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 be given.
Let x1 of type ((CT2 ι) → ι) → (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 be given.
Let x3 of type (ι → ι → ι) → (ι → ι → (ι → ι) → ι) → ι be given.
Assume H0:
∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 . x3 (λ x8 x9 . x2 (λ x10 . 0) (x1 (λ x10 : (ι → ι → ι) → ι . x0 (λ x11 : ι → ι . λ x12 . x1 (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x13 : (ι → ι) → ι → ι . 0)) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . x12) (λ x11 : ι → ι . x9) 0 (λ x11 . x9) (Inj0 0)) (λ x10 . λ x11 : ι → ι . λ x12 x13 . Inj0 (x11 0)) (λ x10 : (ι → ι) → ι → ι . 0)) (Inj1 0) (λ x10 : ι → ι . 0)) (λ x8 x9 . λ x10 : ι → ι . 0) = x2 (λ x8 . setsum (x1 (λ x9 : (ι → ι → ι) → ι . 0) (λ x9 . λ x10 : ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) (Inj0 0))) (x3 (λ x9 x10 . x2 (λ x11 . setsum 0 0) 0 (x0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . 0) 0 (λ x11 . 0) 0) (λ x11 : ι → ι . x2 (λ x12 . 0) 0 0 (λ x12 : ι → ι . 0))) (λ x9 x10 . λ x11 : ι → ι . 0))) (x5 (x5 (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . setsum 0 0)))) (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . 0)) (λ x8 : ι → ι . setsum x7 (x8 (x5 0))).
Assume H1:
∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x8 x9 . 0) (λ x8 x9 . λ x10 : ι → ι . Inj1 (x0 (λ x11 : ι → ι . λ x12 . setsum x12 x9) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . 0) (Inj1 (x3 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . 0))) (λ x11 . x0 (λ x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ι . λ x15 . 0) (λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . 0) (λ x14 : ι → ι . 0) 0 (λ x14 . 0) 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . x13) (λ x12 : ι → ι . 0) (x1 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0)) (λ x12 . 0) x11) 0)) = x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . setsum (setsum (x8 (λ x11 . x0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . 0) (λ x12 : ι → ι . 0) 0 (λ x12 . 0) 0)) 0) (setsum 0 x10)).
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x8 : ι → ι . λ x9 . x3 (λ x10 x11 . x8 (Inj1 0)) (λ x10 x11 . λ x12 : ι → ι . x3 (λ x13 x14 . Inj0 (x0 (λ x15 : ι → ι . λ x16 . 0) (λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . 0) (λ x15 : ι → ι . 0) 0 (λ x15 . 0) 0)) (λ x13 x14 . λ x15 : ι → ι . x15 (setsum 0 0)))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x9 . x6) (λ x8 : ι → ι . x0 (λ x9 : ι → ι . λ x10 . 0) ... ... ... ... ...) ... ... 0 = ...) ⟶ False.