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Proofgold Proof

pf
Let x0 of type (ι((ιι) → ι) → (ιιι) → (ιι) → ιι) → ιιιι be given.
Let x1 of type ((ιι) → (ιιι) → ιι) → ((((ιι) → ιι) → ιι) → ι) → ι be given.
Let x2 of type (ιι) → (ιιιι) → (ιιι) → ιιι be given.
Let x3 of type ((ιι) → (((ιι) → ι) → ι) → CT2 ι) → ιι be given.
Assume H0: ∀ x4 : ι → (ι → ι)ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι)ι → ι → ι) → ι . x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . x7 (λ x11 : ι → ι . λ x12 x13 . Inj1 0)) (Inj0 (x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . x2 (λ x11 . x10 0 0) (λ x11 x12 x13 . 0) (λ x11 x12 . x9 (λ x13 : ι → ι . 0)) (x9 (λ x11 : ι → ι . 0)) (Inj1 0)) (x4 0 (λ x8 . x1 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 . 0) (λ x9 : ((ι → ι)ι → ι)ι → ι . 0)) (x5 (λ x8 . 0))))) = x7 (λ x8 : ι → ι . λ x9 x10 . Inj1 0).
Assume H1: ∀ x4 x5 x6 . ∀ x7 : ι → ι → ι . x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . 0) (setsum (x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . x10 (setsum 0 0) (x7 0 0)) x5) (x7 (x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . 0) x5) (Inj1 (x7 0 0)))) = x6.
Apply FalseE with .........(∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 x7 . x1 (λ x8 : ι → ι . λ x9 : ι → ι → ι . λ x10 . Inj0 (x1 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . x12 0 x10) (λ x11 : ((ι → ι)ι → ι)ι → ι . x9 (x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . 0) 0) ...))) ... = ...)(∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 x7 . x0 (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . Inj1 0) (x0 (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) x7 x6 (Inj1 (x0 (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) (x2 (λ x8 . 0) (λ x8 x9 x10 . 0) (λ x8 x9 . 0) 0 0) (x0 (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0 0) (x2 (λ x8 . 0) (λ x8 x9 x10 . 0) (λ x8 x9 . 0) 0 0)))) x4 0 = x4)(∀ x4 : (((ι → ι) → ι)(ι → ι) → ι) → ι . ∀ x5 : (ι → ι)ι → ι → ι → ι . ∀ x6 : ι → ((ι → ι) → ι)(ι → ι) → ι . ∀ x7 . x0 (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x12) 0 (x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . 0) 0) 0 = x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . Inj0 0) (setsum (Inj0 0) (x0 (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x11 (Inj0 0)) (x2 (λ x8 . 0) (λ x8 x9 x10 . setsum 0 0) (λ x8 x9 . Inj1 0) 0 (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . 0))) (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . x1 (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x10 : ((ι → ι)ι → ι)ι → ι . 0))) (x3 (λ x8 : ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . x1 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . 0) (λ x11 : ((ι → ι)ι → ι)ι → ι . 0)) (x0 (λ x8 . λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0 0)))))False.
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