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lean4/tests/elab/grind_cutsat_omega.lean
Garmelon 08eb78a5b2 chore: switch to new test/bench suite (#12590) 
This PR sets up the new integrated test/bench suite. It then migrates
all benchmarks and some related tests to the new suite. There's also
some documentation and some linting.

For now, a lot of the old tests are left alone so this PR doesn't become
even larger than it already is. Eventually, all tests should be migrated
to the new suite though so there isn't a confusing mix of two systems.
2026-02-25 13:51:53 +00:00

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module
example (_ : (1 : Int) < (0 : Int)) : False := by grind
example (_ : (0 : Int) < (0 : Int)) : False := by grind
example (_ : (0 : Int) < (1 : Int)) : True := by grind
example {x : Int} (_ : 0 ≤ x) (_ : x ≤ 1) : True := by grind
example {x : Int} (_ : 0 ≤ x) (_ : x ≤ -1) : False := by grind
example {x : Int} (_ : x % 2 < x - 2 * (x / 2)) : False := by grind
example {x : Int} (_ : x % 2 > 5) : False := by grind
example {x : Int} (_ : 2 * (x / 2) > x) : False := by grind
example {x : Int} (_ : 2 * (x / 2) ≤ x - 2) : False := by grind
example {x : Nat} : x / 0 = 0 := by grind
example {x : Int} : x / 0 = 0 := by grind
example {x : Int} : x / 2 + x / (-2) = 0 := by grind
example {x : Nat} (_ : x ≠ 0) : 0 < x := by grind
example {a c b : Nat} (_ : a ≤ c) (_ : b ≤ c) : a < Nat.succ c := by grind
example (_ : 7 < 3) : False := by grind
example (_ : 0 < 0) : False := by grind
example {x : Nat} (_ : x > 7) (_ : x < 3) : False := by grind
example {x : Nat} (_ : x ≥ 7) (_ : x ≤ 3) : False := by grind
example {x y : Nat} (_ : x + y > 10) (_ : x < 5) (_ : y < 5) : False := by grind
example {x y : Int} (_ : x + y > 10) (_ : 2 * x < 11) (_ : y < 5) : False := by grind
example {x y : Nat} (_ : x + y > 10) (_ : 2 * x < 11) (_ : y < 5) : False := by grind
example {x y : Int} (_ : 2 * x + 4 * y = 5) : False := by grind
example {x y : Nat} (_ : 2 * x + 4 * y = 5) : False := by grind
example {x y : Int} (_ : 6 * x + 7 * y = 5) : True := by grind
example {x y : Nat} (_ : 6 * x + 7 * y = 5) : False := by grind
example {x y : Nat} (_ : x * 6 + y * 7 = 5) : False := by grind
example {x y : Nat} (_ : 2 * (3 * x) + y * 7 = 5) : False := by grind
example {x y : Nat} (_ : 2 * x * 3 + y * 7 = 5) : False := by grind
example {x y : Nat} (_ : 2 * 3 * x + y * 7 = 5) : False := by grind
example {x : Nat} (_ : x < 0) : False := by grind
example {x y z : Int} (_ : x + y > z) (_ : x < 0) (_ : y < 0) (_ : z > 0) : False := by grind
example {x y : Nat} (_ : x - y = 0) (_ : x > y) : False := by grind
example {x y z : Int} (_ : x - y - z = 0) (_ : x > y + z) : False := by grind
example {x y z : Nat} (_ : x - y - z = 0) (_ : x > y + z) : False := by grind
