Proofgold Proof

Apply unknownprop_50f1b502ede8f73efac5f5638826e50355eb6f972374cae79b4ecf4e1be40675 with ∀ x0 : ((ι → ι → ι → ι) → ι → ι → ι) → ι → ο . ∀ x1 : ((ι → ι) → ι) → (ι → ι) → ι → ο . ∀ x2 : (ι → ι) → ι → ο . ∀ x3 : (ι → ι → ι → ι → ι → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ο . (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . In (setsum 0 (x7 (λ x8 . λ x9 : ι → ι . x7 (λ x10 . λ x11 : ι → ι . 0) (λ x10 . setsum 0 0) 0) (λ x8 . 0) (Inj1 (x6 (λ x8 : (ι → ι) → ι → ι . 0))))) (setsum (x7 (λ x8 . λ x9 : ι → ι . x7 (λ x10 . λ x11 : ι → ι . 0) (λ x10 . Inj1 0) (x6 (λ x10 : (ι → ι) → ι → ι . 0))) (λ x8 . Inj1 (setsum 0 0)) 0) (setsum (x6 (λ x8 : (ι → ι) → ι → ι . 0)) (setsum (setsum 0 0) (Inj1 0)))) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj0 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . x8 (x6 (λ x10 : (ι → ι) → ι → ι . 0)))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . In (Inj1 (setsum (x5 (λ x8 x9 x10 . Inj0 0) (setsum 0 0) (setsum 0 0)) (setsum x6 (x7 (λ x8 . 0))))) x6 ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 (setsum (Inj1 0) x12)) (λ x8 : ι → ι . λ x9 : ι → ι → ι . Inj1 (Inj1 (Inj0 (Inj1 0)))) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 (setsum 0 (setsum (Inj0 0) 0))) (λ x8 : ι → ι . λ x9 : ι → ι → ι . Inj0 (Inj0 (x9 (x7 (λ x10 . 0)) (x7 (λ x10 . 0)))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . In (Inj0 x7) (setsum 0 0) ⟶ x2 (λ x8 . 0) x6 ⟶ x2 (λ x8 . 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . x6) x4 ⟶ In x5 (Inj1 0)) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (x5 (λ x8 : ι → ι → ι . 0)) (x5 (λ x8 : ι → ι → ι . Inj0 (x8 (Inj1 0) (setsum 0 0)))) ⟶ x1 (λ x8 : ι → ι . Inj0 0) (λ x8 . 0) (x5 (λ x8 : ι → ι → ι . 0))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 : ι → ι . x6 (λ x9 . x7) (Inj1 (Inj0 (Inj1 0)))) (λ x8 . setsum (x6 (λ x9 . setsum x9 0) (Inj1 (Inj1 0))) 0) (setsum 0 (Inj1 0)) ⟶ x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . setsum x7 (setsum x10 (x8 (setsum 0 0) 0 (setsum 0 0)))) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . 0) 0 ⟶ x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . 0) (Inj1 x7)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . x10) (Inj0 0) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . 0)) ⟶ False.