Search for blocks/addresses/...

Proofgold Signed Transaction

vin
PrNUD../bb9cc..
PUe9v../affb3..
vout
PrNUD../1a6da.. 0.03 bars
TMLPG../cf99f.. ownership of 4f28e.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
TMWee../cc39b.. ownership of 603d9.. as prop with payaddr PrPhD.. rights free controlledby PrPhD.. upto 0
PUXFL../5a746.. doc published by PrPhD..
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Theorem 4f28e.. : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . ∀ x6 : ι → ο . ∀ x7 : ι → ι . ∀ x8 : ι → ι → ι . ∀ x9 x10 : ι → ι . ∀ x11 : ι → ι → ο . ∀ x12 . ∀ x13 : ι → ι . ∀ x14 x15 : ι → ι → ι . ∀ x16 x17 . ∀ x18 : ι → ι . ∀ x19 : ι → ι → ι . ∀ x20 : ι → ι → ι → ο . ∀ x21 : ι → ι → ι . ∀ x22 . ∀ x23 : ι → ι → ι → ι . ∀ x24 x25 : ι → ι . ∀ x26 x27 x28 : ι → ι → ι . ∀ x29 : ι → ι . ∀ x30 x31 : ι → ι → ι . ∀ x32 x33 : ι → ι . ∀ x34 : ι → ι → ο . ∀ x35 : ι → ο . ∀ x36 x37 x38 x39 . ∀ x40 : ι → ι → ι → ι . ∀ x41 : ι → ι . ∀ x42 x43 : ι → ι → ι . ∀ x44 : ι → ι → ι → ι → ι . ∀ x45 : ι → ι → ι . ∀ x46 x47 x48 . ∀ x49 : ι → ο . ∀ x50 . ∀ x51 : ι → ι . ∀ x52 . ∀ x53 : ι → ι → ι . ∀ x54 . ∀ x55 : ι → ο . ∀ x56 : ι → ι → ο . ∀ x57 : ι → ο . ∀ x58 : ι → ι → ο . ∀ x59 : ι → ι . ∀ x60 : ι → ο . ∀ x61 : ι → ι → ι . ∀ x62 : ι → ι → ο . ∀ x63 : ι → ι . ∀ x64 : ι → ι → ο . ∀ x65 : ι → ι . ∀ x66 : ι → ι → ο . ∀ x67 : ι → ι → ι . ∀ x68 : ι → ι → ι → ι → ι . ∀ x69 x70 : ι → ι → ι . ∀ x71 : ι → ι . ∀ x72 : ι → ο . (∀ x73 x74 . (x72 x74False)x66 x73 (x65 x74)(x73 = x67 (x68 x74 x74 (x69 x74 x73) (x70 x74 x73)) (x71 x73)False)False)(∀ x73 x74 . x72 x74(x74 = x73False)x72 x73False)(∀ x73 x74 . x64 x73 x74x72 x74False)(∀ x73 . x72 x73(x73 = x0False)False)(∀ x73 x74 x75 . x64 x73 x74x66 x74 (x63 x75)x72 x75False)(∀ x73 x74 x75 . x64 x74 x75x66 x75 (x63 x73)(x66 x74 x73False)False)(∀ x73 x74 . x62 x74 x73(x66 x74 (x63 x73)False)False)(∀ x73 x74 . x66 x74 (x63 x73)(x62 x74 x73False)False)(∀ x73 x74 x75 . x64 x74 x75x64 x73 x75x64 x73 (x61 x75 x74)False)(∀ x73 x74 . x64 x74 x73(x64 (x61 x73 x74) x73False)False)(∀ x73 x74 . x66 x73 x74(x72 x74False)(x64 x73 x74False)False)(∀ x73 x74 x75 x76 . x67 x74 x76 = x67 x73 x75(x76 = x75False)False)(∀ x73 x74 x75 x76 . x67 x76 x74 = x67 x75 x73(x76 = x75False)False)(∀ x73 x74 . x64 x74 x73(x66 x74 x73False)False)(∀ x73 . (x62 x73 x73False)False)(∀ x73 x74 x75 x76 . (x72 x76False)(x72 x73False)x66 x75 x76x66 x74 x73(x68 x76 x73 x75 x74 = x67 x75 x74False)False)(∀ x73 . x60 x73(x67 (x59 x73) (x71 x73) = x73False)False)(∀ x73 x74 . (x71 (x67 x74 x73) = x73False)False)(∀ x73 x74 . (x59 (x67 x73 x74) = x73False)False)(∀ x73 . (x1 (x2 x73)False)False)(∀ x73 . (x58 (x2 x73) x73False)False)(∀ x73 . (x3 (x2 x73)False)False)(∀ x73 . (x57 (x2 x73)False)False)((x4 x5False)False)(x72 x5False)(∀ x73 . (x6 x73False)x6 (x7 x73)False)(∀ x73 . (x6 x73False)(x66 (x7 x73) (x63 x73)False)False)(∀ x73 x74 . (x1 (x8 x73 x74)False)False)(∀ x73 x74 . (x56 (x8 x73 x74) x73False)False)(∀ x73 x74 . (x58 (x8 x74 x73) x73False)False)(∀ x73 x74 . (x57 (x8 x73 x74)False)False)(∀ x73 . (x72 x73False)(x6 (x9 x73)False)False)(∀ x73 . (x72 x73False)x72 (x9 x73)False)(∀ x73 . (x72 x73False)(x66 (x9 x73) (x63 x73)False)False)(x55 x54False)((x1 x54False)False)((x57 x54False)False)(∀ x73 . (x72 x73False)(x11 (x10 x73) x73False)False)(∀ x73 . (x72 x73False)(x66 (x10 x73) (x63 x73)False)False)((x1 x12False)False)((x3 x12False)False)((x57 x12False)False)(x72 x12False)(∀ x73 . x11 (x13 x73) x73False)(∀ x73 . (x66 (x13 x73) (x63 x73)False)False)(∀ x73 x74 . (x56 (x14 x73 x74) x73False)False)(∀ x73 x74 . (x58 (x14 x74 x73) x73False)False)(∀ x73 x74 . (x57 (x14 x73 x74)False)False)(∀ x73 x74 . (x72 x74False)(x72 x73False)x72 (x53 x73 x74)False)(∀ x73 x74 . (x72 x74False)(x72 x73False)(x1 (x53 x73 x74)False)False)(∀ x73 x74 . (x72 x74False)(x72 x73False)(x56 (x53 x73 x74) x73False)False)(∀ x73 x74 . (x72 x74False)(x72 x73False)(x58 (x53 x73 x74) x74False)False)(∀ x73 x74 . (x72 x74False)(x72 x73False)(x57 (x53 x73 x74)False)False)(∀ x73 x74 . (x72 x74False)(x72 x73False)(x66 (x53 x73 x74) (x63 (x15 x74 x73))False)False)((x1 x52False)False)((x3 x52False)False)((x57 x52False)False)(x72 x16False)(∀ x73 . (x72 (x51 x73)False)False)(∀ x73 . (x66 (x51 x73) (x63 x73)False)False)((x3 x50False)False)((x57 x50False)False)((x49 x48False)False)((x1 x48False)False)((x57 x48False)False)((x60 x17False)False)((x72 x47False)False)(∀ x73 . (x72 x73False)x72 (x18 x73)False)(∀ x73 . (x72 x73False)(x66 (x18 x73) (x63 x73)False)False)(∀ x73 x74 . (x56 (x19 x73 x74) x73False)False)(∀ x73 x74 . (x58 (x19 x74 x73) x73False)False)(∀ x73 x74 . (x57 (x19 x73 x74)False)False)(∀ x73 x74 . (x72 (x19 x73 x74)False)False)(∀ x73 x74 . (x66 (x19 x73 x74) (x63 (x15 x74 x73))False)False)((x57 x46False)False)(x72 x46False)(∀ x73 x74 . (x1 (x45 x73 x74)False)False)(∀ x73 x74 . (x56 (x45 x73 x74) x73False)False)(∀ x73 x74 . (x58 (x45 x74 x73) x73False)False)(∀ x73 x74 . (x57 (x45 x73 x74)False)False)(∀ x73 x74 . (x66 (x45 x73 x74) (x63 (x15 x74 x73))False)False)(∀ x73 x74 . (x20 (x21 x73 x74) x74 x73False)False)(∀ x73 x74 . (x1 (x21 x73 x74)False)False)(∀ x73 x74 . (x56 (x21 x73 x74) x73False)False)(∀ x73 x74 . (x58 (x21 x74 x73) x73False)False)(∀ x73 x74 . (x57 (x21 x73 x74)False)False)(∀ x73 x74 . (x66 (x21 x73 x74) (x63 (x15 x74 x73))False)False)((x1 x22False)False)((x57 x22False)False)(∀ x73 x74 x75 x76 x77 . (x72 x77False)x66 x73 x77x66 x76 x77x66 x74 (x24 x77)x75 = x68 (x15 x77 x77) (x24 x77) (x68 x77 x77 x73 x76) x74x64 (x68 (x15 x77 x77) (x24 x77) (x68 x77 x77 x73 x76) x74) (x65 x77)(x64 x75 (x23 x77 x73 x76)False)False)(∀ x73 x74 x75 x76 . (x72 x76False)x66 x73 x76x66 x75 x76x64 x74 (x23 x76 x73 x75)(x64 (x68 (x15 x76 x76) (x24 x76) (x68 x76 x76 x73 x75) (x44 x75 x73 x76 x74)) (x65 x76)False)False)(∀ x73 x74 x75 x76 . (x72 x76False)x66 x73 x76x66 x75 x76x64 x74 (x23 x76 x73 x75)(x74 = x68 (x15 x76 x76) (x24 x76) (x68 x76 x76 x73 x75) (x44 x75 x73 x76 x74)False)False)(∀ x73 x74 x75 x76 . (x72 x76False)x66 x73 x76x66 x75 x76x64 x74 (x23 x76 x73 x75)(x66 (x44 x75 x73 x76 x74) (x24 x76)False)False)(∀ x73 x74 x75 x76 x77 . (x72 x77False)x66 x73 x77x66 x76 x77x66 x74 (x24 x77)x75 = x68 (x15 x77 x77) (x24 x77) (x68 x77 x77 x73 x76) x74x73 = x0x1 x74x20 x74 x73 x76x66 x74 (x63 (x15 x73 x76))(x64 x75 (x25 x77)False)False)(∀ x73 x74 x75 x76 x77 . (x72 x77False)x66 x73 x77x66 x76 x77x66 x74 (x24 x77)x75 = x68 (x15 x77 x77) (x24 x77) (x68 x77 x77 x73 x76) x74(x76 = x0False)x1 x74x20 x74 x73 x76x66 x74 (x63 (x15 x73 x76))(x64 x75 (x25 x77)False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)(x66 (x26 x74 x73) (x63 (x15 (x27 x74 x73) (x28 x74 x73)))False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)(x20 (x26 x74 x73) (x27 x74 x73) (x28 x74 x73)False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)(x1 (x26 x74 x73)False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)x28 x74 x73 = x0(x27 x74 x73 = x0False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)(x73 = x68 (x15 x74 x74) (x24 x74) (x68 x74 x74 (x27 x74 x73) (x28 x74 x73)) (x26 x74 x73)False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)(x66 (x26 x74 x73) (x24 x74)False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)(x66 (x28 x74 x73) x74False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x25 x74)(x66 (x27 x74 x73) x74False)False)(∀ x73 x74 x75 x76 . (x72 x76False)x66 x73 x76x66 x75 x76x74 = x30 x73 x75(x64 x74 (x29 x76)False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x29 x74)(x73 = x30 (x42 x74 x73) (x43 x74 x73)False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x29 x74)(x66 (x43 x74 x73) x74False)False)(∀ x73 x74 . (x72 x74False)x64 x73 (x29 x74)(x66 (x42 x74 x73) x74False)False)(∀ x73 x74 x75 x76 . (x57 (x31 (x67 x74 x73) (x67 x76 x75))False)False)(∀ x73 x74 . (x57 (x15 