Proofgold Address

Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Known notE^notE : ∀ x0 : ο . not x0 ⟶ x0 ⟶ False
Known e3ec9..^neq_0_1 : not (0 = 1)
Theorem ad662.. : ∀ x0 : (ι → ι) → (ι → ι → ι) → (ι → (ι → ι) → ι → ι) → ι . ∀ x1 : ((((ι → ι) → ι) → ι → ι) → (((ι → ι) → ι) → ι) → ι → ι → ι) → ι → ι . ∀ x2 : ((((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι) → ι → ι) → (ι → (ι → ι) → ι → ι) → (ι → ι → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x3 : ((ι → ((ι → ι) → ι) → ι) → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι) → ι . (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → ι . x3 (λ x9 : ι → ((ι → ι) → ι) → ι . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . x11 (λ x14 : ι → ι . x0 (λ x15 . x13) (λ x15 x16 . x14 0) (λ x15 . λ x16 : ι → ι . λ x17 . setsum 0 0))) (x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . x13) (x3 (λ x10 : ι → ((ι → ι) → ι) → ι . x10 0 (λ x11 : ι → ι . 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum 0 0)))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) = Inj0 x4) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : ((ι → ι) → ι) → (ι → ι) → ι . x3 (λ x9 : ι → ((ι → ι) → ι) → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0) = x4 (λ x9 . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . setsum x12 x12) (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x11 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x10 x11 x12 . 0) (λ x10 . x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x12 . setsum 0 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x11 x12 x13 . 0) (λ x11 . x9) (Inj1 0) (setsum 0 0)) (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x11 . Inj1 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x10 x11 x12 . 0) (λ x10 . setsum 0 0) 0 (x3 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x11 . x3 (λ x12 : ι → ((ι → ι) → ι) → ι . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (λ x10 . λ x11 : ι → ι . λ x12 . x11 0) (λ x10 x11 x12 . setsum 0 0) (λ x10 . 0) 0 (x3 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))))) (λ x9 x10 . x7 (λ x11 : ι → ι . setsum 0 0) (λ x11 . setsum (x7 (λ x12 : ι → ι . x9) (λ x12 . x3 (λ x13 : ι → ((ι → ι) → ι) → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0))) x10))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x10 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . x11) (λ x9 x10 x11 . x9) (λ x9 . x7) x7 (x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x3 (λ x13 : ι → ((ι → ι) → ι) → ι . x10 (λ x14 : ι → ι . x14 0)) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x10 . Inj0 (Inj1 0)) (λ x9 . λ x10 : ι → ι . λ x11 . x11) (λ x9 x10 x11 . 0) (λ x9 . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . x1 (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 x17 . 0) 0) (setsum 0 0)) (x6 (λ x9 . 0)) (x0 (λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (λ x9 x10 . setsum 0 0) (λ x9 . λ x10 : ι → ι . λ x11 . Inj0 0)))) = setsum (x6 (λ x9 . setsum (x6 (λ x10 . 0)) (x0 (λ x10 . x10) (λ x10 x11 . x7) (λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0)))) (setsum (x0 (λ x9 . Inj0 (setsum 0 0)) (λ x9 x10 . x9) (λ x9 . λ x10 : ι → ι . λ x11 . 0)) 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 : (ι → ι) → ι → ι → ι → ι . x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x10 . x6 (setsum (setsum (x3 (λ x11 : ι → ((ι → ι) → ι) → ι . 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0)) (Inj1 0)) (x0 (λ x11 . x7 (λ x12 . 0) 0 0 0) (λ x11 x12 . setsum 0 0) (λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0))) (Inj0 (x3 (λ x11 : ι → ((ι → ι) → ι) → ι . x10) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . setsum 0 0))) (x0 (λ x11 . x3 (λ x12 : ι → ((ι → ι) → ι) → ι . x9 (λ x13 x14 : ι → ι . 0) (λ x13 x14 . 0)) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (λ x11 x12 . x11) (λ x11 . λ x12 : ι → ι . λ x13 . x12 (x1 (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 x17 . 0) 0)))) (λ x9 . λ x10 : ι → ι . λ x11 . Inj1 (x10 (Inj0 0))) (λ x9 x10 x11 . setsum 0 0) (λ x9 . Inj0 (Inj0 0)) 0 x5 = x6 (Inj1 0) (x7 (λ x9 . x9) (x3 (λ x9 : ι → ((ι → ι) → ι) → ι . x7 (λ x10 . x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x12 . 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x11 x12 x13 . 0) (λ x11 . 0) 0 0) 0 (Inj1 0) (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x11 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x10 x11 x12 . 0) (λ x10 . 0) 0 0)) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum (setsum 0 0) (setsum 0 0))) x4 x5) (setsum 0 (Inj0 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0 = x4 (λ x9 . λ x10 : ι → ι . λ x11 . x9)) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 . x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x0 (setsum (x1 (λ x13 : ((ι → ι) → ι) → ι → ι . λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . x2 (λ x17 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x18 . 0) (λ x17 . λ x18 : ι → ι . λ x19 . 0) (λ x17 x18 x19 . 0) (λ x17 . 0) 0 0) (setsum 0 0))) (λ x13 x14 . x14) (λ x13 . λ x14 : ι → ι . λ x15 . x12)) (setsum (Inj0 (x6 (λ x9 . λ x10 : ι → ι . x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x12 . 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x11 x12 x13 . 0) (λ x11 . 0) 0 0) 0)) (x5 (λ x9 . x0 (λ x10 . x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x12 . 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x11 x12 x13 . 0) (λ x11 . 0) 0 0) (λ x10 x11 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . x1 (λ x13 : ((ι → ι) → ι) → ι → ι . λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . 0) 0)) (λ x9 : ι → ι . Inj0 (x9 0)) (x5 (λ x9 . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0) (λ x9 : ι → ι . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0) 0 x7) 0)) = x0 (λ x9 . x5 (λ x10 . Inj0 (setsum (setsum 0 0) 0)) (λ x10 : ι → ι . x10 x9) (x3 (λ x10 : ι → ((ι → ι) → ι) → ι . x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x12 . x3 (λ x13 : ι → ((ι → ι) → ι) → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x11 . λ x12 : ι → ι . λ x13 . x11) (λ x11 x12 x13 . setsum 0 0) (λ x11 . Inj0 0) (Inj0 0) (Inj0 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ι → ((ι → ι) → ι) → ι . Inj0 0) (λ x14 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . setsum 0 0))) (x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . x3 (λ x14 : ι → ((ι → ι) → ι) → ι . 0) (λ x14 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0)) 0)) (λ x9 x10 . x9) (λ x9 . λ x10 : ι → ι . λ x11 . setsum (setsum 0 (Inj0 (x0 (λ x12 . 0) (λ x12 x13 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0)))) x7)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x9 . x0 (λ x10 . setsum 0 (x7 x6 (λ x11 : ι → ι . λ x12 . Inj1 0))) (λ x10 x11 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . x10)) (λ x9 x10 . x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x12 . x9) (λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x15 . x2 (λ x16 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x17 . x1 (λ x18 : ((ι → ι) → ι) → ι → ι . λ x19 : ((ι → ι) → ι) → ι . λ x20 x21 . 0) 0) (λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x16 x17 x18 . x18) (λ x16 . setsum 0 0) 0 (x14 (λ x16 x17 : ι → ι . 0) (λ x16 x17 . 0))) (λ x14 . λ x15 : ι → ι . λ x16 . setsum (x3 (λ x17 : ι → ((ι → ι) → ι) → ι . 0) (λ x17 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x18 . λ x19 : ι → ι . λ x20 . 0)) (setsum 0 0)) (λ x14 x15 x16 . x1 (λ x17 : ((ι → ι) → ι) → ι → ι . λ x18 : ((ι → ι) → ι) → ι . λ x19 x20 . Inj1 0) (setsum 0 0)) (λ x14 . x13) (Inj1 (Inj1 0)) (setsum 0 x10)) (λ x11 x12 x13 . 0) (λ x11 . setsum (Inj1 0) (x7 (x0 (λ x12 . 0) (λ x12 x13 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0)) (λ x12 : ι → ι . λ x13 . x3 (λ x14 : ι → ((ι → ι) → ι) → ι . 0) (λ x14 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0)))) (Inj0 (Inj1 (Inj1 0))) x9) (λ x9 . λ x10 : ι → ι . λ x11 . 0) = x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x10 . x6) (λ x9 . λ x10 : ι → ι . setsum 0) (λ x9 x10 x11 . Inj1 (Inj1 x11)) (λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι) → ι . x9) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13)) (x3 (λ x9 : ι → ((ι → ι) → ι) → ι . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) (x4 (λ x9 : (ι → ι) → ι → ι . 0) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x10 . x6) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 x10 x11 . Inj1 (x0 (λ x12 . 0) (λ x12 x13 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0))) (λ x9 . setsum x9 (x0 (λ x10 . 0) (λ x10 x11 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0))) 0 (setsum (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x10 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 x10 x11 . 0) (λ x9 . 0) 0 0) (x0 (λ x9 . 0) (λ x9 x10 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0)))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 . 0) (λ x9 x10 . x3 (λ x11 : ι → ((ι → ι) → ι) → ι . 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . x11 (λ x15 : ι → ι . λ x16 . x0 (λ x17 . x2 (λ x18 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x19 . 0) (λ x18 . λ x19 : ι → ι . λ x20 . 0) (λ x18 x19 x20 . 0) (λ x18 . 0) 0 0) (λ x17 x18 . x0 (λ x19 . 0) (λ x19 x20 . 0) (λ x19 . λ x20 : ι → ι . λ x21 . 0)) (λ x17 . λ x18 : ι → ι . λ x19 . x16)) (x3 (λ x15 : ι → ((ι → ι) → ι) → ι . setsum 0 0) (λ x15 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . setsum 0 0)) (Inj1 0))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum x9 (Inj0 (x3 (λ x12 : ι → ((ι → ι) → ι) → ι . setsum 0 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . x2 (λ x16 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . λ x17 . 0) (λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x16 x17 x18 . 0) (λ x16 . 0) 0 0)))) = x3 (λ x9 : ι → ((ι → ι) → ι) → ι . setsum (x3 (λ x10 : ι → ((ι → ι) → ι) → ι . x7) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x5 (λ x10 x11 . x3 (λ x12 : ι → ((ι → ι) → ι) → ι . x1 (λ x13 : ((ι → ι) → ι) → ι → ι . λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . 0) 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . setsum 0 0)))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10)) ⟶ False (proof)
Theorem c3fef.. : ∀ x0 : (ι → ι → ι) → ι → (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . ∀ x1 : (((ι → ι) → (ι → ι → ι) → ι) → ι → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x2 : (ι → ι) → (ι → ((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x3 : ((ι → ι → ι → ι → ι) → ι → ι) → (ι → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 . Inj0 0) (λ x9 . x2 (λ x10 . x7 (x7 0)) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . x3 (λ x14 : ι → ι → ι → ι → ι . λ x15 . setsum 0 (x3 (λ x16 : ι → ι → ι → ι → ι . λ x17 . 0) (λ x16 . 0) 0)) (λ x14 . 0) (x3 (λ x14 : ι → ι → ι → ι → ι . λ x15 . setsum 0 0) (λ x14 . x12) (x0 (λ x14 x15 . 0) 0 (λ x14 : (ι → ι) → ι . 0) (λ x14 x15 . 0))))) (x5 (x2 (λ x9 . x3 (λ x10 : ι → ι → ι → ι → ι . λ x11 . x7 0) (λ x10 . x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . 0))) = x5 (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . setsum (x9 (λ x13 . x0 (λ x14 x15 . 0) 0 (λ x14 : (ι → ι) → ι . 0) (λ x14 x15 . 0)) (λ x13 x14 . 0)) (setsum 0 (x3 (λ x13 : ι → ι → ι → ι → ι . λ x14 . 0) (λ x13 . 0) 0))) (λ x9 : ι → ι . setsum x6 (x9 (x3 (λ x10 : ι → ι → ι → ι → ι . λ x11 . 0) (λ x10 . 0) 0))) (λ x9 : (ι → ι) → ι . λ x10 x11 . Inj0 x10))) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 . x10) (λ x9 . x7 0 0 (λ x10 . 0)) (x7 (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x2 (λ x13 . x2 (λ x14 . 0) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . 0)) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 x16 . x2 (λ x17 . 0) (λ x17 . λ x18 : (ι → ι) → ι . λ x19 x20 . 0))) (λ x9 : ι → ι . Inj0 (x7 0 0 (λ x10 . 0))) (λ x9 : (ι → ι) → ι . λ x10 x11 . x11)) 0 (λ x9 . x5)) = setsum 0 0) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 x7 : ι → ι . x2 (λ x9 . setsum x9 (x7 x9)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . 0) = x6 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x2 (λ x9 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . x0 (λ x13 x14 . Inj0 (Inj0 (x2 (λ x15 . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 x18 . 0)))) (x0 (λ x13 x14 . 0) x12 (λ x13 : (ι → ι) → ι . x12) (λ x13 x14 . Inj0 x12)) (λ x13 : (ι → ι) → ι . setsum (Inj0 x11) 0) (λ x13 x14 . Inj0 0)) = x0 (λ x9 . setsum (Inj1 (setsum (x6 0) (x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0))))) (x2 (λ x9 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . setsum (setsum x9 (x0 (λ x13 x14 . 0) 0 (λ x13 : (ι → ι) → ι . 0) (λ x13 x14 . 0))) (setsum (x10 (λ x13 . 0)) x12))) (λ x9 : (ι → ι) → ι . setsum (setsum (Inj1 (x6 0)) 0) (setsum (Inj0 (x7 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . 0))) 0)) (λ x9 x10 . Inj1 (Inj0 (x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x3 (λ x15 : ι → ι → ι → ι → ι . λ x16 . 0) (λ x15 . 0) 0) (λ x11 : ι → ι . setsum 0 0) (λ x11 : (ι → ι) → ι . λ x12 x13 . x12))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x9 : ι → ι . x2 (λ x10 . x9 (x2 (λ x11 . x3 (λ x12 : ι → ι → ι → ι → ι . λ x13 . 0) (λ x12 . 0) 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . setsum 0 0))) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . x0 (λ x14 x15 . 0) 0 (λ x14 : (ι → ι) → ι . Inj0 (x2 (λ x15 . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 x18 . 0))) (λ x14 x15 . x13))) (λ x9 : (ι → ι) → ι . λ x10 x11 . 0) = x2 (λ x9 . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . x10 (λ x13 . 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x5 x6 x7 . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . setsum 0 x10) (λ x9 : ι → ι . x7) (λ x9 : (ι → ι) → ι . λ x10 x11 . 0) = x7) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 x10 . x3 (λ x11 : ι → ι → ι → ι → ι . λ x12 . x11 (Inj0 (x1 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0) (λ x13 : ι → ι . 0) (λ x13 : (ι → ι) → ι . λ x14 x15 . 0))) x10 x9 (x2 (λ x13 . x0 (λ x14 x15 . 0) 0 (λ x14 : (ι → ι) → ι . 0) (λ x14 x15 . 0)) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 x16 . 0))) (λ x11 . setsum (Inj0 0) 0) (x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x11 : ι → ι . x0 (λ x12 x13 . x11 0) 0 (λ x12 : (ι → ι) → ι . Inj0 0) (λ x12 x13 . x10)) (λ x11 : (ι → ι) → ι . λ x12 x13 . x13))) x7 (λ x9 : (ι → ι) → ι . Inj1 x7) (λ x9 x10 . x10) = x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 . setsum (setsum 0 0) 0) (λ x9 . x0 (λ x10 x11 . x2 (λ x12 . x11) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 x15 . 0)) 0 (λ x10 : (ι → ι) → ι . setsum (Inj1 0) 0) (λ x10 x11 . x0 (λ x12 x13 . x12) (x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) (λ x12 : ι → ι . 0) (λ x12 : (ι → ι) → ι . λ x13 x14 . x13)) (λ x12 : (ι → ι) → ι . setsum 0 x11) (λ x12 x13 . x13))) (Inj0 x7)) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 x10 . x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . λ x12 x13 . setsum (Inj1 (Inj0 0)) (x11 (λ x14 . x11 (λ x15 . 0))))) x5 (λ x9 : (ι → ι) → ι . 0) (λ x9 x10 . x6) = setsum x7 0) ⟶ False (proof)
Theorem d6666.. : ∀ x0 : (ι → ι) → ((((ι → ι) → ι) → ι) → ι → ι → ι) → ι . ∀ x1 : ((((ι → ι) → ι) → ι) → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : ((ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι) → ι → ι . (∀ x4 : ((ι → ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ι → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x6 (x10 (λ x11 : ι → ι . λ x12 . setsum (setsum 0 0) (Inj0 0)) (λ x11 . x0 (λ x12 . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . setsum 0 0)) 0) (λ x11 . setsum (x1 (λ x12 : ((ι → ι) → ι) → ι . x0 (λ x13 . 0) (λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . 0)) (λ x12 . 0)) 0) (x2 (λ x11 . setsum 0 (x0 (λ x12 . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . 0))) 0)) (x4 (λ x9 : ι → ι → ι . x1 (λ x10 : ((ι → ι) → ι) → ι . x10 (λ x11 : ι → ι . x1 (λ x12 : ((ι → ι) → ι) → ι . 0) (λ x12 . 0))) (λ x10 . x0 (λ x11 . setsum 0 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . setsum 0 0))) (λ x9 x10 . x7) (setsum 0 (x6 x7 (λ x9 . Inj1 0) 0))) = setsum x7 (x4 (λ x9 : ι → ι → ι . setsum (x1 (λ x10 : ((ι → ι) → ι) → ι . Inj1 0) (λ x10 . setsum 0 0)) (x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 0) (setsum 0 0))) (λ x9 x10 . x1 (λ x11 : ((ι → ι) → ι) → ι . x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (Inj0 0)) (λ x11 . x7)) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . setsum (x6 0 (λ x11 . 0) 0) (setsum 0 0)) (x4 (λ x9 : ι → ι → ι . setsum 0 0) (λ x9 x10 . x9) (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj0 0) (x10 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . x0 (λ x12 . x1 (λ x13 : ((ι → ι) → ι) → ι . 0) (λ x13 . 0)) (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . Inj1 0)) 0)) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x7) (λ x9 . setsum (x2 (λ x10 . 0) 0) (x1 (λ x10 : ((ι → ι) → ι) → ι . 0) (λ x10 . 0))) (λ x9 . Inj0 x6) (setsum (setsum 0 0) (setsum 0 0)))) = Inj1 (setsum 0 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 . 0) (setsum (x6 (λ x9 : (ι → ι) → ι → ι . x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x1 (λ x12 : ((ι → ι) → ι) → ι . 0) (λ x12 . 0)) (Inj0 0))) (setsum 0 (Inj0 (x2 (λ x9 . 0) 0)))) = x6 (λ x9 : (ι → ι) → ι → ι . x0 (λ x10 . x7 0) (λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . setsum 0 (x9 (λ x13 . setsum 0 0) 0)))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . x7) (Inj0 0) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι) → ι . 0) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x2 (λ x11 . 0) (x1 (λ x11 : ((ι → ι) → ι) → ι . 0) (λ x11 . setsum 0 0)))) = x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . setsum 0 (setsum (setsum 0 0) (setsum x7 0))) (setsum (x4 (x5 (setsum 0 0) (λ x9 . x2 (λ x10 . 0) 0))) x7)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x1 (λ x9 : ((ι → ι) → ι) → ι . x9 (λ x10 : ι → ι . x10 (setsum (x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) 0) (Inj0 0)))) Inj0 = setsum (x2 (λ x9 . 0) (x2 (λ x9 . Inj1 (x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) 0)) (setsum 0 (setsum 0 0)))) 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 . 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x10) = x5 (λ x9 : (ι → ι) → ι . setsum (x2 (λ x10 . x7) (Inj1 0)) (x0 (λ x10 . x9 (λ x11 . Inj1 0)) (λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 0) (x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x0 (λ x9 . x2 (λ x10 . setsum 0 x9) x9) (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x11) = x2 (λ x9 . Inj1 (x7 (λ x10 : ι → ι → ι . setsum (Inj0 0) (x0 (λ x11 . 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0))))) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x0 (λ x11 . x2 (λ x12 . x2 (λ x13 . 0) 0) (setsum 0 0)) (λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . x3 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (setsum 0 0))) 0)) ⟶ False (proof)
Theorem 098cf.. : ∀ x0 : ((ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι) → ((ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x1 : ((((ι → ι → ι) → ι) → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → (ι → ι → (ι → ι) → ι → ι) → ι . ∀ x3 : ((((ι → ι → ι) → ι → ι) → ι) → ι) → ((ι → ι → ι → ι) → ι → ι → ι → ι) → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι) → ι . x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . Inj1 (Inj1 (setsum x6 (setsum 0 0)))) (λ x9 : ι → ι → ι → ι . λ x10 x11 x12 . x11) = Inj0 (x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι → ι . λ x11 . x0 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x3 (λ x15 : ((ι → ι → ι) → ι → ι) → ι . 0) (λ x15 : ι → ι → ι → ι . λ x16 x17 x18 . 0)) (λ x12 : (ι → ι) → ι . x0 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) (λ x13 : (ι → ι) → ι . 0)))) (λ x9 : ι → ι → ι → ι . λ x10 x11 x12 . x3 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x14 : ((ι → ι → ι) → ι) → ι . setsum 0 0) (setsum 0 0)) (λ x13 : ι → ι → ι → ι . λ x14 x15 x16 . x14)))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) (λ x9 : ι → ι → ι → ι . λ x10 x11 x12 . 0) = setsum x5 x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι → ι → ι . x2 (λ x9 . setsum (x7 (x1 (λ x10 : ((ι → ι → ι) → ι) → ι . x1 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) 0) (setsum 0 0)) x9 0 (x5 (Inj1 0) (setsum 0 0))) (x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . x13) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x0 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . x3 (λ x18 : ((ι → ι → ι) → ι → ι) → ι . 0) (λ x18 : ι → ι → ι → ι . λ x19 x20 x21 . 0)) (λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . x0 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x18 . λ x19 : ι → ι . λ x20 . 0) (λ x16 : ι → ι . λ x17 : (ι → ι) → ι → ι . λ x18 : ι → ι . 0) (λ x16 : (ι → ι) → ι . 0)) (λ x13 : (ι → ι) → ι . 0)) (λ x10 : (ι → ι) → ι . Inj1 (setsum 0 0)))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 0) = Inj1 (x7 (setsum (setsum (setsum 0 0) (Inj1 0)) (x4 (x2 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0)))) 0 (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . 0) (λ x14 : ι → ι → ι → ι . λ x15 x16 x17 . x3 (λ x18 : ((ι → ι → ι) → ι → ι) → ι . 0) (λ x18 : ι → ι → ι → ι . λ x19 x20 x21 . 0))) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x9 : (ι → ι) → ι . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x10 : (ι → ι) → ι . x7 0 0 0 0))) (Inj1 (x1 (λ x9 : ((ι → ι → ι) → ι) → ι . Inj0 0) (x1 (λ x9 : ((ι → ι → ι) → ι) → ι . 0) 0))))) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 0) = setsum (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 . x14) (λ x14 x15 . λ x16 : ι → ι . λ x17 . x15)) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x9 (x1 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) (x1 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) 0))) (λ x9 : (ι → ι) → ι . 0)) (x4 (λ x9 . setsum (x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . setsum 0 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x3 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . 0) (λ x13 : ι → ι → ι → ι . λ x14 x15 x16 . 0)) (λ x10 : (ι → ι) → ι . 0)) x5) (x2 (λ x9 . x9) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . setsum 0 0) (λ x13 : ι → ι → ι → ι . λ x14 x15 x16 . x0 (λ x17 : ι → ι . λ x18 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x19 . λ x20 : ι → ι . λ x21 . 0) (λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . 0) (λ x17 : (ι → ι) → ι . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 : ((ι → ι → ι) → ι) → ι . x7) (x4 (setsum 0 (x5 (λ x9 : (ι → ι) → ι → ι . setsum 0 0) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x9 : (ι → ι) → ι . 0))))) = setsum (setsum (x2 (setsum 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . setsum (setsum 0 0) x10)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 : ι → ι . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) (λ x15 : (ι → ι) → ι . 0)) (λ x14 : ι → ι → ι → ι . λ x15 x16 x17 . 0)) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x7) (λ x9 : (ι → ι) → ι . 0))) x7) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : ((ι → ι → ι) → ι) → ι . x9 (λ x10 : ι → ι → ι . x10 0 (x7 0))) x5 = x5) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj0 (Inj0 (x3 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . x13) (λ x14 : ι → ι → ι → ι . λ x15 x16 x17 . x2 (λ x18 . 0) (λ x18 x19 . λ x20 : ι → ι . λ x21 . 0))))) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x9 : (ι → ι) → ι . 0) = x6 (λ x9 : (ι → ι) → ι . x6 (λ x10 : (ι → ι) → ι . x1 (λ x11 : ((ι → ι → ι) → ι) → ι . Inj0 0) (Inj0 (x0 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x11 : (ι → ι) → ι . 0)))) (λ x10 x11 . Inj1 (x3 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . setsum 0 0) (λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0)))) (λ x9 x10 . x10)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum (x1 (λ x14 : ((ι → ι → ι) → ι) → ι . setsum (x3 (λ x15 : ((ι → ι → ι) → ι → ι) → ι . 0) (λ x15 : ι → ι → ι → ι . λ x16 x17 x18 . 0)) 0) (Inj0 x11)) (x1 (λ x14 : ((ι → ι → ι) → ι) → ι . x12 0) 0)) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x11 (x11 (x9 (x11 0)))) (λ x9 : (ι → ι) → ι . x5 (x6 (x6 0)) (λ x10 . 0) (λ x10 . x3 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . Inj0 (Inj1 0)) (λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . 0)) (x2 (λ x10 . x1 (λ x11 : ((ι → ι → ι) → ι) → ι . x9 (λ x12 . 0)) 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0))) = x5 (setsum 0 (x7 (λ x9 : (ι → ι) → ι . λ x10 x11 . x2 (λ x12 . x9 (λ x13 . 0)) (λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj1 0)) (Inj0 (x5 0 (λ x9 . 0) (λ x9 . 0) 0)) (λ x9 . x9))) (λ x9 . Inj0 (x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . setsum x14 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x10 : (ι → ι) → ι . 0))) (λ x9 . Inj0 (x2 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x1 (λ x14 : ((ι → ι → ι) → ι) → ι . 0) 0))) x4) ⟶ False (proof)
