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