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4efaf../8be3e.. bday: 35150 doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem 16160.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ο . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ι → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 . ∀ x8 : ι → ι → ι . ∀ x9 : ι → ο . ∀ x10 : ι → ι → ο . ∀ x11 . ∀ x12 : ι → ι → ι . ∀ x13 : ι → ο . ∀ x14 x15 x16 . ∀ x17 : ι → ι . ∀ x18 x19 x20 . ∀ x21 : ι → ο . ∀ x22 x23 . ∀ x24 : ι → ι → ι → ι . ∀ x25 : ι → ι . ∀ x26 x27 : ι → ο . ∀ x28 x29 x30 . ∀ x31 : ι → ο . ∀ x32 : ι → ι . ∀ x33 : ι → ι → ο . ∀ x34 : ι → ι → ι . ∀ x35 : ι → ο . ∀ x36 : ι → ι . ∀ x37 x38 : ι → ι → ι → ι → ι . ∀ x39 . ∀ x40 : ι → ι . ∀ x41 x42 . ∀ x43 : ι → ο . ∀ x44 . ∀ x45 : ι → ο . ∀ x46 : ι → ι . ∀ x47 . ∀ x48 : ι → ι → ο . ∀ x49 : ι → ι . ∀ x50 x51 x52 . ∀ x53 : ι → ι . ∀ x54 : ι → ο . ∀ x55 : ι → ι → ι → ο . ∀ x56 . ∀ x57 : ι → ι → ι . ∀ x58 : ι → ι → ι → ι . ∀ x59 : ι → ι → ι . ∀ x60 . ∀ x61 : ι → ι → ο . ∀ x62 x63 : ι → ο . ∀ x64 : ι → ι → ο . ∀ x65 : ι → ο . (∀ x66 x67 . x65 x67x65 x66(x64 x67 x66False)(x63 x66False)(x62 x67False)False)(∀ x66 x67 . x0 x67(x67 = x66False)x0 x66False)(∀ x66 x67 . x65 x67x65 x66(x64 x67 x66False)(x62 x67False)(x63 x66False)False)(∀ x66 x67 x68 x69 . x1 x68 (x2 (x3 x69))x9 x66x9 x67x64 x66 (x8 x67 x7)(x4 (x3 x69) (x5 x69 x68 x66 x67) (x6 x69 x68 (x8 x67 x7)) = x6 x69 x68 x66False)False)(∀ x66 x67 . x61 x66 x67x0 x67False)(∀ x66 x67 . x65 x67x65 x66x64 x67 x66(x0 x67False)(x62 x66False)(x63 x67False)False)(∀ x66 . x0 x66(x66 = x60False)False)(∀ x66 x67 x68 . x61 x66 x67x1 x67 (x2 x68)x0 x68False)(∀ x66 x67 . x65 x67x65 x66x64 x67 x66(x0 x66False)(x63 x67False)(x62 x66False)False)(∀ x66 x67 x68 . x61 x67 x68x1 x68 (x2 x66)(x1 x67 x66False)False)(∀ x66 x67 . x65 x67x65 x66x64 x67 x66(x62 x66False)x62 x67False)(∀ x66 x67 . x10 x67 x66(x1 x67 (x2 x66)False)False)(∀ x66 x67 . x1 x67 (x2 x66)(x10 x67 x66False)False)(∀ x66 x67 . x65 x67x65 x66x64 x67 x66(x63 x67False)x63 x66False)(∀ x66 x67 x68 . x61 x67 x68x61 x66 x68x61 x66 (x59 x68 x67)False)(∀ x66 x67 . x61 x67 x66(x61 (x59 x66 x67) x66False)False)(∀ x66 x67 . x1 x66 x67(x0 x67False)(x61 x66 x67False)False)(∀ x66 x67 . x65 x67x65 x66x64 x67 x66x63 x66(x63 x67False)False)(∀ x66 x67 x68 . x1 x67 (x2 (x3 x68))x9 x66(x5 x68 x67 x66 x66 = x58 x68 x67 x66False)False)(∀ x66 x67 . x61 x67 x66(x1 x67 