Theorem c1833.. : ∀ x0 : ((((ι → ι → ι) → ι) → ι) → ι) → (ι → ι → ι → ι) → ι → ((ι → ι) → ι) → ι . ∀ x1 : (((ι → ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ((ι → ι → ι → ι) → ι) → ι → ι → (ι → ι) → ι → ι . ∀ x2 : (ι → ((ι → ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → (ι → ι → ι) → ι) → ι . ∀ x3 : ((ι → ((ι → ι) → ι → ι) → ι → ι) → (((ι → ι) → ι) → (ι → ι) → ι) → ι) → (ι → ((ι → ι) → ι) → ι) → ((ι → ι) → (ι → ι) → ι) → ι → ι . (∀ x4 : (ι → ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x12 (x10 (λ x14 : ι → ι . x1 (λ x15 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x15 : ι → ι → ι → ι . 0) 0 0 (λ x15 . 0) 0) (λ x14 . x1 (λ x15 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x15 : ι → ι → ι → ι . 0) 0 0 (λ x15 . 0) 0)))) (λ x9 . λ x10 : (ι → ι) → ι . x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 . λ x16 : (ι → ι → ι) → ι . λ x17 : ι → ι . λ x18 . x0 (λ x19 : ((ι → ι → ι) → ι) → ι . 0) (λ x19 x20 x21 . x1 (λ x22 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x23 . λ x24 : ι → ι . λ x25 . 0) (λ x22 : ι → ι → ι → ι . 0) 0 0 (λ x22 . 0) 0) (Inj0 0) (λ x19 : ι → ι . Inj0 0)) (λ x15 . λ x16 : ι → ι → ι . x13 (x2 (λ x17 . λ x18 : (ι → ι → ι) → ι . λ x19 : ι → ι . λ x20 . 0) (λ x17 . λ x18 : ι → ι → ι . 0)))) (λ x11 : ι → ι → ι → ι . Inj0 (Inj1 0)) (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x11 (λ x15 x16 x17 . 0) (λ x15 . setsum 0 0)) (λ x11 : ι → ι → ι → ι . x10 (λ x12 . setsum 0 0)) (setsum 0 0) 0 (λ x11 . 0) 0) 0 (λ x11 . x0 (λ x12 : ((ι → ι → ι) → ι) → ι . Inj1 (x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : ι → ι → ι → ι . 0) 0 0 (λ x13 . 0) 0)) (λ x12 x13 x14 . 0) (x10 (λ x12 . x3 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) (λ x13 x14 : ι → ι . 0) 0)) (λ x12 : ι → ι . 0)) (x2 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 . x13 (Inj1 0)) (λ x11 . λ x12 : ι → ι → ι . x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x0 (λ x17 : ((ι → ι → ι) → ι) → ι . 0) (λ x17 x18 x19 . 0) 0 (λ x17 : ι → ι . 0)) (λ x13 : ι → ι → ι → ι . x12 0 0) 0 0 (λ x13 . setsum 0 0) (x0 (λ x13 : ((ι → ι → ι) → ι) → ι . 0) (λ x13 x14 x15 . 0) 0 (λ x13 : ι → ι . 0))))) (λ x9 x10 : ι → ι . x2 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 . x12 (λ x15 . Inj1)) (λ x11 . λ x12 : ι → ι → ι . x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . Inj0 (x15 0)) (λ x13 : ι → ι → ι → ι . x0 (λ x14 : ((ι → ι → ι) → ι) → ι . 0) (λ x14 x15 x16 . x16) (Inj1 0) (λ x14 : ι → ι . 0)) (x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : ι → ι → ι → ι . 0) (setsum 0 0) 0 (λ x13 . Inj1 0) (Inj1 0)) x11 (λ x13 . x11) 0)) 0 = Inj1 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 : ((ι → ι → ι) → ι) → ι . x0 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) (λ x12 x13 x14 . x3 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x16 : ((ι → ι) → ι) → (ι → ι) → ι . Inj1 0) (λ x15 . λ x16 : (ι → ι) → ι . 0) (λ x15 x16 : ι → ι . 0) 0) x7 (λ x12 : ι → ι . x0 (λ x13 : ((ι → ι → ι) → ι) → ι . x12 0) (λ x13 x14 x15 . x3 (λ x16 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x17 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x16 . λ x17 : (ι → ι) → ι . 0) (λ x16 x17 : ι → ι . 0) 0) (x0 (λ x13 : ((ι → ι → ι) → ι) → ι . 0) (λ x13 x14 x15 . 0) 0 (λ x13 : ι → ι . 0)) (λ x13 : ι → ι . 0))) (λ x11 x12 x13 . x12) (Inj1 (x2 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 . x13 0) (λ x11 . λ x12 : ι → ι → ι . x10 (λ x13 . 0)))) (λ x11 : ι → ι . x9)) (λ x9 x10 : ι → ι . Inj1 0) (Inj1 (x4 x6 (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x7) (λ x9 x10 : ι → ι . x6) (setsum 0 0)))) = x0 (λ x9 : ((ι → ι → ι) → ι) → ι . setsum (x2 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 : ι → ι . x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . setsum 0 0) (λ x13 : ι → ι → ι → ι . x13 0 0 0) 0 0 (λ x13 . x12 0)) (λ x10 . λ x11 : ι → ι → ι . x7)) (x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . x0 (λ x12 : ((ι → ι → ι) → ι) → ι . x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : ι → ι → ι → ι . 0) 0 0 (λ x13 . 0) 0) (λ x12 x13 x14 . 0) (x0 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) (λ x12 x13 x14 . 0) 0 (λ x12 : ι → ι . 0)) (λ x12 : ι → ι . x11 (λ x13 : ι → ι . 0) (λ x13 . 0))) (λ x10 . λ x11 : (ι → ι) → ι . x7) (λ x10 x11 : ι → ι . 0) (setsum (Inj1 0) 0))) (λ x9 x10 x11 . Inj1 (setsum (x0 (λ x12 : ((ι → ι → ι) → ι) → ι . x10) (λ x12 x13 x14 . 0) x10 (λ x12 : ι → ι . x12 0)) (x3 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x14 . λ x15 : (ι → ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x14 . λ x15 : ι → ι → ι . 0)) (λ x12 . λ x13 : (ι → ι) → ι . x10) (λ x12 x13 : ι → ι . 0) (setsum 0 0)))) (Inj1 (x5 (λ x9 : ι → ι . λ x10 . 0) (λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x11 . λ x12 : ι → ι → ι . 0)) 0))) (λ x9 : ι → ι . x7)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 . setsum x9 0) (λ x9 . λ x10 : ι → ι → ι . 0) = x6 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x2 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 . Inj0 (setsum x12 0)) (λ x9 . λ x10 : ι → ι → ι . x9) = x6 x5 (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . setsum (Inj0 (x2 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x11 . λ x12 : ι → ι → ι . 0))) (x10 (λ x11 : ι → ι . Inj0 0) (λ x11 . Inj1 0))) (λ x9 . λ x10 : (ι → ι) → ι . x7) (λ x9 x10 : ι → ι . setsum 0 (x10 (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 0 (λ x11 . 0) 0))) 0) 0 0) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 : ι → ι → ι → ι . x5 (λ x10 . λ x11 : ι → ι . λ x12 . x12)) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x10 (Inj1 0))) x6 Inj1 0 = x6) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) (λ x9 : ι → ι → ι → ι . x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . x9 (x2 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 . x13 (λ x16 x17 . 0)) (λ x12 . λ x13 : ι → ι → ι . 0)) x7 (Inj1 (Inj0 0))) (λ x10 x11 : ι → ι . x11 (Inj0 (x0 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) (λ x12 x13 x14 . 0) 0 (λ x12 : ι → ι . 0)))) (setsum x7 x6)) 0 (setsum x5 (x1 (λ x9 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) (λ x9 : ι → ι → ι → ι . x0 (λ x10 : ((ι → ι → ι) → ι) → ι . setsum 0 0) (λ x10 x11 x12 . x11) (Inj1 0) (λ x10 : ι → ι . 0)) x5 (x0 (λ x9 : ((ι → ι → ι) → ι) → ι . Inj1 0) (λ x9 x10 x11 . x10) (x2 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0) (λ x9 . λ x10 : ι → ι → ι . 0)) (λ x9 : ι → ι . x2 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x10 . λ x11 : ι → ι → ι . 0))) (λ x9 . 0) (setsum (setsum 0 0) x5))) (λ x9 . Inj0 (Inj0 0)) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . setsum (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x11 (λ x15 x16 x17 . 0) (λ x15 . 0)) (λ x11 : ι → ι → ι → ι . 0) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x11 x12 : ι → ι . 0) 0) (x2 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x11 . λ x12 : ι → ι → ι . 0)) (λ x11 . setsum 0 0) x6) (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . Inj0 0) (Inj0 0) (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 0 (λ x11 . 0) 0) (λ x11 . x2 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x12 . λ x13 : ι → ι → ι . 0)) (x0 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 x12 x13 . 0) 0 (λ x11 : ι → ι . 0)))) (λ x9 . λ x10 : (ι → ι) → ι . x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . 0) x9 (setsum x9 (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 0 (λ x11 . 0) 0)) (λ x11 . x10 (λ x12 . x9)) (setsum x6 x6)) (λ x9 x10 : ι → ι . setsum (Inj0 (Inj0 0)) (setsum (x10 0) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x11 x12 : ι → ι . 0) 0))) (Inj1 0)) = x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . Inj1 x7) (λ x9 . λ x10 : (ι → ι) → ι . x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . x3 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι . setsum (x0 (λ x16 : ((ι → ι → ι) → ι) → ι . 0) (λ x16 x17 x18 . 0) 0 (λ x16 : ι → ι . 0)) (x14 0 (λ x16 : ι → ι . λ x17 . 0) 0)) (λ x14 . λ x15 : (ι → ι) → ι . x1 (λ x16 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 . x18 0) (λ x16 : ι → ι → ι → ι . x15 (λ x17 . 0)) (x0 (λ x16 : ((ι → ι → ι) → ι) → ι . 0) (λ x16 x17 x18 . 0) 0 (λ x16 : ι → ι . 0)) (x0 (λ x16 : ((ι → ι → ι) → ι) → ι . 0) (λ x16 x17 x18 . 0) 0 (λ x16 : ι → ι . 0)) (λ x16 . x14) x14) (λ x14 x15 : ι → ι . 0)) (λ x11 : ι → ι → ι → ι . setsum (x2 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x12 . λ x13 : ι → ι → ι . x13 0 0)) (x0 (λ x12 : ((ι → ι → ι) → ι) → ι . x10 (λ x13 . 0)) (λ x12 x13 x14 . x0 (λ x15 : ((ι → ι → ι) → ι) → ι . 0) (λ x15 x16 x17 . 0) 0 (λ x15 : ι → ι . 0)) (Inj1 0) (λ x12 : ι → ι . 0))) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . x10 (λ x13 . x1 (λ x14 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x14 : ι → ι → ι → ι . 0) 0 0 (λ x14 . 0) 0)) (λ x11 . λ x12 : (ι → ι) → ι . x3 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . x12 (λ x15 . 0)) (λ x13 . λ x14 : (ι → ι) → ι . 0) (λ x13 x14 : ι → ι . x3 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x16 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . 0) (λ x15 x16 : ι → ι . 0) 0) x11) (λ x11 x12 : ι → ι . x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x13 (λ x17 x18 x19 . 0) (λ x17 . 0)) (λ x13 : ι → ι → ι → ι . 0) (setsum 0 0) (x12 0) (λ x13 . 0) 0) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x11 x12 : ι → ι . x2 (λ x13 . λ x14 : (ι → ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x13 . λ x14 : ι → ι → ι . 0)) x6)) (x2 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x11 . λ x12 : ι → ι → ι . x3 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . Inj1 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) (λ x13 x14 : ι → ι . x3 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x16 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . 0) (λ x15 x16 : ι → ι . 0) 0) 0)) (λ x11 . setsum x9 (Inj0 (x10 (λ x12 . 0)))) (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x11 (λ x15 x16 x17 . x16) (λ x15 . setsum 0 0)) (λ x11 : ι → ι → ι → ι . 0) (setsum (Inj0 0) (x0 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 x12 x13 . 0) 0 (λ x11 : ι → ι . 0))) x6 (λ x11 . setsum 0 (setsum 0 0)) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . x3 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) (λ x13 x14 : ι → ι . 0) 0) (λ x11 x12 : ι → ι . x11 0) x9))) (λ x9 x10 : ι → ι . setsum (setsum x6 (setsum (x1 (λ x11 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 0 (λ x11 . 0) 0) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x11 x12 : ι → ι . 0) 0))) (x9 (x9 (setsum 0 0)))) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . x9 (x0 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 x12 x13 . x13) (x0 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 x12 x13 . 0) 0 (λ x11 : ι → ι . 0)) (λ x11 : ι → ι . x2 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x12 . λ x13 : ι → ι → ι . 0))) (λ x11 : ι → ι . λ x12 . x2 (λ x13 . λ x14 : (ι → ι → ι) → ι . λ x15 : ι → ι . λ x16 . x0 (λ x17 : ((ι → ι → ι) → ι) → ι . 0) (λ x17 x18 x19 . 0) 0 (λ x17 : ι → ι . 0)) (λ x13 . λ x14 : ι → ι → ι . setsum 0 0)) (Inj1 (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x11 x12 : ι → ι . 0) 0))) (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 x10 : ι → ι . 0) x7)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → ι . x0 (λ x9 : ((ι → ι → ι) → ι) → ι . x5 (λ x10 . x6 0)) (λ x9 x10 x11 . x10) (x2 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 . x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . Inj0 (x3 (λ x17 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x18 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x17 . λ x18 : (ι → ι) → ι . 0) (λ x17 x18 : ι → ι . 0) 0)) (λ x13 : ι → ι → ι → ι . setsum (setsum 0 0) 0) (x0 (λ x13 : ((ι → ι → ι) → ι) → ι . x2 (λ x14 . λ x15 : (ι → ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x14 . λ x15 : ι → ι → ι . 0)) (λ x13 x14 x15 . x0 (λ x16 : ((ι → ι → ι) → ι) → ι . 0) (λ x16 x17 x18 . 0) 0 (λ x16 : ι → ι . 0)) x9 (λ x13 : ι → ι . setsum 0 0)) (setsum (setsum 0 0) (x0 (λ x13 : ((ι → ι → ι) → ι) → ι . 0) (λ x13 x14 x15 . 0) 0 (λ x13 : ι → ι . 0))) (λ x13 . Inj1 0) (x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x15 0) (λ x13 : ι → ι → ι → ι . x11 0) (x10 (λ x13 x14 . 0)) (setsum 0 0) (λ x13 . x11 0) (x1 (λ x13 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : ι → ι → ι → ι . 0) 0 0 (λ x13 . 0) 0))) (λ x9 . λ x10 : ι → ι → ι . setsum (x0 (λ x11 : ((ι → ι → ι) → ι) → ι . x1 (λ x12 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x12 : ι → ι → ι → ι . 0) 0 0 (λ x12 . 0) 0) (λ x11 x12 x13 . x10 0 0) x9 (λ x11 : ι → ι . x9)) 0)) (λ x9 : ι → ι . x2 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : ((ι → ι → ι) → ι) → ι . setsum 0 (Inj1 0)) (λ x14 x15 x16 . 0) (Inj0 (x0 (λ x14 : ((ι → ι → ι) → ι) → ι . 0) (λ x14 x15 x16 . 0) 0 (λ x14 : ι → ι . 0))) (λ x14 : ι → ι . 0)) (λ x10 . λ x11 : ι → ι → ι . x2 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 . x0 (λ x16 : ((ι → ι → ι) → ι) → ι . x3 (λ x17 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x18 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x17 . λ x18 : (ι → ι) → ι . 0) (λ x17 x18 : ι → ι . 0) 0) (λ x16 x17 x18 . setsum 0 0) (x1 (λ x16 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0) (λ x16 : ι → ι → ι → ι . 0) 0 0 (λ x16 . 0) 0) (λ x16 : ι → ι . x1 (λ x17 : (ι → ι → ι → ι) → (ι → ι) → ι . λ x18 . λ x19 : ι → ι . λ x20 . 0) (λ x17 : ι → ι → ι → ι . 0) 0 0 (λ x17 . 0) 0)) (λ x12 . λ x13 : ι → ι → ι . x12))) = Inj1 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . Inj1 0) (λ x9 . setsum (x5 (λ x10 . x0 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 x12 x13 . 0) 0 (λ x11 : ι → ι . 0))) 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 : ((ι → ι → ι) → ι) → ι . x7) (λ x9 x10 x11 . Inj0 x10) (Inj0 x6) (λ x9 : ι → ι . x7) = x7) ⟶ False (proof)
Theorem 464b5.. : ∀ x0 : (ι → ι) → ι → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι) → (((ι → ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι → ι) → ι . ∀ x2 : (ι → ι) → ι → (ι → (ι → ι) → ι) → ι . ∀ x3 : (ι → ((ι → ι) → ι) → ι) → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . λ x10 : (ι → ι) → ι . x9) 0 = x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x6 : (ι → ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x3 (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 . 0) (setsum 0 x7) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x3 (λ x13 . λ x14 : (ι → ι) → ι . 0) (Inj0 (x2 (λ x13 . 0) 0 (λ x13 . λ x14 : ι → ι . 0)))) (λ x11 : ι → ι . x7) (λ x11 . x0 (λ x12 . x2 (λ x13 . x12) (x2 (λ x13 . 0) 0 (λ x13 . λ x14 : ι → ι . 0)) (λ x13 . λ x14 : ι → ι . x2 (λ x15 . 0) 0 (λ x15 . λ x16 : ι → ι . 0))) (setsum x11 x9) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x3 (λ x14 . λ x15 : (ι → ι) → ι . 0) (x0 (λ x14 . 0) 0 (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) (λ x14 : ι → ι . 0) (λ x14 . 0))) (λ x12 : ι → ι . setsum 0 (setsum 0 0)) (λ x12 . x2 (λ x13 . setsum 0 0) (x0 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 : ι → ι . 0) (λ x13 . 0)) (λ x13 . λ x14 : ι → ι . setsum 0 0)))) (x6 (λ x9 x10 . 0) 0 (λ x9 . x3 (λ x10 . λ x11 : (ι → ι) → ι . Inj0 (x11 (λ x12 . 0))) (x1 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 . Inj0 0) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . x11) (λ x10 . Inj1 0) (λ x10 x11 . 0)))) = x6 (λ x9 x10 . Inj0 0) (x5 (λ x9 : ι → ι → ι . λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 . Inj0 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . x10) (λ x12 . x11) (λ x12 x13 . x2 (λ x14 . setsum 0 0) (Inj0 0) (λ x14 . λ x15 : ι → ι . 0)))) (λ x9 . x3 (λ x10 . λ x11 : (ι → ι) → ι . x2 (λ x12 . x11 (λ x13 . x1 (λ x14 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 . 0) (λ x14 : (ι → ι → ι) → ι → ι . λ x15 . 0) (λ x14 . 0) (λ x14 x15 . 0))) (x11 (λ x12 . 0)) (λ x12 . λ x13 : ι → ι . x10)) (x2 (λ x10 . setsum (x1 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 . 0) (λ x11 : (ι → ι → ι) → ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 x12 . 0)) x9) 0 (λ x10 . λ x11 : ι → ι . x9)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x9 . x9) (Inj1 (x5 (λ x9 : (ι → ι) → ι . 0))) (λ x9 . λ x10 : ι → ι . Inj0 (Inj1 (setsum (x0 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x11 : ι → ι . 0) (λ x11 . 0)) x7))) = x5 (λ x9 : (ι → ι) → ι . Inj1 (Inj1 (x1 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 . x1 (λ x12 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 . 0) (λ x12 x13 . 0)) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . x3 (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (λ x10 . x10) (λ x10 x11 . 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . x9) 0 (λ x9 . λ x10 : ι → ι . 0) = setsum (x2 (λ x9 . 0) 0 (λ x9 . λ x10 : ι → ι . x7)) (Inj0 x5)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) (x7 (Inj0 x10)) (λ x11 . λ x12 : ι → ι . x3 (λ x13 . λ x14 : (ι → ι) → ι . x12 (setsum 0 0)) 0)) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . x6 (λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 . Inj1 (x0 (λ x15 . 0) 0 (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0) (λ x15 : ι → ι . 0) (λ x15 . 0))) (setsum (x2 (λ x14 . 0) 0 (λ x14 . λ x15 : ι → ι . 0)) (setsum 0 0)) (λ x14 . λ x15 : ι → ι . 0))) (λ x9 . Inj0 0) (λ x9 x10 . x7 (x7 x9)) = Inj0 (x0 (λ x9 . setsum (setsum x9 (setsum 0 0)) (x0 (λ x10 . 0) (x2 (λ x10 . 0) 0 (λ x10 . λ x11 : ι → ι . 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x0 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0) (λ x12 . 0)) (λ x10 : ι → ι . x6 (λ x11 . λ x12 : ι → ι . λ x13 . 0)) (λ x10 . x1 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 . 0) (λ x11 : (ι → ι → ι) → ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 x12 . 0)))) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 : ι → ι . 0) (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 . x7 (setsum 0 0)) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . x1 (λ x12 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 . x2 (λ x14 . 0) 0 (λ x14 . λ x15 : ι → ι . 0)) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 . x0 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 : ι → ι . 0) (λ x13 . 0)) (λ x12 x13 . 0)) x7 (λ x10 x11 . x11)))) ⟶ (∀ x4 : (ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ι . x1 (λ x9 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . x6) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . setsum (Inj0 (x0 (λ x11 . x0 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0) (λ x12 . 0)) (Inj1 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x11 (λ x13 . 0) 0) (λ x11 : ι → ι . x11 0) (λ x11 . x1 (λ x12 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 . 0) (λ x12 x13 . 0)))) (x9 (λ x11 x12 . x10) 0)) (λ x9 . x5 (λ x10 . λ x11 : ι → ι . λ x12 . 0)) (λ x9 x10 . Inj1 0) = x6) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 . 0) (x0 (λ x9 . 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 . x9)) (x1 (λ x9 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) x6 (λ x11 . λ x12 : ι → ι . x10)) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . x3 (λ x11 . λ x12 : (ι → ι) → ι . setsum 0 0) (x3 (λ x11 . λ x12 : (ι → ι) → ι . 0) 0)) (λ x9 . Inj0 (x0 (λ x10 . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x10 : ι → ι . 0) (λ x10 . 0))) (λ x9 x10 . Inj0 (Inj1 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x10 (Inj0 (x1 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 . 0) (λ x11 : (ι → ι → ι) → ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 x12 . 0)))) (λ x9 : ι → ι . setsum (Inj0 0) (x9 (x9 0))) (λ x9 . Inj0 (Inj0 (Inj1 0)))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x0 (λ x11 . x3 (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (x10 x6) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . Inj0 0) (λ x11 : ι → ι . x0 (λ x12 . 0) (x0 (λ x12 . setsum 0 0) (x2 (λ x12 . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x3 (λ x14 . λ x15 : (ι → ι) → ι . 0) 0) (λ x12 : ι → ι . x2 (λ x13 . 0) 0 (λ x13 . λ x14 : ι → ι . 0)) (λ x12 . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x1 (λ x14 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 . x12 (λ x16 . 0) 0) (λ x14 : (ι → ι → ι) → ι → ι . λ x15 . setsum 0 0) (λ x14 . setsum 0 0) (λ x14 x15 . 0)) (λ x12 : ι → ι . setsum (x3 (λ x13 . λ x14 : (ι → ι) → ι . 0) 0) 0) (λ x12 . x12)) (λ x11 . 0)) (λ x9 : ι → ι . setsum (x3 (λ x10 . λ x11 : (ι → ι) → ι . x11 (λ x12 . 0)) (Inj0 0)) (setsum x6 (x5 (λ x10 : ι → ι . x9 0) 0 (λ x10 . setsum 0 0) (x5 (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0)))) (λ x9 . x6) = x0 (λ x9 . x9) (x3 (λ x9 . λ x10 : (ι → ι) → ι . Inj1 (Inj0 0)) x6) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . setsum (x2 (λ x11 . setsum (x9 (λ x12 . 0) 0) (x0 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0) (λ x12 . 0))) (x2 (λ x11 . 0) x6 (λ x11 . λ x12 : ι → ι . 0)) (λ x11 . λ x12 : ι → ι . x0 (λ x13 . x1 (λ x14 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 . 0) (λ x14 : (ι → ι → ι) → ι → ι . λ x15 . 0) (λ x14 . 0) (λ x14 x15 . 0)) (Inj1 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . Inj0 0) (λ x13 : ι → ι . x2 (λ x14 . 0) 0 (λ x14 . λ x15 : ι → ι . 0)) (λ x13 . 0))) (Inj1 0)) (λ x9 : ι → ι . setsum (x9 (x9 (x5 (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0))) 0) (λ x9 . Inj1 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 . x3 (λ x10 . λ x11 : (ι → ι) → ι . x9) 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 : ι → ι . 0) (λ x9 . 0) = x3 (λ x9 . λ x10 : (ι → ι) → ι . Inj0 x6) x4) ⟶ False (proof)
