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fc34d../a6787.. bday: 35145 doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem b6c37.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ο . ∀ x7 x8 x9 : ι → ι → ι → ο . ∀ x10 : ι → ι → ο . ∀ x11 : ι → ι . ∀ x12 : ι → ι → ι → ι . ∀ x13 . ∀ x14 : ι → ι → ι . ∀ x15 x16 x17 x18 : ι → ι . ∀ x19 : ι → ι → ο . ∀ x20 : ι → ι . ∀ x21 : ι → ο . ∀ x22 . ∀ x23 : ι → ι . ∀ x24 . ∀ x25 : ι → ι → ο . ∀ x26 x27 : ι → ι . ∀ x28 : ι → ι → ι . ∀ x29 . ∀ x30 x31 : ι → ι → ι → ι . ∀ x32 : ι → ι . ∀ x33 : ι → ι → ι → ι → ι → ι . ∀ x34 : ι → ι → ι . ∀ x35 : ι → ο . ∀ x36 x37 x38 x39 . ∀ x40 : ι → ο . ∀ x41 x42 : ι → ι → ι → ι → ι . ∀ x43 : ι → ι → ι . ∀ x44 : ι → ι → ι → ι → ι . ∀ x45 . ∀ x46 : ι → ι . ∀ x47 : ι → ι → ι . ∀ x48 . ∀ x49 : ι → ι → ι . ∀ x50 : ι → ι → ο . ∀ x51 : ι → ι . ∀ x52 . ∀ x53 x54 : ι → ο . ∀ x55 . ∀ x56 : ι → ο . ∀ x57 x58 : ι → ι . ∀ x59 : ι → ι → ο . ∀ x60 : ι → ι . ∀ x61 x62 : ι → ι → ι → ι . ∀ x63 : ι → ι → ι . ∀ x64 : ι → ι → ι → ι → ι . ∀ x65 x66 x67 x68 x69 x70 x71 . ∀ x72 : ι → ι → ο . ∀ x73 . ∀ x74 : ι → ο . (∀ x75 x76 . x74 x76(x76 = x75False)x74 x75False)(∀ x75 x76 . x0 x75 x76x74 x76False)(∀ x75 . x74 x75(x75 = x73False)False)(∀ x75 x76 x77 . x0 x75 x76x2 x76 (x1 x77)x74 x77False)(∀ x75 x76 x77 . x0 x76 x77x2 x77 (x1 x75)(x2 x76 x75False)False)(∀ x75 . (x3 x73 x75 = x73False)False)(∀ x75 x76 . x72 x76 x75(x2 x76 (x1 x75)False)False)(∀ x75 x76 . x2 x76 (x1 x75)(x72 x76 x75False)False)(∀ x75 . (x3 x75 x73 = x75False)False)(∀ x75 x76 . x2 x75 x76(x74 x76False)(x0 x75 x76False)False)(∀ x75 x76 . x0 x76 x75(x2 x76 x75False)False)(∀ x75 x76 x77 x78 . x4 x78x7 x78 x75 x76x2 x78 (x1 (x5 x75 x76))x4 x77x7 x77 x75 x76x2 x77 (x1 (x5 x75 x76))x6 x75 x76 x78 x77(x6 x75 x76 x77 x78False)False)(x74 x71False)(∀ x75 x76 x77 x78 . x4 x78x7 x78 x75 x76x2 x78 (x1 (x5 x75 x76))x4 x77x7 x77 x75 x76x2 x77 (x1 (x5 x75 x76))(x6 x75 x76 x78 x78False)False)(∀ x75 . (x72 x75 x75False)False)(∀ x75 x76 x77 x78 . x4 x78x7 x78 x75 x76x2 x78 (x1 (x5 x75 x76))x4 x77x7 x77 x75 x76x2 x77 (x1 (x5 x75 x76))x78 = x77(x6 x75 x76 x78 x77False)False)(∀ x75 x76 x77 x78 . x4 x78x7 x78 x75 x76x2 x78 (x1 (x5 x75 x76))x4 x77x7 x77 x75 x76x2 x77 (x1 (x5 x75 x76))x6 x75 x76 x78 x77(x78 = x77False)False)(∀ x75 x76 x77 . (x74 x77False)(x74 x75False)x2 x75 (x1 x77)x2 x76 x75(x8 x76 x77 x75False)False)(∀ x75 x76 x77 . (x74 x77False)(x74 x75False)x2 x75 (x1 x77)x8 x76 x77 x75(x2 x76 x75False)False)(∀ x75 x76 x77 . (x74 x77False)x10 x75 x77x2 x76 x75(x9 x76 x77 x75False)False)(∀ x75 x76 x77 . (x74 x77False)x10 x75 x77x9 x76 