108 lines
3.1 KiB
Text
108 lines
3.1 KiB
Text
module
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opaque f [Inhabited α] : α → α
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theorem feq [Inhabited α] [Add α] [One α] (x : α) : f x = f (f x) + 1 := sorry
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opaque g [Inhabited α] : α → α → α
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theorem geq [Inhabited α] (x : α) : g x x = x := sorry
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/--
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error: `grind` failed
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case grind
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α : Type u_1
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inst : Inhabited α
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inst_1 : Add α
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inst_2 : One α
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x z y : α
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h : g y z = z
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h_1 : g z y = g y x
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h_2 : ¬f x = g x x
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] g y z = z
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[prop] g z y = g y x
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[prop] ¬f x = g x x
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[prop] f x = f (f x) + 1
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[prop] g x x = x
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[prop] f (f x) = f (f (f x)) + 1
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[prop] f (f (f x)) = f (f (f (f x))) + 1
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[eqc] False propositions
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[prop] f x = g x x
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[eqc] Equivalence classes
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[eqc] {x, g x x}
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[eqc] {z, g y z}
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[eqc] {f x, f (f x) + 1}
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[eqc] {g z y, g y x}
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[eqc] {f (f x), f (f (f x)) + 1}
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[eqc] {f (f (f x)), f (f (f (f x))) + 1}
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[ematch] E-matching patterns
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[thm] feq: [@f #4 #3 #0]
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[thm] geq: [@g #2 #1 #0 #0]
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[limits] Thresholds reached
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[limit] maximum term generation has been reached, threshold: `(gen := 3)`
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[grind] Diagnostics
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[thm] E-Matching instances
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[thm] feq ↦ 3
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[thm] geq ↦ 1
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-/
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#guard_msgs (error) in
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example [Inhabited α] [Add α] [One α] (x z y : α) : g y z = z → g z y = g y x → f x = g x x := by
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grind (gen := 3) [= feq, = geq]
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/--
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error: `grind` failed
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case grind
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x z y : Int
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h : g y z = z
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h_1 : g z y = g y x
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h_2 : ¬f (f x) = g x x
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] g y z = z
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[prop] g z y = g y x
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[prop] ¬f (f x) = g x x
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[prop] f x + -1 * f (f x) + -1 = 0
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[prop] f (f x) + -1 * f (f (f x)) + -1 = 0
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[prop] g x x = x
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[prop] f (f (f x)) + -1 * f (f (f (f x))) + -1 = 0
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[eqc] False propositions
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[prop] f (f x) = g x x
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[eqc] Equivalence classes
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[eqc] {x, g x x}
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[eqc] {z, g y z}
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[eqc] {0, f x + -1 * f (f x) + -1, f (f x) + -1 * f (f (f x)) + -1, f (f (f x)) + -1 * f (f (f (f x))) + -1}
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[eqc] {g z y, g y x}
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[eqc] {f x + -1 * f (f x), f (f x) + -1 * f (f (f x)), f (f (f x)) + -1 * f (f (f (f x)))}
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[ematch] E-matching patterns
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[thm] feq: [@f #4 #3 #0]
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[thm] geq: [@g #2 #1 #0 #0]
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[cutsat] Assignment satisfying linear constraints
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[assign] x := 5
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[assign] z := 3
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[assign] y := 2
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[assign] f x := 1
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[assign] f (f x) := 0
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[assign] g x x := 5
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[assign] g z y := 4
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[assign] g y x := 4
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[assign] g y z := 3
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[assign] f (f (f x)) := -1
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[assign] f (f (f (f x))) := -2
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[assoc] Operator `HAdd.hAdd`
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[basis] Basis
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[_] f (f (f x)) + -1 * f (f (f (f x))) = f x + -1 * f (f x)
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[_] f (f x) + -1 * f (f (f x)) = f x + -1 * f (f x)
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[_] f x + (-1 * f (f x) + -1) = 0
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[properties] Properties
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[_] commutative
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[_] identity: `0`
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[limits] Thresholds reached
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[limit] maximum term generation has been reached, threshold: `(gen := 2)`
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[grind] Diagnostics
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[thm] E-Matching instances
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[thm] feq ↦ 3
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[thm] geq ↦ 1
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-/
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#guard_msgs (error) in
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example (x z y : Int) : g y z = z → g z y = g y x → f (f x) = g x x := by
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grind (gen := 2) -ring [= feq, = geq]
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