Theorem 83068.. : ∀ x0 : (ι → ι) → ι → ι → ι → ι → ι → ι . ∀ x1 : (((((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι) → ι → ι) → ι → (((ι → ι) → ι → ι) → ι) → ι . ∀ x2 : ((ι → ((ι → ι) → ι) → ι) → ι) → ((ι → ι) → ι → (ι → ι) → ι) → ι . ∀ x3 : (((ι → (ι → ι) → ι) → ι) → (ι → ι → ι → ι) → ι) → ((ι → ι → ι → ι) → ι) → (ι → ι) → ι . (∀ x4 : ((ι → ι) → ι) → ι → ι . ∀ x5 : (ι → ι → ι) → (ι → ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → ι → ι → ι . x3 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 : ι → ι → ι → ι . 0) (λ x9 . 0) = x7 (Inj1 (Inj0 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum 0 0)))) 0 (setsum 0 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . x0 (λ x10 . x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 : ι → ι → ι → ι . 0) (λ x11 . 0)) (x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x11 . 0) 0 (λ x10 : (ι → ι) → ι → ι . 0)) 0 (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0)) 0 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x9 (x2 (λ x12 : ι → ((ι → ι) → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0))))) (x3 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 : ι → ι → ι → ι . 0) (λ x9 . 0))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x3 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 : ι → ι → ι → ι . x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . x10 (x3 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 : ι → ι → ι → ι . 0) (λ x13 : ι → ι → ι → ι . Inj1 0) (λ x13 . Inj1 0)) (x0 (λ x13 . x12 0 0 0) (x0 (λ x13 . 0) 0 0 0 0 0) (Inj0 0) (setsum 0 0) (x10 0 0 0) (x0 (λ x13 . 0) 0 0 0 0 0)) (x9 (λ x13 . λ x14 : ι → ι . x3 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 : ι → ι → ι → ι . 0) (λ x15 : ι → ι → ι → ι . 0) (λ x15 . 0)))) (λ x11 : ι → ι → ι → ι . Inj0 (x1 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x13 . Inj1 0) 0 (λ x12 : (ι → ι) → ι → ι . x10 0 0 0))) (λ x11 . 0)) (λ x9 : ι → ι → ι → ι . x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x11 . x2 (λ x12 : ι → ((ι → ι) → ι) → ι . x3 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 : ι → ι → ι → ι . x1 (λ x15 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x16 . 0) 0 (λ x15 : (ι → ι) → ι → ι . 0)) (λ x13 : ι → ι → ι → ι . setsum 0 0) (λ x13 . x12 0 (λ x14 : ι → ι . 0))) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . x3 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 : ι → ι → ι → ι . setsum 0 0) (λ x15 : ι → ι → ι → ι . Inj0 0) (λ x15 . x1 (λ x16 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x17 . 0) 0 (λ x16 : (ι → ι) → ι → ι . 0)))) (setsum 0 (Inj0 (x5 0))) (λ x10 : (ι → ι) → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x13 . x1 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x15 . 0) 0 (λ x14 : (ι → ι) → ι → ι . 0)) (setsum 0 0) (λ x12 : (ι → ι) → ι → ι . Inj1 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . x3 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 : ι → ι → ι → ι . x0 (λ x16 . 0) 0 0 0 0 0) (λ x14 : ι → ι → ι → ι . x1 (λ x15 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x16 . 0) 0 (λ x15 : (ι → ι) → ι → ι . 0)) (λ x14 . x0 (λ x15 . 0) 0 0 0 0 0)))) (λ x9 . 0) = setsum 0 (x0 (λ x9 . Inj1 0) 0 (setsum 0 (x5 (x4 0 0 0 0))) (Inj0 (x7 (λ x9 x10 x11 . setsum 0 0))) (setsum 0 (setsum (x4 0 0 0 0) (x6 0 0 (λ x9 . 0) 0))) (x6 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . x2 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x0 (λ x12 . 0) 0 0 0 0 0)) (Inj0 0) (λ x9 . x5 0) (x4 (Inj0 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 . 0) 0 (λ x9 : (ι → ι) → ι → ι . 0)) 0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → ((ι → ι) → ι) → ι . setsum 0 (x9 (x5 (x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x11 . 0) 0 (λ x10 : (ι → ι) → ι → ι . 0))) (λ x10 : ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x13 . 0) 0 (λ x12 : (ι → ι) → ι → ι . 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0)))) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x13 . x0 (λ x14 . x14) 0 (x0 (λ x14 . setsum 0 0) (x1 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x15 . 0) 0 (λ x14 : (ι → ι) → ι → ι . 0)) (x3 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 : ι → ι → ι → ι . 0) (λ x14 : ι → ι → ι → ι . 0) (λ x14 . 0)) (x11 0) (x2 (λ x14 : ι → ((ι → ι) → ι) → ι . 0) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . 0)) x10) (x1 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x15 . Inj0 0) 0 (λ x14 : (ι → ι) → ι → ι . x12 (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . 0))) (Inj1 (x11 0)) (setsum (x12 (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0)) (x12 (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0)))) (x11 (Inj0 (x2 (λ x12 : ι → ((ι → ι) → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0)))) (λ x12 : (ι → ι) → ι → ι . 0)) = x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 . x9 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . Inj0 (x3 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 : ι → ι → ι → ι . setsum 0 0) (λ x14 : ι → ι → ι → ι . Inj0 0) (λ x14 . setsum 0 0)))) x7 (λ x9 : (ι → ι) → ι → ι . Inj0 (setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x11 . setsum 0 0) (Inj0 0) (λ x10 : (ι → ι) → ι → ι . 0)) (setsum (x0 (λ x10 . 0) 0 0 0 0 0) 0)))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι) → ι) → ι → ι . x2 (λ x9 : ι → ((ι → ι) → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x11 (Inj1 (x1 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x13 . x1 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x15 . 0) 0 (λ x14 : (ι → ι) → ι → ι . 0)) (x3 (λ x12 : (ι → (ι → ι) → ι) → ι . λ x13 : ι → ι → ι → ι . 0) (λ x12 : ι → ι → ι → ι . 0) (λ x12 . 0)) (λ x12 : (ι → ι) → ι → ι . 0)))) = x4 (x4 (Inj0 (setsum (x5 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) 0)) (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → ((ι → ι) → ι) → ι . x9 (setsum 0 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0))) (λ x9 : ι → ι . λ x10 . x10)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 . 0) (Inj0 0) (λ x9 : (ι → ι) → ι → ι . Inj0 (Inj1 0)) = x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum (Inj0 0) x6) (x3 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 : ι → ι → ι → ι . x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . Inj0 (x11 (λ x13 . λ x14 : ι → ι . 0))) (λ x11 : ι → ι → ι → ι . 0) (λ x11 . 0)) (λ x9 : ι → ι → ι → ι . setsum (x5 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x0 (λ x12 . 0) 0 0 0 0 0) (setsum 0 0) (λ x10 . x0 (λ x11 . 0) 0 0 0 0 0) (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0))) 0) (λ x9 . x7)) (λ x9 . x3 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 : ι → ι → ι → ι . Inj0 (x10 x9 x7 (x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 : ι → ι → ι → ι . 0) (λ x11 . 0)))) (λ x10 . Inj1 (setsum (setsum 0 0) (setsum 0 0)))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 . x0 (λ x11 . x11) (Inj1 (x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . Inj0 0) (λ x11 : ι → ι → ι → ι . x10) (λ x11 . x10))) (setsum x10 0) (Inj0 (x7 (λ x11 x12 x13 . Inj0 0))) (x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . setsum 0 (Inj1 0)) (λ x11 : ι → ι → ι → ι . Inj1 (x3 (λ x12 : (ι → (ι → ι) → ι) → ι . λ x13 : ι → ι → ι → ι . 0) (λ x12 : ι → ι → ι → ι . 0) (λ x12 . 0))) (λ x11 . 0)) (x7 (λ x11 x12 x13 . x0 (λ x14 . 0) (x0 (λ x14 . 0) 0 0 0 0 0) (x1 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x15 . 0) 0 (λ x14 : (ι → ι) → ι → ι . 0)) (x3 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 : ι → ι → ι → ι . 0) (λ x14 : ι → ι → ι → ι . 0) (λ x14 . 0)) x11 0))) (x3 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 : ι → ι → ι → ι . x2 (λ x10 : ι → ((ι → ι) → ι) → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x13 . 0) 0 (λ x12 : (ι → ι) → ι → ι . 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . x12 (Inj0 0))) (λ x9 . 0)) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x11 . x3 (λ x12 : (ι → (ι → ι) → ι) → ι . λ x13 : ι → ι → ι → ι . x0 (λ x14 . x14) 0 (x12 (λ x14 . λ x15 : ι → ι . 0)) x11 0 0) (λ x12 : ι → ι → ι → ι . x3 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 : ι → ι → ι → ι . setsum 0 0) (λ x13 : ι → ι → ι → ι . x1 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x15 . 0) 0 (λ x14 : (ι → ι) → ι → ι . 0)) (λ x13 . 0)) (λ x12 . Inj1 (setsum 0 0))) (x5 (λ x10 : ι → ι → ι . x1 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x12 . x11 (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0)) (x1 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x12 . 0) 0 (λ x11 : (ι → ι) → ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . setsum 0 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x12 . setsum 0 0) 0 (λ x11 : (ι → ι) → ι → ι . 0)) (λ x10 . 0) (x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x11 . 0) 0 (λ x10 : (ι → ι) → ι → ι . x7 (λ x11 x12 x13 . 0)))) (λ x10 : (ι → ι) → ι → ι . 0)) = setsum (x3 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 : ι → ι → ι → ι . x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . Inj1 (x12 0 0 0)) (λ x11 : ι → ι → ι → ι . x2 (λ x12 : ι → ((ι → ι) → ι) → ι . Inj1 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . x3 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 : ι → ι → ι → ι . 0) (λ x15 : ι → ι → ι → ι . 0) (λ x15 . 0))) (λ x11 . x10 (x2 (λ x12 : ι → ((ι → ι) → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0)) (setsum 0 0) (x9 (λ x12 . λ x13 : ι → ι . 0)))) (λ x9 : ι → ι → ι → ι . x6 (λ x10 : ι → ι . 0) 0 (λ x10 . x7 (λ x11 x12 x13 . x11)) (Inj0 (x9 0 0 0))) (λ x9 . Inj0 0)) 0) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 . 0) 0 0 (setsum (setsum x7 0) (Inj1 (Inj1 (setsum 0 0)))) 0 (x5 0) = setsum 0 0) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x7 . x0 (λ x9 . 0) 0 (x4 (λ x9 : (ι → ι) → ι → ι . 0)) (setsum 0 0) (Inj1 0) (x0 (λ x9 . x6 (λ x10 : ι → ι . setsum (x3 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 : ι → ι → ι → ι . 0) (λ x11 . 0)) (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . 0) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0))) x9 (λ x10 . x7)) 0 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . Inj1 (setsum 0 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x2 (λ x12 : ι → ((ι → ι) → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . Inj0 0))) 0 (x0 (λ x9 . 0) x7 0 (x3 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 : ι → ι → ι → ι . setsum 0 0) (λ x9 : ι → ι → ι → ι . setsum 0 0) (λ x9 . x6 (λ x10 : ι → ι . 0) 0 (λ x10 . 0))) (Inj1 (setsum 0 0)) (Inj1 (x4 (λ x9 : (ι → ι) → ι → ι . 0)))) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . x9 x7 (λ x10 : ι → ι . x7)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . Inj0 x7))) = x4 (λ x9 : (ι → ι) → ι → ι . setsum (Inj1 0) (setsum x7 (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . setsum 0 0))))) ⟶ False (proof)
Theorem acb5d.. : ∀ x0 : (ι → (ι → ι) → ι → (ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x1 : (ι → ι → (ι → ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι . ∀ x2 : (((((ι → ι) → ι → ι) → (ι → ι) → ι) → ι) → ι → (ι → ι → ι) → ι) → ι → ι → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → ι → ι → ι . x3 (λ x9 . x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . setsum 0 0) x9 (Inj0 x6)) x4 = setsum x6 (Inj0 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι → ι . x3 (λ x9 . x7 (λ x10 : (ι → ι) → ι . setsum (setsum (x0 (λ x11 . λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0) 0 (λ x11 . 0)) (Inj1 0)) (x10 (λ x11 . Inj1 0))) (Inj0 (Inj1 0))) (x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . setsum 0 (setsum 0 (x0 (λ x13 . λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . 0) 0 (λ x13 . 0)))) (x4 (x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) x5 (λ x9 . 0))) (λ x9 . x0 (λ x10 . λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . x10) (x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . x12 0 0) (x0 (λ x10 . λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0) 0 (λ x10 . 0)) (x1 (λ x10 x11 . λ x12 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0))) (λ x10 . 0))) = Inj1 (x1 (λ x9 x10 . λ x11 : ι → ι → ι . x7 (λ x12 : (ι → ι) → ι . x12 (λ x13 . x2 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x15 . λ x16 : ι → ι → ι . 0) 0 0)) 0) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 x11 . λ x12 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . x10 (λ x13 x14 . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x11 (x0 (λ x12 . λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . setsum (setsum 0 0) x14) (x11 (x9 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) 0) (λ x12 . x1 (λ x13 x14 . λ x15 : ι → ι → ι . Inj1 0) (λ x13 : (ι → ι → ι) → ι . x10))) (x11 (x1 (λ x12 x13 . λ x14 : ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . Inj1 0)) 0)) (x1 (λ x9 x10 . λ x11 : ι → ι → ι . x9) (λ x9 : (ι → ι → ι) → ι . x6 (x9 (λ x10 x11 . x11)))) (x3 (λ x9 . Inj0 x5) (Inj1 (x1 (λ x9 x10 . λ x11 : ι → ι → ι . x0 (λ x12 . λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . 0) 0 (λ x12 . 0)) (λ x9 : (ι → ι → ι) → ι . setsum 0 0)))) = Inj0 (x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . x2 (λ x13 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x14 . λ x15 : ι → ι → ι . x13 (λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0)) (Inj1 (setsum 0 0)) x9) 0 (λ x9 . 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . Inj0 (Inj0 (setsum (x9 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) (Inj1 0)))) (x3 (λ x9 . Inj0 x5) x7) (Inj0 (x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . 0) (setsum (Inj1 0) (x3 (λ x9 . 0) 0)) 0)) = x3 (λ x9 . x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . x10 (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x0 (λ x15 . λ x16 : ι → ι . λ x17 . λ x18 : ι → ι . x3 (λ x19 . 0) 0) 0 (λ x15 . x0 (λ x16 . λ x17 : ι → ι . λ x18 . λ x19 : ι → ι . 0) 0 (λ x16 . 0)))) (setsum (setsum (Inj1 0) 0) (x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . 0) (Inj0 0) (Inj1 0))) x5) (setsum (x1 (λ x9 x10 . λ x11 : ι → ι → ι . x7) (λ x9 : (ι → ι → ι) → ι . Inj1 (x1 (λ x10 x11 . λ x12 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0)))) (Inj0 (setsum x5 (x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) 0 (λ x9 . 0)))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 x10 . λ x11 : ι → ι → ι . Inj1 (Inj1 x10)) (λ x9 : (ι → ι → ι) → ι . setsum x5 (setsum x7 0)) = x6) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . λ x11 : ι → ι → ι . setsum 0 (x2 (λ x12 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . x0 (λ x15 . λ x16 : ι → ι . λ x17 . λ x18 : ι → ι . 0) (x14 0 0) (λ x15 . 0)) x10 0)) (λ x9 : (ι → ι → ι) → ι . Inj0 0) = setsum (x1 (λ x9 x10 . λ x11 : ι → ι → ι . x0 (λ x12 . λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . setsum (x3 (λ x16 . 0) 0) x14) (setsum 0 (Inj0 0)) (λ x12 . 0)) (λ x9 : (ι → ι → ι) → ι . Inj1 x6)) 0) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) (x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . 0) (setsum (setsum 0 0) x5) 0) (λ x9 . x0 (λ x10 . λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . x11 (x3 (λ x14 . 0) (x1 (λ x14 x15 . λ x16 : ι → ι → ι . 0) (λ x14 : (ι → ι → ι) → ι . 0)))) (x0 (λ x10 . λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0) 0 (λ x10 . x0 (λ x11 . λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . x14 0) (x1 (λ x11 x12 . λ x13 : ι → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0)) (λ x11 . x3 (λ x12 . 0) 0))) (λ x10 . setsum x10 x10)) = x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . x11) (Inj0 (Inj1 0)) (λ x9 . setsum (x3 (λ x10 . setsum 0 0) 0) 0)) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) 0 (λ x9 . x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . 0) x9 (x6 (λ x10 : ι → ι → ι . x2 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . x10 0 0) (Inj1 0) (x6 (λ x11 : ι → ι → ι . 0))))) = Inj0 (x1 (λ x9 x10 . λ x11 : ι → ι → ι . setsum (x0 (λ x12 . λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . x15 0) (x1 (λ x12 x13 . λ x14 : ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . 0)) (λ x12 . x3 (λ x13 . 0) 0)) (x3 (λ x12 . 0) (x3 (λ x12 . 0) 0))) (λ x9 : (ι → ι → ι) → ι . setsum (setsum (x6 (λ x10 : ι → ι → ι . 0)) (x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . 0) 0 0)) 0))) ⟶ False (proof)
Theorem 60ce1.. : ∀ x0 : (ι → ι → ι) → (((ι → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι) → (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → ι → ι → ι → ι → ι . ∀ x2 : (ι → (ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x3 : (((ι → ι → ι) → ι → ι → ι → ι) → ι → ((ι → ι) → ι → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 : (ι → ι → ι) → ι → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) x7 (x9 (λ x12 x13 . x2 (λ x14 . λ x15 : ι → ι → ι . 0) (λ x14 : ι → ι . x12)) (x11 (λ x12 . x1 (λ x13 . 0) 0 0 0 0 0) (x3 (λ x12 : (ι → ι → ι) → ι → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) 0 0)) (setsum 0 (Inj0 0)) x7)) (x5 0 (λ x9 : ι → ι . 0)) (x1 (λ x9 . x7) (x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) 0 (x1 (λ x9 . setsum 0 0) 0 0 (x2 (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 : ι → ι . 0)) (Inj0 0) 0)) (Inj0 0) (x0 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : (ι → ι → ι) → ι → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x0 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 : ι → ι . λ x14 . 0)) 0 (x0 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . 0) (λ x10 : (ι → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . 0))) (λ x9 : ι → ι . λ x10 . setsum 0 (x6 0))) (x5 (x2 (λ x9 . λ x10 : ι → ι → ι . x2 (λ x11 . λ x12 : ι → ι → ι . 0) (λ x11 : ι → ι . 0)) (λ x9 : ι → ι . x9 0)) (λ x9 : ι → ι . x5 (Inj0 0) (λ x10 : ι → ι . x9 0))) (Inj1 (Inj1 (x2 (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 : ι → ι . 0))))) = Inj1 (Inj1 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . x1 (λ x15 . x15) 0 (setsum (x11 (λ x15 . 0) 0) (x3 (λ x15 : (ι → ι → ι) → ι → ι → ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . 0) 0 0)) 0 0 (Inj1 (x13 (λ x15 . 0) 0))) (λ x12 : (ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . 0)) (Inj1 (setsum (x4 (x6 0) (λ x9 . x6 0)) 0)) 0 = x0 (λ x9 x10 . x2 (λ x11 . λ x12 : ι → ι → ι . x12 (x1 (λ x13 . Inj0 0) 0 x9 (setsum 0 0) (x3 (λ x13 : (ι → ι → ι) → ι → ι → ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) 0 0) 0) (Inj0 0)) (λ x11 : ι → ι . Inj1 (setsum (x2 (λ x12 . λ x13 : ι → ι → ι . 0) (λ x12 : ι → ι . 0)) 0))) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . x1 (λ x12 . 0) (setsum (Inj0 (x2 (λ x12 . λ x13 : ι → ι → ι . 0) (λ x12 : ι → ι . 0))) 0) 0 0 0 (x0 (λ x12 x13 . x13) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . x3 (λ x15 : (ι → ι → ι) → ι → ι → ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . x2 (λ x18 . λ x19 : ι → ι → ι . 0) (λ x18 : ι → ι . 0)) (Inj1 0) 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . Inj1 0))) (λ x9 : (ι → ι) → ι . x7) (λ x9 : ι → ι . λ x10 . Inj1 x7)) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 . λ x10 : ι → ι → ι . x7 x9 (x7 (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x2 (λ x14 . λ x15 : ι → ι → ι . 0) (λ x14 : ι → ι . 0)) (x0 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . 0) (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . λ x12 . 0)) (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0 0)) 0)) (λ x9 : ι → ι . setsum (x1 (λ x10 . x6 (λ x11 : ι → ι → ι . 0) 0) (x1 (λ x10 . x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0 0) (x5 0 (λ x10 : ι → ι . λ x11 . 0)) (Inj1 0) (Inj1 0) (x2 (λ x10 . λ x11 : ι → ι → ι . 0) (λ x10 : ι → ι . 0)) 0) (x5 (setsum 0 0) (λ x10 : ι → ι . λ x11 . x10 0)) 0 0 (x6 (λ x10 : ι → ι → ι . setsum 0 0) 0)) (x1 (λ x10 . x9 (x9 0)) (x0 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . x2 (λ x13 . λ x14 : ι → ι → ι . 0) (λ x13 : ι → ι . 0)) (λ x10 : (ι → ι) → ι . x10 (λ x11 . 0)) (λ x10 : ι → ι . λ x11 . x11)) (x5 0 (λ x10 : ι → ι . λ x11 . x10 0)) 0 0 (Inj1 0))) = x7 (x5 0 (λ x9 : ι → ι . λ x10 . x6 (λ x11 : ι → ι → ι . 0) (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . 0) 0) (Inj0 0) (x1 (λ x11 . 0) 0 0 0 0 0)))) (Inj1 x4)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 . λ x10 : ι → ι → ι . setsum 0 x7) (λ x9 : ι → ι . Inj0 (x0 (λ x10 x11 . Inj0 x10) (λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . x10 (λ x13 x14 . Inj1 0)) (λ x10 : (ι → ι) → ι . x7) (λ x10 : ι → ι . λ x11 . x0 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . 0) (λ x12 : (ι → ι) → ι . x2 (λ x13 . λ x14 : ι → ι → ι . 0) (λ x13 : ι → ι . 0)) (λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ι → ι → ι . 0) (λ x14 : ι → ι . 0))))) = x6) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . ∀ x7 . x1 (λ x9 . x7) 0 0 (setsum (setsum (x2 (λ x9 . λ x10 : ι → ι → ι . x7) (λ x9 : ι → ι . 0)) (Inj1 (x6 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 . 0) (λ x9 . 0)))) (x0 (λ x9 x10 . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x0 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 : ι → ι . λ x14 . 0)) (λ x11 . 0) (λ x11 . 0)) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . x7) (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . x0 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . 0) (λ x11 : (ι → ι) → ι . x3 (λ x12 : (ι → ι → ι) → ι → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) 0 0) (λ x11 : ι → ι . λ x12 . Inj0 0)))) (setsum (setsum (x6 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x1 (λ x11 . 0) 0 0 0 0 0) (λ x9 . x7) (λ x9 . x1 (λ x10 . 0) 0 0 0 0 0)) (x6 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 . x1 (λ x10 . 0) 0 0 0 0 0) (λ x9 . x7))) x7) 0 = x7) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x1 (λ x9 . Inj1 0) 0 (setsum (x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x9 (λ x12 x13 . setsum 0 0) x10 (x2 (λ x12 . λ x13 : ι → ι → ι . 0) (λ x12 : ι → ι . 0)) (Inj1 0)) (Inj0 0) 0) 0) (Inj0 x4) x4 (Inj0 0) = setsum x5 0) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x7 . x0 (λ x9 x10 . x6 (λ x11 x12 . setsum 0 x9) (λ x11 : ι → ι . x9) x7) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . 0) (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . setsum (Inj0 (x0 (λ x11 x12 . x10) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . x2 (λ x14 . λ x15 : ι → ι → ι . 0) (λ x14 : ι → ι . 0)) (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . λ x12 . setsum 0 0))) (x1 (λ x11 . 0) (Inj0 x10) (x0 (λ x11 x12 . setsum 0 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . Inj0 0) (λ x11 : (ι → ι) → ι . setsum 0 0) (λ x11 : ι → ι . λ x12 . x11 0)) (x6 (λ x11 x12 . setsum 0 0) (λ x11 : ι → ι . x0 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . 0)) (Inj0 0)) (setsum (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0 0) (x6 (λ x11 x12 . 0) (λ x11 : ι → ι . 0) 0)) (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . setsum 0 0) (setsum 0 0) 0))) = x6 (λ x9 x10 . x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x12) (x6 (λ x11 x12 . 0) (λ x11 : ι → ι . x10) (x2 (λ x11 . λ x12 : ι → ι → ι . setsum 0 0) (λ x11 : ι → ι . 0))) (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x0 (λ x14 x15 . 0) (λ x14 : (ι → ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 . x3 (λ x17 : (ι → ι → ι) → ι → ι → ι → ι . λ x18 . λ x19 : (ι → ι) → ι → ι . 0) 0 0) (λ x14 : (ι → ι) → ι . setsum 0 0) (λ x14 : ι → ι . λ x15 . 0)) (Inj1 x9) (setsum (x1 (λ x11 . 0) 0 0 0 0 0) 0))) (λ x9 : ι → ι . x5) (x2 (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 : ι → ι . x7))) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x0 (λ x9 x10 . setsum (Inj1 (setsum 0 0)) x7) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . x9 (λ x12 x13 . x0 (λ x14 x15 . 0) (λ x14 : (ι → ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 . Inj0 (setsum 0 0)) (λ x14 : (ι → ι) → ι . x11) (λ x14 : ι → ι . λ x15 . 0))) (λ x9 : (ι → ι) → ι . x6 x7) (λ x9 : ι → ι . λ x10 . x7) = setsum 0 (x0 (λ x9 x10 . setsum (Inj1 0) 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj0 (setsum (setsum 0 0) (setsum 0 0))) (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . 0))) ⟶ False (proof)
Theorem 8ab24.. : ∀ x0 : (ι → ι) → ι → ι → ι → ι . ∀ x1 : (ι → ι) → ι → ι . ∀ x2 : (((ι → ι → ι) → ι) → ι) → (((ι → ι) → ι) → ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x3 : (ι → ι → ι) → ι → ι . (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 x10 . setsum (setsum 0 0) (x0 (λ x11 . x7) (Inj1 (Inj1 0)) x7 x10)) 0 = x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 x10 . x3 (λ x11 x12 . setsum x11 0) (Inj0 (x2 (λ x11 : (ι → ι → ι) → ι . x11 (λ x12 x13 . 0)) (λ x11 : (ι → ι) → ι . λ x12 . x2 (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . λ x14 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x12 0)))) (x5 (setsum (x3 (λ x9 x10 . 0) (x3 (λ x9 x10 . 0) 0))) (λ x9 : ι → ι . λ x10 . x10) (λ x9 . 0)) = x3 (λ x9 x10 . Inj1 0) (x2 (λ x9 : (ι → ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . λ x10 . x0 (λ x11 . x10) 0 0 x7) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x1 (λ x11 . x0 (λ x12 . 0) (x9 (λ x12 . 0) 0) 0 x7) 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 x11 . Inj1 (x7 (x7 0 (λ x12 . 0)) (λ x12 . x11))) (x1 (λ x10 . setsum (x9 (λ x11 x12 . 0)) (x2 (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0))) (Inj1 (x3 (λ x10 x11 . 0) 0)))) (λ x9 : (ι → ι) → ι . λ x10 . setsum (x7 (x9 (λ x11 . x2 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0))) (λ x11 . x10)) 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . setsum (x9 (λ x11 . 0) (x0 (λ x11 . x3 (λ x12 x13 . 0) 0) (x0 (λ x11 . 0) 0 0 0) (setsum 0 0) (setsum 0 0))) 0) = x3 (λ x9 x10 . Inj1 (x1 (λ x11 . 0) (x7 (setsum 0 0) (λ x11 . 0)))) (x3 (λ x9 x10 . setsum 0 (setsum (Inj1 0) (x3 (λ x11 x12 . 0) 0))) (x2 (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 . x3 (λ x11 x12 . 0) 0) (Inj0 0)) (λ x9 : (ι → ι) → ι . setsum (x7 0 (λ x10 . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 x11 . 0) (setsum (setsum 0 (x1 (λ x10 . 0) 0)) (Inj1 (x5 0)))) (λ x9 : (ι → ι) → ι . λ x10 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . setsum (x6 (λ x11 . λ x12 : ι → ι . x0 (λ x13 . 0) (x2 (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . λ x14 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0)) 0 0)) (x9 (λ x11 . x7) (Inj0 x7))) = x3 (λ x9 x10 . x2 (λ x11 : (ι → ι → ι) → ι . x7) (λ x11 : (ι → ι) → ι . λ x12 . x11 (λ x13 . x12)) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (Inj1 (x5 (x0 (λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) (x6 (λ x9 . λ x10 : ι → ι . 0)) (Inj0 0) 0)))) ⟶ (∀ x4 : ((ι → ι) → ι → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι . x1 Inj1 (setsum 0 0) = Inj0 (x7 (x0 (λ x9 . setsum 0 (x6 (λ x10 . λ x11 : ι → ι . λ x12 . 0))) 0 0 (setsum (setsum 0 0) x5)) (λ x9 : ι → ι . λ x10 . x2 (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . λ x12 . Inj0 (setsum 0 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x2 (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . λ x14 . setsum 0 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x13 (λ x15 . 0) 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x9 . setsum x9 (Inj1 (x7 (λ x10 : (ι → ι) → ι → ι . x7 (λ x11 : (ι → ι) → ι → ι . 0))))) (x1 (λ x9 . x6) (setsum 0 (x7 (λ x9 : (ι → ι) → ι → ι . 0)))) = Inj1 (x1 (λ x9 . x0 (λ x10 . x10) x5 (x2 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . λ x11 . x7 (λ x12 : (ι → ι) → ι → ι . 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . setsum 0 0)) (setsum 0 0)) (x2 (λ x9 : (ι → ι → ι) → ι . x5) (λ x9 : (ι → ι) → ι . λ x10 . x1 (λ x11 . x3 (λ x12 x13 . 0) 0) (Inj0 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x6)))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . x0 (λ x9 . x9) (x6 x4) x4 (setsum x4 x4) = setsum (x0 (λ x9 . x5 (x2 (λ x10 : (ι → ι → ι) → ι . x9) (λ x10 : (ι → ι) → ι . λ x11 . x10 (λ x12 . 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) (λ x10 : ι → ι . λ x11 . x11) 0) (setsum 0 (x6 0)) (x5 (Inj1 (Inj1 0)) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . x1 (λ x12 . 0) 0) (x6 0)) x4) (x1 (λ x9 . 0) (x7 (λ x9 : ι → ι . x2 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) (λ x9 x10 . x10) (λ x9 . x5 0 (λ x10 : ι → ι . λ x11 . 0) 0)))) (setsum (Inj1 (x3 (λ x9 x10 . 0) 0)) (x1 (λ x9 . setsum (x1 (λ x10 . 0) 0) 0) (x3 (λ x9 x10 . x2 (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . 0) 0 0 (x2 (λ x9 : (ι → ι → ι) → ι . x5) (λ x9 : (ι → ι) → ι . λ x10 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x9 (λ x11 . x0 (λ x12 . setsum 0 0) (x3 (λ x12 x13 . 0) 0) (x2 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) 0) 0)) = x2 (λ x9 : (ι → ι → ι) → ι . x9 (λ x10 x11 . 0)) (λ x9 : (ι → ι) → ι . λ x10 . x2 (λ x11 : (ι → ι → ι) → ι . setsum (x0 (λ x12 . x11 (λ x13 x14 . 0)) (Inj0 0) (x1 (λ x12 . 0) 0) 0) x10) (λ x11 : (ι → ι) → ι . λ x12 . Inj1 (x1 (λ x13 . x10) x10)) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . Inj0 (x9 (λ x11 . 0) x6))) ⟶ False (proof)