x77 x75(x2 x76 x75False)False)(∀ x75 . (x11 x75 = x1 x75False)False)((x70 = x69False)False)(∀ x75 x76 x77 . x2 x76 (x1 x77)(x12 x77 x76 x75 = x3 x76 x75False)False)((x68 = x67False)False)((x13 = x73False)False)((x66 = x65False)False)(∀ x75 x76 . (x74 x76False)x10 x75 x76(x14 x76 x75 = x15 x75False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x77x2 x75 (x1 (x5 x78 x77))x2 x76 x78(x64 x78 x77 x75 x76 = x63 x75 x76False)False)(∀ x75 . (x16 x75 = x17 x75False)False)(∀ x75 x76 x77 . (x74 x77False)x2 x75 x77x10 x76 x77(x61 x77 x75 x76 = x62 x77 x75 x76False)False)(∀ x75 . (x74 x75False)(x19 (x18 x75) x75False)False)(∀ x75 . (x74 x75False)(x2 (x18 x75) (x1 x75)False)False)(∀ x75 . (x74 x75False)(x21 (x20 x75)False)False)(∀ x75 . (x74 x75False)x74 (x20 x75)False)(∀ x75 . (x74 x75False)(x10 (x20 x75) x75False)False)(∀ x75 . x19 (x60 x75) x75False)(∀ x75 . (x2 (x60 x75) (x1 x75)False)False)(∀ x75 . (x59 (x58 x75) x75False)False)(∀ x75 . x74 (x58 x75)False)(∀ x75 . (x2 (x58 x75) (x1 (x1 (x11 x75)))False)False)(x74 x22False)(∀ x75 . (x74 (x57 x75)False)False)(∀ x75 . (x2 (x57 x75) (x1 x75)False)False)((x56 x55False)False)((x4 x55False)False)((x54 x55False)False)(∀ x75 . (x74 x75False)(x21 (x23 x75)False)False)(∀ x75 . (x74 x75False)x74 (x23 x75)False)(∀ x75 . (x74 x75False)(x10 (x23 x75) x75False)False)((x53 x52False)False)((x74 x24False)False)(∀ x75 . (x74 x75False)x74 (x51 x75)False)(∀ x75 . (x74 x75False)(x2 (x51 x75) (x1 x75)False)False)(∀ x75 x76 . (x50 (x49 x75 x76) x75False)False)(∀ x75 x76 . (x25 (x49 x76 x75) x75False)False)(∀ x75 x76 . (x54 (x49 x75 x76)False)False)(∀ x75 x76 . (x74 (x49 x75 x76)False)False)(∀ x75 x76 . (x2 (x49 x75 x76) (x1 (x5 x76 x75))False)False)(∀ x75 . (x59 (x26 x75) x75False)False)(∀ x75 . (x2 (x26 x75) (x1 (x1 (x11 x75)))False)False)(∀ x75 x76 x77 . x54 x77x50 x77 x75x54 x76(x50 (x3 x77 x76) x75False)False)(∀ x75 x76 . x54 x76x4 x76x56 x76(x53 (x63 x76 x75)False)False)(∀ x75 x76 x77 . x54 x77x25 x77 x75x54 x76(x25 (x3 x77 x76) x75False)False)((x53 x69False)False)(∀ x75 . x74 (x15 x75)False)(x74 x48False)((x53 x67False)False)((x74 x73False)False)(∀ x75 . x74 (x1 x75)False)(∀ x75 . x74 (x17 x75)False)(∀ x75 x76 . (x74 x76False)(x74 x75False)x74 (x5 x76 x75)False)(∀ x75 x76 . (x74 x76False)(x74 x75False)x2 x75 (x1 x76)(x8 (x47 x75 x76) x76 x75False)False)(∀ x75 . (x2 (x27 x75) x75False)False)(∀ x75 . (x10 (x46 x75) x75False)False)(∀ x75 x76 . (x74 x76False)x10 x75 x76(x9 (x28 x75 x76) x76 x75False)False)((x74 x45False)False)(∀ x75 x76 x77 . (x74 x77False)(x74 x75False)x2 x75 (x1 x77)x8 x76 x77 x75(x2 x76 x77False)False)(∀ x75 x76 . x10 x76 x75(x2 x76 (x1 (x1 x75))False)False)(∀ x75 x76 x77 . (x74 x77False)x10 x75 x77x9 x76 x77 x75(x2 x76 (x1 x77)False)False)(∀ x75 . (x2 (x11 x75) (x1 (x1 x75))False)False)((x2 x70 x48False)False)(∀ x75 x76 x77 . x2 x76 (x1 x77)(x2 (x12 x77 x76 x75) (x1 x77)False)False)((x2 x68 x48False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x2 x77 (x1 (x16 x78))x10 x76 x78(x2 (x44 x78 x75 x77 x76) (x1 (x5 x78 x48))False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x2 x77 (x1 (x16 x78))x10 x76 x78(x7 (x44 x78 x75 x77 x76) x78 x48False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x2 x77 (x1 (x16 x78))x10 x76 x78(x4 (x44 x78 x75 x77 x76)False)False)((x8 x13 x29 x66False)False)((x2 x66 (x1 x29)False)False)(∀ x75 x76 x77 . (x74 x77False)x10 x75 x77x2 x76 (x1 (x16 x77))(x10 (x30 x77 x75 x76) x77False)False)(∀ x75 x76 . (x74 x76False)x10 x75 x76(x2 (x14 x76 x75) (x1 (x16 x76))False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x77x2 x75 (x1 (x5 x78 x77))x2 x76 x78(x2 (x64 x78 x77 x75 x76) x77False)False)(∀ x75 x76 . (x74 x76False)x2 x75 (x1 (x16 x76))(x10 (x43 x76 x75) x76False)False)(∀ x75 . (x2 (x16 x75) (x1 (x1 (x11 x75)))False)False)(∀ x75 . (x59 (x16 x75) x75False)False)(∀ x75 x76 x77 . (x74 x77False)x4 x75x7 x75 x77 x48x2 x75 (x1 (x5 x77 x48))x10 x76 x77(x2 (x31 x77 x75 x76) (x1 (x5 x77 x48))False)False)(∀ x75 x76 x77 . (x74 x77False)x4 x75x7 x75 x77 x48x2 x75 (x1 (x5 x77 x48))x10 x76 x77(x7 (x31 x77 x75 x76) x77 x48False)False)(∀ x75 x76 x77 . (x74 x77False)x4 x75x7 x75 x77 x48x2 x75 (x1 (x5 x77 x48))x10 x76 x77(x4 (x31 x77 x75 x76)False)False)(∀ x75 x76 x77 . (x74 x77False)x2 x75 x77x10 x76 x77(x9 (x61 x77 x75 x76) x77 x76False)False)(∀ x75 . (x74 x75False)(x2 (x32 x75) (x1 (x5 x75 x48))False)False)(∀ x75 . (x74 x75False)(x7 (x32 x75) x75 x48False)False)(∀ x75 . (x74 x75False)(x4 (x32 x75)False)False)(∀ x75 x76 x77 . (x74 x77False)x2 x75 x77x10 x76 x77(x2 (x62 x77 x75 x76) (x1 x77)False)False)(∀ x75 x76 x77 . (x74 x77False)x10 x75 x77x2 x76 (x1 (x16 x77))(x30 x77 x75 x76 = x43 x77 (x12 (x16 x77) x76 (x14 x77 x75))False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x2 x75 x78x10 x77 x78x2 x76 (x1 x78)x0 x75 x76x0 x76 x77(x76 = x62 x78 x75 x77False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x2 x75 x78x10 x77 x78x2 x76 (x1 x78)x76 = x62 x78 x75 x77(x0 x76 x77False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x2 x75 x78x10 x77 x78x2 x76 (x1 x78)x76 = x62 x78 x75 x77(x0 x75 x76False)False)((x69 = x71False)False)((x73 = x45False)False)((x67 = x13False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x10 