Search for blocks/addresses/...

Proofgold Proof

pf
Apply unknownprop_50f1b502ede8f73efac5f5638826e50355eb6f972374cae79b4ecf4e1be40675 with ∀ x0 : ((ι → ι)ι → (ι → ι → ι) → ι)ι → ο . ∀ x1 : (ι → (ι → ι)((ι → ι)ι → ι)ι → ι)((ι → ι) → ι)(ι → ι)(ι → ι → ι) → ο . ∀ x2 : (((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) → ο . ...(∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . ...)(∀ x4 : ((ι → ι)(ι → ι)ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι)((ι → ι)ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι)(ι → ι)ι → ι) → ι . In (Inj1 (setsum 0 (setsum 0 0))) (Inj1 0)x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι)(ι → ι) → ι . λ x10 . 0) (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x8 (Inj0 (setsum 0 0)) (x9 (setsum 0 0))))x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι)(ι → ι) → ι . λ x10 . setsum (setsum (setsum (x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (setsum 0 0)) (Inj1 (setsum 0 0))) (x9 (λ x11 . setsum (Inj1 0) (x8 (λ x12 . λ x13 : ι → ι . 0))) (λ x11 . 0))) (x4 (λ x8 x9 : ι → ι . λ x10 . x8 0)))(∀ x4 : (ι → (ι → ι) → ι)(ι → ι → ι)ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι)(ι → ι) → ι . λ x10 . 0) 0x3 (λ x8 : ((ι → ι → ι)ι → ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0))(∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : (ι → (ι → ι)ι → ι)ι → ι → ι → ι . ∀ x6 x7 . In (Inj0 (x4 (λ x8 x9 x10 . 0))) (Inj0 0)x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι)(ι → ι) → ι . λ x10 . Inj1 x7) 0x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι)ι → ι . λ x11 . Inj1 (x9 x8)) (λ x8 : ι → ι . Inj1 (setsum (x8 (setsum 0 0)) (Inj0 (Inj0 0)))) (λ x8 . Inj1 (Inj0 0)) (λ x8 x9 . 0))(∀ x4 . ∀ x5 : ((ι → ι)(ι → ι)ι → ι)ι → (ι → ι)ι → ι . ∀ x6 x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι)ι → ι . λ x11 . Inj0 (x10 (λ x12 . 0) x8)) (λ x8 : ι → ι . setsum x7 (setsum (setsum 0 (setsum 0 0)) x7)) (λ x8 . 0) (λ x8 x9 . 0)In (Inj1 (setsum (x5 (λ x8 x9 : ι → ι . λ x10 . Inj0 0) x4 (λ x8 . setsum 0 0) x7) (Inj0 0))) (setsum (setsum x7 (setsum 0 (setsum 0 0))) (setsum (setsum (setsum 0 0) x4) x6)))(∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . In x7 (setsum 0 0)x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι)(ι → ι) → ι . λ x10 . Inj1 (setsum 0 (Inj0 0))) (x6 (setsum (setsum (x6 0) 0) (x6 (Inj1 0))))x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . Inj1 0) (x6 (Inj0 (setsum (setsum 0 0) 0))))(∀ x4 : (ι → (ι → ι)ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι)ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . In (Inj0 (Inj1 0)) x5x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . x8 x9) (x4 (λ x8 . λ x9 : ι → ι . λ x10 . 0))x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . 0) 0)False.
...