Theorem 51ded.. : ∀ x0 : (ι → ι) → ((ι → ι → ι → ι) → ι) → ι . ∀ x1 : (ι → ((ι → ι → ι) → ι) → ι → (ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι → (ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ι → ι . ∀ x3 : ((ι → ι → (ι → ι) → ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x9 (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . x3 (λ x11 : ι → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . setsum 0 0)) (λ x10 : ι → (ι → ι) → ι . x9 0 (x1 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0)) (λ x11 . 0) 0)) 0 (λ x10 . Inj1 x7) 0) (λ x9 : ι → (ι → ι) → ι . Inj0 0) = Inj1 x7) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ι → ι . x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0) = x5) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x2 (λ x9 x10 . x10) (x2 (λ x9 x10 . 0) (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . setsum 0 x5) (λ x9 : ι → (ι → ι) → ι . Inj0 x6))) = x2 (λ x9 x10 . setsum x6 0) (setsum x6 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 x10 . x6 (λ x11 : ι → ι → ι . 0)) (x0 (λ x9 . x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . x6 (λ x11 : ι → ι → ι . 0)) (λ x10 : ι → (ι → ι) → ι . x0 (λ x11 . x2 (λ x12 x13 . 0) 0) (λ x11 : ι → ι → ι → ι . x0 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0)))) (λ x9 : ι → ι → ι → ι . 0)) = Inj1 0) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . x0 (λ x13 . Inj1 0) (λ x13 : ι → ι → ι → ι . x11)) (λ x9 : (ι → ι → ι) → ι . Inj1 x7) (x2 (λ x9 x10 . 0) (setsum (setsum (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0)) (setsum 0 0)) 0)) (λ x9 . 0) = Inj0 (setsum (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . Inj0 (x5 0)) (λ x9 : ι → (ι → ι) → ι . Inj1 x7)) (x2 (λ x9 x10 . 0) (Inj0 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0)))))) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . x9) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) (Inj1 (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x10 : ι → (ι → ι) → ι . x9 (λ x11 x12 . 0)))) (λ x10 . Inj1 0)) (x5 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . Inj1 (Inj0 0)) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 . x0 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . 0)) (λ x12 : ι → ι → ι → ι . Inj1 0)) (x2 (λ x11 x12 . 0) (setsum 0 0)) (λ x11 . 0)) (setsum (Inj1 0) 0)) (λ x9 . x6 (λ x10 . setsum 0 (Inj0 (x3 (λ x11 : ι → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . 0)))) (Inj0 (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . x3 (λ x11 : ι → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . 0))))) = setsum x4 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x7) (λ x9 : ι → (ι → ι) → ι . 0))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . Inj0 0) (λ x9 : ι → ι → ι → ι . 0) = setsum (setsum x4 (x0 (λ x9 . x9) (λ x9 : ι → ι → ι → ι . x2 (λ x10 x11 . x11) (x1 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0))))) x4) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → ι → ι → ι . ∀ x6 x7 . x0 (λ x9 . x6) (λ x9 : ι → ι → ι → ι . x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . x2 (λ x11 x12 . x1 (λ x13 . λ x14 : (ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι . x2 (λ x17 x18 . 0) 0) (λ x13 : (ι → ι → ι) → ι . setsum 0 0) (x9 0 0 0) (λ x13 . setsum 0 0)) (x1 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . x13) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . x11))) (λ x10 : ι → (ι → ι) → ι . 0)) = Inj1 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x2 (λ x10 x11 . x0 (λ x12 . x3 (λ x13 : ι → ι → (ι → ι) → ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . 0)) (λ x12 : ι → ι → ι → ι . Inj0 0)) 0) (λ x9 : ι → (ι → ι) → ι . 0))) ⟶ False (proof)
Theorem efa1a.. : ∀ x0 : (ι → (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι . ∀ x1 : (ι → ((ι → ι) → ι → ι → ι) → ι) → (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x2 : ((((ι → ι) → (ι → ι) → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x3 : ((ι → ι) → (((ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → ι → ι . (∀ x4 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x9 . 0) (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 : ι → ι → ι . λ x12 x13 . Inj1 x12) 0) = Inj1 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x9 . x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . λ x13 x14 . x11 (x0 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 : ι → ι → ι . λ x18 x19 . 0) 0) (λ x15 . x15) 0) (setsum (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x10 x11 . 0)) 0)) x7)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . x1 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . Inj1 x11) (λ x11 : (ι → ι) → ι → ι . Inj0 (x0 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 : ι → ι → ι . λ x15 x16 . x13 0 (λ x17 . 0) 0) (x11 (λ x12 . 0) 0))) (x1 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . setsum (x1 (λ x13 . λ x14 : (ι → ι) → ι → ι → ι . 0) (λ x13 : (ι → ι) → ι → ι . 0) 0) (x2 (λ x13 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 x14 . 0))) (λ x11 : (ι → ι) → ι → ι . x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι . x11 (λ x14 . 0) 0) (λ x12 . x2 (λ x13 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 x14 . 0)) (x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x12 . 0) 0)) (setsum (Inj1 0) (x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0))))) (λ x9 . Inj0 (Inj1 (Inj1 (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x10 x11 . 0))))) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . x10 (x6 0)) (λ x9 x10 . x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x0 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 : ι → ι → ι . λ x16 x17 . x14 0 (λ x18 . 0) 0) (setsum 0 0)) (λ x11 . x10) (x1 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x12 . 0) 0) (setsum 0 0)))) = setsum (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 : ι → ι → ι . λ x12 x13 . x10 (setsum 0 0) (λ x14 . x13) (Inj0 (x10 0 (λ x14 . 0) 0))) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 x10 . x6 (x1 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0) 0)))) 0) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 x10 . x1 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0) (setsum (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . λ x14 x15 . setsum 0 0) x9) (x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x2 (λ x13 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 x14 . 0)) (λ x11 . 0) 0))) = setsum x7 (Inj0 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . setsum 0 (setsum 0 (x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 . 0) 0) (λ x11 . x10 0) (setsum 0 0)))) (λ x9 x10 . x9) = Inj1 (Inj1 (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 : ι → ι → ι . λ x12 x13 . x3 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → ι . x1 (λ x16 . λ x17 : (ι → ι) → ι → ι → ι . 0) (λ x16 : (ι → ι) → ι → ι . 0) 0) (λ x14 . x14) x12) 0))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x1 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x11 x12 . Inj1 x9)) (λ x9 : (ι → ι) → ι → ι . Inj1 (x1 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 : ι → ι → ι . λ x15 x16 . Inj0 0) 0) (λ x10 : (ι → ι) → ι → ι . x1 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . x11) (λ x11 : (ι → ι) → ι → ι . Inj1 0) (x6 (λ x11 . 0))) (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . λ x13 x14 . x0 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 : ι → ι → ι . λ x18 x19 . 0) 0) (Inj1 0)))) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . 0) (λ x9 x10 . x10)) = x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . setsum 0 (setsum 0 (Inj0 (setsum 0 0)))) (λ x9 x10 . x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x11 (x0 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 : ι → ι → ι . λ x16 x17 . 0) (setsum 0 0))) (λ x11 . 0) (x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . setsum (x12 (λ x13 : ι → ι . λ x14 . 0)) (x12 (λ x13 : ι → ι . λ x14 . 0))) (λ x11 . Inj1 0) 0))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x7 0) (λ x9 : (ι → ι) → ι → ι . setsum (x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 . x10) (x2 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x11 : ι → ι . x11 0) (λ x10 x11 . x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x12 . 0) 0))) (Inj1 (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . λ x13 x14 . x2 (λ x15 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x16 : ι → ι . 0) (λ x15 x16 . 0)) (Inj0 0)))) 0 = Inj0 (x4 (setsum 0 x5) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . λ x14 x15 . x1 (λ x16 . λ x17 : (ι → ι) → ι → ι → ι . 0) (λ x16 : (ι → ι) → ι → ι . 0) 0) (setsum 0 0)) (λ x9 x10 . setsum (setsum 0 0) x6)) (λ x9 . setsum 0 (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι . λ x13 x14 . Inj1 0) (Inj0 0))) (x1 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . Inj1 (setsum 0 0)) (λ x9 : (ι → ι) → ι → ι . Inj1 (x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 . 0) 0)) (x4 (Inj0 0) (Inj0 0) (λ x9 . Inj1 0) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x9 . 0) 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 : ι → ι → ι . λ x12 x13 . 0) (x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . x6) (λ x9 x10 . Inj0 (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . λ x14 x15 . x3 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → ι . 0) (λ x16 . 0) 0) (x1 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0) 0)))) = x2 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x10 : ι → ι . x6) (λ x9 x10 . Inj0 (setsum (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . λ x14 x15 . x1 (λ x16 . λ x17 : (ι → ι) → ι → ι → ι . 0) (λ x16 : (ι → ι) → ι → ι . 0) 0) x7) (setsum (setsum 0 0) (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . λ x14 x15 . 0) 0))))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 : ι → ι → ι . λ x12 x13 . x13) (setsum 0 0) = x6 (setsum (Inj0 (x4 (x4 0 0 0 0) (Inj0 0) 0 0)) 0) (λ x9 x10 . Inj1 (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι . λ x14 x15 . x15) (x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x1 (λ x13 . λ x14 : (ι → ι) → ι → ι → ι . 0) (λ x13 : (ι → ι) → ι → ι . 0) 0) (λ x11 . Inj0 0) (x2 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x11 x12 . 0)))))) ⟶ False (proof)
Theorem 35436.. : ∀ x0 : (((ι → ι) → ι) → ι) → ι → (ι → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → ((ι → ι) → ι) → ι) → (ι → ι → ι → ι → ι) → ι . ∀ x2 : (ι → (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ι . ∀ x3 : (((((ι → ι) → ι) → ι) → ι → ι → ι → ι) → ((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . (∀ x4 x5 . ∀ x6 x7 : ι → ι . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x10 : (ι → ι) → ι . x10 (λ x11 . x10 (λ x12 . x0 (λ x13 : (ι → ι) → ι . 0) (setsum 0 0) (λ x13 . λ x14 : ι → ι . λ x15 . 0)))) (λ x9 : ι → ι . 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι . Inj1 (setsum x9 (Inj1 0))) (λ x9 x10 x11 x12 . 0)) 0 = x1 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 : (ι → ι) → ι . Inj1 (Inj0 0)) 0 (λ x12 . λ x13 : ι → ι . λ x14 . 0)) (λ x9 x10 x11 x12 . setsum x10 (setsum 0 x12))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x10 : (ι → ι) → ι . 0) (λ x9 : ι → ι . x6) (setsum 0 x6) x5 = x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . setsum (Inj1 x9) (setsum 0 (x3 (λ x13 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x13 : ι → ι . 0) 0 0))) (λ x11 : ι → ι . λ x12 : ι → ι → ι . 0)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x10 0 (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x11) (λ x11 : ι → ι . λ x12 : ι → ι → ι . Inj1 (x11 0)))) = Inj0 x4) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x0 (λ x11 : (ι → ι) → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj0 (Inj1 0)) (λ x12 : ι → ι . λ x13 : ι → ι → ι . x3 (λ x14 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x15 : (ι → ι) → ι . 0) (λ x14 : ι → ι . x2 (λ x15 . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x15 : ι → ι . λ x16 : ι → ι → ι . 0)) (setsum 0 0) (x13 0 0))) (Inj1 x6) (λ x11 . λ x12 : ι → ι . λ x13 . x10 (x12 (setsum 0 0)) (x12 (x1 (λ x14 x15 . λ x16 : (ι → ι) → ι . 0) (λ x14 x15 x16 x17 . 0))))) = x0 (λ x9 : (ι → ι) → ι . x1 (λ x10 x11 . λ x12 : (ι → ι) → ι . Inj0 0) (λ x10 x11 x12 x13 . x11)) x4 (λ x9 . λ x10 : ι → ι . λ x11 . Inj1 (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x2 (λ x16 . λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x16 : ι → ι . λ x17 : ι → ι → ι . 0)) (λ x14 : ι → ι . λ x15 : ι → ι → ι . x3 (λ x16 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x17 : (ι → ι) → ι . 0) (λ x16 : ι → ι . 0) 0 0)) (λ x12 : ι → ι . λ x13 : ι → ι → ι . setsum 0 (x1 (λ x14 x15 . λ x16 : (ι → ι) → ι . 0) (λ x14 x15 x16 x17 . 0)))))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι . Inj1 0) (λ x9 x10 x11 x12 . x10) = x7 (λ x9 . x6)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x1 (λ x13 x14 . λ x15 : (ι → ι) → ι . x15 (λ x16 . x15 (λ x17 . x2 (λ x18 . λ x19 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x18 : ι → ι . λ x19 : ι → ι → ι . 0)))) (λ x13 x14 x15 x16 . setsum (Inj0 (x3 (λ x17 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x18 : (ι → ι) → ι . 0) (λ x17 : ι → ι . 0) 0 0)) x13)) = Inj0 (setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x7 0)) 0)) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 : (ι → ι) → ι . Inj0 (Inj0 (setsum 0 (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x11 : (ι → ι) → ι . 0) (λ x10 : ι → ι . 0) 0 0)))) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . setsum (x9 0) (Inj0 0))) (λ x9 . λ x10 : ι → ι . λ x11 . Inj0 0) = x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x11 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x12 : (ι → ι) → ι . x9) (λ x11 : ι → ι . 0) (setsum (setsum 0 (x1 (λ x11 x12 . λ x13 : (ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0))) x6) (Inj1 0)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . setsum 0 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x0 (λ x9 : (ι → ι) → ι . x7 (λ x10 : (ι → ι) → ι → ι . 0)) (setsum 0 (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x13 (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0) 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . setsum 0 0)) (λ x9 x10 x11 x12 . 0))) (λ x9 . λ x10 : ι → ι . λ x11 . Inj1 (x3 (λ x12 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x13 : (ι → ι) → ι . x10 (Inj1 0)) (λ x12 : ι → ι . x3 (λ x13 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x14 : (ι → ι) → ι . Inj0 0) (λ x13 : ι → ι . 0) 0 (Inj1 0)) (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . 0)) (x3 (λ x12 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x13 : (ι → ι) → ι . x3 (λ x14 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x15 : (ι → ι) → ι . 0) (λ x14 : ι → ι . 0) 0 0) (λ x12 : ι → ι . Inj0 0) (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . 0)) x11))) = x7 (λ x9 : (ι → ι) → ι → ι . setsum (Inj1 (x1 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) (λ x10 x11 x12 x13 . 0))) (x7 (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . λ x12 : (ι → ι) → ι . x9 (λ x13 . 0) 0) (λ x11 : ι → ι . x7 (λ x12 : (ι → ι) → ι → ι . 0)) x6 (x7 (λ x11 : (ι → ι) → ι → ι . 0)))))) ⟶ False (proof)
Theorem 5ce35.. : ∀ x0 : (ι → ι) → ι → ι → (ι → ι → ι) → ι . ∀ x1 : (((ι → ι) → ι) → (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x2 : ((ι → ι) → ι) → (((ι → ι → ι) → (ι → ι) → ι) → ι) → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι → ι . x3 (λ x9 . 0) (x1 (λ x9 : (ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → ι) → ι . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . λ x18 . Inj0 (setsum 0 0)) (setsum (Inj1 0) (x1 (λ x14 : (ι → ι) → ι . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . λ x18 . 0) 0))) 0) = Inj0 (Inj1 (Inj1 0))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 . setsum (x1 (λ x10 : (ι → ι) → ι . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . setsum 0 0) x9) (x0 (λ x10 . x2 (λ x11 : ι → ι . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι . x9)) (x2 (λ x10 : ι → ι . x9) (λ x10 : (ι → ι → ι) → (ι → ι) → ι . x9)) (x2 (λ x10 : ι → ι . setsum 0 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι . 0)) (λ x10 x11 . Inj1 (Inj0 0)))) (x0 (λ x9 . Inj1 0) 0 (Inj1 (setsum 0 (x2 (λ x9 : ι → ι . 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . 0)))) (λ x9 x10 . 0)) = x0 (λ x9 . x1 (λ x10 : (ι → ι) → ι . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x0 (λ x15 . Inj1 (x2 (λ x16 : ι → ι . 0) (λ x16 : (ι → ι → ι) → (ι → ι) → ι . 0))) (x11 (λ x15 : ι → ι . λ x16 . 0)) 0 (λ x15 . setsum 0)) 0) (setsum 0 (x3 (λ x9 . x0 (λ x10 . setsum 0 0) (x5 0 (λ x10 : ι → ι . 0) 0) (Inj1 0) (λ x10 x11 . x7)) 0)) (x0 (λ x9 . x0 (λ x10 . x2 (λ x11 : ι → ι . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι . x1 (λ x12 : (ι → ι) → ι . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . 0) 0)) x9 (x2 (λ x10 : ι → ι . x2 (λ x11 : ι → ι . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι . 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι . Inj1 0)) (λ x10 x11 . x11)) x7 (x1 (λ x9 : (ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x13) 0) (λ x9 x10 . x6)) (λ x9 x10 . x9)) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 : ι → ι . x7 (x7 (setsum (x0 (λ x10 . 0) 0 0 (λ x10 x11 . 0)) 0))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . x9 (λ x10 x11 . 0) (λ x10 . x7 (x7 0))) = setsum (x3 (λ x9 . 0) (x7 (Inj0 (x3 (λ x9 . 0) 0)))) (x6 (λ x9 : ι → ι . λ x10 . x10))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x9 : ι → ι . x7 (x9 (Inj0 (x7 0 0))) (setsum (Inj1 0) (setsum (Inj1 0) 0))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . x1 (λ x10 : (ι → ι) → ι . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x11 (λ x15 : ι → ι . λ x16 . 0)) (Inj1 x5)) = x1 (λ x9 : (ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 : ι → ι . x2 (λ x15 : ι → ι . x14 (x3 (λ x16 . 0) 0)) (λ x15 : (ι → ι → ι) → (ι → ι) → ι . x3 (λ x16 . x16) 0)) (λ x14 : (ι → ι → ι) → (ι → ι) → ι . x1 (λ x15 : (ι → ι) → ι . λ x16 : ((ι → ι) → ι → ι) → ι . λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . Inj1 (setsum 0 0)) (setsum (setsum 0 0) 0))) (x0 (λ x9 . x1 (λ x10 : (ι → ι) → ι . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) (x7 (x3 (λ x10 . 0) 0) (Inj1 0))) (setsum (x4 (setsum 0 0)) (setsum (Inj1 0) (setsum 0 0))) (x2 (λ x9 : ι → ι . 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . 0)) (λ x9 x10 . x3 (λ x11 . 0) 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 : (ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x12 (x3 (λ x14 . x12 (Inj0 0)) 0)) x7 = x7) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ι . x1 (λ x9 : (ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 = x4) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x0 (λ x9 . 0) (x1 (λ x9 : (ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x11 (x0 (λ x14 . Inj1 0) 0 (setsum 0 0) (λ x14 x15 . x1 (λ x16 : (ι → ι) → ι . λ x17 : ((ι → ι) → ι → ι) → ι . λ x18 : ι → ι → ι . λ x19 : ι → ι . λ x20 . 0) 0)) (x10 (λ x14 : ι → ι . λ x15 . x3 (λ x16 . 0) 0))) (Inj0 (setsum (x7 0 (λ x9 : ι → ι . λ x10 . 0) 0 0) (x4 0)))) x5 (λ x9 x10 . 0) = Inj1 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 x7 . x0 (λ x9 . x1 (λ x10 : (ι → ι) → ι . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x13 (x13 (x13 0))) (Inj0 x9)) (x1 (λ x9 : (ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 : ι → ι . setsum (x3 (λ x15 . 0) 0) x13) (λ x14 : (ι → ι → ι) → (ι → ι) → ι . 0)) (Inj0 0)) x7 (λ x9 x10 . x9) = setsum (setsum (x4 (setsum 0 x6) (Inj0 0)) x5) 0) ⟶ False (proof)
Theorem fbca8.. : ∀ x0 : ((ι → (ι → ι → ι) → ι) → (((ι → ι) → ι → ι) → ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x1 : (((ι → ι) → (ι → ι → ι) → ι) → ι) → ι → ι . ∀ x2 : (((ι → ι → ι) → ι) → ι → (ι → ι → ι) → ι → ι → ι) → ι → (ι → (ι → ι) → ι) → ι . ∀ x3 : (ι → ι) → (ι → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . x2 (λ x15 : (ι → ι → ι) → ι . λ x16 . λ x17 : ι → ι → ι . λ x18 x19 . x17 (x3 (λ x20 . 0) (λ x20 . 0)) 0) (setsum 0 (x1 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . 0) 0)) (λ x15 . λ x16 : ι → ι . x15)) 0 (λ x10 . λ x11 : ι → ι . x7)) (λ x9 . x9) = x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x13) (Inj0 x4) (λ x9 . λ x10 : ι → ι . x6)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 : ι → ι . x3 (λ x9 . setsum (x7 (x7 0)) (Inj0 0)) (λ x9 . 0) = setsum (x3 (λ x9 . x5 (λ x10 . 0) (λ x10 : ι → ι . λ x11 . x10 0)) (λ x9 . x7 (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι → ι) → ι → ι . λ x12 . 0) (λ x10 : ι → ι . x10 0)))) (setsum 0 (setsum 0 (setsum (x7 0) (setsum 0 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x2 (λ x14 : (ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . x17) (x11 0 (setsum x13 (Inj0 0))) (λ x14 . λ x15 : ι → ι . Inj1 0)) x7 (λ x9 . λ x10 : ι → ι . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι → ι) → ι → ι . λ x13 . x0 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι → ι) → ι → ι . λ x16 . Inj1 (setsum 0 0)) (λ x14 : ι → ι . x12 (λ x15 : ι → ι . λ x16 . Inj0 0) (Inj1 0))) (λ x11 : ι → ι . 0)) = Inj1 (x3 (λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . x1 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . Inj1 0) 0) (x3 (λ x10 . x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . 0) 0) (λ x10 . x10)) (λ x10 . λ x11 : ι → ι . setsum x10 (x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . 0) 0))) (λ x9 . Inj1 x5))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x2 (λ x14 : (ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . 0) (setsum (setsum x12 (x0 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι → ι) → ι → ι . λ x16 . 0) (λ x14 : ι → ι . 0))) 0) (λ x14 . λ x15 : ι → ι . 0)) (x3 (λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι → ι . λ x13 . x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . x14 (λ x15 . 0) (λ x15 x16 . 0))) (Inj0 0) (λ x10 . λ x11 : ι → ι . 0)) (λ x9 . 0)) (λ x9 . λ x10 : ι → ι . setsum (setsum 0 (x3 (λ x11 . setsum 0 0) (λ x11 . setsum 0 0))) 0) = x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . setsum (setsum x10 (Inj0 0)) (x3 (λ x14 . 0) (λ x14 . Inj0 (setsum 0 0)))) (Inj1 (setsum (x4 (Inj1 0) (λ x9 : ι → ι . λ x10 . 0) (x6 0) 0) 0)) (λ x9 . λ x10 : ι → ι . x9)) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . setsum 0 (x3 (λ x10 . 0) (λ x10 . setsum (x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . 0) 0) (x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . 0) 0)))) 0 = x5) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . x9 (λ x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι → ι) → ι → ι . λ x13 . 0) (λ x11 : ι → ι . 0)) (λ x10 x11 . setsum (Inj0 (setsum 0 0)) x10)) (x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . setsum (x3 (λ x14 . 0) (λ x14 . 0)) (x2 (λ x14 : (ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . 0) (setsum 0 0) (λ x14 . λ x15 : ι → ι . 0))) (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . 0) (setsum 0 0)) (λ x9 . λ x10 : ι → ι . x2 (λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . setsum 0 (x0 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : ((ι → ι) → ι → ι) → ι → ι . λ x18 . 0) (λ x16 : ι → ι . 0))) (setsum 0 0) (λ x11 . λ x12 : ι → ι . 0))) = x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 . setsum 0) (setsum x4 (x6 (λ x9 x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι → ι) → ι → ι . λ x13 . setsum 0 0) (λ x11 : ι → ι . 0)))) (λ x9 . λ x10 : ι → ι . Inj1 (Inj1 (Inj0 (x10 0))))) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 . 0) (λ x9 : ι → ι . x2 (λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . setsum 0 (setsum 0 (setsum 0 0))) (x9 (setsum 0 x5)) (λ x10 . λ x11 : ι → ι . Inj1 (x3 (λ x12 . 0) (λ x12 . Inj1 0)))) = setsum 0 (Inj0 (x6 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 . Inj1 (setsum 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 . x2 (λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0) 0 (λ x12 . λ x13 : ι → ι . Inj1 0)) (λ x9 : ι → ι . 0) = Inj0 (Inj1 (Inj0 x6))) ⟶ False (proof)