x66False)False)(∀ x66 x67 . x65 x67x65 x66x64 x67 x66x62 x67(x62 x66False)False)((x1 x60 x11False)False)(∀ x66 . (x57 x66 x60 = x66False)False)(∀ x66 x67 . x9 x67x9 x66x64 x67 x66x64 (x12 x66 x7) x67False)(∀ x66 x67 . x9 x67x9 x66(x64 (x12 x66 x7) x67False)(x64 x67 x66False)False)(∀ x66 x67 x68 . x13 x68x13 x66x13 x67(x8 (x8 x68 x66) x67 = x8 x68 (x8 x66 x67)False)False)((x1 x7 x56False)False)((x1 x7 x14False)False)((x55 x7 x56 x14False)False)((x62 x7False)False)(x0 x7False)((x64 x7 x7False)False)(∀ x66 x67 . x54 x67x54 x66(x64 x67 x67False)False)(∀ x66 . (x10 x66 x66False)False)(∀ x66 x67 x68 . (x0 x68False)(x0 x66False)x1 x66 (x2 x68)x1 x67 x66(x55 x67 x68 x66False)False)(∀ x66 x67 x68 . (x0 x68False)(x0 x66False)x1 x66 (x2 x68)x55 x67 x68 x66(x1 x67 x66False)False)((x14 = x11False)False)(∀ x66 x67 x68 . x1 x67 (x2 x68)x1 x66 (x2 x68)(x4 x68 x67 x66 = x57 x67 x66False)False)(∀ x66 . (x53 x66 = x3 x66False)False)(∀ x66 x67 . x9 x67x1 x66 x14(x12 x67 x66 = x8 x67 x66False)False)((x9 x52False)False)(x0 x52False)((x54 x51False)False)((x0 x51False)False)((x65 x50False)False)((x54 x50False)False)((x13 x50False)False)((x0 x50False)False)(∀ x66 . (x0 x66False)(x48 (x49 x66) x66False)False)(∀ x66 . (x0 x66False)(x1 (x49 x66) (x2 x66)False)False)((x9 x47False)False)((x63 x15False)False)((x54 x15False)False)((x65 x16False)False)((x63 x16False)False)((x54 x16False)False)((x13 x16False)False)(∀ x66 . x48 (x17 x66) x66False)(∀ x66 . (x1 (x17 x66) (x2 x66)False)False)((x62 x18False)False)((x54 x18False)False)((x65 x19False)False)((x62 x19False)False)((x54 x19False)False)((x13 x19False)False)(x0 x20False)(∀ x66 . (x0 (x46 x66)False)False)(∀ x66 . (x1 (x46 x66) (x2 x66)False)False)((x45 x44False)False)((x21 x44False)False)((x43 x44False)False)(x0 x44False)((x45 x42False)False)(x0 x42False)((x1 x42 (x2 x56)False)False)((x54 x22False)False)((x65 x41False)False)((x0 x23False)False)(∀ x66 . (x0 x66False)x0 (x40 x66)False)(∀ x66 . (x0 x66False)(x1 (x40 x66) (x2 x66)False)False)((x45 x39False)False)(∀ x66 x67 x68 . x1 x67 (x2 x68)x1 x66 (x2 x68)(x4 x68 x67 x67 = x67False)False)(∀ x66 . (x57 x66 x66 = x66False)False)(∀ x66 x67 x68 x69 x70 x71 . x1 x70 (x2 (x3 x71))x9 x66x1 x69 (x2 (x3 x71))x67 = x69x9 x68x64 x66 x68x69 = x58 x71 x70 x68(x61 x67 (x24 x71 x70 x66)False)False)(∀ x66 x67 x68 x69 . x1 x68 (x2 (x3 x69))x9 x66x61 x67 (x24 x69 x68 x66)(x38 x66 x68 x69 x67 = x58 x69 x68 (x37 x66 x68 