Let x0 of type (ι → (ι → (ι → ι) → ι → ι) → ι) → ((ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι) → ι be given.
Let x1 of type (ι → (ι → ι) → (ι → ι → ι) → ι → ι) → (ι → ι) → ι be given.
Let x2 of type (ι → ι → ι → (ι → ι) → ι → ι) → ι → ι → CN (ι → ι) be given.
Let x3 of type (ι → ι) → ι → ι be given.
Assume H0:
∀ x4 : ι → (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x8 . 0) (setsum 0 (x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 . 0) 0) 0 (x7 0 (λ x10 x11 . 0)) (λ x10 : ι → ι . λ x11 . x9 0 (λ x12 . 0) 0) (λ x10 . setsum 0 0) 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . setsum (x8 0 (λ x10 . 0) 0) 0))) = x6 (λ x8 : (ι → ι) → ι . x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x9 . x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . x10) (λ x10 : ι → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . x9))) (λ x8 . setsum (x5 (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . x10 0 (λ x11 . 0) 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . setsum 0 0)) (λ x9 . x8)) (x6 (λ x9 : (ι → ι) → ι . x8) (λ x9 . x9) (λ x9 . 0) (x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 . 0) 0) (setsum 0 0) (Inj0 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . Inj1 0) x8))) (λ x8 . Inj1 x8) (Inj1 (x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . 0))).
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . setsum (Inj0 (x9 (setsum 0 0) (λ x10 . x1 (λ x11 . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . 0) (λ x11 . 0)) 0)) (x3 (λ x10 . x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . x2 (λ x13 x14 x15 . λ x16 : ι → ι . ...) 0 0 ... ... 0)) ...)) ... = ...) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 . x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . Inj1 (setsum (setsum 0 0) x12)) 0 (setsum 0 (x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . setsum 0 0) 0 (setsum 0 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . x8) (x9 0 (λ x10 . 0) 0))) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . x9 x10 (λ x11 . x2 (λ x12 x13 x14 . λ x15 : ι → ι . λ x16 . x15 0) 0 x11 (λ x12 : ι → ι . λ x13 . x1 (λ x14 . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 . 0) (λ x14 . 0)) (λ x12 . Inj1 0) 0) x10) 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . x7) = setsum (setsum 0 x4) (x5 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . setsum (Inj1 0) (x12 0 (λ x13 . 0) 0)) (λ x11 : ι → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . 0)) 0)) ⟶ False.