Theorem 27d8b.. : ∀ x0 : ((ι → (ι → ι) → ι) → ι → ι → (ι → ι) → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → (ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x1 : ((ι → ι → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → (((ι → ι) → ι → ι) → ι) → ι → ι → (ι → ι) → ι . ∀ x3 : (ι → (((ι → ι) → ι) → ι) → ι) → (((ι → ι) → (ι → ι) → ι) → ι → ι) → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . x1 (λ x11 : ι → ι → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → ι . 0) (λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 . setsum (x10 (λ x14 : ι → ι . 0)) 0)) (Inj1 x9)) (λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) = x1 (λ x9 : ι → ι → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . x10) (λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 . Inj1 (x10 (λ x12 . x10 (λ x13 . 0) (λ x13 . 0)) (λ x12 . x11)))) (setsum (x5 (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . Inj0 0) (λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . 0) (λ x11 : (ι → ι) → (ι → ι) → ι . λ x12 . 0)))) (Inj0 0))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . x7) (λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) = setsum (setsum x6 0) (setsum 0 (setsum x6 (setsum (x0 (λ x9 : ι → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 : ι → ι . 0) (λ x9 : (ι → ι) → ι . 0)) (x2 (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . 0) 0 0 (λ x9 . 0)))))) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x9 . setsum 0 0) (λ x9 : (ι → ι) → ι → ι . x2 (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . Inj1 0) (x0 (λ x10 : ι → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . setsum 0 (Inj1 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 : ι → ι . 0) (λ x10 : (ι → ι) → ι . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 . Inj1 0))) (x0 (λ x10 : ι → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . setsum 0 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 : ι → ι . x2 (λ x12 . Inj1 0) (λ x12 : (ι → ι) → ι → ι . Inj1 0) 0 (x10 (λ x12 : ι → ι . λ x13 . 0) 0 0) (λ x12 . x11 0)) (λ x10 : (ι → ι) → ι . 0)) (λ x10 . setsum (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x10) (λ x11 : (ι → ι) → (ι → ι) → ι . λ x12 . 0)))) 0 (x2 (λ x9 . Inj0 (Inj1 x7)) (λ x9 : (ι → ι) → ι → ι . Inj1 x7) (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 . x11 (λ x13 . 0) 0)) (λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . setsum (x9 (λ x11 . 0) (λ x11 . 0)) (setsum 0 0))) x4 (λ x9 . Inj1 0)) (λ x9 . Inj1 (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0))) = setsum 0 (setsum x5 (x0 (λ x9 : ι → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x12 x10) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 : ι → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x0 (λ x13 : ι → (ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 : ι → ι . 0) (λ x13 : (ι → ι) → ι . 0)) (λ x11 : (ι → ι) → (ι → ι) → ι . λ x12 . 0)) (λ x9 : (ι → ι) → ι . x7)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . x2 (λ x9 . x9) (λ x9 : (ι → ι) → ι → ι . setsum (x0 (λ x10 : ι → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . x10 x11 (λ x14 . x13 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 : ι → ι . x11 0) (λ x10 : (ι → ι) → ι . 0)) (Inj1 0)) 0 (setsum 0 (x7 (λ x9 x10 : ι → ι . 0) 0 (λ x9 . 0) (Inj1 (Inj1 0)))) (λ x9 . x0 (λ x10 : ι → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . x11) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 : ι → ι . x7 (λ x12 x13 : ι → ι . x13 (x2 (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . 0) 0 0 (λ x14 . 0))) (Inj1 (x10 (λ x12 : ι → ι . λ x13 . 0) 0 0)) (λ x12 . x9) 0) (λ x10 : (ι → ι) → ι . x10 (λ x11 . setsum x11 0))) = setsum (setsum (setsum (Inj0 (x2 (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . 0) 0 0 (λ x9 . 0))) (x0 (λ x9 : ι → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . setsum 0 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 : ι → ι . x6) (λ x9 : (ι → ι) → ι . x5))) x6) (Inj0 (x7 (λ x9 x10 : ι → ι . setsum (setsum 0 0) (x9 0)) (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . setsum 0 0) (λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj0 0)) (λ x9 . 0) 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → ι → ι . 0) x7 = setsum 0 (setsum (setsum (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . 0) (λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 0)) (setsum 0 0)) (x5 x4 (Inj1 x7) (λ x9 . Inj0 (x2 (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . 0) 0 0 (λ x10 . 0))) 0))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x1 (λ x9 : ι → ι → ι . x9 0 0) 0 = x6 0 (λ x9 : ι → ι . setsum (Inj1 (x7 (λ x10 x11 x12 . x0 (λ x13 : ι → (ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 : ι → ι . 0) (λ x13 : (ι → ι) → ι . 0)))) (x6 (x0 (λ x10 : ι → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . 0) (λ x14 : (ι → ι) → (ι → ι) → ι . λ x15 . 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 : ι → ι . 0) (λ x10 : (ι → ι) → ι . x2 (λ x11 . 0) (λ x11 : (ι → ι) → ι → ι . 0) 0 0 (λ x11 . 0))) (λ x10 : ι → ι . 0)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 : ι → ι . x7) (λ x9 : (ι → ι) → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . setsum (x9 (λ x12 . 0)) (Inj1 0)) (λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 . x1 (λ x12 : ι → ι → ι . Inj0 0) x7)) = Inj1 x7) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . Inj1 (setsum x10 0)) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 : ι → ι . setsum (x1 (λ x11 : ι → ι → ι . 0) (x10 (setsum 0 0))) (x6 (x2 (λ x11 . Inj0 0) (λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : ι → ι → ι . 0) 0) 0 0 (λ x11 . x9 (λ x12 : ι → ι . λ x13 . 0) 0 0)))) (λ x9 : (ι → ι) → ι . x6 0) = Inj0 (x0 (λ x9 : ι → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x0 (λ x13 : ι → (ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . x15) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 : ι → ι . 0) (λ x13 : (ι → ι) → ι . 0)) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 : ι → ι . 0) (λ x9 : (ι → ι) → ι . x6 (x0 (λ x10 : ι → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . Inj1 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 : ι → ι . Inj1 0) (λ x10 : (ι → ι) → ι . 0))))) ⟶ False (proof)
Theorem a0efe.. : ∀ x0 : ((ι → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ι) → ((ι → ι) → ((ι → ι) → ι → ι) → ι) → ι . ∀ x1 : ((((ι → ι) → ι → ι) → ι) → ι → ι) → ((((ι → ι) → ι) → ι) → ι) → ι . ∀ x2 : (ι → ι) → ι → ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x3 : (ι → ι) → (ι → ι) → (ι → (ι → ι) → ι) → (ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : ι → ι → ι . x3 (λ x9 . 0) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . setsum (setsum (setsum 0 (x3 (λ x11 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) (λ x11 . 0))) (x3 (λ x11 . x11) (λ x11 . x7 0 0) (λ x11 . λ x12 : ι → ι . setsum 0 0) (λ x11 . 0))) (setsum 0 0)) (λ x9 . Inj1 (Inj1 x9)) = setsum (Inj0 x4) (Inj1 (x7 (setsum (Inj0 0) (Inj1 0)) x5))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 . x9) (λ x9 . x7) (λ x9 . λ x10 : ι → ι . x9) (λ x9 . Inj0 (Inj0 (x3 (λ x10 . x6) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 . 0)) (λ x10 . x7)))) = setsum (x1 (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 . x9 (λ x11 : ι → ι . λ x12 . setsum 0 (setsum 0 0))) (λ x9 : ((ι → ι) → ι) → ι . 0)) (Inj0 (x5 (λ x9 : (ι → ι) → ι → ι . x3 (λ x10 . 0) (λ x10 . x0 (λ x11 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . 0)) (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 . 0)) (λ x10 . 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . x2 (λ x9 . x1 (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . x1 (λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι) → ι . Inj1 x9)) (λ x10 : ((ι → ι) → ι) → ι . x3 (λ x11 . x0 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x10 (λ x13 : ι → ι . 0)) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . x10 (λ x14 : ι → ι . 0))) (λ x11 . Inj1 0) (λ x11 . λ x12 : ι → ι . setsum x9 x9) (λ x11 . Inj1 (x3 (λ x12 . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 . 0))))) (x2 (λ x9 . setsum 0 (x2 (λ x10 . x2 (λ x11 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0) (setsum 0 0) (λ x10 x11 : ι → ι . λ x12 . 0) 0)) (x3 (λ x9 . x3 (λ x10 . x0 (λ x11 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . 0)) (λ x10 . setsum 0 0) (λ x10 . λ x11 : ι → ι . 0) (λ x10 . x7 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . 0) 0 0)) (λ x9 . x7 (λ x10 : ι → ι . x3 (λ x11 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) (λ x11 . 0)) (λ x10 : ι → ι . 0) x6 x6) (λ x9 . λ x10 : ι → ι . x2 (λ x11 . x10 0) (setsum 0 0) (λ x11 x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x14 : ι → ι . λ x15 : (ι → ι) → ι → ι . 0)) (setsum 0 0)) (λ x9 . x7 (λ x10 : ι → ι . Inj1 0) (λ x10 : ι → ι . 0) (x1 (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι) → ι . 0)) (x2 (λ x10 . 0) 0 (λ x10 x11 : ι → ι . λ x12 . 0) 0))) (λ x9 x10 : ι → ι . λ x11 . 0) x5) (λ x9 x10 : ι → ι . λ x11 . x11) (Inj1 0) = x2 (λ x9 . x1 (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι) → ι . setsum (x7 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . x1 (λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι) → ι . 0)) (x3 (λ x11 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) (λ x11 . 0)) (x1 (λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → ι . 0))) 0)) x6 (λ x9 x10 : ι → ι . λ x11 . x9 (Inj1 (setsum 0 (setsum 0 0)))) (x2 (λ x9 . x7 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . setsum (Inj0 0) 0) 0 0) (setsum x6 (x7 (λ x9 : ι → ι . Inj0 0) (λ x9 : ι → ι . x0 (λ x10 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . 0)) 0 0)) (λ x9 x10 : ι → ι . λ x11 . 0) x4)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 . x3 (λ x10 . x7) (λ x10 . x6) (λ x10 . λ x11 : ι → ι . setsum (setsum (x11 0) x9) (x1 (λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . setsum 0 0) (λ x12 : ((ι → ι) → ι) → ι . Inj1 0))) (λ x10 . 0)) (Inj0 0) (λ x9 x10 : ι → ι . λ x11 . Inj0 (Inj0 (x3 (λ x12 . x0 (λ x13 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0)) (λ x12 . setsum 0 0) (λ x12 . λ x13 : ι → ι . x3 (λ x14 . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . 0) (λ x14 . 0)) (λ x12 . 0)))) x6 = Inj1 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 . Inj0 0) (λ x9 : ((ι → ι) → ι) → ι . Inj1 (x9 (λ x10 : ι → ι . 0))) = x7 (setsum (x0 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x0 (λ x10 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x11 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 . 0))) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x3 (λ x11 . x1 (λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι) → ι . 0)) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . x1 (λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . 0) (λ x13 : ((ι → ι) → ι) → ι . 0)) (λ x11 . x9 0))) x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x7 . x1 (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 . setsum (x3 (λ x11 . x9 (λ x12 : ι → ι . λ x13 . 0)) (λ x11 . Inj1 (setsum 0 0)) (λ x11 . λ x12 : ι → ι . 0) (λ x11 . 0)) (setsum (x6 (λ x11 . λ x12 : ι → ι . λ x13 . x13) (λ x11 . x3 (λ x12 . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 . 0)) (x9 (λ x11 : ι → ι . λ x12 . 0)) 0) (x6 (λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 . 0) 0 (λ x14 x15 : ι → ι . λ x16 . 0) 0) (λ x11 . Inj0 0) x10 0))) (λ x9 : ((ι → ι) → ι) → ι . x1 (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . x2 (λ x12 . x2 (λ x13 . x3 (λ x14 . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . 0) (λ x14 . 0)) (setsum 0 0) (λ x13 x14 : ι → ι . λ x15 . x14 0) (x2 (λ x13 . 0) 0 (λ x13 x14 : ι → ι . λ x15 . 0) 0)) 0 (λ x12 x13 : ι → ι . λ x14 . x11) (x1 (λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . setsum 0 0) (λ x12 : ((ι → ι) → ι) → ι . x11))) (λ x10 : ((ι → ι) → ι) → ι . setsum 0 (x3 (λ x11 . 0) (λ x11 . x10 (λ x12 : ι → ι . 0)) (λ x11 . λ x12 : ι → ι . Inj0 0) (λ x11 . x7)))) = x1 (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 . Inj0 (Inj1 (x3 (λ x11 . 0) (λ x11 . x3 (λ x12 . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 . 0)) (λ x11 . λ x12 : ι → ι . 0) (λ x11 . 0)))) (λ x9 : ((ι → ι) → ι) → ι . Inj1 (x6 (λ x10 . λ x11 : ι → ι . λ x12 . x10) (λ x10 . x2 (λ x11 . Inj0 0) x10 (λ x11 x12 : ι → ι . λ x13 . 0) (x3 (λ x11 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) (λ x11 . 0))) 0 (x2 (λ x10 . x2 (λ x11 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0) (x9 (λ x10 : ι → ι . 0)) (λ x10 x11 : ι → ι . λ x12 . x3 (λ x13 . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 . 0)) (x3 (λ x10 . 0) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . 0) (λ x10 . 0)))))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj0 (Inj1 (Inj1 (setsum 0 0)))) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . 0) = setsum 0 (Inj0 x5)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x9 (setsum 0 (x2 (λ x10 . x10) 0 (λ x10 x11 : ι → ι . λ x12 . x1 (λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . 0) (λ x13 : ((ι → ι) → ι) → ι . 0)) (Inj0 0))) (λ x10 : ι → ι . λ x11 . setsum (x2 (λ x12 . setsum 0 0) 0 (λ x12 x13 : ι → ι . λ x14 . Inj1 0) (setsum 0 0)) (Inj0 (x0 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . 0)))) (λ x10 . x7 (x7 (Inj0 0)))) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x2 (λ x11 . x0 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum 0 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . x11)) (x7 0) (λ x11 x12 : ι → ι . λ x13 . x1 (λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . x1 (λ x16 : ((ι → ι) → ι → ι) → ι . λ x17 . x0 (λ x18 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x18 : ι → ι . λ x19 : (ι → ι) → ι → ι . 0)) (λ x16 : ((ι → ι) → ι) → ι . x0 (λ x17 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . 0))) (λ x14 : ((ι → ι) → ι) → ι . Inj0 x13)) (x1 (λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → ι . 0))) = setsum 0 (setsum 0 0)) ⟶ False (proof)
Theorem 23307.. : ∀ x0 : ((((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι) → (ι → ι) → (ι → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x1 : ((ι → ι) → ι) → (ι → ι → ι → ι) → ι . ∀ x2 : (ι → (ι → ι → ι) → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → ι → ι → ι . ∀ x7 . x3 (λ x9 . x9) (x1 (λ x9 : ι → ι . 0) (λ x9 x10 x11 . 0)) = x1 (λ x9 : ι → ι . x5) (λ x9 x10 x11 . x11)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x3 (λ x9 . Inj0 x5) (Inj1 (x6 (x1 (λ x9 : ι → ι . setsum 0 0) (λ x9 x10 x11 . setsum 0 0)))) = x4 0 (x2 (λ x9 . λ x10 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . x1 (λ x10 : ι → ι . 0) (λ x10 x11 x12 . 0)) (λ x9 x10 x11 . x9)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 . λ x10 : ι → ι → ι . x2 (λ x11 . λ x12 : ι → ι → ι . 0) 0) x5 = setsum (x2 (λ x9 . λ x10 : ι → ι → ι . 0) (setsum (x4 x5) 0)) (x3 (λ x9 . x7 (x6 (λ x10 . setsum 0 0) (x0 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 : ι → ι . λ x12 : ι → ι → ι . 0) 0 (λ x10 . 0)) (x3 (λ x10 . 0) 0))) 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ι . x2 (λ x9 . λ x10 : ι → ι → ι . 0) (setsum (Inj1 (x7 (λ x9 : (ι → ι) → ι . λ x10 x11 . x9 (λ x12 . 0)))) x4) = x6 (λ x9 : (ι → ι) → ι . setsum 0 (x6 (λ x10 : (ι → ι) → ι . 0) (x7 (λ x10 : (ι → ι) → ι . λ x11 x12 . 0)))) x4) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → ι . x3 (λ x10 . x1 (λ x11 : ι → ι . setsum (x0 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . 0) 0 (λ x12 . 0)) (setsum 0 0)) (λ x11 x12 x13 . x3 (λ x14 . x12) (Inj0 0))) (setsum (x5 (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0) (λ x10 . x2 (λ x11 . λ x12 : ι → ι → ι . 0) 0) (setsum 0 0)) x7)) (λ x9 x10 x11 . setsum 0 (Inj0 (Inj0 (x3 (λ x12 . 0) 0)))) = setsum x7 0) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . x1 (λ x9 : ι → ι . 0) (λ x9 x10 x11 . x2 (λ x12 . λ x13 : ι → ι → ι . setsum (x2 (λ x14 . λ x15 : ι → ι → ι . 0) x10) 0) (x1 (λ x12 : ι → ι . 0) (λ x12 x13 x14 . 0))) = x2 (λ x9 . λ x10 : ι → ι → ι . Inj1 (x10 (x1 (λ x11 : ι → ι . x1 (λ x12 : ι → ι . 0) (λ x12 x13 x14 . 0)) (λ x11 x12 x13 . x2 (λ x14 . λ x15 : ι → ι → ι . 0) 0)) x9)) (x3 (λ x9 . 0) (Inj0 (Inj0 (x3 (λ x9 . 0) 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . x1 (λ x12 : ι → ι . 0) (λ x12 x13 x14 . Inj0 (x11 0 (x11 0 0)))) (x3 (λ x9 . Inj0 x6) x6) (λ x9 . 0) = Inj0 (Inj1 (setsum (x2 (λ x9 . λ x10 : ι → ι → ι . setsum 0 0) (setsum 0 0)) (x4 (x3 (λ x9 . 0) 0))))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 : ι → ι . x0 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . x0 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . x14 (x3 (λ x15 . x2 (λ x16 . λ x17 : ι → ι → ι . 0) 0) (x1 (λ x15 : ι → ι . 0) (λ x15 x16 x17 . 0))) 0) (x11 (x2 (λ x12 . λ x13 : ι → ι → ι . 0) (x11 0 0)) 0) (λ x12 . x2 (λ x13 . λ x14 : ι → ι → ι . x13) 0)) (Inj0 (x6 (x7 0))) (λ x9 . setsum 0 0) = x0 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . Inj0 0) (Inj0 (Inj1 (x0 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . x10 0) (x0 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . 0) 0 (λ x9 . 0)) (λ x9 . x1 (λ x10 : ι → ι . 0) (λ x10 x11 x12 . 0))))) (λ x9 . Inj0 (Inj1 (setsum (x6 0) (x7 0))))) ⟶ False (proof)
Theorem c725c.. : ∀ x0 : ((ι → ι → ι) → ι) → ι → (ι → ι → ι) → ι . ∀ x1 : ((ι → ι → ι) → ι) → (ι → ι → (ι → ι) → ι) → ι . ∀ x2 : (((ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → (ι → ι → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x3 : ((ι → (ι → ι → ι) → ι) → ι) → ι → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ι → (ι → ι → ι) → ι . setsum x5 0) 0 = setsum x7 (Inj0 x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι . 0) (Inj0 0) = x5) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x10 : ι → ι → ι → ι . x9 (λ x11 . λ x12 : ι → ι . setsum (x2 (λ x13 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x14 : ι → ι → ι → ι . x11) (λ x13 x14 . x2 (λ x15 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x16 : ι → ι → ι → ι . 0) (λ x15 x16 . 0))) (x0 (λ x13 : ι → ι → ι . Inj1 0) 0 (λ x13 x14 . 0))) (x6 (x0 (λ x11 : ι → ι → ι . Inj0 0) (x10 0 0 0) (λ x11 x12 . x11))) (λ x11 . 0) (setsum (x1 (λ x11 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . Inj0 0)) (Inj1 (x3 (λ x11 : ι → (ι → ι → ι) → ι . 0) 0)))) (λ x9 x10 . setsum (x6 x10) (Inj0 (setsum x9 0))) = x4 (x6 (Inj0 (x1 (λ x9 : ι → ι → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι . 0) 0) (λ x9 x10 . λ x11 : ι → ι . x11 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . x2 (λ x9 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x10 : ι → ι → ι → ι . setsum (Inj0 (x6 (setsum 0 0) (λ x11 . setsum 0 0))) (x0 (λ x11 : ι → ι → ι . x10 (setsum 0 0) (x1 (λ x12 : ι → ι → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0)) 0) (Inj1 (x0 (λ x11 : ι → ι → ι . 0) 0 (λ x11 x12 . 0))) (λ x11 x12 . Inj1 (Inj1 0)))) (λ x9 x10 . x10) = x5 (x3 (λ x9 : ι → (ι → ι → ι) → ι . x0 (λ x10 : ι → ι → ι . x6 (setsum 0 0) (λ x11 . x7 (λ x12 . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0))) (x6 (x0 (λ x10 : ι → ι → ι . 0) 0 (λ x10 x11 . 0)) (λ x10 . 0)) (λ x10 x11 . x1 (λ x12 : ι → ι → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0))) x4)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → ι . ∀ x5 x6 x7 . x1 (λ x9 : ι → ι → ι . x1 (λ x10 : ι → ι → ι . x2 (λ x11 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 . x1 (λ x13 : ι → ι → ι . x12) (λ x13 x14 . λ x15 : ι → ι . setsum 0 0))) (λ x10 x11 . λ x12 : ι → ι . setsum (x0 (λ x13 : ι → ι → ι . 0) (setsum 0 0) (λ x13 x14 . 0)) 0)) (λ x9 x10 . λ x11 : ι → ι . x0 (λ x12 : ι → ι → ι . 0) 0 (λ x12 x13 . x13)) = x1 (λ x9 : ι → ι → ι . setsum (x3 (λ x10 : ι → (ι → ι → ι) → ι . x1 (λ x11 : ι → ι → ι . x9 0 0) (λ x11 x12 . λ x13 : ι → ι . 0)) x6) (setsum 0 0)) (λ x9 x10 . λ x11 : ι → ι . x10)) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ι . x1 (λ x9 : ι → ι → ι . 0) (λ x9 x10 . λ x11 : ι → ι . setsum (x7 (λ x12 : (ι → ι) → ι → ι . x0 (λ x13 : ι → ι → ι . x10) 0 (λ x13 x14 . setsum 0 0)) 0 (λ x12 . setsum (Inj1 0) x9) (x2 (λ x12 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι → ι . 0) (λ x12 x13 . x2 (λ x14 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x15 : ι → ι → ι → ι . 0) (λ x14 x15 . 0)))) x9) = x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . x0 (λ x9 : ι → ι → ι . x7 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x14 : ι → ι → ι → ι . setsum 0 0) (λ x13 x14 . Inj0 (x2 (λ x15 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x16 : ι → ι → ι → ι . 0) (λ x15 x16 . 0)))) (λ x10 x11 . x7 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x1 (λ x15 : ι → ι → ι . x3 (λ x16 : ι → (ι → ι → ι) → ι . 0) 0) (λ x15 x16 . λ x17 : ι → ι . Inj0 0)) (λ x12 x13 . x0 (λ x14 : ι → ι → ι . 0) (Inj0 0) (λ x14 x15 . setsum 0 0)))) x5 (λ x9 x10 . x0 (λ x11 : ι → ι → ι . Inj1 x9) x6 (λ x11 x12 . 0)) = Inj1 (x1 (λ x9 : ι → ι → ι . x9 (x0 (λ x10 : ι → ι → ι . x0 (λ x11 : ι → ι → ι . 0) 0 (λ x11 x12 . 0)) (setsum 0 0) (λ x10 x11 . x2 (λ x12 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι → ι . 0) (λ x12 x13 . 0))) (x1 (λ x10 : ι → ι → ι . x6) (λ x10 x11 . λ x12 : ι → ι . x11))) (λ x9 x10 . λ x11 : ι → ι . 0))) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι → ι . x0 (λ x9 : ι → ι → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι . x6 (λ x11 . x10 (x2 (λ x12 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x13 : ι → ι → ι → ι . 0) (λ x12 x13 . 0)) (λ x12 x13 . 0))) (x6 (λ x10 . Inj1 (x1 (λ x11 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0))))) (x6 (λ x9 . 0)) (λ x9 x10 . x9) = x6 (λ x9 . x9)) ⟶ False (proof)
