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