Let x0 of type (ι → ι) → ι → ι → ι → ι → ι → ι be given.
Let x1 of type (((CN (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 → (ι → ι) → ι) → ι be given.
Let x3 of type (((ι → (ι → ι) → ι) → ι) → CT3 ι) → (CT3 ι) → (ι → ι) → ι be given.
Assume H0:
∀ x4 : ((ι → ι) → ι) → ι → ι . ∀ x5 : (ι → ι → ι) → (ι → ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → ι → ι → ι . x3 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : ι → ι → ι → ι . 0) (λ x8 : ι → ι → ι → ι . 0) (λ x8 . 0) = x7 (Inj1 (Inj0 (x2 (λ x8 : ι → ((ι → ι) → ι) → ι . 0) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . setsum 0 0)))) 0 (setsum 0 (x2 (λ x8 : ι → ((ι → ι) → ι) → ι . x0 (λ x9 . x3 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 : ι → ι → ι → ι . 0) (λ x10 . 0)) (x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 . 0) 0 (λ x9 : (ι → ι) → ι → ι . 0)) 0 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0)) 0 0) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . x8 (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . 0) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0))))) (x3 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : ι → ι → ι → ι . 0) (λ x8 : ι → ι → ι → ι . 0) (λ x8 . 0)).
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x1 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 . x0 (λ x10 . x10) (Inj1 (x3 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 : ι → ι → ι → ι . Inj0 0) (λ x10 : ι → ι → ι → ι . x9) (λ x10 . x9))) (setsum x9 0) (Inj0 (x7 (λ x10 x11 x12 . Inj0 0))) (x3 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 : ι → ι → ι → ι . setsum 0 (Inj1 0)) ... ...) ...) ... ... = ...) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x8 . 0) 0 0 (setsum (setsum x7 0) (Inj1 (Inj1 (setsum 0 0)))) 0 (x5 0) = setsum 0 0) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x7 . x0 (λ x8 . 0) 0 (x4 (λ x8 : (ι → ι) → ι → ι . 0)) (setsum 0 0) (Inj1 0) (x0 (λ x8 . x6 (λ x9 : ι → ι . setsum (x3 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 : ι → ι → ι → ι . 0) (λ x10 . 0)) (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0))) x8 (λ x9 . x7)) 0 (x2 (λ x8 : ι → ((ι → ι) → ι) → ι . Inj1 (setsum 0 0)) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι . 0) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . Inj0 0))) 0 (x0 (λ x8 . 0) x7 0 (x3 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : ι → ι → ι → ι . setsum 0 0) (λ x8 : ι → ι → ι → ι . setsum 0 0) (λ x8 . x6 (λ x9 : ι → ι . 0) 0 (λ x9 . 0))) (Inj1 (setsum 0 0)) (Inj1 (x4 (λ x8 : (ι → ι) → ι → ι . 0)))) (x2 (λ x8 : ι → ((ι → ι) → ι) → ι . x8 x7 (λ x9 : ι → ι . x7)) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . Inj0 x7))) = x4 (λ x8 : (ι → ι) → ι → ι . setsum (Inj1 0) (setsum x7 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum 0 0))))) ⟶ False.