil : Knot :=
  ⟨3, [(⟨0, by omega⟩, ⟨1, by omega⟩, ⟨2, by omega⟩),
       (⟨1, by omega⟩, ⟨2, by omega⟩, ⟨0, by omega⟩),
       (⟨2, by omega⟩, ⟨0, by omega⟩, ⟨1, by omega⟩)]⟩

theorem exists_nonisotopic_knots : ∃ K₁ K₂ : Knot, ¬ K₁.Isotopic K₂ :=
  ⟨unknot, trefoil, by native_decide⟩

end Submission

WorkspaceTest.lean

import Lean

open Lean

def comparatorExists (comparatorBin : String) : IO Bool := do
  if comparatorBin.contains '/' then
    return (← System.FilePath.pathExists comparatorBin)
  try
    let child ← IO.Process.spawn {
      cmd := "sh"
      args := #["-c", "command -v \"$1\" >/dev/null 2>&1", "sh", comparatorBin]
    }
    let exitCode ← child.wait
    return exitCode == 0
  catch _ =>
    return false

def main : IO UInt32 := do
  let comparatorBin := (← IO.getEnv "COMPARATOR_BIN").getD "comparator"
  if !(← comparatorExists comparatorBin) then
    IO.eprintln s!"Failed to run comparator via `{comparatorBin}`."
    IO.eprintln "Make sure `comparator` is installed and on your `PATH`, or set `COMPARATOR_BIN=/path/to/comparator`."
    IO.eprintln "See the root repository README for comparator setup details, including landrun and lean4export."
    pure 1
  else
    try
      let child ← IO.Process.spawn {
        cmd := "lake"
        args := #["env", comparatorBin, "config.json"]
      }
      let exitCode ← child.wait
      pure exitCode
    catch err =>
      IO.eprintln s!"Failed to run comparator via `{comparatorBin}`."
      IO.eprintln "Make sure `comparator` is installed and on your `PATH`, or set `COMPARATOR_BIN=/path/to/comparator`."
      IO.eprintln "See the root repository README for comparator setup details, including landrun and lean4export."
      IO.eprintln s!"Original error: {err}"
      pure 1