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PUQi7ZkqusvjVNCGWPdXvFK5PhSDC1GxgHS
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0be8f../25b58.. bday: 35144 doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem c048a.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . ∀ x2 x3 : ι → ι → ο . ∀ x4 . ∀ x5 : ι → ι → ι → ο . ∀ x6 x7 : ι → ο . ∀ x8 : ι → ι . ∀ x9 : ι → ι → ο . ∀ x10 : ι → ι . ∀ x11 : ι → ο . ∀ x12 . ∀ x13 : ι → ι . ∀ x14 x15 . ∀ x16 : ι → ι . ∀ x17 : ι → ι → ι . ∀ x18 x19 x20 : ι → ο . ∀ x21 . ∀ x22 : ι → ο . ∀ x23 : ι → ι . ∀ x24 x25 x26 x27 x28 x29 : ι → ο . ∀ x30 x31 x32 . ∀ x33 : ι → ι → ι → ι . ∀ x34 : ι → ι → ι . ∀ x35 : ι → ο . ∀ x36 . ∀ x37 x38 : ι → ο . ∀ x39 : ι → ι → ι . ∀ x40 : ι → ο . ∀ x41 . ∀ x42 : ι → ο . ∀ x43 . ∀ x44 : ι → ι → ο . ∀ x45 . ∀ x46 : ι → ο . ∀ x47 . ∀ x48 : ι → ο . ∀ x49 : ι → ι → ι . ∀ x50 x51 : ι → ο . ∀ x52 . ∀ x53 : ι → ι → ι → ι . ∀ x54 : ι → ι → ο . ∀ x55 x56 . ∀ x57 : ι → ι → ι . ∀ x58 . ∀ x59 : ι → ι → ι → ο . ∀ x60 : ι → ι → ι → ι . ∀ x61 : ι → ι → ο . ∀ x62 : ι → ι → ι . ∀ x63 : ι → ο . ∀ x64 . ∀ x65 : ι → ο . (∀ x66 x67 . x65 x67(x67 = x66False)x65 x66False)(∀ x66 x67 . x0 x66 x67x65 x67False)(∀ x66 . x65 x66(x66 = x64False)False)(∀ x66 x67 x68 . x0 x66 x67x2 x67 (x1 x68)x65 x68False)(∀ x66 x67 x68 . x0 x67 x68x2 x68 (x1 x66)(x2 x67 x66False)False)(∀ x66 x67 . x3 x67 x66(x2 x67 (x1 x66)False)False)(∀ x66 x67 . x2 x67 (x1 x66)(x3 x67 x66False)False)(∀ x66 x67 . x2 x66 x67(x65 x67False)(x0 x66 x67False)False)(∀ x66 x67 . x0 x67 x66(x2 x67 x66False)False)((x2 x64 x4False)False)(∀ x66 x67 x68 x69 . (x65 x69False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x69 x58x2 x66 (x1 (x62 x69 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x69 x58x2 x67 (x1 (x62 x69 x58))x54 x68 (x57 x56 x55)x63 x68x59 x68 x69 x58x2 x68 (x1 (x62 x69 x58))x61 x66 x67x61 x68 x67(x61 (x60 x69 x66 x68) x67False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x61 x66 (x60 x68 x66 x67)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x61 (x53 x68 x66 x67) x66False)False)((x2 x55 x58False)False)((x2 x55 x52False)False)((x5 x55 x58 x52False)False)((x51 x55False)False)(x65 x55False)(∀ x66 . (x3 x66 x66False)False)(∀ x66 x67 . x6 x67x63 x67x7 x67x6 x66x63 x66x7 x66(x61 x67 x67False)False)(∀ x66 x67 x68 . (x65 x68False)(x65 x66False)x2 x66 (x1 x68)x2 x67 x66(x5 x67 x68 x66False)False)(∀ x66 x67 x68 . (x65 x68False)(x65 x66False)x2 x66 (x1 x68)x5 x67 x68 x66(x2 x67 x66False)False)((x56 = x64False)False)((x52 = x4False)False)(∀ x66 x67 . x50 x67x50 x66(x57 x67 x66 = x49 x67 x66False)False)(∀ x66 . (x65 x66False)(x9 (x8 x66) x66False)False)(∀ x66 . (x65 x66False)(x2 (x8 x66) (x1 x66)False)False)(∀ x66 . x9 (x10 x66) x66False)(∀ x66 . (x2 (x10 x66) (x1 x66)False)False)((x11 x12False)False)((x48 x12False)False)(x65 x12False)(x65 x47False)(∀ x66 . (x65 (x13 x66)False)False)(∀ x66 . (x2 (x13 x66) (x1 x66)False)False)((x48 x14False)False)(x65 x14False)((x65 x15False)False)((x46 x45False)False)((x63 x45False)False)((x6 x45False)False)(∀ x66 . (x65 x66False)x65 (x16 x66)False)(∀ x66 . (x65 x66False)(x2 (x16 x66) (x1 x66)False)False)(∀ x66 x67 . (x54 (x17 x66 x67) x66False)False)(∀ x66 x67 . (x44 (x17 x67 x66) x66False)False)(∀ x66 x67 . (x6 (x17 x66 x67)False)False)(∀ x66 x67 . (x65 (x17 x66 x67)False)False)(∀ x66 x67 . (x2 (x17 x66 x67) (x1 (x62 x67 x66))False)False)((x48 x43False)False)(x65 x43False)((x42 x41False)False)((x18 x41False)False)((x40 x41False)False)((x19 x41False)False)(x65 x41False)((x2 x41 (x1 x58)False)False)(∀ x66 x67 . (x65 x67False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x67 x58x2 x66 (x1 (x62 x67 x58))(x39 x67 (x39 x67 x66) = x66False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x60 x68 x66 x66 = x66False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x53 x68 x66 x66 = x66False)False)(∀ x66 x67 . x48 x67(x46 (x62 x66 x67)False)False)(x38 x58False)(∀ x66 x67 . x20 x67(x54 (x62 x66 x67) x21False)False)(∀ x66 x67 . x37 x67(x54 (x62 x66 x67) x36False)False)(∀ x66 x67 . x18 x67(x7 (x62 x66 x67)False)False)(∀ x66 x67 . x40 x67(x35 (x62 x66 x67)False)False)(∀ x66 x67 . x19 x67(x22 (x62 x66 x67)False)False)(x38 x36False)(x38 x21False)((x48 x4False)False)((x20 x21False)False)((x11 x4False)False)((x11 x21False)False)((x11 x36False)False)((x11 x58False)False)(x65 x21False)((x37 x36False)False)(x65 x36False)((x18 x58False)False)((x65 x64False)False)(∀ x66 . x65 (x1 x66)False)(x65 x58False)(∀ x66 x67 . (x65 x67False)(x65 x66False)x65 (x62 x67 x66)False)(∀ x66 x67 . (x65 x67False)(x65 x66False)x2 x66 (x1 x67)(x5 (x34 x66 x67) x67 x66False)False)(∀ x66 . (x2 (x23 x66) x66False)False)(∀ x66 x67 x68 . (x65 x68False)(x65 x66False)x2 x66 (x1 x68)x5 x67 x68 x66(x2 x67 x68False)False)((x5 x56 x58 x52False)False)((x2 x52 (x1 x58)False)False)(∀ x66 x67 . (x65 x67False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x67 x58x2 x66 (x1 (x62 x67 x58))(x2 (x39 x67 x66) (x1 (x62 x67 x58))False)False)(∀ x66 x67 . (x65 x67False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x67 x58x2 x66 (x1 (x62 x67 x58))(x59 (x39 x67 x66) x67 x58False)False)(∀ x66 x67 . (x65 x67False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x67 x58x2 x66 (x1 (x62 x67 x58))(x63 (x39 x67 x66)False)False)(∀ x66 x67 . (x65 x67False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x67 x58x2 x66 (x1 (x62 x67 x58))(x54 (x39 x67 x66) (x57 x56 x55)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x2 (x60 x68 x66 x67) (x1 (x62 x68 x58))False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x59 (x60 x68 x66 x67) x68 x58False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x63 (x60 x68 x66 x67)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x54 (x60 x68 x66 x67) (x57 x56 x55)False)False)(∀ x66 x67 . x50 x67x50 x66(x2 (x57 x67 x66) (x1 x58)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x2 (x33 x68 x66 x67) (x1 (x62 x68 x58))False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x59 (x33 x68 x66 x67) x68 x58False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x63 (x33 x68 x66 x67)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x54 (x33 x68 x66 x67) (x57 x56 x55)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x2 (x53 x68 x66 x67) (x1 (x62 x68 x58))False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x59 (x53 x68 x66 x67) x68 x58False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x63 (x53 x68 x66 x67)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x54 (x53 x68 x66 x67) (x57 x56 x55)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x33 x68 x66 x67 = x53 x68 x66 (x39 x68 x67)False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x60 x68 x66 x67 = x60 x68 x67 x66False)False)(∀ x66 x67 x68 . (x65 x68False)x54 x66 (x57 x56 x55)x63 x66x59 x66 x68 x58x2 x66 (x1 (x62 x68 x58))x54 x67 (x57 x56 x55)x63 x67x59 x67 x68 x58x2 x67 (x1 (x62 x68 x58))(x53 x68 x66 x67 = x53 x68 x67 x66False)False)(∀ x66 . x65 x66x6 x66(x46 x66False)False)(∀ x66 . x65 x66x6 x66(x6 x66False)False)(∀ x66 . x2 x66 (x1 x36)(x37 x66False)False)(∀ x66 . x6 x66x46 x66(x7 x66False)False)(∀ x66 . x6 x66x46 x66(x6 x66False)False)(∀ x66 . x2 x66 (x1 x58)(x18 x66False)False)(∀ x66 . x6 x66x46 x66(x54 x66 x36False)False)(∀ x66 . x6 x66x46 x66(x6 x66False)False)(∀ x66 . x6 x66x7 x66(x22 x66False)False)(∀ x66 . x6 x66x7 x66(x6 x66False)False)(∀ x66 . x6 x66x7 x66(x35 x66False)False)(∀ x66 . x6 x66x7 x66(x6 x66False)False)(∀ x66 . x18 x66(x19 x66False)False)(∀ x66 . x2 x66 (x1 x58)x65 x66(x42 x66False)False)(∀ x66 . x6 x66x54 x66 x36(x7 x66False)False)(∀ x66 . x6 x66x54 x66 x36(x6 x66False)False)(∀ x66 x67 . x65 x67x2 x66 (x1 x67)x9 x66 x67False)(∀ x66 x67 x68 . x65 x68x2 x66 (x1 (x62 x67 x68))(x65 x66False)False)(∀ x66 . x18 x66(x40 x66False)False)(∀ x66 . x6 x66x54 x66 x21(x7 x66False)False)(∀ x66 . x6 x66x54 x66 x21(x6 x66False)False)(∀ x66 x67 . (x65 x67False)x2 x66 (x1 x67)x65 x66(x9 x66 x67False)False)(∀ x66 x67 x68 . x65 x68x2 x66 (x1 (x62 x68 x67))(x65 x66False)False)(∀ x66 . x37 x66(x18 x66False)False)(∀ x66 . x6 x66x54 x66 x52(x46 x66False)False)(∀ x66 . x6 x66x54 x66 x52(x6 x66False)False)(∀ x66 . x6 x66x54 x66 x58(x7 x66False)False)(∀ x66 . x6 