Search for blocks/addresses/...

Proofgold Signed Transaction

vin
PrNUD../c4810..
PUact../3df84..
vout
PrNUD../83687.. 0.02 bars
TMWLj../7909e.. ownership of 2076f.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
TMRwP../dcebf.. ownership of 46062.. as prop with payaddr PrPhD.. rightscost 0.00 controlledby PrPhD.. upto 0
PULeR../17a63.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem 2076f.. : ∀ x0 : ι → ο . ∀ x1 : ι → ι → ο . ∀ x2 . ∀ x3 : ι → ι → ο . ∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ο . ∀ x8 : ι → ι . ∀ x9 x10 x11 x12 x13 x14 x15 x16 . ∀ x17 : ι → ο . ∀ x18 x19 x20 x21 x22 x23 . ∀ x24 : ι → ο . ∀ x25 : ι → ι → ι . ∀ x26 x27 : ι → ο . ∀ x28 . ∀ x29 x30 x31 x32 : ι → ο . ∀ x33 . ∀ x34 : ι → ι . ∀ x35 x36 : ι → ο . ∀ x37 x38 : ι → ι . ∀ x39 x40 x41 x42 x43 . ∀ x44 : ι → ο . ∀ x45 x46 x47 x48 : ι → ι → ι . ∀ x49 . ∀ x50 x51 : ι → ι . ∀ x52 : ι → ο . ∀ x53 . ∀ x54 : ι → ι . ∀ x55 x56 : ι → ι → ι . ∀ x57 . ∀ x58 : ι → ο . ∀ x59 : ι → ι → ο . ∀ x60 : ι → ι . ∀ x61 x62 : ι → ο . ∀ x63 : ι → ι → ο . ∀ x64 : ι → ο . (∀ x65 x66 . x64 x66x64 x65(x63 x66 x65False)(x62 x65False)(x61 x66False)False)(∀ x65 x66 . x0 x66(x66 = x65False)x0 x65False)(∀ x65 x66 . x64 x66x64 x65(x63 x66 x65False)(x61 x66False)(x62 x65False)False)(∀ x65 x66 . x1 x65 x66x0 x66False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x0 x66False)(x61 x65False)(x62 x66False)False)(∀ x65 . x0 x65(x65 = x2False)False)(∀ x65 x66 x67 . x1 x65 x66x59 x66 (x60 x67)x0 x67False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x0 x65False)(x62 x66False)(x61 x65False)False)(∀ x65 . x58 x65(x56 x57 x65 = x57False)False)(∀ x65 x66 x67 . x1 x66 x67x59 x67 (x60 x65)(x59 x66 x65False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x61 x65False)x61 x66False)(∀ x65 x66 . x3 x66 x65(x59 x66 (x60 x65)False)False)(∀ x65 x66 . x59 x66 (x60 x65)(x3 x66 x65False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65(x62 x66False)x62 x65False)(∀ x65 x66 . x59 x65 x66(x0 x66False)(x1 x65 x66False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65x62 x65(x62 x66False)False)(∀ x65 . x58 x65(x55 x65 x57 = x57False)False)(∀ x65 x66 . x1 x66 x65(x59 x66 x65False)False)(∀ x65 x66 . x64 x66x64 x65x63 x66 x65x61 x66(x61 x65False)False)((x59 x2 x4False)False)(∀ x65 x66 x67 . x58 x67x58 x65x58 x66(x55 (x55 x67 x65) x66 = x55 x67 (x55 x65 x66)False)False)(∀ x65 x66 x67 . x58 x67x58 x65x58 x66(x55 x67 (x56 x65 x66) = x56 (x55 x67 x65) x66False)False)(∀ x65 x66 . x58 x66x58 x65(x55 x66 (x54 x65) = x56 x66 x65False)False)(∀ x65 x66 . x58 x66x58 x65(x56 (x54 x66) (x54 x65) = x56 x65 x66False)False)(∀ x65 x66 . x58 x66x58 x65(x55 (x54 x66) (x54 x65) = x54 (x55 x66 x65)False)False)((x59 x6 x5False)False)((x59 x6 x53False)False)((x7 x6 x5 x53False)False)((x0 x6False)False)((x8 x6 = x6False)False)((x55 x6 x6 = x6False)False)((x63 x6 x6False)False)(∀ x65 x66 . x52 x66x52 x65(x63 x66 x66False)False)(∀ x65 . (x3 x65 x65False)False)(∀ x65 x66 x67 . (x0 x67False)(x0 x65False)x59 x65 (x60 x67)x59 x66 x65(x7 x66 x67 x65False)False)(∀ x65 x66 x67 . (x0 x67False)(x0 x65False)x59 x65 (x60 x67)x7 x66 x67 x65(x59 x66 x65False)False)((x57 = x2False)False)((x53 = x4False)False)(∀ x65 . x59 x65 x49(x51 x65 = x50 x65False)False)((x9 = x10False)False)(∀ x65 x66 . x59 x66 x49x59 x65 x49(x47 x66 x65 = x48 x66 x65False)False)((x11 = x12False)False)(∀ x65 x66 . x59 x66 x49x59 x65 x49(x45 x66 x65 = x46 x66 x65False)False)((x52 x13False)False)((x0 x13False)False)((x64 x14False)False)((x52 x14False)False)((x58 x14False)False)((x0 x14False)False)((x62 x15False)False)((x52 x15False)False)((x64 x16False)False)((x62 x16False)False)((x52 x16False)False)((x58 x16False)False)((x17 x18False)False)((x44 x18False)False)(x0 x18False)(x64 x43False)((x62 x43False)False)((x52 x43False)False)((x61 x19False)False)((x52 x19False)False)((x64 x20False)False)((x61 x20False)False)((x52 x20False)False)((x58 x20False)False)(x0 x21False)((x44 x42False)False)(x0 x42False)(x64 x41False)((x61 x41False)False)((x52 x41False)False)((x52 x22False)False)((x64 x40False)False)((x0 x23False)False)((x44 x39False)False)(x0 x39False)(∀ x65 . x59 x65 x49(x38 (x38 x65) = x38 x65False)False)(∀ x65 . x58 x65(x54 (x54 x65) = x65False)False)(∀ x65 . x58 x65(x8 (x8 x65) = x65False)False)(∀ x65 . x52 x65(x50 (x50 x65) = x65False)False)(∀ x65 . x59 x65 x49(x51 (x51 x65) = x65False)False)(∀ x65 x66 x67 x68 . x64 x68x64 x65x58 x67x58 x66x68 = x67x65 = x66(x48 x68 x65 = x56 x67 x66False)False)(∀ x65 x66 . x64 x66x58 x65x66 = x65(x37 x66 = x54 x65False)False)(∀ x65 x66 x67 x68 . x64 x68x64 x65x58 x67x58 x66x68 = x67x65 = x66(x46 x68 x65 = x55 x67 x66False)False)(∀ x65 x66 . x64 x66x58 x65x66 = x65(x50 x66 = x8 x65False)False)(∀ x65 x66 . x64 x66x64 x65(x64 (x56 x66 x65)False)False)(x36 x5False)(∀ x65 x66 . x64 x66x64 x65(x64 (x55 x66 x65)False)False)((x44 x4False)False)(x0 x49False)((x17 x4False)False)((x17 x5False)False)((x62 x10False)False)(∀ x65 . x64 x65(x64 (x54 x65)False)False)(∀ x65 . x64 x65(x58 (x54 x65)False)False)((x52 (x37 x12)False)False)((x0 (x37 x12)False)False)((x52 (x37 x10)False)False)((x0 (x37 x10)False)False)(∀ x65 x66 . x64 x66x64 x65(x64 (x48 x66 x65)False)False)(∀ x65 x66 . x64 x66x64 x65(x52 (x48 x66 x65)False)False)((x61 x12False)False)(∀ x65 . x64 x65(x64 (x8 x65)False)False)(∀ x65 . x64 x65(x58 (x8 x65)False)False)((x35 