Theorem 1af22.. : ∀ x0 : (((((ι → ι) → ι) → ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x2 : (ι → ι) → ((ι → ι → ι) → ι) → ι . ∀ x3 : ((((ι → ι → ι) → ι) → ι) → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 : ((ι → ι → ι) → ι) → ι . x2 (λ x10 . 0) (λ x10 : ι → ι → ι . Inj0 (Inj0 (x2 (λ x11 . 0) (λ x11 : ι → ι → ι . 0))))) (setsum (x2 (λ x9 . setsum x7 x7) (λ x9 : ι → ι → ι . 0)) (x6 (λ x9 : ι → ι → ι . Inj0 0))) = x2 (λ x9 . setsum (setsum (setsum (x3 (λ x10 : ((ι → ι → ι) → ι) → ι . 0) 0) (setsum 0 0)) (x0 (λ x10 : (((ι → ι) → ι) → ι → ι) → ι . x6 (λ x11 : ι → ι → ι . 0)) (λ x10 : ι → ι . λ x11 . setsum 0 0))) (x0 (λ x10 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . setsum 0 (setsum 0 0)))) (λ x9 : ι → ι → ι . x9 x7 x7)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι . x3 (λ x9 : ((ι → ι → ι) → ι) → ι . x1 (λ x10 . 0) (x7 (λ x10 . setsum (x1 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0) 0 0 0))) (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum (x0 (λ x12 : (((ι → ι) → ι) → ι → ι) → ι . x10 (λ x13 . 0) 0) (λ x12 : ι → ι . λ x13 . x11)) 0) 0 (setsum (x9 (λ x10 : ι → ι → ι . 0)) 0) 0) (x1 (λ x9 . Inj1 (Inj0 (x0 (λ x10 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . 0)))) x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0) (setsum 0 0) (x3 (λ x9 : ((ι → ι → ι) → ι) → ι . setsum 0 (setsum 0 0)) 0) (Inj0 (setsum (setsum 0 0) 0))) = Inj1 x6) ⟶ (∀ x4 : ((ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 . 0) (λ x9 : ι → ι → ι . Inj0 (x5 (Inj1 (x2 (λ x10 . 0) (λ x10 : ι → ι → ι . 0))) (λ x10 x11 . x9 0 (x3 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) 0)))) = x7) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 . Inj1 0) (λ x9 : ι → ι → ι . x0 (λ x10 : (((ι → ι) → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι . λ x12 . Inj1 0)) (λ x10 : ι → ι . λ x11 . 0)) = Inj1 x6) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x1 (λ x9 . 0) (x1 (λ x9 . Inj0 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . x0 (λ x11 : (((ι → ι) → ι) → ι → ι) → ι . setsum (x2 (λ x12 . 0) (λ x12 : ι → ι → ι . 0)) (x3 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) 0)) (λ x11 : ι → ι . λ x12 . x0 (λ x13 : (((ι → ι) → ι) → ι → ι) → ι . setsum 0 0) (λ x13 : ι → ι . λ x14 . x2 (λ x15 . 0) (λ x15 : ι → ι → ι . 0)))) 0 (Inj1 0) (Inj1 (x3 (λ x9 : ((ι → ι → ι) → ι) → ι . Inj1 0) (setsum 0 0)))) (λ x9 : (ι → ι) → ι → ι . λ x10 . x10) (Inj0 (Inj1 x5)) (x3 (λ x9 : ((ι → ι → ι) → ι) → ι . setsum (Inj1 0) (x9 (λ x10 : ι → ι → ι . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) 0))) (x1 (λ x9 . x1 (λ x10 . 0) (setsum 0 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum 0 0) 0 x5 x5) x4 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0) 0 (x1 (λ x9 . x1 (λ x10 . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0) 0 0 0) (x2 (λ x9 . 0) (λ x9 : ι → ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . 0) 0 (x1 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0) 0 0 0) (x7 0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0))) 0)) (x6 x5) = setsum (x6 (x2 (λ x9 . setsum 0 (x7 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0))) (λ x9 : ι → ι → ι . setsum (x0 (λ x10 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x10 : ι → ι . λ x11 . 0)) (Inj0 0)))) (Inj1 (setsum x5 (setsum 0 (x6 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x9 . x5 0 (λ x10 : ι → ι . λ x11 . x0 (λ x12 : (((ι → ι) → ι) → ι → ι) → ι . Inj0 x11) (λ x12 : ι → ι . λ x13 . x10 (x12 0))) (λ x10 . Inj0 x9)) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . x10) (λ x11 : ι → ι → ι . x3 (λ x12 : ((ι → ι → ι) → ι) → ι . setsum 0 (x1 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι → ι . λ x14 . 0) 0 0 0)) 0)) 0 x6 (x7 (Inj0 (x0 (λ x9 : (((ι → ι) → ι) → ι → ι) → ι . setsum 0 0) (λ x9 : ι → ι . λ x10 . 0)))) = x5 (x0 (λ x9 : (((ι → ι) → ι) → ι → ι) → ι . x1 (λ x10 . 0) (Inj0 (setsum 0 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 . x10 (λ x12 . setsum 0 0) 0) 0 (setsum (x3 (λ x10 : ((ι → ι → ι) → ι) → ι . 0) 0) (x5 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0))) (x5 (x2 (λ x10 . 0) (λ x10 : ι → ι → ι . 0)) (λ x10 : ι → ι . λ x11 . x0 (λ x12 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x10 . 0))) (λ x9 : ι → ι . λ x10 . 0)) (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . setsum (Inj1 x10) 0) (x2 (λ x11 . x2 (λ x12 . 0) (λ x12 : ι → ι → ι . setsum 0 0)) (λ x11 : ι → ι → ι . x0 (λ x12 : (((ι → ι) → ι) → ι → ι) → ι . x12 (λ x13 : (ι → ι) → ι . λ x14 . 0)) (λ x12 : ι → ι . λ x13 . Inj1 0)))) (λ x9 . x5 x6 (λ x10 : ι → ι . λ x11 . x9) (λ x10 . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . x3 (λ x12 : ((ι → ι → ι) → ι) → ι . x12 (λ x13 : ι → ι → ι . 0)) (x0 (λ x12 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x12 : ι → ι . λ x13 . 0))) (setsum (setsum 0 0) (Inj0 0))))) ⟶ (∀ x4 x5 : ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . Inj1 0) = x5 (Inj1 (setsum 0 0)) (x5 (Inj0 (x7 (Inj1 0) (λ x9 : ι → ι . x3 (λ x10 : ((ι → ι → ι) → ι) → ι . 0) 0) (λ x9 . 0))) (x4 (x3 (λ x9 : ((ι → ι → ι) → ι) → ι . x2 (λ x10 . 0) (λ x10 : ι → ι → ι . 0)) 0) (x3 (λ x9 : ((ι → ι → ι) → ι) → ι . x6 (λ x10 . 0)) (Inj0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (ι → ι) → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ((ι → ι) → ι) → ι → ι → ι . x0 (λ x9 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 . 0) = setsum (Inj0 0) (x2 (λ x9 . x0 (λ x10 : (((ι → ι) → ι) → ι → ι) → ι . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (Inj0 0)) (λ x10 : ι → ι . λ x11 . x7 (λ x12 : ι → ι . Inj0 0) (x10 0) (x1 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0) 0 0 0))) (λ x9 : ι → ι → ι . setsum (setsum (Inj1 0) (x2 (λ x10 . 0) (λ x10 : ι → ι → ι . 0))) (Inj0 (x5 (λ x10 . 0) (λ x10 . 0)))))) ⟶ False (proof)
Theorem aa8c7.. : ∀ x0 : (ι → ι) → (ι → ι) → (ι → ι) → ι . ∀ x1 : (((((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι) → ι → ι → ι → ι) → (ι → (ι → ι → ι) → ι) → ι . ∀ x2 : (ι → ι) → ι → ι → (ι → ι) → ι → ι → ι . ∀ x3 : ((ι → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x3 (λ x9 : ι → ι . 0) (x2 (λ x9 . x5 (x2 (λ x10 . setsum 0 0) (x5 0 0) (Inj1 0) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x12 x13 x14 . 0) (λ x11 . λ x12 : ι → ι → ι . 0)) (x5 0 0) 0) (x6 0)) (x2 (λ x9 . x2 (λ x10 . x9) (setsum 0 0) (x7 (λ x10 . λ x11 : ι → ι . 0)) (λ x10 . 0) x9 (x5 0 0)) (x3 (λ x9 : ι → ι . x2 (λ x10 . 0) 0 0 (λ x10 . 0) 0 0) (x3 (λ x9 : ι → ι . 0) 0 0) (x7 (λ x9 . λ x10 : ι → ι . 0))) (x7 (λ x9 . λ x10 : ι → ι . Inj1 0)) (λ x9 . x5 0 (setsum 0 0)) (x3 (λ x9 : ι → ι . 0) 0 (setsum 0 0)) (x3 (λ x9 : ι → ι . Inj1 0) (x2 (λ x9 . 0) 0 0 (λ x9 . 0) 0 0) (setsum 0 0))) (x6 0) (λ x9 . setsum (Inj1 (x3 (λ x10 : ι → ι . 0) 0 0)) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . 0))) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . Inj0 (x0 (λ x13 . 0) (λ x13 . 0) (λ x13 . 0))) (λ x9 . λ x10 : ι → ι → ι . 0)) (setsum (x5 (x6 0) (x0 (λ x9 . 0) (λ x9 . 0) (λ x9 . 0))) 0)) (x3 (λ x9 : ι → ι . 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . 0) (λ x9 . λ x10 : ι → ι → ι . setsum 0 0)) (x5 (x7 (λ x9 . λ x10 : ι → ι . 0)) 0)) = x2 (λ x9 . x9) (Inj0 x4) (Inj0 x4) (λ x9 . x5 0 (x7 (λ x10 . λ x11 : ι → ι . x3 (λ x12 : ι → ι . x12 0) 0 (x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x13 x14 x15 . 0) (λ x12 . λ x13 : ι → ι → ι . 0))))) (Inj0 (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . 0) (λ x9 . λ x10 : ι → ι → ι . Inj1 0))) (setsum 0 (x7 (λ x9 . λ x10 : ι → ι . x10 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x3 (λ x9 : ι → ι . x0 (λ x10 . Inj0 (x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x12 x13 x14 . setsum 0 0) (λ x11 . λ x12 : ι → ι → ι . 0))) (λ x10 . Inj0 (x0 (λ x11 . setsum 0 0) (λ x11 . 0) (λ x11 . x7 (λ x12 . 0) (λ x12 : ι → ι . 0) (λ x12 . 0) 0))) (λ x10 . Inj0 (x9 0))) (Inj0 (setsum 0 (Inj0 x5))) (x7 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . x0 (λ x14 . setsum 0 0) (λ x14 . x1 (λ x15 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x16 x17 x18 . 0) (λ x15 . λ x16 : ι → ι → ι . 0)) (λ x14 . 0)) (λ x10 . λ x11 : ι → ι → ι . 0)) (λ x9 : ι → ι . Inj1 (setsum (x0 (λ x10 . 0) (λ x10 . 0) (λ x10 . 0)) (setsum 0 0))) (λ x9 . 0) (Inj0 0)) = Inj0 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x2 (λ x9 . x9) (Inj1 0) (x3 (λ x9 : ι → ι . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . Inj1 (x3 (λ x12 : ι → ι . 0) 0 0))) (x4 (x5 (λ x9 : (ι → ι) → ι → ι . x3 (λ x10 : ι → ι . 0) 0 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . 0) (λ x9 . λ x10 : ι → ι → ι . 0)) (λ x9 . 0))) (setsum (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . x11) (λ x9 . λ x10 : ι → ι → ι . x3 (λ x11 : ι → ι . 0) 0 0)) (x5 (λ x9 : (ι → ι) → ι → ι . Inj1 0) 0 (λ x9 . setsum 0 0)))) (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . Inj1 (setsum 0 (setsum 0 0)))) (setsum (x0 (λ x9 . x0 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x12 x13 x14 . 0) (λ x11 . λ x12 : ι → ι → ι . 0)) (λ x10 . Inj0 0) (λ x10 . 0)) (λ x9 . 0) (λ x9 . x5 (λ x10 : (ι → ι) → ι → ι . x7 0 (λ x11 : ι → ι . λ x12 . 0)) x9 (λ x10 . 0))) (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . x2 (λ x11 . x3 (λ x12 : ι → ι . 0) 0 0) (x7 0 (λ x11 : ι → ι . λ x12 . 0)) (x3 (λ x11 : ι → ι . 0) 0 0) (λ x11 . x2 (λ x12 . 0) 0 0 (λ x12 . 0) 0 0) (x3 (λ x11 : ι → ι . 0) 0 0) (setsum 0 0)))) 0 = x3 (λ x9 : ι → ι . x7 (x9 (x3 (λ x10 : ι → ι . x2 (λ x11 . 0) 0 0 (λ x11 . 0) 0 0) 0 (Inj0 0))) (λ x10 : ι → ι . λ x11 . x2 (λ x12 . 0) 0 0 (λ x12 . 0) 0 0)) (x2 (λ x9 . x0 (λ x10 . 0) (λ x10 . 0) (λ x10 . x7 (Inj0 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 . 0) (λ x13 . 0) (λ x13 . 0)))) (x4 0) 0 (λ x9 . 0) (setsum 0 (setsum (x3 (λ x9 : ι → ι . 0) 0 0) (x0 (λ x9 . 0) (λ x9 . 0) (λ x9 . 0)))) (x2 (λ x9 . x7 0 (λ x10 : ι → ι . λ x11 . x9)) 0 (x2 (λ x9 . x9) (x7 0 (λ x9 : ι → ι . λ x10 . 0)) (setsum 0 0) (λ x9 . 0) (x4 0) 0) (λ x9 . x3 (λ x10 : ι → ι . x6 (λ x11 : ι → ι → ι . λ x12 : ι → ι . 0)) (x6 (λ x10 : ι → ι → ι . λ x11 : ι → ι . 0)) (setsum 0 0)) (setsum 0 (x0 (λ x9 . 0) (λ x9 . 0) (λ x9 . 0))) (Inj0 (x7 0 (λ x9 : ι → ι . λ x10 . 0))))) (setsum (x5 (λ x9 : (ι → ι) → ι → ι . x5 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . x10)) (setsum 0 (x4 0)) (λ x9 . 0)) 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 . x2 (λ x10 . 0) (Inj1 0) (x0 (λ x10 . setsum x7 (setsum 0 0)) (λ x10 . 0) (λ x10 . 0)) (λ x10 . x10) x6 0) 0 x5 (λ x9 . x9) x5 0 = x5) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . x11) (λ x9 . λ x10 : ι → ι → ι . 0) = x5) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . Inj0 (x9 (λ x13 : (ι → ι) → ι → ι . x1 (λ x14 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x15 x16 x17 . Inj0 0) (λ x14 . λ x15 : ι → ι → ι . x15 0 0)) (setsum (x0 (λ x13 . 0) (λ x13 . 0) (λ x13 . 0)) (x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x14 x15 x16 . 0) (λ x13 . λ x14 : ι → ι → ι . 0))) (λ x13 . setsum x10 0))) (λ x9 . λ x10 : ι → ι → ι . x7 (λ x11 . 0)) = x7 (λ x9 . x2 (λ x10 . x6 0) x9 (setsum (x7 (λ x10 . 0)) (x7 (λ x10 . Inj0 0))) (λ x10 . x2 (λ x11 . 0) 0 (x6 0) (λ x11 . x7 (λ x12 . 0)) (x3 (λ x11 : ι → ι . x0 (λ x12 . 0) (λ x12 . 0) (λ x12 . 0)) (Inj1 0) 0) x9) (setsum (x3 (λ x10 : ι → ι . x2 (λ x11 . 0) 0 0 (λ x11 . 0) 0 0) 0 x5) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . x1 (λ x14 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x15 x16 x17 . 0) (λ x14 . λ x15 : ι → ι → ι . 0)) (λ x10 . λ x11 : ι → ι → ι . x0 (λ x12 . 0) (λ x12 . 0) (λ x12 . 0)))) (x6 (x0 (λ x10 . x2 (λ x11 . 0) 0 0 (λ x11 . 0) 0 0) (λ x10 . x7 (λ x11 . 0)) (λ x10 . setsum 0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . x2 (λ x14 . Inj1 (setsum 0 0)) 0 (setsum x12 (x2 (λ x14 . 0) 0 0 (λ x14 . 0) 0 0)) (λ x14 . x14) (setsum (x3 (λ x14 : ι → ι . 0) 0 0) (x1 (λ x14 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x15 x16 x17 . 0) (λ x14 . λ x15 : ι → ι → ι . 0))) (Inj1 (Inj1 0))) (λ x10 . λ x11 : ι → ι → ι . Inj0 (x2 (λ x12 . x9) (setsum 0 0) (x0 (λ x12 . 0) (λ x12 . 0) (λ x12 . 0)) (λ x12 . x12) (setsum 0 0) (x0 (λ x12 . 0) (λ x12 . 0) (λ x12 . 0))))) (λ x9 . Inj0 0) (λ x9 . 0) = x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 . setsum 0) (λ x9 . λ x10 : ι → ι → ι . x3 (λ x11 : ι → ι . Inj1 (x3 (λ x12 : ι → ι . 0) x9 (x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x13 x14 x15 . 0) (λ x12 . λ x13 : ι → ι → ι . 0)))) (setsum (Inj0 0) (x2 (λ x11 . 0) (Inj1 0) (x3 (λ x11 : ι → ι . 0) 0 0) (λ x11 . 0) (Inj0 0) (setsum 0 0))) 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → (ι → ι → ι) → ι . x0 (λ x9 . x3 (λ x10 : ι → ι . x0 (λ x11 . Inj0 (Inj1 0)) (λ x11 . setsum (x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x13 x14 x15 . 0) (λ x12 . λ x13 : ι → ι → ι . 0)) 0) (λ x11 . x0 (λ x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x14 x15 x16 . 0) (λ x13 . λ x14 : ι → ι → ι . 0)) (λ x12 . setsum 0 0) (λ x12 . 0))) (Inj1 (x7 (λ x10 : ι → ι . 0) (λ x10 x11 . x0 (λ x12 . 0) (λ x12 . 0) (λ x12 . 0)))) (setsum (Inj1 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . 0))) (x0 (λ x10 . Inj1 0) (λ x10 . x6 0) (λ x10 . x7 (λ x11 : ι → ι . 0) (λ x11 x12 . 0))))) (λ x9 . 0) (λ x9 . setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . x0 (λ x12 . x12) (λ x12 . x0 (λ x13 . 0) (λ x13 . 0) (λ x13 . 0)) (λ x12 . x9))) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . x11) (λ x10 . λ x11 : ι → ι → ι . x11 0 (x7 (λ x12 : ι → ι . 0) (λ x12 x13 . 0))))) = x3 (λ x9 : ι → ι . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x10 . λ x11 : ι → ι → ι . x7 (λ x12 : ι → ι . 0) (λ x12 x13 . x0 (λ x14 . x13) (λ x14 . x11 0 0) (λ x14 . x1 (λ x15 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x16 x17 x18 . 0) (λ x15 . λ x16 : ι → ι → ι . 0))))) (setsum 0 (x6 (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . λ x10 x11 x12 . x3 (λ x13 : ι → ι . 0) 0 0) (λ x9 . λ x10 : ι → ι → ι . x6 0)))) x5) ⟶ False (proof)
Theorem 7ec4f.. : ∀ x0 : ((ι → ι → ι → ι) → ι) → ((((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι) → ι . ∀ x1 : (((((ι → ι) → ι → ι) → ι → ι) → ι) → ι) → ι → ι . ∀ x2 : (((((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι) → ι) → (ι → (ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι) → (ι → ι → (ι → ι) → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . 0) = x6) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → (ι → ι) → ι . x3 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → ι → ι) → ι . Inj0 (x12 (λ x13 : (ι → ι) → ι → ι . λ x14 . x12 (λ x15 : (ι → ι) → ι → ι . λ x16 . 0)))) x10) = x1 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x10 . λ x11 x12 : ι → ι . λ x13 . x11 (x11 x10))) (setsum 0 (Inj0 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι → ι . x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x9 . λ x10 x11 : ι → ι . λ x12 . x0 (λ x13 : ι → ι → ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 : ι → ι → ι . x2 (λ x15 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x15 . λ x16 x17 : ι → ι . λ x18 . setsum (x0 (λ x19 : ι → ι → ι → ι . 0) (λ x19 : ((ι → ι) → ι → ι) → ι . λ x20 : ι → ι → ι . 0)) (setsum 0 0)))) = x0 (λ x9 : ι → ι → ι → ι . x3 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . 0)) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x1 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) 0)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . Inj0 0) (λ x9 . λ x10 x11 : ι → ι . λ x12 . 0) = setsum 0 (x4 (setsum (x4 (setsum 0 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) 0) (λ x9 . 0)) (x3 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . setsum 0 0))) (x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x0 (λ x10 : ι → ι → ι → ι . x7 (λ x11 : ι → ι → ι . 0)) (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . x7 (λ x12 : ι → ι → ι . 0))) (λ x9 . λ x10 x11 : ι → ι . λ x12 . 0)) (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x2 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x11 . λ x12 x13 : ι → ι . λ x14 . 0)) (setsum 0 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum (x0 (λ x10 : ι → ι → ι → ι . x10 0 x7 0) (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . x3 (λ x12 . x10 (λ x13 : ι → ι . λ x14 . 0)) (λ x12 x13 . λ x14 : ι → ι . 0))) (Inj0 0)) 0 = Inj1 x4) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → (ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x5) (Inj1 0) = Inj0 (x3 (λ x9 . x7 (x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x6 (λ x11 x12 : ι → ι . 0) (λ x11 . 0)) (λ x10 . λ x11 x12 : ι → ι . λ x13 . setsum 0 0)) (Inj1 0) (λ x10 . x2 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x10) (λ x11 . λ x12 x13 : ι → ι . λ x14 . x12 0)) (Inj0 0)) (λ x9 x10 . λ x11 : ι → ι . x9))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι → ι . x0 (λ x9 : ι → ι → ι → ι . x6) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x3 (λ x11 . Inj0 (setsum x11 (x7 (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0))) (λ x11 x12 . λ x13 : ι → ι . setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (x13 0)))) = x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x9 : ι → ι → ι → ι . setsum (Inj1 (setsum 0 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) 0))) (Inj1 0)) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . setsum x6 (Inj0 (x10 (x2 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x11 . λ x12 x13 : ι → ι . λ x14 . 0)) (x10 0 0)))) = x7 0 (λ x9 : ι → ι . x9 0)) ⟶ False (proof)
Theorem 212f6.. : ∀ x0 : ((ι → ι) → ι → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x1 : (ι → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → ((ι → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x3 : (ι → ι → ι) → (ι → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 x10 . x9) (λ x9 . x1 (λ x10 . 0) x5) = Inj0 (x3 (λ x9 x10 . 0) (λ x9 . x7))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x9 x10 . 0) (λ x9 . x5 x9 (λ x10 . x7 (λ x11 : (ι → ι) → ι . 0)) (λ x10 . setsum 0 (x1 (λ x11 . x10) 0)) (x5 (setsum (setsum 0 0) (x5 0 (λ x10 . 0) (λ x10 . 0) 0)) (λ x10 . setsum x6 (setsum 0 0)) (λ x10 . Inj0 (x3 (λ x11 x12 . 0) (λ x11 . 0))) (setsum x9 0))) = x5 (x3 (λ x9 x10 . 0) (λ x9 . Inj0 0)) (λ x9 . x1 (λ x10 . x2 (λ x11 . 0) (setsum (x7 (λ x11 : (ι → ι) → ι . 0)) (setsum 0 0)) (λ x11 : ι → ι → ι . λ x12 : ι → ι . x0 (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0) (Inj1 0) (x2 (λ x13 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x13 : ι → ι . 0))) (λ x11 : ι → ι . 0)) 0) (λ x9 . x7 (λ x10 : (ι → ι) → ι . 0)) (Inj1 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . x6 0) (x0 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x1 Inj1 (setsum (setsum 0 0) (Inj0 0))) x4 (setsum (Inj1 (Inj0 0)) (Inj0 x4))) (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0) (λ x9 : ι → ι . 0) = setsum 0 (setsum (setsum 0 (setsum 0 (setsum 0 0))) (x0 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . setsum x13 x13) x7 (x1 (λ x9 . x5) 0)))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x2 (λ x9 . setsum (x5 (x3 (λ x10 x11 . x11) (λ x10 . Inj0 0))) (setsum (x0 (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . x11) 0 (x3 (λ x10 x11 . 0) (λ x10 . 0))) (x3 (λ x10 x11 . 0) (λ x10 . 0)))) (x1 (λ x9 . 0) x7) (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj1 (x1 (λ x11 . 0) (x3 (λ x11 x12 . Inj0 0) (λ x11 . x2 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0))))) (λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . x13) 0 0) = Inj1 x7) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . x1 (λ x10 . 0) (setsum 0 x5)) (setsum 0 x7) = x1 (λ x9 . setsum (Inj1 (Inj1 (x1 (λ x10 . 0) 0))) (x3 (λ x10 x11 . x7) (λ x10 . x9))) x6) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 . x9) 0 = x7 (x2 (λ x9 . x3 (λ x10 x11 . x0 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . x2 (λ x17 . 0) 0 (λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) (λ x17 : ι → ι . 0)) (x1 (λ x12 . 0) 0) 0) (λ x10 . x3 (λ x11 x12 . 0) (λ x11 . 0))) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . setsum x6 (Inj0 (setsum 0 0))) (λ x9 : ι → ι . x1 (λ x10 . Inj0 0) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . Inj0 (setsum (x1 (λ x14 . 0) (Inj0 0)) x13)) x7 (Inj1 (Inj0 0)) = x7) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x0 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x12) (setsum 0 x5) x5 = setsum (x1 (λ x9 . setsum 0 (x3 (λ x10 x11 . Inj0 0) (λ x10 . x2 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x11 : ι → ι . 0)))) (x2 (λ x9 . x9) (x4 0 (x7 (λ x9 : (ι → ι) → ι → ι . 0)) (x0 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . 0) 0 0) (setsum 0 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . x7 (λ x11 : (ι → ι) → ι → ι . x3 (λ x12 x13 . 0) (λ x12 . 0))) (λ x9 : ι → ι . x7 (λ x10 : (ι → ι) → ι → ι . Inj1 0)))) (x2 (λ x9 . x6 0 (λ x10 : ι → ι . λ x11 . 0)) (x3 (λ x9 x10 . x2 (λ x11 . x11) (x7 (λ x11 : (ι → ι) → ι → ι . 0)) (λ x11 : ι → ι → ι . λ x12 : ι → ι . x2 (λ x13 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x13 : ι → ι . 0)) (λ x11 : ι → ι . 0)) (λ x9 . x5)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0) (λ x9 : ι → ι . x3 (λ x10 x11 . x0 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . setsum 0 0) (x2 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0)) (x3 (λ x12 x13 . 0) (λ x12 . 0))) (setsum 0)))) ⟶ False (proof)
Theorem e23eb.. : ∀ x0 : (ι → ι → ι → ι) → (ι → ι) → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι → ι) → ι → ((ι → ι) → ι → ι) → ι) → ι → ι → ι → ι . ∀ x2 : ((ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x7 . x3 (λ x9 . 0) (λ x9 : ι → ι . setsum 0 (x0 (λ x10 x11 x12 . 0) (λ x10 . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . Inj0 0) (x6 (λ x11 : (ι → ι) → ι . 0) 0) (x2 (λ x11 : ι → ι . 0) (λ x11 x12 . 0)) (setsum 0 0)))) 0 (x2 (λ x9 : ι → ι . x5 (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 . x0 (λ x12 x13 x14 . 0) (λ x12 . 0)) (λ x11 : ι → ι . Inj0 0) 0 0 (setsum 0 0))) (λ x9 x10 . x0 (λ x11 x12 x13 . 0) (λ x11 . 0))) (setsum 0 0) = x2 (λ x9 : ι → ι . x9 (Inj1 (setsum (Inj0 0) (x9 0)))) (λ x9 x10 . Inj0 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x3 (λ x10 . 0) (λ x10 : ι → ι . x3 (λ x11 . Inj1 0) (λ x11 : ι → ι . x11 0) (x6 (x3 (λ x11 . 0) (λ x11 : ι → ι . 0) 0 0 0)) (x10 (x10 0)) 0) (x3 (λ x10 . x3 (λ x11 . setsum 0 0) (λ x11 : ι → ι . x0 (λ x12 x13 x14 . 0) (λ x12 . 0)) (Inj1 0) (x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0 0 0) (x2 (λ x11 : ι → ι . 0) (λ x11 x12 . 0))) (λ x10 : ι → ι . 0) (Inj1 x5) x5 (Inj0 0)) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x2 (λ x13 : ι → ι . setsum 0 0) (λ x13 x14 . x0 (λ x15 x16 x17 . 0) (λ x15 . 0))) x9 (setsum x5 0) x7) (Inj1 (Inj0 (Inj0 0)))) (λ x9 : ι → ι . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . setsum (x10 (λ x13 . λ x14 : ι → ι . λ x15 . x0 (λ x16 x17 x18 . 0) (λ x16 . 0)) (x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) 0 0 0)) (x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) 0 0 (Inj1 0))) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) x5 (x3 (λ x10 . x0 (λ x11 x12 x13 . 0) (λ x11 . 0)) (λ x10 : ι → ι . 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . 0) 0 0 0) (setsum 0 0) (x6 0)) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) 0 (x9 0) (setsum 0 0))) 0 x7) (setsum 0 (x6 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (Inj1 0) 0 0))) (x3 (λ x9 . x2 (λ x10 : ι → ι . x2 (λ x11 : ι → ι . 0) (λ x11 x12 . x11)) (λ x10 x11 . 0)) (λ x9 : ι → ι . 0) x7 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x9 (λ x12 . λ x13 : ι → ι . λ x14 . x11 (λ x15 . 0) 0) (x11 (λ x12 . 0) 0)) 0 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . 0) 0 0 0) (x2 (λ x9 : ι → ι . 0) (λ x9 x10 . 0)) x5 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) 0 0 0)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . Inj0 0) (x3 (λ x9 . 0) (λ x9 : ι → ι . 0) 0 0 0) x7 0)) 0) (x6 0) = x3 (λ x9 . Inj0 (Inj0 x7)) (λ x9 : ι → ι . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x2 (λ x13 : ι → ι . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . Inj1 0) 0 0 (Inj1 0)) (λ x13 x14 . Inj1 0)) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 . Inj0 0) (λ x13 : ι → ι . x12 (λ x14 . 0) 0) (setsum 0 0) (x0 (λ x13 x14 x15 . 0) (λ x13 . 0)) (x10 (λ x13 . λ x14 : ι → ι . λ x15 . 0) 0)) x7 (setsum (x3 (λ x10 . 0) (λ x10 : ι → ι . 0) 0 0 0) (x2 (λ x10 : ι → ι . 0) (λ x10 x11 . 0))) (Inj0 (x2 (λ x10 : ι → ι . 0) (λ x10 x11 . 0)))) (setsum 0 (x2 (λ x10 : ι → ι . x0 (λ x11 x12 x13 . 0) (λ x11 . 0)) (λ x10 x11 . Inj0 0))) (x0 (λ x10 x11 x12 . x10) (λ x10 . x9 0))) x7 (setsum (Inj0 x7) (x0 (λ x9 x10 x11 . setsum (x0 (λ x12 x13 x14 . 0) (λ x12 . 0)) (x2 (λ x12 : ι → ι . 0) (λ x12 x13 . 0))) (λ x9 . x0 (λ x10 x11 x12 . x2 (λ x13 : ι → ι . 0) (λ x13 x14 . 0)) (λ x10 . x9)))) (Inj0 0)) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 . Inj0 (Inj0 0)) (λ x11 : ι → ι . Inj0 (Inj1 0)) (x0 (λ x11 x12 x13 . x10 (λ x14 . 0) 0) (λ x11 . x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) 0 0 0)) (x2 (λ x11 : ι → ι . setsum 0 0) (λ x11 x12 . 0)) (setsum (x6 (λ x11 : (ι → ι) → ι → ι . 0) 0 0) (x10 (λ x11 . 0) 0))) (x3 (λ x10 . 0) (λ x10 : ι → ι . x2 (λ x11 : ι → ι . setsum 0 0) (λ x11 x12 . x3 (λ x13 . 0) (λ x13 : ι → ι . 0) 0 0 0)) (setsum (x2 (λ x10 : ι → ι . 0) (λ x10 x11 . 0)) (x9 0)) (x2 (λ x10 : ι → ι . x7) (λ x10 x11 . 0)) (setsum (x0 (λ x10 x11 x12 . 0) (λ x10 . 0)) (setsum 0 0))) (x0 (λ x10 x11 x12 . x10) (λ x10 . x0 (λ x11 x12 x13 . x13) (λ x11 . x9 0)))) (λ x9 x10 . Inj1 0) = Inj1 (Inj1 (x0 (λ x9 x10 x11 . x2 (λ x12 : ι → ι . 0) (λ x12 x13 . x10)) (λ x9 . setsum 0 (x6 (λ x10 : (ι → ι) → ι → ι . 0) 0 0))))) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ι → ι . 0) (λ x9 x10 . 0) = Inj0 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : ι → ι . 0) (λ x12 x13 . x0 (λ x14 x15 x16 . x15) (λ x14 . x12))) 0 x7 x7)) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . setsum 0 (setsum 0 (setsum 0 0))) (x11 (λ x12 . x12) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . x11 (λ x15 . 0) 0) x10 (x0 (λ x12 x13 x14 . 0) (λ x12 . 0)) 0)) (setsum (setsum 0 (x2 (λ x12 : ι → ι . 0) (λ x12 x13 . 0))) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (x11 (λ x12 . 0) 0) (x11 (λ x12 . 0) 0) (Inj1 0))) (setsum (x2 (λ x12 : ι → ι . setsum 0 0) (λ x12 x13 . 0)) (setsum 0 (x2 (λ x12 : ι → ι . 0) (λ x12 x13 . 0))))) 0 0 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . setsum 0 (Inj0 (Inj0 0))) x6 0 x4) = x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . x3 (λ x13 . Inj1 (x11 (λ x14 . 0) 0)) (λ x13 : ι → ι . x2 (λ x14 : ι → ι . setsum 0 0) (λ x14 x15 . x2 (λ x16 : ι → ι . 0) (λ x16 x17 . 0))) 0 (x11 (λ x13 . 0) (setsum 0 0)) (Inj1 (x3 (λ x13 . 0) (λ x13 : ι → ι . 0) 0 0 0))) (x11 (λ x12 . x11 (λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) 0 0 0) 0) x10) (setsum 0 (setsum (x2 (λ x12 : ι → ι . 0) (λ x12 x13 . 0)) (setsum 0 0))) (setsum (x11 (λ x12 . x10) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) 0 0 0)) (x0 (λ x12 x13 x14 . setsum 0 0) (λ x12 . Inj0 0)))) x7 (x2 (λ x9 : ι → ι . x0 (λ x10 x11 x12 . 0) (λ x10 . 0)) (λ x9 x10 . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x12) 0 x7 (x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . Inj0 0) (x0 (λ x11 x12 x13 . 0) (λ x11 . 0)) 0 x6))) x4) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . Inj0 (setsum 0 (Inj1 0))) (Inj0 0) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . x0 (λ x15 x16 x17 . Inj0 0) (λ x15 . x2 (λ x16 : ι → ι . 0) (λ x16 x17 . 0))) 0 (Inj0 (x2 (λ x12 : ι → ι . 0) (λ x12 x13 . 0))) (x3 (λ x12 . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) 0 0 0) (λ x12 : ι → ι . Inj1 0) (x9 (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0) 0 (Inj0 0))) 0) 0 (x0 (λ x9 x10 x11 . x2 (λ x12 : ι → ι . x12 (x3 (λ x13 . 0) (λ x13 : ι → ι . 0) 0 0 0)) (λ x12 x13 . x13)) (λ x9 . x6 (λ x10 . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x0 (λ x14 x15 x16 . 0) (λ x14 . 0)) (setsum 0 0) (x0 (λ x11 x12 x13 . 0) (λ x11 . 0)) (x3 (λ x11 . 0) (λ x11 : ι → ι . 0) 0 0 0)))) (Inj1 0) = Inj0 (setsum (x6 (λ x9 . x3 (λ x10 . x10) (λ x10 : ι → ι . x3 (λ x11 . 0) (λ x11 : ι → ι . 0) 0 0 0) (x6 (λ x10 . 0)) (Inj1 0) (x7 (λ x10 . λ x11 : ι → ι . λ x12 . 0)))) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 x10 x11 . setsum 0 x7) (λ x9 . 0) = x5 0 (x2 (λ x9 : ι → ι . x6 0) (λ x9 x10 . 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x9 x10 x11 . x7 x10 (λ x12 : ι → ι . x10)) (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x11) (setsum x5 (Inj0 (x7 0 (λ x10 : ι → ι . 0)))) (Inj1 (setsum 0 (setsum 0 0))) (x7 (x3 (λ x10 . x2 (λ x11 : ι → ι . 0) (λ x11 x12 . 0)) (λ x10 : ι → ι . Inj1 0) (setsum 0 0) x9 (setsum 0 0)) (λ x10 : ι → ι . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) (Inj1 0) x6 x6))) = x7 (setsum (setsum 0 (x4 (x3 (λ x9 . 0) (λ x9 : ι → ι . 0) 0 0 0))) x6) (λ x9 : ι → ι . x5)) ⟶ False (proof)