x77 x78x4 x76x7 x76 x78 x48x2 x76 (x1 (x5 x78 x48))x64 x78 x48 x76 (x42 x76 x77 x75 x78) = x70x64 x78 x48 x76 (x42 x76 x77 x75 x78) = x68(x76 = x31 x78 x75 x77False)False)(∀ x75 x76 x77 x78 x79 . (x74 x79False)x4 x75x7 x75 x79 x48x2 x75 (x1 (x5 x79 x48))x10 x78 x79x4 x76x7 x76 x79 x48x2 x76 (x1 (x5 x79 x48))x64 x79 x48 x76 (x42 x76 x78 x75 x79) = x70x2 x77 x79x0 x77 (x61 x79 (x42 x76 x78 x75 x79) x78)x64 x79 x48 x75 x77 = x70(x76 = x31 x79 x75 x78False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x10 x77 x78x4 x76x7 x76 x78 x48x2 x76 (x1 (x5 x78 x48))(x64 x78 x48 x75 (x41 x76 x77 x75 x78) = x70False)x64 x78 x48 x76 (x42 x76 x77 x75 x78) = x68(x76 = x31 x78 x75 x77False)False)(∀ x75 x76 x77 x78 x79 . (x74 x79False)x4 x75x7 x75 x79 x48x2 x75 (x1 (x5 x79 x48))x10 x78 x79x4 x76x7 x76 x79 x48x2 x76 (x1 (x5 x79 x48))(x64 x79 x48 x75 (x41 x76 x78 x75 x79) = x70False)x2 x77 x79x0 x77 (x61 x79 (x42 x76 x78 x75 x79) x78)x64 x79 x48 x75 x77 = x70(x76 = x31 x79 x75 x78False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x10 x77 x78x4 x76x7 x76 x78 x48x2 x76 (x1 (x5 x78 x48))(x0 (x41 x76 x77 x75 x78) (x61 x78 (x42 x76 x77 x75 x78) x77)False)x64 x78 x48 x76 (x42 x76 x77 x75 x78) = x68(x76 = x31 x78 x75 x77False)False)(∀ x75 x76 x77 x78 x79 . (x74 x79False)x4 x75x7 x75 x79 x48x2 x75 (x1 (x5 x79 x48))x10 x78 x79x4 x76x7 x76 x79 x48x2 x76 (x1 (x5 x79 x48))(x0 (x41 x76 x78 x75 x79) (x61 x79 (x42 x76 x78 x75 x79) x78)False)x2 x77 x79x0 x77 (x61 x79 (x42 x76 x78 x75 x79) x78)x64 x79 x48 x75 x77 = x70(x76 = x31 x79 x75 x78False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x10 x77 x78x4 x76x7 x76 x78 x48x2 x76 (x1 (x5 x78 x48))(x2 (x41 x76 x77 x75 x78) x78False)x64 x78 x48 x76 (x42 x76 x77 x75 x78) = x68(x76 = x31 x78 x75 x77False)False)(∀ x75 x76 x77 x78 x79 . (x74 x79False)x4 x75x7 x75 x79 x48x2 x75 (x1 (x5 x79 x48))x10 x78 x79x4 x76x7 x76 x79 x48x2 x76 (x1 (x5 x79 x48))(x2 (x41 x76 x78 x75 x79) x79False)x2 x77 x79x0 x77 (x61 x79 (x42 x76 x78 x75 x79) x78)x64 x79 x48 x75 x77 = x70(x76 = x31 x79 x75 x78False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x10 x77 x78x4 x76x7 x76 x78 x48x2 x76 (x1 (x5 x78 x48))(x2 (x42 x76 x77 x75 x78) x78False)(x76 = x31 x78 x75 x77False)False)(∀ x75 x76 x77 x78 x79 . (x74 x79False)x4 x75x7 x75 x79 x48x2 x75 (x1 (x5 x79 x48))x10 x78 x79x4 x76x7 x76 x79 x48x2 x76 (x1 (x5 x79 x48))x76 = x31 x79 x75 x78x2 x77 x79(x64 x79 x48 x75 (x33 x77 x76 x78 x75 x79) = x70False)(x64 x79 x48 x76 x77 = x68False)False)(∀ x75 x76 x77 x78 x79 . (x74 x79False)x4 x75x7 x75 x79 x48x2 x75 (x1 (x5 x79 x48))x10 x78 x79x4 