example {a b c d e f : Nat} (_ : a - b - c - d - e - f = 0) (_ : a > b + c + d + e + f) :
False := by
grind
example {x y : Nat} (h₁ : x - y ≤ 0) (h₂ : y < x) : False := by grind
example {x y : Int} (_ : x / 2 - y / 3 < 1) (_ : 3 * x ≥ 2 * y + 6) : False := by grind
example {x y : Nat} (_ : x / 2 - y / 3 < 1) (_ : 3 * x ≥ 2 * y + 6) : False := by grind
example {x y : Nat} (_ : x / 2 - y / 3 < 1) (_ : 3 * x ≥ 2 * y + 4) : False := by grind
example {x y : Nat} (_ : x / 2 - y / 3 < x % 2) (_ : 3 * x ≥ 2 * y + 4) : False := by grind
example {x : Int} (h₁ : 5 ≤ x) (h₂ : x ≤ 4) : False := by grind
example {x : Nat} (h₁ : 5 ≤ x) (h₂ : x ≤ 4) : False := by grind
example {x : Nat} (h₁ : x / 3 ≥ 2) (h₂ : x < 6) : False := by grind
example {x : Int} {y : Nat} (_ : 0 < x) (_ : x + y ≤ 0) : False := by grind
example {a b c : Nat} (_ : a - (b - c) ≤ 5) (_ : b ≥ c + 3) (_ : a + c ≥ b + 6) : False := by grind
example {x : Nat} : 1 < (1 + ((x + 1 : Nat) : Int) + 2) / 2 := by grind
example {x : Nat} : (x + 4) / 2 ≤ x + 2 := by grind
example {x : Int} {m : Nat} (_ : 0 < m) (_ : ¬x % ↑m < (↑m + 1) / 2) : -↑m / 2 ≤ x % ↑m - ↑m := by
grind
example (h : (7 : Int) = 0) : False := by grind
example (h : (7 : Int) ≤ 0) : False := by grind
example (h : (-7 : Int) + 14 = 0) : False := by grind
example (h : (-7 : Int) + 14 ≤ 0) : False := by grind
example (h : (1 : Int) + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 0) : False := by
grind
example (h : (7 : Int) - 14 = 0) : False := by grind
example (h : (14 : Int) - 7 ≤ 0) : False := by grind
example (h : (1 : Int) - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 = 0) : False := by
grind
example (h : -(7 : Int) = 0) : False := by grind
example (h : -(-7 : Int) ≤ 0) : False := by grind
example (h : 2 * (7 : Int) = 0) : False := by grind
example (h : (7 : Int) < 0) : False := by grind
example {x : Int} (h : x + x + 1 = 0) : False := by grind
example {x : Int} (h : 2 * x + 1 = 0) : False := by grind
example {x y : Int} (h : x + x + y + y + 1 = 0) : False := by grind
example {x y : Int} (h : 2 * x + 2 * y + 1 = 0) : False := by grind
example {x : Int} (h₁ : 0 ≤ -7 + x) (h₂ : 0 ≤ 3 - x) : False := by grind
example {x : Int} (h₁ : 0 ≤ -7 + x) (h₂ : 0 < 4 - x) : False := by grind
example {x : Int} (h₁ : 0 ≤ 2 * x + 1) (h₂ : 2 * x + 1 ≤ 0) : False := by grind
example {x : Int} (h₁ : 0 < 2 * x + 2) (h₂ : 2 * x + 1 ≤ 0) : False := by grind
example {x y : Int} (h₁ : 0 ≤ 2 * x + 1) (h₂ : x = y) (h₃ : 2 * y + 1 ≤ 0) : False := by grind
example {x y z : Int} (h₁ : 0 ≤ 2 * x + 1) (h₂ : x = y) (h₃ : y = z) (h₄ : 2 * z + 1 ≤ 0) :
False := by grind
example {x1 x2 x3 x4 x5 x6 : Int} (h : 0 ≤ 2 * x1 + 1) (h : x1 = x2) (h : x2 = x3) (h : x3 = x4)
(h : x4 = x5) (h : x5 = x6) (h : 2 * x6 + 1 ≤ 0) : False := by grind
