Let x0 of type (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 be given.
Let x2 of type ((CT2 ι) → (ι → ι) → ((ι → ι) → ι) → ι) → (ι → 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 be given.
Assume H0:
∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x3 (λ x8 . 0) (λ x8 : ι → ι . λ x9 x10 x11 . x1 (λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . setsum 0 0) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 . x14)) = x1 (λ x8 : ι → ι → ι → ι . λ x9 x10 : ι → ι . x8 (x10 (Inj1 (Inj1 0))) (x9 (x0 (λ x11 . 0) (setsum 0 0))) 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 . Inj1 0).
Assume H1:
∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x8 . Inj0 x8) (λ x8 : ι → ι . λ x9 x10 x11 . x11) = setsum 0 (x4 (λ x8 . λ x9 : ι → ι . λ x10 . setsum (setsum (x1 (λ x11 : ι → ι → ι → ι . λ x12 x13 : ι → ι . 0) (λ x11 : ι → (ι → ι) → ι → ι . λ x12 x13 . 0)) x10) (x9 (x2 (λ x11 : (ι → ι → ι) → ι . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 : (ι → ι) → ι → ι . 0)))) (λ x8 : ι → ι . x5 0)).
Assume H2:
∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x2 (λ x8 : (ι → ι → ι) → ι . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . Inj0 (setsum 0 0)) (λ x8 x9 x10 x11 . Inj1 0) (λ x8 : (ι → ι) → ι → ι . x1 (λ x9 : ι → ι → ι → ι . λ x10 x11 : ι → ι . Inj0 (Inj0 (x11 0))) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . Inj1 (x0 (λ x12 . 0) (x1 (λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . 0) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 . 0))))) = Inj0 0.
Assume H3: ∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 x7 . x2 (λ x8 : (ι → ι → ι) → ι . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . x7) (λ x8 x9 x10 x11 . x11) (λ x8 : (ι → ι) → ι → ι . 0) = x7.
Assume H4: ∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x8 : ι → ι → ι → ι . λ x9 x10 : ι → ι . x10 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 . x10) = x5 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x9 (x9 (x0 (λ x11 . x0 (λ x12 . 0) 0) 0))).
Apply FalseE with
(∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x8 : ι → ι → ι → ι . λ x9 x10 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 . setsum x10 (x8 x10 (λ x11 . setsum (setsum 0 0) 0) (x0 (λ x11 . 0) x9))) = setsum 0 (x3 (λ x8 . 0) (λ x8 : ι → ι . λ x9 x10 x11 . Inj0 (x8 x10)))) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι → ι → ι . x0 (λ x8 . 0) 0 = x4) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x8 . x5 (x0 (λ x9 . x3 (λ x10 . Inj0 0) (λ x10 : ι → ι . λ x11 x12 x13 . x10 0)) (x0 (λ x9 . x8) (x0 (λ x9 . 0) 0)))) 0 = Inj1 (x3 (λ x8 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x12) (λ x9 : (ι → ι) → ι → ι . Inj1 (Inj0 0))) (λ x8 : ι → ι . λ x9 x10 x11 . x8 (x0 (λ x12 . Inj1 0) (Inj1 0))))) ⟶ False.