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Proofgold Asset

asset id
a3ccd2affea1742e6919a4cdf09a52be44e016f0301bf3311d1a932c3da6a843
asset hash
9f13a28537d91d55d20fe4fd7060dfe2a849b2fd30091df01f784f3038fd8903
bday / block
38739
tx
53841..
preasset
doc published by PrCmT..
Known 02f51.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13In x4 x0∀ x14 : ο . (∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0not (x6 x15 (x1 (x3 x4 x16) (x9 x17 x18 x16)) x19 = x4)(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x1 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x3 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x2 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0x5 x20 x21 = x2 (x1 x21 x20) (x1 x20 x21))(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x5 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0∀ x22 . In x22 x0x6 x20 x21 x22 = x2 (x1 x20 (x1 x21 x22)) (x1 (x1 x20 x21) x22))(∀ x20 . In x20 x0∀ x21 . In x21 x0∀ x22 . In x22 x0In (x6 x20 x21 x22) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0x7 x20 x21 = x2 x20 (x1 x21 x20))(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x7 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0∀ x22 . In x22 x0x8 x20 x21 x22 = x2 (x1 x21 x20) (x1 x21 (x1 x20 x22)))(∀ x20 . In x20 x0∀ x21 . In x21 x0∀ x22 . In x22 x0In (x8 x20 x21 x22) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0∀ x22 . In x22 x0x9 x20 x21 x22 = x3 (x1 (x1 x22 x20) x21) (x1 x20 x21))(∀ x20 . In x20 x0∀ x21 . In x21 x0∀ x22 . In x22 x0In (x9 x20 x21 x22) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0x10 x20 x21 = x1 x20 (x1 x21 (x2 x20 x4)))(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x10 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0x12 x20 x21 = x1 (x2 x20 x21) (x2 (x2 x20 x4) x4))(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x12 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0x11 x20 x21 = x1 (x1 (x3 x4 x20) x21) x20)(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x11 x20 x21) x0)(∀ x20 . In x20 x0∀ x21 . In x21 x0x13 x20 x21 = x1 (x3 x4 (x3 x4 x20)) (x3 x21 x20))(∀ x20 . In x20 x0∀ x21 . In x21 x0In (x13 x20 x21) x0)(∀ x20 . In x20 x0x1 x4 x20 = x20)(∀ x20 . In x20 x0x1 x20 x4 = x20)(∀ x20 . In x20 x0∀ x21 . In x21 x0x2 x20 (x1 x20 x21) = x21)(∀ x20 . In x20 x0∀ x21 . In x21 x0x1 x20 (x2 x20 x21) = x21)(∀ x20 . In x20 x0∀ x21 . In x21 x0x3 (x1 x20 x21) x21 = x20)(∀ x20 . In x20 x0∀ x21 . In x21 x0x1 (x3 x20 x21) x21 = x20)x14)x14
Known notEnotE : ∀ x0 : ο . not x0x0False
Theorem e6d86..conj_AIM2_TMSybA3Bk2mZ86dwnoZJ8eVA86eLhWZbLNp : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13In x4 x0(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 x17))))))))))))))))))) = x17)(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 x17))))))))))))))) = x17)(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0x10 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x10 x14 x17)))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x8 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x8 x14 x15 x18)))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x10 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x10 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x12 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x7 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x13 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x7 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x13 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x13 x14 (x12 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0x10 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x10 x14 (x10 x15 x18))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0x8 x14 x15 (x7 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0x9 x14 x15 (x7 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x9 x14 x15 (x7 x16 x19))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0x8 x14 x15 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0x8 x14 x15 (x12 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x12 x16 x20))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21)))))(∀ x14 . In x14 x0∀ x15 . In x15 x0∀ x16 . In x16 x0∀ x17 . In x17 x0∀ x18 . In x18 x0∀ x19 . In x19 x0∀ x20 . In x20 x0∀ x21 . In x21 x0x9 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21)))))False (proof)