example {x : Int} (_ : 1 ≤ -3 * x) (_ : 1 ≤ 2 * x) : False := by grind
example {x y : Int} (_ : 2 * x + 3 * y = 0) (_ : 1 ≤ x) (_ : 1 ≤ y) : False := by grind
example {x y z : Int} (_ : 2 * x + 3 * y = 0) (_ : 3 * y + 4 * z = 0) (_ : 1 ≤ x) (_ : 1 ≤ -z) :
False := by grind
example {x y z : Int} (_ : 2 * x + 3 * y + 4 * z = 0) (_ : 1 ≤ x + y) (_ : 1 ≤ y + z)
(_ : 1 ≤ x + z) : False := by grind
example {x y : Int} (_ : 1 ≤ 3 * x) (_ : y ≤ 2) (_ : 6 * x - 2 ≤ y) : False := by grind
example {x y : Int} (_ : y = x) (_ : 0 ≤ x - 2 * y) (_ : x - 2 * y ≤ 1) (_ : 1 ≤ x) : False := by
grind
example {x y : Int} (_ : y = x) (_ : 0 ≤ x - 2 * y) (_ : x - 2 * y ≤ 1) (_ : x ≥ 1) : False := by
grind
example {x y : Int} (_ : y = x) (_ : 0 ≤ x - 2 * y) (_ : x - 2 * y ≤ 1) (_ : 0 < x) : False := by
grind
example {x y : Int} (_ : y = x) (_ : 0 ≤ x - 2 * y) (_ : x - 2 * y ≤ 1) (_ : x > 0) : False := by
grind
example {x : Nat} (_ : 10 ∣ x) (_ : ¬ 5 ∣ x) : False := by grind
example {x y : Nat} (_ : 5 ∣ x) (_ : ¬ 10 ∣ x) (_ : y = 7) (_ : x - y ≤ 2) (_ : x ≥ 6) : False := by
grind
example (x : Nat) : x % 4 - x % 8 = 0 := by grind
example {n : Nat} (_ : n > 0) : (2*n - 1) % 2 = 1 := by grind
example (x : Int) (_ : x > 0 ∧ x < -1) : False := by grind
example (x : Int) (_ : x > 7) : x < 0 ∨ x > 3 := by grind
example (_ : ∃ n : Nat, n < 0) : False := by grind
example (_ : { x : Int // x < 0 ∧ x > 0 }) : False := by grind
example {x y : Int} (_ : x < y) (z : { z : Int // y ≤ z ∧ z ≤ x }) : False := by grind
example (a b c d e : Int)
(ha : 2 * a + b + c + d + e = 4)
(hb : a + 2 * b + c + d + e = 5)
(hc : a + b + 2 * c + d + e = 6)
(hd : a + b + c + 2 * d + e = 7)
(he : a + b + c + d + 2 * e = 8) : e = 3 := by grind
example (a b c d e : Int)
(ha : 2 * a + b + c + d + e = 4)
(hb : a + 2 * b + c + d + e = 5)
(hc : a + b + 2 * c + d + e = 6)
(hd : a + b + c + 2 * d + e = 7)
(he : a + b + c + d + 2 * e = 8 ∨ e = 3) : e = 3 := by
grind
example {x : Int} (h : x = 7) : x.natAbs = 7 := by
grind
example {x y : Int} (_ : (x - y).natAbs < 3) (_ : x < 5) (_ : y > 15) : False := by
grind
example {a b : Int} (h : a < b) (w : b < a) : False := by grind
example (_e b c a v0 v1 : Int) (_h1 : v0 = 5 * a) (_h2 : v1 = 3 * b) (h3 : v0 + v1 + c = 10) :
v0 + 5 + (v1 - 3) + (c - 2) = 10 := by grind
example (h : (1 : Int) < 0) (_ : ¬ (37 : Int) < 42) (_ : True) (_ : (-7 : Int) < 5) :
(3 : Int) < 7 := by grind
example (A B : Int) (h : 0 < A * B) : 0 < 8 * (A * B) := by grind
example (A B : Nat) (h : 7 < A * B) : 0 < A*B/8 := by grind
example (A B : Int) (h : 7 < A * B) : 0 < A*B/8 := by grind
example (ε : Int) (h1 : ε > 0) : ε / 2 + ε / 3 + ε / 7 < ε := by grind
example (x y z : Int) (h1 : 2*x < 3*y) (h2 : -4*x + z/2 < 0) (h3 : 12*y - z < 0) : False := by grind
example (ε : Int) (h1 : ε > 0) : ε / 2 < ε := by grind
