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