x69 x67)False)False)(∀ x66 x67 x68 x69 . x1 x68 (x2 (x3 x69))x9 x66x61 x67 (x24 x69 x68 x66)(x64 x66 (x37 x66 x68 x69 x67)False)False)(∀ x66 x67 x68 x69 . x1 x68 (x2 (x3 x69))x9 x66x61 x67 (x24 x69 x68 x66)(x9 (x37 x66 x68 x69 x67)False)False)(∀ x66 x67 x68 x69 . x1 x68 (x2 (x3 x69))x9 x66x61 x67 (x24 x69 x68 x66)(x67 = x38 x66 x68 x69 x67False)False)(∀ x66 x67 x68 x69 . x1 x68 (x2 (x3 x69))x9 x66x61 x67 (x24 x69 x68 x66)(x1 (x38 x66 x68 x69 x67) (x2 (x3 x69))False)False)(∀ x66 x67 . (x63 x67False)x65 x67(x63 x66False)x65 x66x63 (x8 x67 x66)False)((x45 x11False)False)(x0 x11False)(∀ x66 x67 . x65 x67x65 x66(x65 (x8 x67 x66)False)False)(∀ x66 x67 . (x0 x67False)x0 (x57 x66 x67)False)(∀ x66 x67 . (x0 x67False)x0 (x57 x67 x66)False)(∀ x66 x67 . x9 x67(x0 x66False)x9 x66x0 (x8 x66 x67)False)(∀ x66 . x45 x66(x45 (x36 x66)False)False)(∀ x66 x67 . x9 x67(x0 x66False)x9 x66x0 (x8 x67 x66)False)(∀ x66 . (x35 (x3 x66)False)False)(∀ x66 . x0 (x3 x66)False)((x0 x60False)False)(∀ x66 . x0 (x2 x66)False)(∀ x66 x67 . x9 x67x9 x66(x9 (x8 x67 x66)False)False)(∀ x66 x67 . x63 x67x65 x67(x62 x66False)x65 x66(x63 (x8 x66 x67)False)False)(∀ x66 x67 . x63 x67x65 x67(x62 x66False)x65 x66(x63 (x8 x67 x66)False)False)(∀ x66 x67 . x62 x67x65 x67(x63 x66False)x65 x66(x62 (x8 x66 x67)False)False)(∀ x66 x67 . x62 x67x65 x67(x63 x66False)x65 x66(x62 (x8 x67 x66)False)False)(∀ x66 x67 . (x62 x67False)x65 x67(x62 x66False)x65 x66x62 (x8 x67 x66)False)(∀ x66 x67 . (x0 x67False)(x0 x66False)x1 x66 (x2 x67)(x55 (x34 x66 x67) x67 x66False)False)(∀ x66 . (x1 (x25 x66) x66False)False)(∀ x66 . (x33 (x32 x66) x66False)False)(∀ x66 x67 x68 . (x0 x68False)(x0 x66False)x1 x66 (x2 x68)x55 x67 x68 x66(x1 x67 x68False)False)(∀ x66 x67 . x33 x67 x66(x35 x67False)False)(∀ x66 x67 . x33 x67 x66x0 x67False)(∀ x66 x67 x68 . x1 x67 (x2 (x53 x68))x9 x66(x1 (x58 x68 x67 x66) (x2 (x53 x68))False)False)((x1 x14 (x2 x56)False)False)(∀ x66 x67 x68 . x1 x67 (x2 x68)x1 x66 (x2 x68)(x1 (x4 x68 x67 x66) (x2 x68)False)False)(∀ x66 . (x33 (x53 x66) x66False)False)(∀ x66 x67 . x9 x67x1 x66 x14(x55 (x12 x67 x66) x56 x14False)False)(∀ x66 x67 x68 . x1 x67 (x2 (x3 x68))x9 x66(x1 (x6 x68 x67 x66) (x2 (x3 x68))False)False)(∀ x66 x67 x68 x69 . x1 x68 (x2 (x3 x69))x9 x66x9 x67(x1 (x5 x69 x68 x66 x67) (x2 (x3 x69))False)False)(∀ x66 x67 x68 . x1 x67 (x2 (x3 x68))x9 x66(x6 x68 x67 x66 = x36 (x24 x68 x67 x66)False)False)(∀ x66 x67 . x54 