Theorem e2aee.. : ∀ x0 : (((ι → ι → ι → ι) → ι) → ι → (ι → ι) → ι) → ι → ι . ∀ x1 : (((ι → ι) → (ι → ι → ι) → ι → ι) → ι → (ι → ι) → ι) → (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x2 : (((ι → ι) → (ι → ι → ι) → ι) → ι) → (ι → ι → ι → ι → ι) → ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x3 : (ι → ι → ι → ι) → ((((ι → ι) → ι) → ι) → (ι → ι → ι) → ι → ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 x10 x11 . 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . Inj0 0) (λ x13 : (ι → ι) → ι . λ x14 . x13 (λ x15 . x3 (λ x16 x17 x18 . x0 (λ x19 : (ι → ι → ι → ι) → ι . λ x20 . λ x21 : ι → ι . 0) 0) (λ x16 : ((ι → ι) → ι) → ι . λ x17 : ι → ι → ι . λ x18 x19 . x18) (λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . x1 (λ x18 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x19 . λ x20 : ι → ι . 0) (λ x18 : (ι → ι) → ι . λ x19 . 0) (λ x18 . 0) 0))) (λ x13 . x10 (x0 (λ x14 : (ι → ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι . setsum 0 0) (setsum 0 0)) (x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x14 x15 x16 x17 . 0) x11 (λ x14 : ι → ι . λ x15 . setsum 0 0) x12 (setsum 0 0))) 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x3 (λ x11 x12 x13 . x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . x1 (λ x15 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x16 . λ x17 : ι → ι . x14 (λ x18 . 0) (λ x18 x19 . 0)) (λ x15 : (ι → ι) → ι . λ x16 . Inj0 0) (λ x15 . 0) (Inj1 0)) (λ x14 x15 x16 x17 . 0) 0 (λ x14 : ι → ι . λ x15 . x2 (λ x16 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x16 x17 x18 x19 . x16) (x0 (λ x16 : (ι → ι → ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0) (λ x16 : ι → ι . λ x17 . 0) 0 (setsum 0 0)) 0 (setsum (Inj1 0) x11)) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . setsum (x1 (λ x15 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x16 . λ x17 : ι → ι . Inj0 0) (λ x15 : (ι → ι) → ι . λ x16 . x15 (λ x17 . 0)) (λ x15 . Inj1 0) (x3 (λ x15 x16 x17 . 0) (λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι → ι . λ x17 x18 . 0) (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0))) 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x11 (λ x13 . x3 (λ x14 x15 x16 . setsum 0 0) (λ x14 : ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . Inj0 0)) 0)) = Inj0 (Inj0 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x9 x10 x11 . setsum 0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . x9) (λ x12 x13 x14 x15 . Inj0 (x2 (λ x16 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x16 x17 x18 x19 . 0) 0 (λ x16 : ι → ι . λ x17 . 0) 0 0)) 0 (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . Inj0 0) (λ x14 : (ι → ι) → ι . λ x15 . 0) (λ x14 . setsum 0 0) 0) (x0 (λ x12 : (ι → ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0) (x7 (λ x12 : (ι → ι) → ι . 0)))) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x0 (λ x13 : (ι → ι → ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) (x9 (λ x13 : ι → ι . Inj0 (x3 (λ x14 x15 x16 . 0) (λ x14 : ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0))))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . setsum (x3 (λ x11 x12 x13 . Inj1 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (x7 (λ x11 : (ι → ι) → ι . x0 (λ x12 : (ι → ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . setsum 0 0) (setsum 0 0)))) = setsum 0 (Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . Inj1 (x3 (λ x10 x11 x12 . Inj1 (x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x13 x14 x15 x16 . 0) 0 (λ x13 : ι → ι . λ x14 . 0) 0 0)) (λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . x13) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x0 (λ x12 : (ι → ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x15 x16 x17 x18 . 0) 0 (λ x15 : ι → ι . λ x16 . 0) 0 0) 0))) (λ x9 x10 x11 x12 . x3 (λ x13 x14 x15 . x14) (λ x13 : ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . Inj0 (Inj1 (x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x15 x16 x17 x18 . 0) 0 (λ x15 : ι → ι . λ x16 . 0) 0 0)))) 0 (λ x9 : ι → ι . λ x10 . x3 (λ x11 x12 x13 . 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . x14) (λ x15 x16 x17 x18 . 0) (setsum 0 0) (λ x15 : ι → ι . λ x16 . x13) (Inj0 0) (Inj1 (x3 (λ x15 x16 x17 . 0) (λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι → ι . λ x17 x18 . 0) (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0)))) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . x11 (λ x14 . 0) (setsum 0 0)) (λ x13 x14 x15 x16 . x16) x10 (λ x13 : ι → ι . λ x14 . setsum 0 (x0 (λ x15 : (ι → ι → ι → ι) → ι . λ x16 . λ x17 : ι → ι . 0) 0)) (Inj0 (x12 0)) (x0 (λ x13 : (ι → ι → ι → ι) → ι . λ x14 . λ x15 : ι → ι . setsum 0 0) (x9 0)))) (x0 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . 0) 0) x5 = Inj1 (Inj1 (x4 0))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . x0 (λ x13 : (ι → ι → ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) 0) (Inj1 (x7 (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x10 x11 x12 x13 . 0) 0 (λ x10 : ι → ι . λ x11 . 0) 0 0)))) (λ x9 x10 x11 x12 . x11) 0 (λ x9 : ι → ι . λ x10 . x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x11 x12 x13 x14 . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . setsum (x1 (λ x16 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x17 . λ x18 : ι → ι . 0) (λ x16 : (ι → ι) → ι . λ x17 . 0) (λ x16 . 0) 0) (setsum 0 0)) (λ x15 x16 x17 x18 . 0) 0 (λ x15 : ι → ι . λ x16 . x15 (Inj0 0)) (Inj0 (x0 (λ x15 : (ι → ι → ι → ι) → ι . λ x16 . λ x17 : ι → ι . 0) 0)) 0) x6 (λ x11 : ι → ι . λ x12 . setsum 0 (x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . x12) (λ x13 x14 x15 x16 . x14) (setsum 0 0) (λ x13 : ι → ι . λ x14 . x11 0) x10 (setsum 0 0))) 0 0) 0 (setsum (x0 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x12 x13 x14 x15 . x2 (λ x16 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x16 x17 x18 x19 . 0) 0 (λ x16 : ι → ι . λ x17 . 0) 0 0) (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι . λ x13 . 0) 0 0) (λ x12 : ι → ι . λ x13 . x3 (λ x14 x15 x16 . 0) (λ x14 : ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0)) x10 (x11 0)) 0) 0) = Inj1 x6) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι → ι) → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . setsum (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . x1 (λ x13 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . x12 (λ x16 . 0) (λ x16 x17 . 0)) (λ x13 : (ι → ι) → ι . λ x14 . 0) (λ x13 . x0 (λ x14 : (ι → ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι . 0) 0) 0) (λ x12 x13 x14 x15 . x13) (x11 (setsum 0 0)) (λ x12 : ι → ι . λ x13 . 0) 0 x10) 0) (λ x9 : (ι → ι) → ι . λ x10 . x9 (λ x11 . x7 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . setsum 0 0) (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι . λ x13 . x13) 0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι . λ x13 . 0) 0 0)))) (λ x9 . Inj1 (Inj0 (x0 (λ x10 : (ι → ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . x11) 0))) 0 = x5) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . x11 0) (λ x9 : (ι → ι) → ι . λ x10 . Inj0 (x3 (λ x11 x12 . Inj1) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . x11 (λ x15 : ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . Inj1 (x11 (λ x13 . 0) 0)))) (λ x9 . x5) (x0 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . setsum 0 (setsum 0 (x9 (λ x12 x13 x14 . 0)))) 0) = Inj0 (setsum (x0 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . x11 (x9 (λ x12 x13 x14 . 0))) (setsum (x3 (λ x9 x10 x11 . 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)) (x0 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . 0) 0))) x6)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . x3 (λ x12 x13 x14 . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x11 (x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . setsum 0 0) (λ x14 x15 x16 x17 . x2 (λ x18 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x18 x19 x20 x21 . 0) 0 (λ x18 : ι → ι . λ x19 . 0) 0 0) (x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . 0) (λ x14 : (ι → ι) → ι . λ x15 . 0) (λ x14 . 0) 0) (λ x14 : ι → ι . λ x15 . setsum 0 0) 0 (x12 (λ x14 . 0) 0)))) 0 = setsum (setsum x7 (x4 (λ x9 x10 x11 . 0) x7 (x3 (λ x9 x10 x11 . x7) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x13 x14 x15 x16 . 0) 0 (λ x13 : ι → ι . λ x14 . 0) 0 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)))) 0) ⟶ (∀ x4 : (ι → ι) → ι → ι → ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι . Inj0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . x10) (λ x12 x13 x14 x15 . setsum (x2 (λ x16 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x16 x17 x18 x19 . 0) 0 (λ x16 : ι → ι . λ x17 . 0) 0 0) (x0 (λ x16 : (ι → ι → ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0)) x10 (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . 0) (λ x14 : (ι → ι) → ι . λ x15 . Inj0 0) (λ x14 . setsum 0 0) (x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x14 x15 x16 x17 . 0) 0 (λ x14 : ι → ι . λ x15 . 0) 0 0)) (x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x15 x16 x17 x18 . 0) 0 (λ x15 : ι → ι . λ x16 . 0) 0 0) (λ x12 : (ι → ι) → ι . λ x13 . setsum 0 0) (λ x12 . setsum 0 0) 0) 0)) (Inj1 0) = x7 (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . setsum 0 (Inj1 (x0 (λ x12 : (ι → ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0))) (λ x9 : (ι → ι) → ι . λ x10 . Inj0 0) (λ x9 . 0) (x3 (λ x9 x10 x11 . Inj0 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . 0) (λ x11 x12 x13 x14 . setsum 0 0) 0 (λ x11 : ι → ι . λ x12 . Inj1 0) (x3 (λ x11 x12 x13 . 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (x3 (λ x11 x12 x13 . 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)))))) ⟶ False (proof)
Theorem d392e.. : ∀ x0 : (((((ι → ι) → ι → ι) → ι → ι → ι) → ι) → ι) → ι → ι . ∀ x1 : (ι → ι) → ((ι → ι) → (ι → ι → ι) → (ι → ι) → ι) → ι . ∀ x2 : (ι → ((ι → ι) → (ι → ι) → ι) → ι) → (((ι → ι) → ι) → ι → ι → ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 . 0) (Inj0 (x1 (setsum 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . x11 (Inj1 0)))) = x6) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 . 0) (x6 (setsum (x6 (Inj0 0) (λ x9 . 0) (λ x9 . 0) 0) (x3 (λ x9 . setsum 0 0) 0)) (λ x9 . x9) (λ x9 . 0) (x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) (x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x2 (λ x10 . λ x11 : (ι → ι) → (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . λ x11 x12 x13 . 0)) (x1 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . 0))))) = x6 (setsum (x5 (setsum (x1 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . 0)) 0)) (x3 (λ x9 . x3 (λ x10 . setsum 0 0) (x5 0)) (Inj1 (x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) 0)))) (λ x9 . Inj1 (x7 (λ x10 . x6 (x6 0 (λ x11 . 0) (λ x11 . 0) 0) (λ x11 . x0 (λ x12 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) 0) (λ x11 . 0) 0))) (λ x9 . setsum (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . Inj1 0) (setsum 0 (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) 0))) (x1 (λ x10 . Inj1 (x7 (λ x11 . 0))) (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x1 (λ x13 . 0) (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . x0 (λ x16 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) 0)))) (x6 0 (λ x9 . x9) (λ x9 . 0) (x5 (x1 (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . x0 (λ x12 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x2 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . setsum 0 0) (λ x9 : (ι → ι) → ι . λ x10 x11 x12 . 0) = Inj0 0) ⟶ (∀ x4 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) (x2 (λ x11 . λ x12 : (ι → ι) → (ι → ι) → ι . x0 (λ x13 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) (setsum 0 0)) (λ x11 : (ι → ι) → ι . λ x12 x13 x14 . x14))) (λ x9 : (ι → ι) → ι . λ x10 x11 x12 . 0) = x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . Inj1 0) (setsum (x6 (λ x9 : (ι → ι) → ι . x1 (λ x10 . Inj1 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x0 (λ x13 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . 0) 0))) 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → (ι → ι) → ι . ∀ x7 . x1 (λ x9 . x7) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . Inj0 (x9 (x1 (λ x12 . Inj1 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0)))) = x7) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : (ι → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι) → ι . x1 (λ x9 . x5 (λ x10 x11 . x10) (λ x10 . x6)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . 0) = x5 (λ x9 x10 . setsum 0 (x3 (λ x11 . setsum 0 (x1 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0))) 0)) (λ x9 . Inj0 (x7 (λ x10 : ι → ι → ι . x3 (λ x11 . x1 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x10 . Inj1 (x3 (λ x11 . x7 0) (x1 (λ x11 . 0) (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0)))) (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x10 0)) (Inj0 (x2 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . λ x10 x11 x12 . setsum (Inj0 0) (Inj0 0)))) = setsum (Inj1 (x2 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . x9) (λ x9 : (ι → ι) → ι . λ x10 x11 x12 . x11))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . Inj0 0)) 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x3 (λ x13 . 0) 0)) 0 = x1 (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x6) (Inj0 x7)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . setsum (Inj1 (x0 (λ x12 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x10 0 0) 0)) x7)) ⟶ False (proof)
Theorem d256b.. : ∀ x0 : ((ι → ι → ι) → ι → ι) → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι) → ι) → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι) → ((((ι → ι) → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x3 : ((((ι → ι → ι) → ι) → ι) → ι) → (ι → ι) → (((ι → ι) → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x3 (λ x9 : ((ι → ι → ι) → ι) → ι . x9 (λ x10 : ι → ι → ι . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . x3 (λ x13 : ((ι → ι → ι) → ι) → ι . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 x14 . 0) (λ x13 . 0)) (λ x12 . x3 (λ x13 : ((ι → ι → ι) → ι) → ι . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 x14 . 0) (λ x13 . 0))) (λ x11 . 0) (λ x11 : (ι → ι) → ι . setsum (setsum 0 0) (x0 (λ x12 : ι → ι → ι . λ x13 . 0) 0)) (λ x11 x12 . x1 (λ x13 : (ι → (ι → ι) → ι) → ι . x11) (λ x13 . 0)) (λ x11 . x7))) (λ x9 . setsum (x3 (λ x10 : ((ι → ι → ι) → ι) → ι . Inj1 0) (λ x10 . 0) (λ x10 : (ι → ι) → ι . x6 (λ x11 . setsum 0 0) (x3 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0) (λ x11 x12 . 0) (λ x11 . 0)) (λ x11 . 0)) (λ x10 x11 . x10) (λ x10 . Inj1 (setsum 0 0))) (Inj1 x7)) (λ x9 : (ι → ι) → ι . x6 (λ x10 . Inj1 (x6 (λ x11 . x11) (Inj0 0) (λ x11 . x0 (λ x12 : ι → ι → ι . λ x13 . 0) 0))) (x9 (λ x10 . 0)) Inj1) (λ x9 x10 . x9) (λ x9 . Inj0 0) = setsum (x6 (λ x9 . x3 (λ x10 : ((ι → ι → ι) → ι) → ι . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . x3 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0) (λ x12 . 0)) (λ x11 . x3 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0) (λ x12 . 0)) (λ x11 : (ι → ι) → ι . x3 (λ x12 : ((ι → ι → ι) → ι) → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 x13 . 0) (λ x12 . 0)) (λ x11 x12 . x3 (λ x13 : ((ι → ι → ι) → ι) → ι . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 x14 . 0) (λ x13 . 0)) (λ x11 . setsum 0 0)) (λ x10 . setsum (Inj1 0) (setsum 0 0)) (λ x10 : (ι → ι) → ι . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 . x2 (λ x12 . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x11 : (ι → ι) → ι . x9) (λ x11 x12 . 0) (λ x11 . x2 (λ x12 . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0))) (λ x10 x11 . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . 0) (λ x12 . x10)) (λ x10 . Inj0 x7)) 0 (λ x9 . Inj1 (Inj0 0))) (x3 (λ x9 : ((ι → ι → ι) → ι) → ι . Inj0 0) (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . Inj0 (x0 (λ x11 : ι → ι → ι . λ x12 . 0) 0)) (λ x10 . 0)) (λ x9 : (ι → ι) → ι . setsum 0 (x3 (λ x10 : ((ι → ι → ι) → ι) → ι . x0 (λ x11 : ι → ι → ι . λ x12 . 0) 0) (λ x10 . Inj0 0) (λ x10 : (ι → ι) → ι . x7) (λ x10 x11 . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . 0) (λ x12 . 0)) (λ x10 . x10))) (λ x9 x10 . x9) (λ x9 . Inj0 (x0 (λ x10 : ι → ι → ι . λ x11 . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . 0) (λ x12 . 0)) (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 . x3 (λ x9 : ((ι → ι → ι) → ι) → ι . x9 (λ x10 : ι → ι → ι . x10 (x3 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 . Inj0 0) (λ x11 : (ι → ι) → ι . x11 (λ x12 . 0)) (λ x11 x12 . x0 (λ x13 : ι → ι → ι . λ x14 . 0) 0) (λ x11 . Inj1 0)) (x6 0 (λ x11 : ι → ι . λ x12 . Inj0 0) 0 0))) (λ x9 . x0 (λ x10 : ι → ι → ι . λ x11 . x0 (λ x12 : ι → ι → ι . λ x13 . x13) x9) 0) (λ x9 : (ι → ι) → ι . Inj1 x7) (λ x9 x10 . x9) (λ x9 . x7) = setsum x7 0) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → (ι → ι) → ι . ∀ x7 . x2 (λ x9 . Inj0 (setsum 0 0)) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . Inj1 0) = x6 (λ x9 . 0) (λ x9 . x3 (λ x10 : ((ι → ι → ι) → ι) → ι . Inj1 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . x10 (λ x12 : ι → ι → ι . 0)) (λ x11 . x0 (λ x12 : ι → ι → ι . λ x13 . 0) 0))) (λ x10 . Inj0 0) (λ x10 : (ι → ι) → ι . 0) (λ x10 x11 . x9) (λ x10 . setsum (x2 (λ x11 . x9) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x14)) (x2 (λ x11 . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . 0) (λ x12 . 0)) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x14))))) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι . x2 (λ x9 . x7 (λ x10 . λ x11 : ι → ι . 0) (x6 (x3 (λ x10 : ((ι → ι → ι) → ι) → ι . 0) (λ x10 . setsum 0 0) (λ x10 : (ι → ι) → ι . 0) (λ x10 x11 . 0) (λ x10 . x0 (λ x11 : ι → ι → ι . λ x12 . 0) 0)))) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x11 (x10 (λ x13 . x3 (λ x14 : ((ι → ι → ι) → ι) → ι . 0) (λ x14 . x14) (λ x14 : (ι → ι) → ι . Inj1 0) (λ x14 x15 . x12) (λ x14 . x2 (λ x15 . 0) (λ x15 : ((ι → ι) → ι) → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0))))) = setsum (x0 (λ x9 : ι → ι → ι . λ x10 . 0) 0) 0) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι → (ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . x2 (λ x10 . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . setsum (x0 (λ x12 : ι → ι → ι . λ x13 . 0) 0) (x0 (λ x12 : ι → ι → ι . λ x13 . 0) 0)) (λ x11 . setsum (x7 0 0 (λ x12 . 0)) (x7 0 0 (λ x12 . 0)))) (λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13)) (λ x9 . 0) = setsum (setsum (x4 (x0 (λ x9 : ι → ι → ι . λ x10 . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0) (λ x11 x12 . 0) (λ x11 . 0)) x5) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . 0) (λ x10 . 0)) (λ x9 . 0)) (λ x9 . 0)) (x2 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . 0) (λ x10 . Inj1 0)) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))) 0) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . 0) (λ x9 . x0 (λ x10 : ι → ι → ι . λ x11 . 0) (x3 (λ x10 : ((ι → ι → ι) → ι) → ι . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . x2 (λ x12 . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x11 . x2 (λ x12 . 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x11 : (ι → ι) → ι . x7) (λ x11 x12 . x12) (λ x11 . x7)) (λ x10 . Inj0 0) (λ x10 : (ι → ι) → ι . 0) (λ x10 x11 . x2 (λ x12 . x0 (λ x13 : ι → ι → ι . λ x14 . 0) 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . Inj0 0)) (λ x10 . x2 (λ x11 . 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0)))) = Inj1 x6) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι) → ι . x0 (λ x9 : ι → ι → ι . λ x10 . x2 (λ x11 . x7 (λ x12 x13 . x2 (λ x14 . 0) (λ x14 : ((ι → ι) → ι) → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . x2 (λ x18 . 0) (λ x18 : ((ι → ι) → ι) → ι . λ x19 : (ι → ι) → ι . λ x20 : ι → ι . λ x21 . 0)))) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x14)) (x2 (λ x9 . x0 (λ x10 : ι → ι → ι . λ x11 . x0 (λ x12 : ι → ι → ι . λ x13 . Inj0 0) 0) (x7 (λ x10 x11 . 0))) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x10 (λ x13 . x11 (x10 (λ x14 . 0))))) = setsum (x0 (λ x9 : ι → ι → ι . λ x10 . x2 (λ x11 . 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x14)) 0) (x6 (λ x9 : ι → ι . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . x7 (λ x11 x12 . x2 (λ x13 . 0) (λ x13 : ((ι → ι) → ι) → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0))) (λ x10 . x6 (λ x11 : ι → ι . 0))))) ⟶ (∀ x4 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι . x0 (λ x9 : ι → ι → ι . λ x10 . x7 (setsum (x2 (λ x11 . 0) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x14)) (setsum x10 (x6 0 0))) (λ x11 x12 . Inj0 (Inj0 (setsum 0 0))) (λ x11 . 0)) 0 = x7 (x3 (λ x9 : ((ι → ι → ι) → ι) → ι . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . 0) (λ x10 . 0)) (λ x9 . x7 x9 (λ x10 x11 . x11) (λ x10 . 0)) (λ x9 : (ι → ι) → ι . 0) (λ x9 x10 . x7 0 (λ x11 x12 . 0) (λ x11 . setsum x9 x9)) (λ x9 . Inj0 (setsum (x7 0 (λ x10 x11 . 0) (λ x10 . 0)) x5))) (λ x9 x10 . x3 (λ x11 : ((ι → ι → ι) → ι) → ι . x2 (λ x12 . x0 (λ x13 : ι → ι → ι . λ x14 . x2 (λ x15 . 0) (λ x15 : ((ι → ι) → ι) → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0)) (x3 (λ x13 : ((ι → ι → ι) → ι) → ι . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 x14 . 0) (λ x13 . 0))) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x3 (λ x16 : ((ι → ι → ι) → ι) → ι . setsum 0 0) (λ x16 . x13 (λ x17 . 0)) (λ x16 : (ι → ι) → ι . setsum 0 0) (λ x16 x17 . 0) (λ x16 . 0))) (λ x11 . 0) (λ x11 : (ι → ι) → ι . x2 (λ x12 . setsum 0 (setsum 0 0)) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x2 (λ x16 . setsum 0 0) (λ x16 : ((ι → ι) → ι) → ι . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . λ x19 . Inj1 0))) (λ x11 x12 . x11) (λ x11 . x9)) (λ x9 . x2 (λ x10 . x10) (λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0))) ⟶ False (proof)
