Let x0 of type (((ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι) → (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 x1 of type (((ι → ι) → CT2 ι) → ι → ι → (ι → ι) → ι) → ι → ι → ι → (ι → ι) → 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 be given.
Assume H0:
∀ x4 : (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x8 x9 . 0) (λ x8 : ((ι → ι) → ι) → ι → ι . x3 (λ x9 x10 . setsum 0 (x7 0)) (λ x9 : ((ι → ι) → ι) → ι → ι . x9 (λ x10 : ι → ι . setsum (setsum 0 0) (x7 0)) (Inj1 (setsum 0 0)))) = x3 (λ x8 x9 . Inj0 (setsum x6 (setsum 0 x9))) (λ x8 : ((ι → ι) → ι) → ι → ι . setsum 0 (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . x11 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x2 (λ x12 . x0 (λ x13 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x14 : ι → ι → ι → ι . λ x15 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . 0) (λ x13 . 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0)) (Inj1 0)) (λ x9 . Inj1 (x1 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 0 0 (λ x10 . 0) 0)) (λ x9 : ι → ι . λ x10 . Inj0 (x7 0)) (λ x9 . x7 0))).
Assume H1:
∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι) → ι → ι . x3 (λ x8 x9 . setsum (x0 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . setsum 0 0) (λ x10 . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . x10)) x8) (λ x8 : ((ι → ι) → ι) → ι → ι . setsum (x8 (λ x9 : ι → ι . x2 (λ x10 . Inj0 0) (x3 (λ x10 x11 . 0) (λ x10 : ((ι → ι) → ι) → ι → ι . 0))) (x2 (λ x9 . x0 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) (λ x10 . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0)) (Inj0 0))) 0) = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x0 (λ x8 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x9 : ι → ι → ι → ι . λ x10 : ι → ι . x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . Inj1 (x14 x12)) (Inj0 (setsum (x2 (λ x11 . 0) 0) 0)) 0 0 (λ x11 . x2 (λ x12 . setsum (setsum 0 0) (x2 (λ x13 . 0) 0)) 0) x7) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . setsum (Inj1 (Inj0 (x8 0))) 0) (λ x8 . setsum 0 (setsum x7 (Inj1 (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . 0) 0 0 0 (λ x9 . 0) 0)))) (λ x8 : ι → ι . λ x9 . x6) (λ x8 . x6) = x1 (λ x8 : (ι → ι) → (ι → ι → ι) → ι . λ x9 x10 . λ x11 : ι → ι . x11 (x3 (λ x12 x13 . Inj1 0) (λ x12 : ((ι → ι) → ι) → ι → ι . x10))) (setsum (setsum 0 x7) (Inj1 x6)) (Inj1 (Inj0 (setsum (x0 (λ x8 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x9 : ι → ι → ι → ι . λ x10 : ι → ι . 0) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . 0) (λ x8 . 0) (λ x8 : ι → ι . λ x9 . 0) ...) ...))) ... ... ...) ⟶ False.