61 lines
1.5 KiB
Text
61 lines
1.5 KiB
Text
module
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example (x y : Int) :
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27 ≤ 11*x + 13*y →
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11*x + 13*y ≤ 45 →
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-10 ≤ 7*x - 9*y →
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7*x - 9*y ≤ 4 → False := by
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-- `omega` fails in this example
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grind
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example (x : Int) : 100 ≤ x → x ≤ 10000 → 20000 ∣ 3*x → False := by
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grind
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abbrev problem₁ [∀ n, OfNat α n] [Neg α] [Mul α] [Sub α] [Add α] [LE α] (x y : α) : Prop :=
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27 ≤ 11*x + 13*y ∧
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11*x + 13*y ≤ 45 ∧
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-10 ≤ 7*x - 9*y ∧
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7*x - 9*y ≤ 4
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/--
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trace: [grind.cutsat.model] x := 241/154
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[grind.cutsat.model] y := 1
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-/
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#guard_msgs (trace) in
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set_option trace.grind.cutsat.model true in
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example (x y : Int) : problem₁ x y → False := by
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fail_if_success grind +qlia -- Rational counterexamples allowed
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sorry
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/-- info: true -/
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#guard_msgs in
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open Std.Internal in
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#eval problem₁ (241/154 : Rat) (1 : Rat)
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theorem ex₁ (x y : Int) :
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27 ≤ 13*x + 11*y → 13*x + 11*y ≤ 30 →
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-10 ≤ 9*x - 7*y → 9*x - 7*y ≤ 4 → False := by
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grind
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theorem ex₂ (x y : Int) :
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27 ≤ 11*x + 13*y → 11*x + 13*y ≤ 45 →
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-10 ≤ 7*x - 9*y → 7*x - 9*y ≤ 4 → False := by
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grind
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theorem ex₃ (x y : Int) :
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5 ≤ x + y → x + 2*y ≤ 14 → 7 ∣ x → 4 ∣ y → y ≥ 4 → False := by
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grind
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theorem ex₄ (x y : Int) :
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5 ≤ 2*x + y → 3*x + 2*y ≤ 14 → 7 ∣ x → 4 ∣ y → y ≥ 4 → False := by
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grind
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theorem ex₅ (x y : Int) : 1 ≤ x + y → 100 ∣ x + y → 100 ≤ x + y := by
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grind
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open Int.Linear
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#print ex₁
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#print ex₂
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#print ex₃
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#print ex₄
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#print ex₅
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