x5False)False)(∀ x65 x66 . x64 x66x64 x65(x64 (x46 x66 x65)False)False)(∀ x65 x66 . x64 x66x64 x65(x52 (x46 x66 x65)False)False)(∀ x65 . x64 x65(x64 (x37 x65)False)False)(∀ x65 . x64 x65(x52 (x37 x65)False)False)(∀ x65 x66 . x0 x66x52 x66x52 x65(x52 (x46 x66 x65)False)False)(∀ x65 x66 . x0 x66x52 x66x52 x65(x0 (x46 x66 x65)False)False)(∀ x65 x66 . (x0 x66False)x52 x66(x0 x65False)x52 x65(x52 (x46 x66 x65)False)False)(∀ x65 x66 . (x0 x66False)x52 x66(x0 x65False)x52 x65x0 (x46 x66 x65)False)(∀ x65 x66 . x52 x66(x61 x66False)x52 x65(x61 x65False)x62 (x48 x66 x65)False)(∀ x65 x66 . x52 x66(x61 x66False)x52 x65(x61 x65False)(x52 (x48 x66 x65)False)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x62 x65False)x62 (x48 x66 x65)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x62 x65False)(x52 (x48 x66 x65)False)False)(∀ x65 x66 . (x61 x66False)x64 x66(x61 x65False)x64 x65x62 (x56 x66 x65)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x61 x65False)x61 (x48 x65 x66)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x61 x65False)(x52 (x48 x65 x66)False)False)(∀ x65 x66 . (x62 x66False)x64 x66(x62 x65False)x64 x65x62 (x56 x66 x65)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x61 x65False)x61 (x48 x66 x65)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x61 x65False)(x52 (x48 x66 x65)False)False)(∀ x65 x66 . (x62 x66False)x64 x66(x61 x65False)x64 x65x61 (x56 x65 x66)False)(∀ x65 . x52 x65(x62 x65False)x62 (x37 x65)False)(∀ x65 . x52 x65(x62 x65False)(x52 (x37 x65)False)False)(∀ x65 x66 . (x62 x66False)x64 x66(x61 x65False)x64 x65x61 (x56 x66 x65)False)(∀ x65 . x52 x65(x61 x65False)x61 (x37 x65)False)(∀ x65 . x52 x65(x61 x65False)(x52 (x37 x65)False)False)(∀ x65 . (x62 x65False)x64 x65x62 (x54 x65)False)(∀ x65 . (x62 x65False)x64 x65(x58 (x54 x65)False)False)((x52 x10False)False)(x64 x12False)((x24 x49False)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x62 x65False)x62 (x46 x66 x65)False)(∀ x65 x66 . x52 x66(x62 x66False)x52 x65(x62 x65False)(x52 (x46 x66 x65)False)False)(∀ x65 . x62 x65x64 x65(x62 (x54 x65)False)False)(∀ x65 . x62 x65x64 x65(x58 (x54 x65)False)False)(∀ x65 x66 . x52 x66(x61 x66False)x52 x65(x61 x65False)x62 (x46 x66 x65)False)(∀ x65 x66 . x52 x66(x61 x66False)x52 x65(x61 x65False)(x52 (x46 x66 x65)False)False)(∀ x65 . (x61 x65False)x64 x65x61 (x54 x65)False)(∀ x65 . (x61 x65False)x64 x65(x58 (x54 x65)False)False)(∀ x65 x66 . x52 x66(x61 x66False)x52 x65(x62 x65False)x61 (x46 x66 x65)False)(∀ x65 x66 . x52 x66(x61 x66False)x52 x65(x62 x65False)(x52 (x46 x66 x65)False)False)(∀ x65 . x61 x65x64 x65(x61 (x54 x65)False)False)(∀ x65 . x61 x65x64 x65(x58 (x54 x65)False)False)(∀ x65 x66 . x52 x66x61 x66x52 x65x61 x65(x61 (x46 x66 x65)False)False)(∀ x65 x66 . x52 x66x61 x66x52 x65x61 x65(x52 (x46 x66 x65)False)False)(∀ x65 x66 . (x62 x66False)x64 x66(x62 x65False)x64 x65x62 (x55 x66 x65)False)(∀ x65 x66 . x52 x66x62 x66x52 x65x62 x65(x61 (x46 x66 x65)False)False)(∀ x65 x66 . x52 x66x62 x66x52 x65x62 x65(x52 (x46 x66 x65)False)False)(∀ x65 x66 . (x61 x66False)x64 x66(x61 x65False)x64 x65x62 (x55 x66 x65)False)(∀ x65 x66 . x52 x66x61 x66x52 x65x62 x65(x62 (x46 x66 x65)False)False)(∀ x65 x66 . x52 x66x61 x66x52 x65x62 x65(x52 (x46 x66 x65)False)False)(∀ x65 x66 . (x61 x66False)x64 x66(x62 x65False)x64 x65x61 (x55 x65 x66)False)(∀ x65 x66 . (x61 x66False)x64 x66(x62 x65False)x64 x65x61 (x55 x66 x65)False)(∀ x65 . x64 x65(x64 (x50 x65)False)False)(∀ x65 . x64 x65(x52 (x50 x65)False)False)((x52 x12False)False)(x64 x10False)((x0 x2False)False)(x0 x5False)(∀ x65 . x59 x65 x49x62 (x38 x65)False)(∀ x65 . x52 x65x62 x65(x61 (x50 x65)False)False)(∀ x65 . x52 x65x62 x65(x52 (x50 x65)False)False)(∀ x65 . x52 x65x61 x65(x62 (x50 x65)False)False)(∀ x65 . x52 x65x61 x65(x52 (x50 x65)False)False)(∀ x65 . (x62 x65False)x64 x65x61 (x8 x65)False)(∀ x65 . (x62 x65False)x64 x65(x58 (x8 x65)False)False)(∀ x65 . x52 x65(x62 x65False)x61 (x50 x65)False)(∀ x65 . x52 x65(x62 x65False)(x52 (x50 x65)False)False)(∀ x65 . (x61 x65False)x64 x65x62 (x8 x65)False)(∀ x65 . (x61 x65False)x64 x65(x58 (x8 x65)False)False)(∀ x65 . x52 x65(x61 x65False)x62 (x50 x65)False)(∀ x65 . x52 x65(x61 x65False)(x52 (x50 x65)False)False)(∀ x65 x66 . (x0 x66False)(x0 x65False)x59 x65 (x60 x66)(x7 (x25 x65 x66) x66 x65False)False)(∀ x65 . (x59 (x34 x65) x65False)False)(∀ x65 x66 x67 . (x0 x67False)(x0 x65False)x59 x65 (x60 x67)x7 x66 x67 x65(x59 x66 x67False)False)((x59 x33 x49False)False)(∀ x65 x66 . x52 x66x52 x65(x52 (x48 x66 x65)False)False)((x7 x57 x5 x53False)False)(∀ x65 . x52 x65(x52 (x37 x65)False)False)(∀ x65 . x58 x65(x58 (x54 x65)False)False)((x59 x53 (x60 x5)False)False)(∀ x65 x66 . x52 x66x52 x65(x52 (x46 x66 x65)False)False)(∀ x65 . x58 x65(x58 (x8 x65)False)False)(∀ x65 . x59 x65 x49(x59 (x38 x65) x49False)False)(∀ x65 . x52 x65(x52 (x50 x65)False)False)(∀ x65 . x59 x65 x49(x59 (x51 x65) x49False)False)((x59 x9 x49False)False)(∀ x65 x66 . x59 x66 x49x59 x65 x49(x59 (x47 x66 x65) x49False)False)((x59 x11 x49False)False)(∀ x65 x66 . x59 x66 x49x59 x65 x49(x59 (x45 x66 x65) x49False)False)(∀ x65 x66 . x52 x66x52 x65(x48 x66 x65 = x46 x66 (x37 x65)False)False)(∀ x65 . x59 x65 x49(x63 x57 x65False)(x38 x65 = x51 x65False)False)(∀ x65 . x59 x65 x49x63 x57 x65(x38 x65 = x65False)False)(∀ x65 x66 . x52 x66x52 x65(x63 x66 x65False)(x63 