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Proofgold Proof

pf
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with ∀ x0 : (ι → ι)ι → ι → ο . ∀ x1 : ((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)(((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 → ι → ι)ι → ο . .........(∀ x4 : ι → ι . ∀ x5 x6 x7 . ......x2 (λ x8 . Inj0 x8) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι)ι → ι . λ x10 x11 . x8 (λ x12 : ι → ι . 0)) (λ x8 : (ι → ι) → ι . λ x9 x10 . setsum x7 0) (setsum (setsum 0 0) 0) (λ x8 . Inj0 ...) 0)(∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . In (setsum (Inj0 (Inj0 (Inj1 0))) (setsum 0 x5)) (x4 (setsum (setsum x5 (setsum 0 0)) (Inj1 x5)))x2 (λ x8 . setsum (x7 (λ x9 x10 x11 . 0)) x5) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι)ι → ι . λ x10 x11 . 0) (λ x8 : (ι → ι) → ι . λ x9 x10 . x8 (λ x11 . setsum x10 0)) (setsum 0 (setsum (Inj1 0) (Inj0 x5))) (λ x8 . x7 (λ x9 x10 x11 . setsum (setsum (setsum 0 0) (Inj1 0)) (Inj0 (Inj1 0)))) (Inj1 (Inj1 0))x1 (λ x8 : ι → ι . 0) (λ x8 : ι → ι → ι → ι . Inj1 0) (λ x8 x9 x10 . x10))(∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι)((ι → ι)ι → ι)(ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x1 (λ x8 : ι → ι . Inj1 (setsum (x7 (λ x9 . λ x10 : ι → ι . 0)) (setsum 0 0))) (λ x8 : ι → ι → ι → ι . x6 (λ x9 x10 . x9) (λ x9 : ι → ι . λ x10 . x8 0 (x8 (setsum 0 0) (Inj1 0) (Inj0 0)) 0) (λ x9 . Inj1 (Inj0 0))) (λ x8 x9 x10 . x9)x0 (λ x8 . setsum 0 (Inj1 (setsum 0 (x7 (λ x9 . λ x10 : ι → ι . 0))))) 0 (setsum (setsum (setsum (x6 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0) (λ x8 . 0)) 0) (setsum 0 (setsum 0 0))) (x6 (λ x8 x9 . x7 (λ x10 . λ x11 : ι → ι . Inj1 0)) (λ x8 : ι → ι . λ x9 . x8 (setsum 0 0)) (λ x8 . setsum 0 (x7 (λ x9 . λ x10 : ι → ι . 0))))))(∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι)ι → ι) → ι)ι → ι → ι . ∀ x7 . x0 (λ x8 . 0) (setsum (Inj1 (x6 (λ x8 : (ι → ι)ι → ι . 0) (Inj0 0) 0)) x7) (setsum (x4 (λ x8 x9 x10 . Inj0 (setsum 0 0))) 0)x0 (λ x8 . setsum (setsum (Inj1 (Inj0 0)) (setsum (Inj0 0) 0)) (x5 0 (Inj0 (setsum 0 0)))) (Inj1 (Inj1 (x5 (x6 (λ x8 : (ι → ι)ι → ι . 0) 0 0) (Inj0 0)))) (Inj1 (Inj1 (Inj1 0))))(∀ x4 x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι)((ι → ι) → ι)ι → ι → ι . x0 (λ x8 . x5) 0 (setsum 0 x5)False)False.
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