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Proofgold Signed Transaction

vin
PrS5Z../f8ff7..
PUi12../b839a..
vout
PrS5Z../e0f74.. 24.98 bars
TMcrh../3794e.. ownership of e92bb.. as prop with payaddr PrDsC.. rights free controlledby PrDsC.. upto 0
TMPUV../361c6.. ownership of 40683.. as prop with payaddr PrDsC.. rights free controlledby PrDsC.. upto 0
PUeHT../11e98.. doc published by PrDsC..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem e92bb..t10_sin_cos8 : ∀ x0 : ι → ο . ∀ x1 . ∀ x2 : ι → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ι . ∀ x5 : ι → ι → ι → ο . ∀ x6 x7 : ι → ο . ∀ x8 x9 : ι → ι → ο . ∀ x10 x11 x12 x13 x14 x15 : ι → ο . ∀ x16 x17 x18 x19 . ∀ x20 : ι → ι . ∀ x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 . ∀ x34 : ι → ο . ∀ x35 . ∀ x36 x37 x38 x39 : ι → ο . ∀ x40 : ι → ι → ο . ∀ x41 : ι → ι → ι . ∀ x42 . ∀ x43 : ι → ο . ∀ x44 : ι → ι . ∀ x45 : ι → ο . ∀ x46 . ∀ x47 x48 : ι → ι → ι . ∀ x49 : ι → ι . ∀ x50 . ∀ x51 : ι → ι . ∀ x52 . ∀ x53 : ι → ι → ι . ∀ x54 : ι → ι . ∀ x55 : ι → ι → ι . ∀ x56 : ι → ι . ∀ x57 : ι → ι → ι . (x57 (x54 (x48 x52 x50)) (x55 (x56 x52) (x54 x50)) = x48 (x51 x52) (x49 x50)x57 (x54 (x53 x52 x50)) (x55 (x56 x52) (x54 x50)) = x53 (x51 x52) (x49 x50)False)(∀ x58 x59 . (x57 (x53 (x49 x59) (x49 x58)) (x53 x1 (x55 (x49 x59) (x49 x58))) = x49 (x53 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x57 (x48 (x49 x59) (x49 x58)) (x48 x1 (x55 (x49 x59) (x49 x58))) = x49 (x48 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x53 (x55 (x56 x59) (x54 x58)) (x55 (x54 x59) (x56 x58)) = x56 (x53 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x48 (x55 (x56 x59) (x54 x58)) (x55 (x54 x59) (x56 x58)) = x56 (x48 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x53 (x55 (x54 x59) (x54 x58)) (x55 (x56 x59) (x56 x58)) = x54 (x53 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x48 (x55 (x54 x59) (x54 x58)) (x55 (x56 x59) (x56 x58)) = x54 (x48 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 x60 . (x2 x60False)(x2 x58False)(x3 x59 x58False)x5 x59 x58 x60x3 x60 (x4 x58)False)(∀ x58 x59 x60 . (x2 x60False)(x2 x58False)(x3 x59 x60False)x5 x59 x58 x60x3 x60 (x4 x58)False)(∀ x58 x59 x60 . (x53 (x57 x58 x59) (x57 x60 x59) = x57 (x53 x58 x60) x59False)x6 x60x6 x59x6 x58False)(∀ x58 x59 x60 . (x48 (x57 x58 x59) (x57 x60 x59) = x57 (x48 x58 x60) x59False)x6 x60x6 x59x6 x58False)(∀ x58 x59 x60 . (x48 (x55 x58 x60) (x55 x59 x60) = x55 (x48 x58 x59) x60False)x6 x60x6 x59x6 x58False)(∀ x58 x59 . (x2 x59False)(x2 x58False)(x5 (x47 x58 x59) x58 x59False)x3 x59 (x4 x58)False)(∀ x58 x59 x60 . (x2 x60False)(x2 x58False)(x5 x59 x60 x58False)x3 x59 x58x3 x58 (x4 x60)False)(∀ x58 x59 x60 . (x60 = x46False)(x57 (x55 x59 x60) (x55 x58 x60) = x57 x59 x58False)x6 x58x6 x59x6 x60False)(∀ x58 x59 x60 . (x55 (x55 x58 x59) x60 = x55 x58 (x55 x59 x60)False)x6 x60x6 x59x6 x58False)(∀ x58 x59 x60 . (x48 (x48 x58 x59) x60 = x48 x58 (x48 x59 x60)False)x6 x60x6 x59x6 x58False)(∀ x58 x59 x60 . (x57 (x55 x58 x59) x60 = x55 x58 (x57 x59 x60)False)x6 x60x6 x59x6 x58False)(∀ x58 x59 . (x45 x59False)(x45 x58False)x0 x59x0 x58x45 (x48 x58 x59)False)(∀ x58 x59 . (x45 x59False)(x45 x58False)x0 x59x0 x58x7 (x57 x58 x59)False)(∀ x58 x59 . (x45 x59False)(x45 x58False)x0 x59x0 x58x7 (x55 x58 x59)False)(∀ x58 x59 . (x7 x59False)(x45 x58False)x0 x58x0 x59x45 (x53 x58 x59)False)(∀ x58 x59 . (x7 x59False)(x45 x58False)x0 x58x0 x59x45 (x57 x59 x58)False)(∀ x58 x59 . (x7 x59False)(x45 x58False)x0 x58x0 x59x45 (x57 x58 x59)False)(∀ x58 x59 . (x7 x59False)(x45 x58False)x0 x58x0 x59x7 (x53 x59 x58)False)(∀ x58 x59 . (x7 x59False)(x45 x58False)x0 x59x0 x58x45 (x55 x58 x59)False)(∀ x58 x59 . (x7 x59False)(x45 x58False)x0 x59x0 x58x45 (x55 x59 x58)False)(∀ x58 x59 . (x7 x59False)(x7 x58False)x0 x59x0 x58x7 (x57 x58 x59)False)(∀ x58 x59 . (x7 x59False)(x7 x58False)x0 x59x0 x58x7 (x55 x58 x59)False)(∀ x58 x59 . (x7 x59False)(x7 x58False)x0 x59x0 x58x7 (x48 x58 x59)False)(∀ x58 x59 . (x48 (x44 x59) (x44 x58) = x44 (x48 x59 x58)False)x6 x58x6 x59False)(∀ x58 x59 x60 . (x3 x59 x60False)x8 x59 x58x3 x58 (x4 x60)False)(∀ x58 x59 . (x2 x59False)x43 x59x43 x58x2 (x48 x58 x59)False)(∀ x58 x59 . (x2 x59False)x43 x59x43 x58x2 (x48 x59 x58)False)(∀ x58 x59 . (x3 (x41 x59 x58) x42False)x0 x58x3 x59 x42False)(∀ x58 x59 x60 . x2 x60x8 x59 x58x3 x58 (x4 x60)False)(∀ x58 x59 . (x45 x59False)(x45 (x53 x58 x59)False)x0 x59x0 x58x45 x58False)(∀ x58 x59 . (x45 x59False)(x7 (x53 x59 x58)False)x0 x59x0 x58x45 x58False)(∀ x58 x59 . (x45 x59False)(x7 (x48 x58 x59)False)x0 x59x0 x58x7 x58False)(∀ x58 x59 . (x45 x59False)(x7 (x48 x59 x58)False)x0 x59x0 x58x7 x58False)(∀ x58 x59 . (x7 x59False)(x45 (x53 x59 x58)False)x0 x59x0 x58x7 x58False)(∀ x58 x59 . (x7 x59False)(x45 (x48 x58 x59)False)x0 x59x0 x58x45 x58False)(∀ x58 x59 . (x7 x59False)(x45 (x48 x59 x58)False)x0 x59x0 x58x45 x58False)(∀ x58 x59 . (x7 x59False)(x7 (x53 x58 x59)False)x0 x59x0 x58x7 x58False)(∀ x58 x59 . (x41 x59 x58 = x57 x59 x58False)x0 x58x3 x59 x42False)(∀ x58 x59 . (x53 (x44 x59) (x44 x58) = x53 x58 x59False)x6 x58x6 x59False)(∀ x58 x59 . (x2 x59False)(x7 x59False)(x45 x58False)x0 x58x0 x59x40 x59 x58False)(∀ x58 x59 . (x2 x59False)(x7 x58False)(x45 x59False)x0 x59x0 x58x40 x58 x59False)(∀ x58 x59 . (x45 x59False)x0 x59x0 x58x45 x58x40 x58 x59False)(∀ x58 x59 . (x45 x59False)x0 x59x0 x58x45 x58x40 x58 x59False)(∀ x58 x59 . (x7 x59False)x0 x58x0 x59x7 x58x40 x59 x58False)(∀ x58 x59 . (x7 x59False)x0 x58x0 x59x7 x58x40 x59 x58False)(∀ x58 x59 . (x48 x59 (x44 x58) = x53 x59 x58False)x6 x58x6 x59False)(∀ x58 x59 . (x9 x59 x58False)x3 x59 (x4 x58)False)(∀ x58 x59 . x8 x58 x59x8 x59 x58False)(∀ x58 x59 . (x43 (x55 x59 x58)False)x43 x58x43 x59False)(∀ x58 x59 . (x43 (x48 x59 x58)False)x43 x58x43 x59False)(∀ x58 x59 . (x0 (x53 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x0 (x57 