Let x0 of type (ι → ι → ι) → ι → (ι → (ι → ι) → ι) → ι be given.
Let x1 of type ((ι → CN (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) → ι be given.
Let x3 of type (ι → ι) → ((ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι) → ι be given.
Assume H0:
∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . x6 (Inj1 x7)) (λ x8 : ι → ι . λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) = Inj1 (setsum (x3 (λ x8 . x8) (λ x8 : ι → ι . λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . Inj0 (x9 0 0))) (Inj0 (x1 (λ x8 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . 0)))).
Assume H1:
∀ x4 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x8 . x8) (λ x8 : ι → ι . λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) = Inj1 0.
Assume H2:
∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x2 (λ x8 x9 x10 . setsum x7 0) (λ x8 : ι → ι → ι . λ x9 . x0 (λ x10 x11 . x11) 0 (λ x10 . λ x11 : ι → ι . Inj0 x10)) = x0 (λ x8 x9 . Inj1 0) (x5 (λ x8 . λ x9 : ι → ι . λ x10 . 0) (λ x8 : ι → ι . λ x9 . x9)) (λ x8 . λ x9 : ι → ι . Inj1 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj0 0) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0))).
Assume H3: ∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x8 x9 x10 . x10) (λ x8 : ι → ι → ι . λ x9 . 0) = x6 (λ x8 : (ι → ι) → ι → ι . λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . x3 (λ x16 . 0) (λ x16 : ι → ι . λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . 0)))).
Apply FalseE with
... ⟶ ... ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x8 x9 . setsum (x0 (λ x10 x11 . 0) (Inj0 (x2 (λ x10 x11 x12 . 0) (λ x10 : ι → ι → ι . λ x11 . 0))) (λ x10 . λ x11 : ι → ι . Inj1 (x2 (λ x12 x13 x14 . 0) (λ x12 : ι → ι → ι . λ x13 . 0)))) 0) x5 (λ x8 . λ x9 : ι → ι . x7) = ...) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x0 (λ x8 x9 . x8) (Inj1 (Inj0 (x2 (λ x8 x9 x10 . setsum 0 0) (λ x8 : ι → ι → ι . λ x9 . 0)))) (λ x8 . λ x9 : ι → ι . 0) = setsum x6 (x7 (λ x8 x9 : ι → ι . x0 (λ x10 x11 . x2 (λ x12 x13 x14 . x13) (λ x12 : ι → ι → ι . λ x13 . 0)) x6 (λ x10 . λ x11 : ι → ι . Inj1 (x8 0))) (Inj0 0) 0 (x7 (λ x8 x9 : ι → ι . x0 (λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0)) (setsum 0 0) (λ x10 . λ x11 : ι → ι . x8 0)) x6 (x3 (λ x8 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0)) (λ x8 : ι → ι . λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x10 0)) (setsum (x5 (λ x8 x9 x10 . 0) 0) (x3 (λ x8 . 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0)))))) ⟶ False.