x65 x66False)False)(∀ x65 x66 . x52 x66x52 x65(x46 x66 x65 = x46 x65 x66False)False)(∀ x65 x66 . x58 x66x58 x65(x55 x66 x65 = x55 x65 x66False)False)(∀ x65 x66 . x59 x66 x49x59 x65 x49(x45 x66 x65 = x45 x65 x66False)False)(∀ x65 . x52 x65(x61 x65False)(x62 x65False)(x52 x65False)False)(∀ x65 . x52 x65(x61 x65False)(x62 x65False)(x0 x65False)False)(∀ x65 . x59 x65 (x60 x5)(x35 x65False)False)(∀ x65 . x0 x65x52 x65x62 x65False)(∀ x65 . x0 x65x52 x65x61 x65False)(∀ x65 . x0 x65x52 x65(x52 x65False)False)(∀ x65 . x59 x65 (x60 x49)(x24 x65False)False)(∀ x65 . (x0 x65False)x52 x65(x61 x65False)(x62 x65False)False)(∀ x65 . (x0 x65False)x52 x65(x61 x65False)(x52 x65False)False)(∀ x65 . x52 x65x62 x65x61 x65False)(∀ x65 . x52 x65x62 x65(x52 x65False)False)(∀ x65 . x52 x65x62 x65x0 x65False)(∀ x65 . x35 x65(x32 x65False)False)(∀ x65 . (x0 x65False)x52 x65(x62 x65False)(x61 x65False)False)(∀ x65 . (x0 x65False)x52 x65(x62 x65False)(x52 x65False)False)(∀ x65 . x64 x65(x52 x65False)False)(∀ x65 . x35 x65(x24 x65False)False)(∀ x65 . x52 x65x61 x65x62 x65False)(∀ x65 . x52 x65x61 x65(x52 x65False)False)(∀ x65 . x52 x65x61 x65x0 x65False)(∀ x65 . x64 x65(x58 x65False)False)(∀ x65 . x26 x65(x35 x65False)False)(∀ x65 . x52 x65(x61 x65False)(x64 x65False)(x62 x65False)False)(∀ x65 . x52 x65(x61 x65False)(x64 x65False)(x52 x65False)False)(∀ x65 . x31 x65(x52 x65False)False)(∀ x65 . x31 x65(x64 x65False)False)(∀ x65 . x30 x65(x26 x65False)False)(∀ x65 . x0 x65(x17 x65False)False)(∀ x65 . x59 x65 x53(x44 x65False)False)(∀ x65 x66 . x44 x66x59 x65 (x60 x66)(x44 x65False)False)(∀ x65 x66 . x30 x66x59 x65 (x60 x66)(x30 x65False)False)(∀ x65 x66 . x26 x66x59 x65 (x60 x66)(x26 x65False)False)(∀ x65 x66 . x35 x66x59 x65 (x60 x66)(x35 x65False)False)(∀ x65 x66 . x24 x66x59 x65 (x60 x66)(x24 x65False)False)(∀ x65 . x52 x65(x62 x65False)(x64 x65False)(x61 x65False)False)(∀ x65 . x52 x65(x62 x65False)(x64 x65False)(x52 x65False)False)(∀ x65 . x59 x65 x49(x52 x65False)False)(∀ x65 . x59 x65 x5(x64 x65False)False)(∀ x65 . x44 x65(x30 x65False)False)(∀ x65 x66 . x32 x66x59 x65 (x60 x66)(x32 x65False)False)(∀ x65 . x0 x65(x44 x65False)False)(∀ x65 x66 . x44 x66x59 x65 x66(x31 x65False)False)(∀ x65 x66 . x30 x66x59 x65 x66(x29 x65False)False)(∀ x65 x66 . x26 x66x59 x65 x66(x27 x65False)False)(∀ x65 x66 . x35 x66x59 x65 x66(x64 x65False)False)(∀ x65 x66 . x24 x66x59 x65 x66(x52 x65False)False)(∀ x65 x66 . x32 x66x59 x65 x66(x58 x65False)False)(∀ x65 . x59 x65 (x60 x53)(x44 x65False)False)(∀ x65 x66 . x1 x65 x66x1 x66 x65False)(x45 (x38 x28) (x38 (x47 x33 x28)) = x57False)((x28 = x11False)(x28 = x9False)False)((x59 x28 x49False)False)False (proof)