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