x73 x74)False)False)(∀ x73 x74 . (x57 (x32 (x67 x74 x73))False)False)(∀ x73 x74 . x72 (x31 x73 x74)False)(∀ x73 x74 . (x72 x74False)x72 x73(x72 (x30 x74 x73)False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x65 x74)(x1 (x71 x73)False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x65 x74)(x57 (x71 x73)False)False)(∀ x73 . x72 (x32 x73)False)(∀ x73 . x72 (x30 x73 x73)False)(∀ x73 . (x72 x73False)x72 (x65 x73)False)(∀ x73 x74 . (x60 (x67 x73 x74)False)False)((x72 x0False)False)(∀ x73 . x72 (x63 x73)False)(∀ x73 x74 . (x72 x74False)x72 (x30 x73 x74)False)(∀ x73 x74 . (x1 (x32 (x67 x74 x73))False)False)(∀ x73 . (x72 x73False)x72 (x24 x73)False)(∀ x73 . (x72 x73False)(x4 (x24 x73)False)False)(∀ x73 x74 . x57 x74x1 x74x57 x73x1 x73(x4 (x31 x74 x73)False)False)(∀ x73 . x57 x73x1 x73(x4 (x32 x73)False)False)(∀ x73 x74 . (x72 x74False)(x72 x73False)x72 (x15 x74 x73)False)(∀ x73 x74 . (x4 (x30 x73 x74)False)False)(∀ x73 . (x66 (x41 x73) x73False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x65 x74)(x66 (x70 x74 x73) x74False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x65 x74)(x66 (x69 x74 x73) x74False)False)(∀ x73 x74 x75 x76 . (x72 x76False)(x72 x73False)x66 x75 x76x66 x74 x73(x66 (x68 x76 x73 x75 x74) (x15 x76 x73)False)False)(∀ x73 x74 x75 . (x72 x75False)x66 x73 x75x66 x74 x75(x40 x75 x73 x74 = x23 x75 x73 x74False)False)(∀ x73 x74 . (x67 x74 x73 = x31 (x31 x74 x73) (x32 x74)False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x65 x74)(x70 x74 x73 = x71 (x59 x73)False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x65 x74)(x69 x74 x73 = x59 (x59 x73)False)False)(∀ x73 . (x72 x73False)(x65 x73 = x25 x73False)False)(∀ x73 . (x72 x73False)(x24 x73 = x33 (x29 x73)False)False)(∀ x73 x74 . (x31 x74 x73 = x31 x73 x74False)False)(∀ x73 x74 . x4 x74x66 x73 (x63 x74)(x4 x73False)False)(∀ x73 x74 . x72 x74x57 x73x56 x73 x74(x56 x73 x74False)False)(∀ x73 x74 . x72 x74x57 x73x56 x73 x74(x57 x73False)False)(∀ x73 x74 . x72 x74x57 x73x56 x73 x74(x72 x73False)False)(∀ x73 x74 x75 . (x72 x75False)(x72 x73False)x66 x74 (x63 (x15 x75 x73))x1 x74x20 x74 x75 x73(x20 x74 x75 x73False)False)(∀ x73 x74 x75 . (x72 x75False)(x72 x73False)x66 x74 (x63 (x15 x75 x73))x1 x74x20 x74 x75 x73x72 x74False)(∀ x73 x74 x75 . (x72 x75False)(x72 x73False)x66 x74 (x63 (x15 x75 x73))x1 x74x20 x74 x75 x73(x1 x74False)False)(∀ x73 x74 . x4 x74x66 x73 x74(x1 x73False)False)(∀ x73 x74 . x4 x74x66 x73 x74(x57 x73False)False)(∀ x73 x74 . x72 x74x57 x73x58 x73 x74(x58 x73 x74False)False)(∀ x73 x74 . x72 x74x57 x73x58 x73 x74(x57 x73False)False)(∀ x73 x74 . x72 