141 lines
3.2 KiB
Text
141 lines
3.2 KiB
Text
-- In this file we use the `cutsat` frontend for `grind`,
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-- as a minimal test that it is working.
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module
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example (w x y z : Int) :
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2*w + 3*x - 4*y + z = 10 →
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w - x + 2*y - 3*z = 5 →
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3*w - 2*x + y + z = 7 →
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4*w + x - y - z = 3 →
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w = 2 := by
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cutsat
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abbrev test1 (a b c d e : Int) :=
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1337*a + 424242*b - 23*c + 17*d - 101*e ≤ 12345 →
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42*a - 18*b + 23*c - 107*d + 53*e ≥ -10000 →
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a ≥ 0 → b ≥ 0 → c ≥ 0 → d ≥ 0 → e ≥ 0 →
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a ≤ 100
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/--
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trace: [grind.lia.model] a := 101
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[grind.lia.model] b := 0
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[grind.lia.model] c := 5335
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[grind.lia.model] d := 0
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[grind.lia.model] e := 0
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-/
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#guard_msgs (trace) in
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set_option trace.grind.lia.model true in
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example (a b c d e : Int) : test1 a b c d e := by
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(fail_if_success cutsat); sorry
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/-- info: false -/
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#guard_msgs (info) in
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#eval test1 101 0 5335 0 0
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example : ∀ (x y z : Int),
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2*x + 3*y ≤ 100 →
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3*y + 4*z ≤ 200 →
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4*z + 2*x ≤ 300 →
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x ≥ 0 → y ≥ 0 → z ≥ 0 →
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x + y + z ≤ 150 := by
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cutsat
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example : ∀ (x y : Int),
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x > 0 →
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y > 0 →
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x ≤ 100 →
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2 ∣ x →
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y ≤ 100 →
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2*x + 3*y = 47 →
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x = 22 ∨ x = 16 ∨ x = 10 ∨ x = 4 := by
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cutsat
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example : ∀ (x y : Int),
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x + y ≤ 10 →
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2*x + y ≥ 19 →
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3*x - y ≤ 30 →
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x - 2*y ≥ -15 →
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x = 9 ∨ x = 10 := by
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cutsat
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example : ∀ (x y z : Int),
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¬(2*x + 3*y + 4*z ≤ 100 ∧
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3*x + 4*y + 5*z ≥ 101 ∧
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x + y + z = 50 ∧ x ≠ 50 ∧
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x ≥ 0 ∧ y ≥ 0 ∧ z ≥ 0) := by
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cutsat
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example : ∀ (x y : Int),
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2*x + 3*y = 100 →
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x + y = 40 → x = y := by
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cutsat
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example : ∀ (x y z : Int),
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3 * x + 5 * y + 7 * z = 100 →
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2 * x + 3 * y + 4 * z ≥ 50 →
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x + y + z ≤ 30 →
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x ≥ 0 ∧ y ≥ 0 ∧ z ≥ 0 →
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z ≤ 15 := by
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cutsat
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example : ∀ (x y z : Int),
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2 * x + 3 * y + 4 * z = 100 →
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3 * x + 4 * y + 5 * z ≥ 150 →
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x + y + z ≤ 40 →
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x ≥ 0 ∧ y ≥ 0 ∧ z ≥ 0 →
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z ≥ 10 := by
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cutsat
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example : ∀ (x y z : Int),
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x / 4 + y / 3 = 50 →
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x % 4 = 1 →
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y % 3 = 2 →
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x + y + z = 200 →
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x ≥ 0 ∧ y ≥ 0 ∧ z ≥ 0 →
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z ≤ 50 := by
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cutsat
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example : ∀ (x : Int),
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x ≥ 0 →
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x % 2 = 1 →
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x % 3 = 2 →
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x % 5 = 3 →
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x ≥ 23 := by
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cutsat
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example : ∀ (x : Int),
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x / 5 ≥ 20 →
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x % 5 = 3 →
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x ≥ 103 := by
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cutsat
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example : ∀ (x y z : Int),
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z > 0 →
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x + y + z = 100 →
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y = 2 * x →
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x ≤ 33 := by
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cutsat
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example : ∀ (x y : Int),
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2 * x + 3 * y ≤ 10 →
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x + y ≤ 5 →
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x ≥ 0 → y ≥ 0 →
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x + y ≤ 5 := by
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cutsat
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example (x : Int) : x / 1 = x := by cutsat
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example (x : Int) : x % 1 = 0 := by cutsat
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example (x : Nat) : x / 1 = x := by cutsat
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example (x : Nat) : x % 1 = 0 := by cutsat
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example (x : Int) : x / -1 = -x := by cutsat
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example (x : Int) : x % -1 = 0 := by cutsat
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-- Verify that `cutsat` will not use the ring solver.
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example (x : Int) (h : x^2 = 0) : x^3 = 0 := by
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fail_if_success cutsat
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grobner
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-- Verify that `cutsat` will not instantiate theorems.
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example {xs ys zs : List α} : (xs ++ ys) ++ zs = xs ++ (ys ++ zs) := by
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fail_if_success cutsat
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grind
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