example (ε : Int) (_ : ε > 0) : ε - 2 ≤ ε / 3 + ε / 3 + ε / 3 := by grind
example (ε : Int) (_ : ε > 0) : ε / 3 + ε / 3 + ε / 3 ≤ ε := by grind
example (ε : Int) (_ : ε > 0) : ε - 2 ≤ ε / 3 + ε / 3 + ε / 3 ∧ ε / 3 + ε / 3 + ε / 3 ≤ ε := by
grind
example (x : Int) (h : 0 < x) : 0 < x / 1 := by grind
example (x : Int) (h : 5 < x) : 0 < x/2/3 := by grind
example (_a b _c : Nat) (h2 : b + 2 > 3 + b) : False := by grind
example (_a b _c : Int) (h2 : b + 2 > 3 + b) : False := by grind
example (g v V c h : Int) (_ : h = 0) (_ : v = V) (_ : V > 0) (_ : g > 0)
(_ : 0 ≤ c) (_ : c < 1) : v ≤ V := by grind
example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : 12 * y - 4 * z < 0) :
False := by
grind
example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (_h3 : x * y < 5)
(h3 : 12 * y - 4 * z < 0) : False := by grind
example (a b c : Int) (h1 : a > 0) (h2 : b > 5) (h3 : c < -10) (h4 : a + b - c < 3) : False := by
grind
example (_ b _ : Int) (h2 : b > 0) (h3 : ¬ b ≥ 0) : False := by
grind
example (x y z : Int) (hx : x ≤ 3 * y) (h2 : y ≤ 2 * z) (h3 : x ≥ 6 * z) : x = 3 * y := by
grind
example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (_h3 : x * y < 5) :
¬ 12 * y - 4 * z < 0 := by
grind
example (x y z : Int) (hx : ¬ x > 3 * y) (h2 : ¬ y > 2 * z) (h3 : x ≥ 6 * z) : x = 3 * y := by
grind
example (x y : Int) (h : 6 + ((x + 4) * x + (6 + 3 * y) * y) = 3) (h' : (x + 4) * x ≥ 0)
(h'' : (6 + 3 * y) * y ≥ 0) : False := by grind
example (a : Int) (ha : 0 ≤ a) : 0 * 0 ≤ 2 * a := by grind
example (x y : Int) (h : x < y) : x ≠ y := by grind
example (x y : Int) (h : x < y) : ¬ x = y := by grind
example (prime : Nat → Prop) (x y z : Int) (h1 : 2 * x + ((-3) * y) < 0) (h2 : (-4) * x + 2* z < 0)
(h3 : 12 * y + (-4) * z < 0) (_ : prime 7) : False := by grind
example (i n : Nat) (h : (2 : Int) ^ i ≤ 2 ^ n) : (0 : Int) ≤ 2 ^ n - 2 ^ i := by grind
example (prime : Nat → Prop) (_ b _ : Nat) (h2 : b > 0) (h3 : b < 0) : prime 10 := by
grind
example (a b c : Nat) (h2 : (2 : Nat) > 3) : a + b - c ≥ 3 := by grind
example (x y : Int)
(h : 6 + ((x + 4) * x + (6 + 3 * y) * y) = 3 ∧ (x + 4) * x ≥ 0 ∧ (6 + 3 * y) * y ≥ 0) :
False := by grind
example (mess : Nat → Nat) (S n : Nat) :
mess S + (n * mess S + n * 2 + 1) < n * mess S + mess S + (n * 2 + 2) := by grind
example (p n p' n' : Nat) (h : p + n' = p' + n) : n + p' = n' + p := by
grind
example (a b c : Int) (h1 : 32 / a < b) (h2 : b < c) : 32 / a < c := by grind
example (i n : Nat) (hi : i ≤ n := by omega) : i < n + 1 := by
grind
example : 0 = 0 := by
have : 0 = 0 := by grind
grind
example (a b : Int) (h : a < 0 ↔ b < 0) (w : b > 3) : a ≥ 0 := by grind
example (a b : Int) (h : a > 7) (w : b > 2) : a > 0 ↔ b > 0 := by grind
example (a : Int) : a > 0 → a > -1 := by grind
example (x y : Int) : x + 1 ≤ y → ¬ y + 1 ≤ x := by grind
