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Proofgold Proposition

not (∀ x0 : (ι → ι → ι)((ι → ι)((ι → ι) → ι) → ι) → ο . ∀ x1 : ((ι → ι)ι → ι → ι)ι → ο . ∀ x2 : (ι → (ι → (ι → ι)ι → ι)ι → ι → ι)ι → ((ι → ι)ι → ι)ι → ο . ∀ x3 : ((((ι → ι → ι)ι → ι → ι)((ι → ι)ι → ι)(ι → ι) → ι)ι → ι)ι → ο . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (((ι → ι)ι → ι)(ι → ι) → ι)(ι → ι)(ι → ι) → ι . x1 (λ x8 : ι → ι . λ x9 x10 . Inj1 (Inj1 (Inj1 (Inj0 0)))) 0x3 (λ x8 : ((ι → ι → ι)ι → ι → ι)((ι → ι)ι → ι)(ι → ι) → ι . λ x9 . Inj0 (x6 (λ x10 . setsum (setsum 0 0) 0))) (Inj0 0))(∀ x4 : (ι → (ι → ι) → ι)((ι → ι) → ι) → ι . ∀ x5 : (ι → ι)(ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ((ι → ι → ι)ι → ι → ι)((ι → ι)ι → ι)(ι → ι) → ι . λ x9 . x9) (setsum 0 (setsum (setsum (Inj0 0) 0) (x5 (λ x8 . x5 (λ x9 . 0) (λ x9 x10 . 0)) (λ x8 x9 . 0))))x3 (λ x8 : ((ι → ι → ι)ι → ι → ι)((ι → ι)ι → ι)(ι → ι) → ι . λ x9 . x9) (Inj1 0))(∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι)ι → ι) → ι)(ι → ι)(ι → ι)ι → ι . ∀ x7 : ι → ι . x2 (λ x8 . λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . x8) (setsum (Inj1 0) (setsum (setsum (setsum 0 0) 0) (Inj1 (setsum 0 0)))) (λ x8 : ι → ι . λ x9 . setsum (x8 (Inj0 (Inj0 0))) (Inj1 (Inj1 (setsum 0 0)))) (Inj0 (Inj1 (setsum (setsum 0 0) x4)))x2 (λ x8 . λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . 0) (setsum (x7 (setsum x4 (Inj1 0))) x4) (λ x8 : ι → ι . λ x9 . x9) (Inj1 (setsum 0 (Inj0 (x7 0)))))(∀ x4 : (ι → ι)(ι → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 . λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . setsum (setsum x8 (x9 (Inj1 0) (λ x12 . x11) 0)) 0) (Inj1 (setsum (x4 (λ x8 . 0) (λ x8 . x8)) 0)) (λ x8 : ι → ι . λ x9 . setsum (setsum (x7 (Inj1 0)) (x7 (Inj0 0))) (Inj1 (x8 0))) (x5 (λ x8 . Inj1 0))x1 (λ x8 : ι → ι . λ x9 x10 . 0) (Inj0 (Inj1 (setsum 0 (Inj0 0)))))(∀ x4 : (((ι → ι)ι → ι) → ι)(ι → ι) → ι . ∀ x5 : (ι → ι)ι → ι . ∀ x6 . ∀ x7 : (((ι → ι)ι → ι)(ι → ι)ι → ι) → ι . x2 (λ x8 . λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . 0) 0 (λ x8 : ι → ι . λ x9 . 0) (setsum 0 0)x1 (λ x8 : ι → ι . λ x9 x10 . Inj1 0) (x7 (λ x8 : (ι → ι)ι → ι . λ x9 : ι → ι . λ x10 . setsum (Inj0 0) 0)))(∀ x4 x5 . ∀ x6 : (ι → ι)ι → ι → ι . ∀ x7 . In (Inj0 x4) (setsum 0 (x6 (λ x8 . setsum (Inj0 0) (setsum 0 0)) (setsum x4 (Inj1 0)) 0))x1 (λ x8 : ι → ι . λ x9 x10 . x10) 0x2 (λ x8 . λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . setsum 0 x8) (x6 (λ x8 . setsum (setsum x8 x8) 0) 0 (setsum x4 (Inj0 x5))) (λ x8 : ι → ι . λ x9 . Inj1 0) (setsum 0 (Inj1 x7)))(∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 . In (x6 0 (λ x8 : ι → ι . Inj0 0)) x7x0 (λ x8 x9 . setsum x9 x9) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . x9 (λ x10 . setsum (Inj1 (Inj1 0)) 0))x0 (λ x8 x9 . setsum x9 (setsum (Inj0 (setsum 0 0)) (Inj1 (x6 0 (λ x10 : ι → ι . 0))))) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . 0))(∀ x4 : ((ι → ι) → ι)(ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x8 x9 . Inj0 0) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . Inj0 0)In (Inj1 (setsum 0 (x4 (λ x8 : ι → ι . x6) (λ x8 . x5 0)))) x7)False)
type
prop
theory
HF
name
-
proof
PUYCz..
Megalodon
-
proofgold address
TMFCK..
creator
11884 PrGVS../7e8ca..
owner
11884 PrGVS../7e8ca..
term root
7828f..