| not (∀ x0 : (ι → ι → (ι → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ο . ∀ x1 : (ι → (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ο . ∀ x2 : (ι → ι) → (((ι → ι → ι) → (ι → ι) → ι) → ι) → (ι → ι) → ο . ∀ x3 : (ι → ι) → ι → ο . (∀ x4 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 x9 . λ x10 : ι → ι → ι . Inj1 0) (λ x8 . setsum (x7 (setsum 0 x8)) (Inj0 0)) (λ x8 . x8) (x7 (setsum 0 (Inj0 0))) ⟶ x3 (λ x8 . setsum x6 (Inj1 0)) (Inj0 (setsum (x7 0) (setsum (Inj1 0) (Inj1 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (x4 (λ x8 . λ x9 : ι → ι . λ x10 . 0) (λ x8 : ι → ι . λ x9 . x8 0) (λ x8 . 0) 0) (Inj1 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x3 (λ x8 . Inj1 0) 0 ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . Inj1 (setsum 0 x9)) (λ x8 . setsum (Inj1 (Inj0 (Inj1 0))) (Inj0 (setsum 0 (Inj1 0)))) (λ x8 . x8) (Inj1 (x4 (λ x8 . λ x9 : ι → ι . λ x10 . Inj1 (Inj1 0)) (λ x8 : ι → ι . λ x9 . Inj0 0) (λ x8 . 0) x6))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x8 . setsum (setsum x6 x6) x7) (Inj1 0) ⟶ x2 (λ x8 . setsum 0 0) (λ x8 : (ι → ι → ι) → (ι → ι) → ι . 0) (λ x8 . x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 . setsum x6 (setsum 0 (x5 0))) (λ x8 : (ι → ι → ι) → (ι → ι) → ι . 0) (λ x8 . setsum 0 (x7 (setsum (Inj1 0) (Inj0 0)))) ⟶ In (setsum (Inj0 (x5 x4)) 0) (Inj1 (Inj1 (setsum 0 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . In (Inj0 (Inj1 (x5 (λ x8 x9 . 0)))) (x5 (λ x8 x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x11 0) (Inj0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) (λ x8 : ι → ι . Inj0 (x5 (λ x9 x10 . x9))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj0 x10) (λ x8 : ι → ι . Inj1 (Inj0 (x5 (λ x9 x10 . x8 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . In (x5 (Inj1 (setsum (setsum 0 0) (x4 0))) (x7 (λ x8 . setsum (Inj0 0) (x5 0 0)) (λ x8 x9 . Inj1 (setsum 0 0)))) x6 ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum (Inj0 (setsum (setsum 0 0) (setsum 0 0))) (Inj1 (x9 x10 (λ x13 . 0) (setsum 0 0)))) (λ x8 : ι → ι . Inj0 0) ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . 0) (λ x8 . x8) (λ x8 . x5 (x7 (λ x9 . x9) (λ x9 x10 . x8)) (setsum 0 (x7 (λ x9 . Inj0 0) (λ x9 x10 . setsum 0 0)))) 0) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . In (x7 (λ x8 : (ι → ι) → ι . 0)) (Inj1 (Inj1 (x7 (λ x8 : (ι → ι) → ι . setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 0) (λ x8 : ι → ι . x7 (λ x9 : (ι → ι) → ι . setsum (Inj1 0) 0)) ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . 0) (λ x8 . 0) (λ x8 . Inj1 (setsum (setsum (setsum 0 0) (x5 0 0 (λ x9 . 0))) (Inj1 (x7 (λ x9 : (ι → ι) → ι . 0))))) (setsum 0 (x7 (λ x8 : (ι → ι) → ι . Inj0 (Inj0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 x9 . λ x10 : ι → ι → ι . setsum x9 (Inj0 (x10 (setsum 0 0) 0))) (λ x8 . x5 (λ x9 : ι → ι . setsum (Inj1 0) (setsum (setsum 0 0) 0)) (λ x9 x10 . 0) (Inj1 (setsum (setsum 0 0) (x6 0))) 0) (λ x8 . 0) (Inj0 (x5 (λ x8 : ι → ι . 0) (λ x8 x9 . Inj0 0) (setsum 0 (x4 (λ x8 . 0))) (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum x12 (Inj1 x12)) (λ x8 : ι → ι . Inj0 (setsum (Inj0 0) 0))) ⟶ False) |
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