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08eb78a5b2
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.
58 lines
1.9 KiB
Lean4
58 lines
1.9 KiB
Lean4
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-- Turn on `trace.omega` to get detailed information about the processing of hypotheses,
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-- and the justification of the contradiction found.
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-- set_option trace.omega true
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-- Inequalities
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example {x y : Nat} (_ : x + y > 10) (_ : x < 5) (_ : y < 5) : False := by omega
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-- Tightening inequalities over `Int` or `Nat`
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example {x y : Nat} (_ : x + y > 10) (_ : 2 * x < 11) (_ : y < 5) : False := by omega
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-- GCDs not dividing constant terms
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example {x y : Nat} (_ : 2 * x + 4 * y = 5) : False := by omega
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-- Eliminating variables even when no coefficient is ±1
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example {x y : Nat} (_ : 6 * x + 7 * y = 5) : False := by omega
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-- Case bashing on `Nat.sub`
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example {x y z : Nat} (_ : x - y - z = 0) (_ : x > y + z) : False := by omega
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-- Division with constant denominators
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example {x y : Nat} (_ : x / 2 - y / 3 < 1) (_ : 3 * x ≥ 2 * y + 4) : False := by omega
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-- Annoying casts
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example {x : Nat} : 1 < (1 + ((x + 1 : Nat) : Int) + 2) / 2 := by omega
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-- Divisibility
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example {x : Nat} (_ : 10000 ∣ x) (_ : ¬ 100 ∣ x) : False := by omega
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-- Mod
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example (x : Nat) : x % 1024 - x % 2048 = 0 := by omega
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-- Systems of equations
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example (a b c d e : Int)
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(ha : 2 * a + b + c + d + e = 4)
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(hb : a + 2 * b + c + d + e = 5)
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(hc : a + b + 2 * c + d + e = 6)
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(hd : a + b + c + 2 * d + e = 7)
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(he : a + b + c + d + 2 * e = 8) : e = 3 := by omega
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-- Case bashing on disjunctions
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example (a b c d e : Int)
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(ha : 2 * a + b + c + d + e = 4)
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(hb : a + 2 * b + c + d + e = 5)
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(hc : a + b + 2 * c + d + e = 6)
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(hd : a + b + c + 2 * d + e = 7)
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(he : a + b + c + d + 2 * e = 8 ∨ e = 3) : e = 3 := by omega
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-- Case bashing conjunctions in the goal
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example (ε : Int) (_ : ε > 0) : (ε - 2 ≤ ε / 3 + ε / 2 + ε / 2) ∧ (ε / 3 + ε / 4 + ε / 5 ≤ ε) := by
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omega
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-- Fast results with duplicated hypotheses
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example {x : Int} (h₁ : 0 ≤ 2 * x + 1) (h₂ : 2 * x + 1 ≤ 0) : False := by
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iterate 64 have := h₁
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iterate 64 have := h₂
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omega
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