x67x54 x66(x64 x67 x66False)(x64 x66 x67False)False)(∀ x66 x67 x68 . x1 x67 (x2 x68)x1 x66 (x2 x68)(x4 x68 x67 x66 = x4 x68 x66 x67False)False)(∀ x66 x67 . x13 x67x13 x66(x8 x67 x66 = x8 x66 x67False)False)(∀ x66 x67 . (x57 x67 x66 = x57 x66 x67False)False)(∀ x66 x67 . x9 x67x1 x66 x14(x12 x67 x66 = x12 x66 x67False)False)(∀ x66 . x0 x66(x26 x66False)False)(∀ x66 . x54 x66(x62 x66False)(x63 x66False)(x54 x66False)False)(∀ x66 . x54 x66(x62 x66False)(x63 x66False)(x0 x66False)False)(∀ x66 . x1 x66 x11(x9 x66False)False)(∀ x66 . x0 x66x54 x66x63 x66False)(∀ x66 . x0 x66x54 x66x62 x66False)(∀ x66 . x0 x66x54 x66(x54 x66False)False)(∀ x66 . x0 x66(x9 x66False)False)(∀ x66 . (x0 x66False)x54 x66(x62 x66False)(x63 x66False)False)(∀ x66 . (x0 x66False)x54 x66(x62 x66False)(x54 x66False)False)(∀ x66 . x9 x66(x45 x66False)False)(∀ x66 . x54 x66x63 x66x62 x66False)(∀ x66 . x54 x66x63 x66(x54 x66False)False)(∀ x66 . x54 x66x63 x66x0 x66False)(∀ x66 x67 . x45 x67x1 x66 x67(x45 x66False)False)(∀ x66 . (x0 x66False)x54 x66(x63 x66False)(x62 x66False)False)(∀ x66 . (x0 x66False)x54 x66(x63 x66False)(x54 x66False)False)(∀ x66 . x65 x66(x54 x66False)False)(∀ x66 x67 . x0 x67x1 x66 (x2 x67)x48 x66 x67False)(∀ x66 . x0 x66(x31 x66False)False)(∀ x66 . x54 x66x62 x66x63 x66False)(∀ x66 . x54 x66x62 x66(x54 x66False)False)(∀ x66 . x54 x66x62 x66x0 x66False)(∀ x66 . x65 x66(x13 x66False)False)(∀ x66 x67 . (x0 x67False)x1 x66 (x2 x67)x0 x66(x48 x66 x67False)False)(∀ x66 . x0 x66(x45 x66False)False)(∀ x66 . x9 x66x63 x66False)(∀ x66 . x9 x66(x9 x66False)False)(∀ x66 . x9 x66(x54 x66False)False)(∀ x66 . x9 x66(x65 x66False)False)(∀ x66 x67 . (x0 x67False)x1 x66 (x2 x67)(x48 x66 x67False)x0 x66False)(∀ x66 . x43 x66x21 x66(x45 x66False)False)(∀ x66 . x1 x66 x14x63 x66False)(∀ x66 . x1 x66 x56(x65 x66False)False)(∀ x66 x67 . x0 x67x1 x66 (x2 x67)(x0 x66False)False)(∀ x66 . x45 x66(x21 x66False)False)(∀ x66 . x45 x66(x43 x66False)False)(∀ x66 . x9 x66(x9 x66False)False)(∀ x66 . x9 x66(x45 x66False)False)(∀ x66 x67 . x26 x67x1 x66 (x2 x67)(x26 x66False)False)(∀ x66 x67 . x1 x67 (x3 x66)(x27 x67False)False)(∀ x66 x67 . x1 x67 (x3 x66)(x31 x67False)False)(∀ x66 x67 . x61 x66 x67x61 x67 x66False)(x4 (x3 x28) (x58 x28 x29 x30) (x6 x28 x29 (x8 x30 x7)) = x6 x28 x29 x30False)((x9 x30False)False)((x1 x29 (x2 (x3 x28))False)False)False (proof)

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