x74x57 x73x58 x73 x74(x72 x73False)False)(∀ x73 . x72 x73(x4 x73False)False)(∀ x73 x74 x75 . x57 x75x56 x75 x73x66 x74 (x63 x75)(x56 x74 x73False)False)(∀ x73 . x6 x73x57 x73x1 x73(x55 x73False)False)(∀ x73 . x6 x73x57 x73x1 x73(x1 x73False)False)(∀ x73 . x6 x73x57 x73x1 x73(x57 x73False)False)(∀ x73 x74 . x6 x74x66 x73 (x63 x74)(x6 x73False)False)(∀ x73 x74 x75 . x57 x75x58 x75 x73x66 x74 (x63 x75)(x58 x74 x73False)False)(∀ x73 . x57 x73x1 x73(x55 x73False)(x1 x73False)False)(∀ x73 . x57 x73x1 x73(x55 x73False)(x57 x73False)False)(∀ x73 . x57 x73x1 x73(x55 x73False)x6 x73False)(∀ x73 x74 . x72 x74x66 x73 (x63 x74)x11 x73 x74False)(∀ x73 x74 x75 . x72 x75x66 x73 (x63 (x15 x74 x75))(x72 x73False)False)(∀ x73 . x72 x73x57 x73(x3 x73False)False)(∀ x73 . x72 x73x57 x73(x57 x73False)False)(∀ x73 x74 . x66 x74 (x63 (x15 x73 x73))x20 x74 x73 x73(x34 x74 x73False)False)(∀ x73 . x72 x73x57 x73x1 x73(x55 x73False)False)(∀ x73 . x72 x73x57 x73x1 x73(x1 x73False)False)(∀ x73 . x72 x73x57 x73x1 x73(x57 x73False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x63 x74)x72 x73(x11 x73 x74False)False)(∀ x73 x74 x75 . x72 x75x66 x73 (x63 (x15 x75 x74))(x72 x73False)False)(∀ x73 . x72 x73x57 x73(x35 x73False)False)(∀ x73 . x72 x73x57 x73(x57 x73False)False)(∀ x73 x74 x75 . (x72 x75False)x66 x73 (x63 (x15 x74 x75))x20 x73 x74 x75(x34 x73 x74False)False)(∀ x73 x74 . x57 x74x1 x74x66 x73 (x63 x74)(x1 x73False)False)(∀ x73 x74 . (x72 x74False)x66 x73 (x63 x74)(x11 x73 x74False)x72 x73False)(∀ x73 x74 x75 . x66 x75 (x63 (x15 x73 x74))(x56 x75 x74False)False)(∀ x73 x74 x75 . x66 x75 (x63 (x15 x74 x73))(x58 x75 x74False)False)(∀ x73 x74 . x57 x74x66 x73 (x63 x74)(x57 x73False)False)(∀ x73 x74 x75 . (x72 x75False)x72 x73x66 x74 (x63 (x15 x75 x73))x34 x74 x75False)(∀ x73 x74 x75 . x72 x75x66 x73 (x63 (x15 x75 x74))x20 x73 x75 x74(x34 x73 x75False)False)(∀ x73 . x72 x73x57 x73x1 x73(x49 x73False)False)(∀ x73 . x72 x73x57 x73x1 x73(x1 x73False)False)(∀ x73 . x72 x73x57 x73x1 x73(x57 x73False)False)(∀ x73 x74 . x72 x74x66 x73 (x63 x74)(x72 x73False)False)(∀ x73 x74 x75 . x66 x75 (x63 (x15 x73 x74))(x57 x75False)False)(∀ x73 . x72 x73(x57 x73False)False)(∀ x73 x74 x75 . x72 x75x66 x73 (x63 (x15 x75 x74))(x34 x73 x75False)False)(∀ x73 x74 x75 . x66 x74 (x63 (x15 x75 x73))x34 x74 x75(x20 x74 x75 x73False)False)(∀ x73 . x72 x73(x1 x73False)False)(∀ x73 x74 . x64 x73 x74x64 x74 x73False)(x39 = x67 (x68 x36 x36 x38 x37) (x71 x39)False)((x64 x39 (x40 x36 x38 x37)False)False)((x66 x39 (x65 x36)False)False)((x66 x37 x36False)False)((x66 x38 x36False)False)(x72 x36False)False (proof)