x76x7 x76 x79 x48x2 x76 (x1 (x5 x79 x48))x76 = x31 x79 x75 x78x2 x77 x79(x0 (x33 x77 x76 x78 x75 x79) (x61 x79 x77 x78)False)(x64 x79 x48 x76 x77 = x68False)False)(∀ x75 x76 x77 x78 x79 . (x74 x79False)x4 x75x7 x75 x79 x48x2 x75 (x1 (x5 x79 x48))x10 x78 x79x4 x76x7 x76 x79 x48x2 x76 (x1 (x5 x79 x48))x76 = x31 x79 x75 x78x2 x77 x79(x2 (x33 x77 x76 x78 x75 x79) x79False)(x64 x79 x48 x76 x77 = x68False)False)(∀ x75 x76 x77 x78 x79 x80 . (x74 x80False)x4 x75x7 x75 x80 x48x2 x75 (x1 (x5 x80 x48))x10 x79 x80x4 x76x7 x76 x80 x48x2 x76 (x1 (x5 x80 x48))x76 = x31 x80 x75 x79x2 x77 x80x2 x78 x80x0 x78 (x61 x80 x77 x79)x64 x80 x48 x75 x78 = x70(x64 x80 x48 x76 x77 = x70False)False)(∀ x75 x76 . (x74 x76False)x4 x75x7 x75 x76 x48x2 x75 (x1 (x5 x76 x48))x64 x76 x48 x75 (x34 x75 x76) = x70(x75 = x32 x76False)False)(∀ x75 x76 . (x74 x76False)x4 x75x7 x75 x76 x48x2 x75 (x1 (x5 x76 x48))(x2 (x34 x75 x76) x76False)(x75 = x32 x76False)False)(∀ x75 x76 x77 . (x74 x77False)x4 x75x7 x75 x77 x48x2 x75 (x1 (x5 x77 x48))x75 = x32 x77x2 x76 x77(x64 x77 x48 x75 x76 = x70False)False)(∀ x75 x76 x77 x78 . (x74 x78False)x4 x75x7 x75 x78 x48x2 x75 (x1 (x5 x78 x48))x2 x77 (x1 (x16 x78))x10 x76 x78(x44 x78 x75 x77 x76 = x31 x78 x75 (x30 x78 x76 x77)False)False)(∀ x75 x76 . x74 x76x2 x75 (x1 x76)x19 x75 x76False)(∀ x75 x76 x77 . x74 x77x2 x75 (x1 (x5 x76 x77))(x74 x75False)False)(∀ x75 x76 . (x74 x76False)x2 x75 (x1 x76)x74 x75(x19 x75 x76False)False)(∀ x75 x76 x77 . x74 x77x2 x75 (x1 (x5 x77 x76))(x74 x75False)False)(∀ x75 x76 . x2 x76 (x1 (x5 x75 x48))x4 x76x7 x76 x75 x48(x56 x76False)False)(∀ x75 x76 . x2 x76 (x1 (x5 x75 x48))x4 x76x7 x76 x75 x48(x7 x76 x75 x48False)False)(∀ x75 x76 . x2 x76 (x1 (x5 x75 x48))x4 x76x7 x76 x75 x48(x4 x76False)False)(∀ x75 x76 . (x74 x76False)x2 x75 (x1 x76)(x19 x75 x76False)x74 x75False)(∀ x75 x76 x77 . x2 x77 (x1 (x5 x75 x76))(x50 x77 x76False)False)(∀ x75 x76 x77 . x2 x77 (x1 (x5 x76 x75))(x25 x77 x76False)False)(∀ x75 . x2 x75 x48(x53 x75False)False)(∀ x75 x76 . x10 x76 x75(x21 x76False)False)(∀ x75 . x53 x75(x35 x75False)False)(∀ x75 x76 . x74 x76x2 x75 (x1 x76)(x74 x75False)False)(∀ x75 x76 x77 . x2 x77 (x1 (x5 x75 x76))(x54 x77False)False)(∀ x75 . x74 x75(x40 x75False)False)(∀ x75 x76 . (x74 x76False)x10 x75 x76x74 x75False)(∀ x75 x76 . x0 x75 x76x0 x76 x75False)(x6 x36 x48 (x44 x36 (x32 x36) x37 x38) (x32 x36)False)((x10 x38 x36False)False)((x2 x39 (x1 (x5 x36 x48))False)False)((x7 x39 x36 x48False)False)((x4 x39False)False)((x2 x37 (x1 (x17 x36))False)False)(x74 x36False)False (proof)

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