example (x y : Int) (_ : x < y) (_ : ¬ ¬ y < x) : False := by grind
example (a : Nat) (h : a < 0) : Nat → Nat := by grind
example {a₁ a₂ p₁ p₂ : Nat}
(h₁ : a₁ = a₂ → ¬p₁ = p₂) :
(a₁ < a₂ ∨ a₁ = a₂ ∧ p₁ < p₂) ∨ a₂ < a₁ ∨ a₂ = a₁ ∧ p₂ < p₁ := by grind
example {i : Nat} (h1 : i < 330) (_h2 : 7 ∣ (660 + i) * (1319 - i)) : 1319 - i < 1979 := by
grind
example {a : Int} (_ : a < min a b) : False := by grind
example {a : Int} (_ : max a b < b) : False := by grind
example {a : Nat} (_ : a < min a b) : False := by grind
example {a : Nat} (_ : max a b < b) : False := by grind
example {a b : Nat} (_ : a = 7) (_ : b = 3) : min a b = 3 := by grind
example {a b : Nat} (_ : a + b = 9) : (min a b) % 2 + (max a b) % 2 = 1 := by
grind
example {a : Int} (_ : a < if a ≤ b then a else b) : False := by grind
example {a b : Int} : (if a < b then a else b - 1) ≤ b := by grind
example (i j : Nat) (p : i ≥ j) : True := by
let l := j - 1
have _ : i ≥ l := by grind
trivial
example (i j : Nat) (p : i ≥ j) : True := by
let l := j - 1
let k := l
have _ : i ≥ k := by grind
trivial
example (a b : Nat) (h : a % b + 1 = 0) : False := by grind
example (x : Nat) : x < 2 →
(0 = 0 → 0 = 0 → 0 = 0 → 0 = 0 → x < 2) ∧ (0 = 0 → 0 = 0 → 0 = 0 → 0 = 0 → x < 2 → x < 3) := by
grind
example (s : Int) (s0 : s < (0 : Int)) : 63 + (s - 2 ^ 63) ≤ 62 - 2 ^ 63 := by
grind
example (n : Nat) : n * n ≥ 0 := by grind
example (n : Nat) : n * n + n ≥ 0 := by grind
example (i j k l : Nat) : i * j + k + l - k = i * j + l := by grind
example (n : Nat) : n * 2 = n + n := by grind
example (n : Nat) : n * n * 2 = n * n + n * n := by grind
example (n : Nat) : 2 * (n * n) = n * n + n * n := by grind
example (a : Nat) : a * 1 = a := by grind
example (x y : Nat) (_ : 2 ≤ x) (_ : x ≤ 3) (_ : 2 ≤ y) (_ : y ≤ 3) :
4 ≤ (x + y) % 8 ∧ (x + y) % 8 ≤ 6 := by
grind
example : 2^7 < 165 := by grind
example (x : Nat) (_ : x % 2^7 < 3) : x % 128 < 5 := by grind
example (a : Nat) :
(((a + (2 ^ 64 - 1)) % 2 ^ 64 + 1) * 8 - 1 - (a + (2 ^ 64 - 1)) % 2 ^ 64 * 8 + 1) = 8 := by
grind
example (z : Int) : z.toNat = 0 ↔ z ≤ 0 := by grind
example (x : Int) (h : Int.negSucc 0 < x ∧ x < 1) : x = 0 := by grind
-- From Mathlib.Order.RelSeries
theorem RelSeries.inductionOn.extracted_3 (p : Nat) (heq : p = 0) (n : Fin (p + 1)) : n = 0 := by
grind
theorem LTSeries.length_lt_card.extracted_1 (s : Nat) (i j : Fin (s + 1)) (hn : i ≠ j) (hl : ¬i < j) : j < i := by
grind
-- From Mathlib.AlgebraicTopology.SimplexCategory.Basic
theorem SimplexCategory.mkOfLe_refl.extracted_1 {n : Nat} (j : Fin (n + 1)) : j ≤ j := by
grind
theorem SimplexCategory.eq_σ_comp_of_not_injective.extracted_1 {n : Nat}
(x y : Fin ((n + 1) + 1)) (h₂ : ¬x = y) (h : ¬x < y) : y < x := by
omega
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