x66x54 x66 x58(x6 x66False)False)(∀ x66 . x6 x66x54 x66 x21(x54 x66 x36False)False)(∀ x66 . x6 x66x54 x66 x21(x6 x66False)False)(∀ x66 x67 . (x65 x67False)x2 x66 (x1 x67)(x9 x66 x67False)x65 x66False)(∀ x66 x67 x68 . x2 x68 (x1 (x62 x66 x67))(x54 x68 x67False)False)(∀ x66 x67 x68 . x2 x68 (x1 (x62 x67 x66))(x44 x68 x67False)False)(∀ x66 . x20 x66(x37 x66False)False)(∀ x66 . x65 x66(x11 x66False)False)(∀ x66 . x2 x66 x52(x48 x66False)False)(∀ x66 x67 . x48 x67x2 x66 (x1 x67)(x48 x66False)False)(∀ x66 x67 . x20 x67x2 x66 (x1 x67)(x20 x66False)False)(∀ x66 x67 . x37 x67x2 x66 (x1 x67)(x37 x66False)False)(∀ x66 x67 x68 . x48 x68x2 x66 (x1 (x62 x67 x68))(x46 x66False)False)(∀ x66 x67 . x18 x67x2 x66 (x1 x67)(x18 x66False)False)(∀ x66 x67 x68 . x20 x68x2 x66 (x1 (x62 x67 x68))(x54 x66 x21False)False)(∀ x66 x67 . x40 x67x2 x66 (x1 x67)(x40 x66False)False)(∀ x66 . x6 x66x46 x66(x54 x66 x21False)False)(∀ x66 . x6 x66x46 x66(x6 x66False)False)(∀ x66 x67 . x65 x67x2 x66 (x1 x67)(x65 x66False)False)(∀ x66 x67 x68 . x2 x68 (x1 (x62 x66 x67))(x6 x68False)False)(∀ x66 . x48 x66(x20 x66False)False)(∀ x66 . x2 x66 (x1 x58)x42 x66(x24 x66False)False)(∀ x66 x67 x68 . x37 x68x2 x66 (x1 (x62 x67 x68))(x54 x66 x36False)False)(∀ x66 x67 . x19 x67x2 x66 (x1 x67)(x19 x66False)False)(∀ x66 x67 x68 . x18 x68x2 x66 (x1 (x62 x67 x68))(x7 x66False)False)(∀ x66 . x65 x66(x48 x66False)False)(∀ x66 x67 x68 . x40 x68x2 x66 (x1 (x62 x67 x68))(x35 x66False)False)(∀ x66 x67 . x48 x67x2 x66 x67(x25 x66False)False)(∀ x66 x67 x68 . x19 x68x2 x66 (x1 (x62 x67 x68))(x22 x66False)False)(∀ x66 x67 . x20 x67x2 x66 x67(x26 x66False)False)(∀ x66 x67 . x6 x67x46 x67x2 x66 (x1 x67)(x46 x66False)False)(∀ x66 x67 . x37 x67x2 x66 x67(x27 x66False)False)(∀ x66 x67 . x6 x67x54 x67 x21x2 x66 (x1 x67)(x54 x66 x21False)False)(∀ x66 x67 . x18 x67x2 x66 x67(x50 x66False)False)(∀ x66 x67 . x6 x67x54 x67 x36x2 x66 (x1 x67)(x54 x66 x36False)False)(∀ x66 x67 . x40 x67x2 x66 x67(x28 x66False)False)(∀ x66 x67 . x6 x67x7 x67x2 x66 (x1 x67)(x7 x66False)False)(∀ x66 x67 . x19 x67x2 x66 x67(x29 x66False)False)(∀ x66 x67 . x6 x67x35 x67x2 x66 (x1 x67)(x35 x66False)False)(∀ x66 . x2 x66 (x1 x52)(x48 x66False)False)(∀ x66 x67 . x6 x67x22 x67x2 x66 (x1 x67)(x22 x66False)False)(∀ x66 . x2 x66 (x1 x21)(x20 x66False)False)(∀ x66 x67 . x0 x66 x67x0 x67 x66False)(x61 (x60 x31 (x53 x31 x30 x32) (x33 x31 x30 x32)) x30False)((x2 x32 (x1 (x62 x31 x58))False)False)((x59 x32 x31 x58False)False)((x63 x32False)False)((x54 x32 (x57 x56 x55)False)False)((x2 x30 (x1 (x62 x31 x58))False)False)((x59 x30 x31 x58False)False)((x63 x30False)False)((x54 x30 (x57 x56 x55)False)False)(x65 x31False)False (proof)

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