Let x0 of type (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 → 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 be given.
Let x3 of type (ι → ι → ι → (ι → ι) → ι) → ι → ι be given.
Assume H0: ∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x8 x9 x10 . λ x11 : ι → ι . 0) x7 = x7.
Assume H1:
∀ x4 x5 x6 x7 . x3 (λ x8 x9 x10 . λ x11 : ι → ι . x2 (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . Inj0 (Inj0 (setsum 0 0))) (x11 (x2 (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . x2 (λ x15 : ((ι → ι) → ι) → ι . λ x16 x17 . 0) 0) 0))) (x3 (λ x8 x9 x10 . λ x11 : ι → ι . x0 (λ x12 x13 . x1 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 : (ι → ι) → ι → ι . x13) (λ x14 . 0)) (λ x12 : ι → ι → ι → ι . λ x13 . 0) (Inj0 (Inj0 0))) (x2 (λ x8 : ((ι → ι) → ι) → ι . λ x9 x10 . x3 (λ x11 x12 x13 . λ x14 : ι → ι . 0) (Inj1 0)) (setsum (setsum 0 0) (setsum 0 0)))) = Inj1 0.
Assume H2:
∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x2 (λ x8 : ((ι → ι) → ι) → ι . λ x9 x10 . x0 (λ x11 x12 . x10) (λ x11 : ι → ι → ι → ι . λ x12 . x2 (λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . Inj1 0) x10) (x0 (λ x11 x12 . x2 (λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . x14) 0) (λ x11 : ι → ι → ι → ι . λ x12 . Inj1 (x11 0 0 0)) 0)) x7 = setsum 0 (setsum (setsum x7 (Inj1 x5)) (x0 (λ x8 x9 . 0) (λ x8 : ι → ι → ι → ι . λ x9 . x9) 0)).
Assume H3: ∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 : ι → ι . ∀ x7 . x2 (λ x8 : ((ι → ι) → ι) → ι . λ x9 x10 . 0) x7 = x7.
Assume H4:
∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 . x1 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . 0) (λ x8 . x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . 0) (x0 (λ x9 x10 . x8) (λ x9 : ι → ι → ι → ι . λ x10 . 0) (x3 (λ x9 x10 x11 . λ x12 : ι → ι . 0) x8))) = setsum (x2 (λ x8 : ((ι → ι) → ι) → ι . λ x9 x10 . setsum (Inj0 (setsum 0 0)) (x8 (λ x11 : ι → ι . 0))) 0) 0.
Assume H5:
∀ x4 : ((ι → ι) → (ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . setsum (Inj1 (x8 (λ x11 : ι → ι → ι . λ x12 : ι → ι . x2 (λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . 0) 0))) 0) (λ x8 . x8) = x4 (λ x8 x9 : ι → ι . x0 (λ x10 x11 . x2 (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . x14) x11) (λ x10 : ι → ι → ι → ι . λ x11 . x0 (λ x12 x13 . x2 (λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . Inj0 0) (Inj1 0)) (λ x12 : ι → ι → ι → ι . λ x13 . x0 (λ x14 x15 . x14) (λ x14 : ι → ι → ι → ι . λ x15 . setsum 0 0) (x0 (λ x14 x15 . 0) (λ x14 : ι → ι → ι → ι . λ x15 . 0) 0)) 0) (Inj0 0)) (λ x8 . x3 (λ x9 x10 x11 . λ x12 : ι → ι . 0) x6) (x7 (λ x8 . x6) (λ x8 : ι → ι . λ x9 . Inj0 (Inj1 0))).
Apply FalseE with
... ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 x9 . 0) (λ x8 : ι → ι → ι → ι . ...) 0 = ...) ⟶ False.