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x0 (x55 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x0 (x48 x59 x58)False)x0 x58x0 x59False)(∀ x58 x59 . (x10 x59False)x10 x58x3 x59 (x4 x58)False)(∀ x58 x59 . (x39 x59False)x39 x58x3 x59 (x4 x58)False)(∀ x58 x59 . (x11 x59False)x11 x58x3 x59 (x4 x58)False)(∀ x58 x59 . (x38 x59False)x38 x58x3 x59 (x4 x58)False)(∀ x58 x59 . (x12 x59False)x12 x58x3 x59 (x4 x58)False)(∀ x58 x59 . (x37 x59False)x37 x58x3 x59 (x4 x58)False)(∀ x58 x59 . (x40 x58 x59False)(x40 x59 x58False)x13 x58x13 x59False)(∀ x58 x59 . (x3 x59 (x4 x58)False)x9 x59 x58False)(∀ x58 x59 . (x55 x59 x58 = x55 x58 x59False)x6 x58x6 x59False)(∀ x58 x59 . (x48 x59 x58 = x48 x58 x59False)x6 x58x6 x59False)(∀ x58 x59 . (x2 x59False)(x8 x58 x59False)x3 x58 x59False)(∀ x58 x59 . (x7 x59False)(x45 x58False)(x40 x58 x59False)x0 x59x0 x58False)(∀ x58 x59 . (x7 x59False)(x45 x58False)(x40 x58 x59False)x0 x59x0 x58False)(∀ x58 . (x57 (x56 x58) (x54 x58) = x49 x58False)x0 x58False)(∀ x58 . (x41 (x54 x58) (x56 x58) = x51 x58False)x0 x58False)(∀ x58 x59 . (x3 x59 x58False)x8 x59 x58False)(∀ x58 x59 . (x43 x59False)x37 x58x3 x59 x58False)(∀ x58 x59 . (x36 x59False)x10 x58x3 x59 x58False)(∀ x58 x59 . (x14 x59False)x39 x58x3 x59 x58False)(∀ x58 x59 . (x13 x59False)x38 x58x3 x59 x58False)(∀ x58 x59 . (x6 x59False)x12 x58x3 x59 x58False)(∀ x58 x59 . (x0 x59False)x11 x58x3 x59 x58False)(∀ x58 . (x11 x58False)x3 x58 (x4 x42)False)(∀ x58 . (x37 x58False)x3 x58 (x4 x35)False)(∀ x58 x59 . x2 x59x8 x58 x59False)(∀ x58 x59 . (x40 x59 x59False)x13 x58x13 x59False)(∀ x58 . (x45 x58False)x0 x58x7 (x44 x58)False)(∀ x58 . (x7 x58False)x0 x58x45 (x44 x58)False)(∀ x58 . (x55 x58 (x44 x1) = x44 x58False)x6 x58False)(∀ x58 . x7 x58x3 x58 x35False)(∀ x58 . (x3 (x51 x58) x42False)x0 x58False)(∀ x58 . (x40 x1 (x54 x58)False)x0 x58False)(∀ x58 . (x37 x58False)x3 x58 x35False)(∀ x58 . (x0 x58False)x3 x58 x42False)(∀ x58 . (x45 x58False)(x6 (x44 x58)False)x0 x58False)(∀ x58 . (x7 x58False)(x6 (x44 x58)False)x0 x58False)(∀ x58 . x13 x58x7 x58x45 x58False)(∀ x58 . x13 x58x7 x58x45 x58False)(∀ x58 . x13 x58x2 x58x45 x58False)(∀ x58 . x13 x58x2 x58x45 x58False)(∀ x58 . x13 x58x2 x58x7 x58False)(∀ x58 . x13 x58x2 x58x7 x58False)(∀ x58 . (x2 x58False)(x7 x58False)(x45 x58False)x13 x58False)(∀ x58 . (x2 x58False)(x7 x58False)(x45 x58False)x13 x58False)(∀ x58 . (x2 x58False)(x7 x58False)(x45 x58False)x13 x58False)(∀ x58 . (x55 x1 x58 = x58False)x6 x58False)(∀ x58 . (x53 x58 x46 = x58False)x6 x58False)(∀ x58 . (x57 x58 x1 = x58False)x6 x58False)(∀ x58 . (x48 x58 x46 = x58False)x6 x58False)(∀ x58 . (x57 x46 x58 = x46False)x6 x58False)(∀ x58 . (x55 x58 x46 = x46False)x6 x58False)(∀ x58 . (x44 (x44 x58) = x58False)x6 x58False)(∀ x58 . (x6 (x44 x58)False)x6 x58False)(∀ x58 . (x6 (x44 x58)False)x0 x58False)(∀ x58 . (x0 (x44 x58)False)x0 x58False)(∀ x58 x59 . (x59 = x58False)x2 x58x2 x59False)(∀ x58 . (x58 = x46False)x56 x58 = x46x0 x58False)(∀ x58 . (x58 = x46False)x49 x58 = x46x0 x58False)(∀ x58 . x43 x58x7 x58False)(∀ x58 . (x34 x58False)x2 x58False)(∀ x58 . (x15 x58False)x43 x58False)(∀ x58 . (x10 x58False)x37 x58False)(∀ x58 . (x39 x58False)x10 x58False)(∀ x58 . (x11 x58False)x39 x58False)(∀ x58 . (x13 x58False)x43 x58False)(∀ x58 . (x13 x58False)x0 x58False)(∀ x58 . (x38 x58False)x11 x58False)(∀ x58 . (x6 x58False)x0 x58False)(∀ x58 . (x12 x58False)x11 x58False)(∀ x58 . (x37 x58False)x2 x58False)(∀ x58 . (x0 x58False)x43 x58False)(∀ x58 . (x56 x46 = x46False)x0 x58False)(∀ x58 . (x54 x46 = x1False)x0 x58False)(∀ x58 . (x49 x46 = x46False)x0 x58False)(∀ x58 . (x58 = x16False)x2 x58False)(x40 x33 (x44 x1)False)(x40 x1 (x44 x1)False)(x40 x1 x33False)(x2 x17False)(x2 x32False)(x2 x18False)(x2 x31False)(x2 x19False)(x2 x1False)(x52 = x46False)((x5 x33 x42 x35False)False)((x5 x1 x42 x35False)False)((x5 x46 x42 x35False)False)((x40 (x44 x1) (x44 x1)False)False)((x53 (x44 x1) (x44 x1) = x33False)False)(∀ x58 . (x3 (x20 x58) x58False)False)(∀ x58 . (x3 (x56 x58) x42False)False)(∀ x58 . (x3 (x54 x58) x42False)False)(∀ x58 . (x3 (x49 x58) x42False)False)((x53 (x44 x1) x33 = x44 x1False)False)((x48 (x44 x1) x33 = x44 x1False)False)((x57 x1 (x44 x1) = x44 x1False)False)((x48 x33 (x44 x1) = x44 x1False)False)((x40 (x44 x1) x33False)False)((x40 (x44 x1) x1False)False)((x3 x18 (x4 x42)False)False)((x3 x35 (x4 x42)False)False)((x48 (x44 x1) x1 = x33False)False)((x53 x33 (x44 x1) = x1False)False)((x48 x1 (x44 x1) = x33False)False)(∀ x58 . (x9 x58 x58False)False)((x53 x33 x1 = x44 x1False)False)((x40 x33 x33False)False)((x40 x33 x1False)False)((x40 x1 x1False)False)((x3 x33 x42False)False)((x3 x33 x35False)False)((x3 x1 x42False)False)((x3 x1 x35False)False)((x3 x16 x21False)False)((x53 x1 x33 = x1False)False)((x53 x1 x1 = x33False)False)((x57 x1 x1 = x1False)False)((x55 x33 x33 = x33False)False)((x55 x33 x1 = x33False)False)((x55 x1 x33 = x33False)False)((x55 x1 x1 = x1False)False)((x48 x33 x33 = x33False)False)((x48 x33 x1 = x1False)False)((x48 x1 x33 = x1False)False)((x44 (x44 x1) = x1False)False)((x45 x22False)False)((x45 x30False)False)((x45 x1False)False)((x7 x29False)False)((x7 x23False)False)((x34 x17False)False)((x34 x21False)False)((x34 x42False)False)((x15 x18False)False)((x2 x28False)False)((x2 x24False)False)((x2 x27False)False)((x2 x33False)False)((x2 x16False)False)((x11 x42False)False)((x13 x28False)False)((x13 x24False)False)((x13 x29False)False)((x13 x23False)False)((x13 x22False)False)((x13 x30False)False)((x13 x26False)False)((x6 x24False)False)((x6 x23False)False)((x6 x30False)False)((x37 x17False)False)((x37 x31False)False)((x37 x19False)False)((x37 x21False)False)((x0 x24False)False)((x0 x23False)False)((x0 x30False)False)((x0 x25False)False)((x0 x50False)False)((x0 x52False)False)((x44 x33 = x33False)False)((x35 = x21False)False)((x16 = x46False)False)False (proof)