Theorem 96ff9.. : ∀ x0 : (ι → (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι) → ι → ι . ∀ x1 : ((ι → ι → ι) → ι) → (ι → ι) → (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι → ι → ι) → ((ι → (ι → ι) → ι → ι) → ι) → ι . (∀ x4 : (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 x10 x11 . x11) (λ x9 : ι → (ι → ι) → ι → ι . x2 (λ x10 . x10) x7) = Inj0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 x10 x11 . 0) (λ x9 : ι → (ι → ι) → ι → ι . setsum (Inj0 (setsum 0 (x1 (λ x10 : ι → ι → ι . 0) (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)))) (setsum 0 (x3 (λ x10 x11 x12 . 0) (λ x10 : ι → (ι → ι) → ι → ι . x3 (λ x11 x12 x13 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0))))) = x4) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 . 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . Inj1 (Inj1 (x0 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0) 0))) (setsum 0 x7)) = x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . Inj1 (x12 (x2 (λ x13 . setsum 0 0) (x3 (λ x13 x14 x15 . 0) (λ x13 : ι → (ι → ι) → ι → ι . 0))))) (setsum (x1 (λ x9 : ι → ι → ι . 0) (λ x9 . x1 (λ x10 : ι → ι → ι . x7) (λ x10 . x10) (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum 0 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . x7)) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι) → ι . x2 (λ x9 . x6 (λ x10 : ι → ι → ι . x6 (λ x11 : ι → ι → ι . 0))) (x5 (λ x9 . x6 (λ x10 : ι → ι → ι . Inj1 (Inj1 0))) (setsum (x1 (λ x9 : ι → ι → ι . setsum 0 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . x9 (λ x11 . 0) 0)) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 x10 . x3 (λ x11 x12 x13 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0))))) = setsum (x5 (λ x9 . x9) (x2 (λ x9 . setsum 0 0) 0)) (setsum (setsum (x6 (λ x9 : ι → ι → ι . 0)) (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) (setsum 0 0))) (Inj1 (x1 (λ x9 : ι → ι → ι . x7 (λ x10 x11 . 0)) (λ x9 . x7 (λ x10 x11 . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj1 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x1 (λ x9 : ι → ι → ι . x1 (λ x10 : ι → ι → ι . x3 (λ x11 x12 x13 . 0) (λ x11 : ι → (ι → ι) → ι → ι . x2 (λ x12 . Inj0 0) (x9 0 0))) (λ x10 . x10) (λ x10 : (ι → ι) → ι → ι . λ x11 . x11)) (λ x9 . x0 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x3 (λ x14 x15 x16 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0)) 0) (λ x9 : (ι → ι) → ι → ι . Inj1) = Inj0 0) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → ι → ι . x7) (λ x9 . x5 (x1 (λ x10 : ι → ι → ι . Inj1 (x1 (λ x11 : ι → ι → ι . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 . 0))) (λ x10 . x2 (λ x11 . setsum 0 0) (setsum 0 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum (x0 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0) 0)) (x0 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . setsum (setsum 0 0) (x2 (λ x14 . 0) 0)) (x2 (λ x10 . x9) x7)) (λ x10 . 0) (x1 (λ x10 : ι → ι → ι . x9) (λ x10 . x3 (λ x11 x12 x13 . x10) (λ x11 : ι → (ι → ι) → ι → ι . 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 . x11))) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (Inj1 (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x3 (λ x15 x16 x17 . 0) (λ x15 : ι → (ι → ι) → ι → ι . 0)) (x2 (λ x11 . 0) 0))) (x3 (λ x11 x12 x13 . x0 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) x10) (λ x11 : ι → (ι → ι) → ι → ι . setsum 0 0))) = x5 (Inj0 (Inj1 (x3 (λ x9 x10 x11 . setsum 0 0) (λ x9 : ι → (ι → ι) → ι → ι . Inj0 0)))) (x1 (λ x9 : ι → ι → ι . x1 (λ x10 : ι → ι → ι . x1 (λ x11 : ι → ι → ι . x0 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0) (λ x11 . x2 (λ x12 . 0) 0) (λ x11 : (ι → ι) → ι → ι . λ x12 . x11 (λ x13 . 0) 0)) (x9 (setsum 0 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 . x3 (λ x12 x13 x14 . x2 (λ x15 . 0) 0) (λ x12 : ι → (ι → ι) → ι → ι . x12 0 (λ x13 . 0) 0))) (λ x9 . x1 (λ x10 : ι → ι → ι . Inj1 (x2 (λ x11 . 0) 0)) (λ x10 . x10) (λ x10 : (ι → ι) → ι → ι . λ x11 . x7)) (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 (x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0) (Inj0 0)))) (λ x9 . x5 0 x9 (λ x10 . x0 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x12 (λ x15 : ι → ι . λ x16 . x16)) 0) 0) (Inj0 (x2 (λ x9 . x6) (setsum (x3 (λ x9 x10 x11 . 0) (λ x9 : ι → (ι → ι) → ι → ι . 0)) (x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . Inj1 (x1 (λ x13 : ι → ι → ι . x10 (λ x14 : ι → ι . λ x15 . Inj0 0)) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 . x14))) 0 = Inj0 x4) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) (setsum (x4 (x1 (λ x9 : ι → ι → ι . x2 (λ x10 . 0) 0) (λ x9 . x1 (λ x10 : ι → ι → ι . 0) (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . 0))) 0) = x5) ⟶ False (proof)
Theorem 1b320.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → ι → ι . ∀ x2 : (ι → ((ι → ι → ι) → ι → ι) → ι → ι) → ((ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x3 : ((((ι → ι) → ι) → ι) → ι → ι → ι) → ι → ι . (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x3 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x9 (λ x12 : ι → ι . 0)) 0 = x7 x4 (λ x9 : ι → ι . 0) x6) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . x3 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . setsum (x1 (λ x12 . x2 (λ x13 . λ x14 : (ι → ι → ι) → ι → ι . λ x15 . 0) (λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . Inj1 0)) (x7 (λ x12 . λ x13 : ι → ι . x10) (λ x12 . x11) (λ x12 . 0) (x7 (λ x12 . λ x13 : ι → ι . 0) (λ x12 . 0) (λ x12 . 0) 0))) (x7 (λ x12 . λ x13 : ι → ι . x1 (λ x14 x15 . x0 (λ x16 . 0) 0) 0) (λ x12 . 0) (λ x12 . x1 (λ x13 x14 . 0) (x1 (λ x13 x14 . 0) 0)) (Inj0 (x0 (λ x12 . 0) 0)))) 0 = Inj0 0) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → (ι → ι) → (ι → ι) → ι . x2 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x10 (λ x12 . x1 (λ x13 x14 . x14) (x10 (λ x13 . x13) 0)) (x1 (λ x12 x13 . setsum (x1 (λ x14 x15 . 0) 0) (x0 (λ x14 . 0) 0)) 0)) 0 = Inj0 (Inj1 0)) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 . x2 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . x1 (λ x12 x13 . setsum (setsum 0 x13) (x10 (λ x14 x15 . 0) (Inj1 0))) (x0 (λ x12 . x2 (λ x13 . λ x14 : (ι → ι → ι) → ι → ι . λ x15 . 0) (λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . setsum 0 0) (Inj1 0)) (x1 (λ x12 x13 . 0) 0))) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . setsum 0 0) x7 = Inj0 0) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 . x1 (λ x9 x10 . Inj0 (x0 (λ x11 . x10) (x3 (λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) x7))) 0 = x4 (λ x9 . Inj0 (x3 (λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x0 (λ x13 . 0) (setsum 0 0)) (x0 (λ x10 . setsum 0 0) (x3 (λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0)))) (λ x9 : ι → ι . 0) (Inj0 0) (Inj0 0)) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι . x1 (λ x9 x10 . x2 (λ x11 . λ x12 : (ι → ι → ι) → ι → ι . λ x13 . x13) (λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . Inj1 (x11 0)) (Inj1 (x0 (λ x11 . x0 (λ x12 . 0) 0) (setsum 0 0)))) 0 = Inj0 (Inj0 x6)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 . setsum x5 (x6 x7)) 0 = x6 (setsum (x6 x7) x7)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x3 (λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . x12) 0)) (Inj1 (x1 (λ x9 x10 . Inj1 (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0))) 0)) = setsum (x7 0) (x3 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x11) (x0 (λ x9 . x9) 0))) ⟶ False (proof)
Theorem 4acef.. : ∀ x0 : (ι → ι) → ((ι → (ι → ι) → ι) → ι → (ι → ι) → ι) → (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x2 : ((((ι → ι → ι) → ι) → ι → ι) → ι) → (ι → ι) → ι → (ι → ι → ι) → ι . ∀ x3 : ((ι → ι) → ι) → (ι → ((ι → ι) → ι) → ι → ι → ι) → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . x3 (λ x9 : ι → ι . setsum (x0 (λ x10 . setsum 0 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (λ x10 x11 x12 . x11) (λ x10 : ι → ι . λ x11 . x7 (λ x12 . Inj1 0) (λ x12 x13 . x2 (λ x14 : ((ι → ι → ι) → ι) → ι → ι . 0) (λ x14 . 0) 0 (λ x14 x15 . 0)))) 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . Inj0 (x2 (λ x13 : ((ι → ι → ι) → ι) → ι → ι . x1 (λ x14 x15 . x15) (λ x14 : ι → ι . 0)) (λ x13 . x3 (λ x14 : ι → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . x1 (λ x18 x19 . 0) (λ x18 : ι → ι . 0))) 0 (λ x13 . setsum 0))) = x6) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x3 (λ x9 : ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . Inj1) = x6 (λ x9 : ι → ι . λ x10 . x9 (x3 (λ x11 : ι → ι . x10) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . Inj0 (x2 (λ x15 : ((ι → ι → ι) → ι) → ι → ι . 0) (λ x15 . 0) 0 (λ x15 x16 . 0))))) (λ x9 : ι → ι . λ x10 . 0)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ((ι → ι → ι) → ι) → ι → ι . Inj1 (x2 (λ x10 : ((ι → ι → ι) → ι) → ι → ι . x0 (λ x11 . x0 (λ x12 . 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (λ x12 x13 x14 . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . x11 0 (λ x14 . 0)) (λ x11 x12 x13 . x3 (λ x14 : ι → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . 0)) (λ x11 : ι → ι . λ x12 . x1 (λ x13 x14 . 0) (λ x13 : ι → ι . 0))) (λ x10 . x9 (λ x11 : ι → ι → ι . 0) x7) x7 (λ x10 . x9 (λ x11 : ι → ι → ι . 0)))) (λ x9 . x9) x4 (λ x9 x10 . x10) = Inj1 (setsum (x3 (λ x9 : ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . x10 (λ x13 . x11))) x7)) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x2 (λ x9 : ((ι → ι → ι) → ι) → ι → ι . x5 (Inj1 (x0 (λ x10 . setsum 0 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x12 0) (λ x10 x11 x12 . x1 (λ x13 x14 . 0) (λ x13 : ι → ι . 0)) (λ x10 : ι → ι . λ x11 . 0)))) (λ x9 . x5 (Inj1 (x6 (λ x10 . x1 (λ x11 x12 . 0) (λ x11 : ι → ι . 0))))) (Inj1 (setsum (x1 (λ x9 x10 . setsum 0 0) (λ x9 : ι → ι . 0)) 0)) (λ x9 x10 . setsum (x2 (λ x11 : ((ι → ι → ι) → ι) → ι → ι . x11 (λ x12 : ι → ι → ι . Inj1 0) (x3 (λ x12 : ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 x15 . 0))) (λ x11 . 0) (x0 (λ x11 . x11) (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . Inj0 0) (λ x11 x12 x13 . x0 (λ x14 . 0) (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . 0) (λ x14 x15 x16 . 0) (λ x14 : ι → ι . λ x15 . 0)) (λ x11 : ι → ι . λ x12 . x1 (λ x13 x14 . 0) (λ x13 : ι → ι . 0))) (λ x11 x12 . x1 (λ x13 x14 . setsum 0 0) (λ x13 : ι → ι . 0))) 0) = setsum (x3 (λ x9 : ι → ι . Inj1 (Inj1 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 x12 . setsum 0 (Inj0 (Inj1 0)))) x7) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 x10 . 0) (λ x9 : ι → ι . x1 (λ x10 x11 . Inj1 0) (λ x10 : ι → ι . 0)) = x1 (λ x9 x10 . x0 (λ x11 . x1 (λ x12 x13 . x12) (λ x12 : ι → ι . x10)) (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . x12) (λ x11 x12 x13 . x3 (λ x14 : ι → ι . setsum (setsum 0 0) (Inj1 0)) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . x1 (λ x18 x19 . x17) (λ x18 : ι → ι . Inj1 0))) (λ x11 : ι → ι . λ x12 . setsum (x11 0) (x0 (λ x13 . 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . setsum 0 0) (λ x13 x14 x15 . Inj1 0) (λ x13 : ι → ι . λ x14 . x11 0)))) (λ x9 : ι → ι . x0 (λ x10 . x7) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum 0 0) (λ x10 x11 x12 . Inj0 (x2 (λ x13 : ((ι → ι → ι) → ι) → ι → ι . x3 (λ x14 : ι → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . 0)) (λ x13 . x13) (setsum 0 0) (λ x13 x14 . Inj1 0))) (λ x10 : ι → ι . λ x11 . 0))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 . x1 (λ x9 x10 . 0) (λ x9 : ι → ι . x9 (x9 (setsum (x9 0) x5))) = x5) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 . x6) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x2 (λ x12 : ((ι → ι → ι) → ι) → ι → ι . setsum (x2 (λ x13 : ((ι → ι → ι) → ι) → ι → ι . x13 (λ x14 : ι → ι → ι . 0) 0) (λ x13 . x11 0) 0 (λ x13 x14 . setsum 0 0)) (x0 (λ x13 . 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) (λ x13 x14 x15 . x15) (λ x13 : ι → ι . λ x14 . x14))) x11 0 (λ x12 x13 . x0 (λ x14 . x3 (λ x15 : ι → ι . x1 (λ x16 x17 . 0) (λ x16 : ι → ι . 0)) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 x18 . x3 (λ x19 : ι → ι . 0) (λ x19 . λ x20 : (ι → ι) → ι . λ x21 x22 . 0))) (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . x16 0) (λ x14 x15 x16 . setsum (Inj0 0) 0) (λ x14 : ι → ι . λ x15 . x1 (λ x16 x17 . x3 (λ x18 : ι → ι . 0) (λ x18 . λ x19 : (ι → ι) → ι . λ x20 x21 . 0)) (λ x16 : ι → ι . x15)))) (λ x9 x10 x11 . x9) (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ι . x10) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . 0)) = Inj0 (Inj0 (x2 (λ x9 : ((ι → ι → ι) → ι) → ι → ι . x1 (λ x10 x11 . 0) (λ x10 : ι → ι . 0)) (λ x9 . x5) 0 (λ x9 x10 . x1 (λ x11 x12 . x12) (λ x11 : ι → ι . Inj1 0))))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . x6) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x1 (λ x12 x13 . 0) (λ x12 : ι → ι . Inj0 (setsum (x3 (λ x13 : ι → ι . 0) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 x16 . 0)) (x9 0 (λ x13 . 0))))) (λ x9 x10 x11 . x7) (λ x9 : ι → ι . λ x10 . x1 (λ x11 x12 . Inj1 x10) (λ x11 : ι → ι . Inj1 (Inj0 0))) = x6) ⟶ False (proof)
Theorem fc3b7.. : ∀ x0 : (ι → ι) → (ι → ι → (ι → ι) → ι) → ι . ∀ x1 : ((((ι → ι) → (ι → ι) → ι) → ι) → ι → ι → (ι → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι) → (ι → ι → ι) → ι → ((ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 . x0 (λ x10 . Inj1 x9) (λ x10 x11 . λ x12 : ι → ι . x12 (x2 (λ x13 . setsum 0 0) (Inj1 0)))) (λ x9 x10 . x2 (λ x11 . 0) (setsum (x6 (λ x11 . x1 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0) (λ x11 x12 . 0)) (x3 (λ x11 . 0) (λ x11 x12 . setsum 0 0) (setsum 0 0) (λ x11 : ι → ι . x11 0)))) (Inj0 (setsum (setsum (x6 (λ x9 . 0) (λ x9 x10 . 0)) 0) (x0 (λ x9 . setsum 0 0) (λ x9 x10 . λ x11 : ι → ι . x10)))) (λ x9 : ι → ι . 0) = setsum 0 0) ⟶ (∀ x4 : (ι → ι → ι) → ι → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 . x9) (λ x9 x10 . Inj1 0) 0 (λ x9 : ι → ι . setsum (Inj0 (Inj1 0)) (Inj1 (setsum (Inj0 0) (x9 0)))) = setsum 0 (setsum (x2 (λ x9 . x2 (λ x10 . setsum 0 0) (Inj1 0)) (x5 (x3 (λ x9 . 0) (λ x9 x10 . 0) 0 (λ x9 : ι → ι . 0)))) (x0 (λ x9 . x9) (λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 . 0) (x1 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 . 0) 0 = setsum (setsum x4 (setsum x7 x7)) (Inj0 (x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . x9)))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x2 (x1 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . Inj1 0)) 0 = x1 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x2 (λ x13 . 0) (x1 (λ x13 : ((ι → ι) → (ι → ι) → ι) → ι . λ x14 x15 . λ x16 : ι → ι . Inj1 (x0 (λ x17 . 0) (λ x17 x18 . λ x19 : ι → ι . 0))) (setsum 0 x10))) (x4 (Inj1 (Inj0 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . setsum (setsum 0 (x2 (λ x13 . 0) (x12 0))) (x1 (λ x13 : ((ι → ι) → (ι → ι) → ι) → ι . λ x14 x15 . λ x16 : ι → ι . Inj1 (x0 (λ x17 . 0) (λ x17 x18 . λ x19 : ι → ι . 0))) 0)) (x2 (λ x9 . setsum (Inj1 (x2 (λ x10 . 0) 0)) 0) 0) = setsum (Inj0 0) 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . 0) (setsum (Inj0 (x6 (λ x9 : ι → ι → ι . x2 (λ x10 . 0) 0) (λ x9 : ι → ι . x1 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0))) (x3 (λ x9 . x0 (λ x10 . x7 0) (λ x10 x11 . λ x12 : ι → ι . x2 (λ x13 . 0) 0)) (λ x9 x10 . setsum (x1 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0) 0) 0 (λ x9 : ι → ι . 0))) = setsum (x3 (λ x9 . x5 (λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x10 : ι → ι . 0)) (λ x9 x10 . setsum x9 0) (Inj0 0) (λ x9 : ι → ι . 0)) (x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . 0) = x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . setsum (setsum x9 0) 0) = x4) ⟶ False (proof)
Theorem f4c43.. : ∀ x0 : (ι → ι) → ι → (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x1 : (((ι → ι) → ι) → ι → ((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x2 : ((ι → (ι → ι → ι) → ι) → (((ι → ι) → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x3 : ((((ι → ι → ι) → (ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x0 (λ x10 . Inj0 0) x6 (λ x10 . x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι . λ x14 . setsum 0 (setsum 0 0)) (x0 (λ x11 . setsum 0 0) (Inj0 0) (λ x11 . setsum 0 0) (λ x11 : ι → ι . λ x12 . x10))) (λ x10 : ι → ι . λ x11 . 0)) (λ x9 . 0) (setsum (x0 (λ x9 . Inj1 x7) x5 (λ x9 . x7) (λ x9 : ι → ι . λ x10 . 0)) 0) = Inj1 0) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x6) (x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 . 0)) (x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 . x10 (λ x13 : ι → ι . setsum (x13 0) 0)) (Inj1 (Inj1 (x4 0 (λ x9 x10 . 0))))) = x6) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 . 0) (x1 (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . x12) (Inj0 (x0 (λ x9 . x7) (setsum 0 0) (λ x9 . setsum 0 0) (λ x9 : ι → ι . λ x10 . x6 0 0)))) = x1 (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . Inj0 (x9 (λ x13 . x0 (λ x14 . 0) x10 (λ x14 . x2 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 : ((ι → ι) → ι) → ι . λ x17 : ι → ι . λ x18 . 0) 0) (λ x14 : ι → ι . λ x15 . Inj0 0)))) x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 . setsum (setsum (setsum (Inj1 0) (x10 (λ x13 : ι → ι . 0))) (x0 (λ x13 . Inj1 0) (x1 (λ x13 : (ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 . 0) 0) (λ x13 . Inj1 0) (λ x13 : ι → ι . λ x14 . x13 0))) 0) (Inj0 (setsum (x0 (λ x9 . x0 (λ x10 . 0) 0 (λ x10 . 0) (λ x10 : ι → ι . λ x11 . 0)) 0 (λ x9 . Inj0 0) (λ x9 : ι → ι . λ x10 . 0)) 0)) = x7 (x5 (λ x9 . x0 (λ x10 . 0) (Inj1 (Inj1 0)) (λ x10 . x1 (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 . setsum 0 0) 0) (λ x10 : ι → ι . λ x11 . x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x12 (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x12 . x1 (λ x13 : (ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 . 0) 0) 0)) (λ x9 x10 . x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι . λ x14 . Inj0 (x11 0 (λ x15 x16 . 0))) 0)) (x0 (λ x9 . x1 (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 . x12 (λ x14 . x1 (λ x15 : (ι → ι) → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . λ x18 . 0) 0) x11) x6) (x5 (λ x9 . 0) (λ x9 x10 . x1 (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 . x11 (λ x15 . 0)) (Inj0 0))) (λ x9 . Inj0 (x2 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 0) (x1 (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 . 0) 0))) (λ x9 : ι → ι . λ x10 . x6))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : (ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x1 (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . x1 (λ x13 : (ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 . x0 (λ x17 . Inj1 (setsum 0 0)) (setsum (x3 (λ x17 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x17 . 0) 0) x16) (λ x17 . setsum x17 (x3 (λ x18 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x18 . 0) 0)) (λ x17 : ι → ι . λ x18 . x17 (x1 (λ x19 : (ι → ι) → ι . λ x20 . λ x21 : (ι → ι) → ι → ι . λ x22 . 0) 0))) x10) 0 = Inj1 (setsum (x5 (x4 (λ x9 . x6 0 0 0)) (λ x9 : ι → ι . x9 (x1 (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 . 0) 0))) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . 0) 0 = x7 (x1 (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . x11 (λ x13 . x0 (λ x14 . x0 (λ x15 . 0) 0 (λ x15 . 0) (λ x15 : ι → ι . λ x16 . 0)) (Inj1 0) (λ x14 . x1 (λ x15 : (ι → ι) → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . λ x18 . 0) 0) (λ x14 : ι → ι . λ x15 . 0)) 0) (x1 (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . x12) (x1 (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . Inj0 0) x4)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι → ι . x0 (λ x9 . x5) (Inj1 (x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 0) 0) (λ x9 . Inj0 (setsum 0 0)) x4)) (λ x9 . x6 0) (λ x9 : ι → ι . λ x10 . 0) = x5) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 . x9) 0 (λ x9 . x3 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι . λ x14 . x13 (x11 0 (λ x15 x16 . 0))) x7) (λ x10 . setsum (x1 (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 . x2 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 : ((ι → ι) → ι) → ι . λ x17 : ι → ι . λ x18 . 0) 0) 0) 0) 0) (λ x9 : ι → ι . λ x10 . setsum 0 (setsum (x3 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x0 (λ x12 . 0) 0 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x11 . setsum 0 0) x7) x7)) = x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x3 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x10 . 0) 0) (λ x9 . setsum (setsum (x1 (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 . 0) (x5 (λ x10 : ι → ι . λ x11 . 0))) (x0 (λ x10 . 0) 0 (λ x10 . x9) (λ x10 : ι → ι . λ x11 . x0 (λ x12 . 0) 0 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0)))) (x3 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . setsum (x0 (λ x11 . 0) 0 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0)) 0) (λ x10 . 0) 0)) (x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . Inj0 x6) (λ x9 . x7) (x0 (λ x9 . 0) (x0 (λ x9 . setsum 0 0) x4 (λ x9 . x9) (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x11 . 0) 0)) (λ x9 . x0 (λ x10 . Inj0 0) 0 (λ x10 . Inj0 0) (λ x10 : ι → ι . λ x11 . setsum 0 0)) (λ x9 : ι → ι . λ x10 . x6)))) ⟶ False (proof)
Theorem 99c9f.. : ∀ x0 : ((ι → (ι → ι → ι) → ι → ι → ι) → ι) → (ι → ((ι → ι) → ι) → ι → ι) → ι . ∀ x1 : ((ι → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ((ι → ι → ι) → ι → (ι → ι) → ι → ι) → ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x3 : ((ι → ι → ι) → ι → ι) → ι → ι . (∀ x4 : ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : ι → ι → ι . λ x10 . Inj0 (Inj1 x10)) (x1 (λ x9 : ι → ι . x1 (λ x10 : ι → ι . 0) (x5 (λ x10 x11 . setsum 0 0) (λ x10 : ι → ι . λ x11 . x1 (λ x12 : ι → ι . 0) 0))) (Inj0 (x4 (λ x9 : ι → ι . λ x10 . x10) (λ x9 : ι → ι . λ x10 . x9 0) (λ x9 . x2 (λ x10 . 0) (λ x10 : ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) 0 (λ x10 x11 . 0) (λ x10 . 0) 0)))) = setsum (x3 (λ x9 : ι → ι → ι . λ x10 . x10) (x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . setsum 0 (x9 0 (λ x10 x11 . 0) 0 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . setsum (x0 (λ x12 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 . 0)) (Inj0 0)))) 0) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 : ι → ι → ι . λ x10 . 0) 0 = x4) ⟶ (∀ x4 : ((ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x7 : (ι → ι) → (ι → ι) → ι → ι → ι . x2 (λ x9 . Inj0 0) (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) (setsum (setsum (x5 0) (x4 (λ x9 : ι → ι . λ x10 . Inj0 0))) (x3 (λ x9 : ι → ι → ι . λ x10 . x7 (λ x11 . Inj0 0) (λ x11 . setsum 0 0) (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x11 : ι → ι . 0) 0) (x0 (λ x11 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 . 0))) (setsum (setsum 0 0) 0))) (λ x9 x10 . x10) Inj0 0 = Inj0 (x4 (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ι . x3 (λ x12 : ι → ι → ι . λ x13 . 0) x10) x10))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x9 . Inj1 x7) (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (setsum 0 0) (λ x9 x10 . x1 (λ x11 : ι → ι . Inj1 (setsum (x2 (λ x12 . 0) (λ x12 : ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) 0 (λ x12 x13 . 0) (λ x12 . 0) 0) (x1 (λ x12 : ι → ι . 0) 0))) x7) (λ x9 . Inj1 (Inj1 (setsum 0 (x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))))) (x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 . setsum (x1 (λ x13 : ι → ι . 0) 0) 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . setsum (setsum x11 x7) (Inj0 (Inj1 0)))) = x1 (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι → ι → ι . x10 (x6 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . 0))) (λ x11 x12 . x9 (x3 (λ x13 : ι → ι → ι . λ x14 . 0) 0)) 0 (x6 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ι → ι → ι . λ x15 . 0) 0))) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 . setsum 0 (x0 (λ x13 : ι → (ι → ι → ι) → ι → ι → ι . x1 (λ x14 : ι → ι . 0) 0) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 . 0)))) (Inj1 (x1 (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 . x12)) x5))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι → ι . x1 (λ x9 : ι → ι . 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . Inj1 (Inj0 (x9 0 (λ x10 x11 . 0) 0 0))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . 0)) = setsum (setsum x6 0) 0) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 : ι → ι . setsum x5 (x1 (λ x10 : ι → ι . 0) (setsum (setsum 0 0) (setsum 0 0)))) (setsum (setsum x5 x5) (x4 (λ x9 x10 x11 . setsum (Inj1 0) x10))) = setsum (x1 (λ x9 : ι → ι . x6 (λ x10 . x2 (λ x11 . 0) (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . x14) x7 (λ x11 x12 . x10) (λ x11 . x3 (λ x12 : ι → ι → ι . λ x13 . 0) 0) x7) (x2 (λ x10 . x2 (λ x11 . 0) (λ x11 : ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) 0 (λ x11 x12 . 0) (λ x11 . 0) 0) (λ x10 : ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (x3 (λ x10 : ι → ι → ι . λ x11 . 0) 0) (λ x10 x11 . Inj1 0) (λ x10 . Inj1 0) 0)) (x1 (λ x9 : ι → ι . 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . x1 (λ x12 : ι → ι . 0) 0)))) 0) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . 0) = setsum (x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . x7) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . setsum (x1 (λ x12 : ι → ι . x10 (λ x13 . 0)) (setsum 0 0)) (x1 (λ x12 : ι → ι . x3 (λ x13 : ι → ι → ι . λ x14 . 0) 0) 0))) (setsum (x3 (λ x9 : ι → ι → ι . λ x10 . x1 (λ x11 : ι → ι . setsum 0 0) 0) (x2 (λ x9 . 0) (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) 0 (λ x9 x10 . x3 (λ x11 : ι → ι → ι . λ x12 . 0) 0) (λ x9 . setsum 0 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . 0)))) (Inj0 (x2 (λ x9 . 0) (λ x9 : ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0) 0 (λ x9 x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 . 0)) (λ x9 . 0) (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . x0 (λ x12 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 . 0)) = x0 (λ x9 : ι → (ι → ι → ι) → ι → ι → ι . Inj0 (x7 (x2 (λ x10 . 0) (λ x10 : ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13) 0 (λ x10 x11 . x2 (λ x12 . 0) (λ x12 : ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) 0 (λ x12 x13 . 0) (λ x12 . 0) 0) (λ x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 . 0)) 0) (Inj0 0))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 . Inj1 (x10 (λ x12 . 0)))) ⟶ False (proof)
Theorem b241d.. : ∀ x0 : (ι → ι) → ((ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x1 : (ι → ι) → ((ι → (ι → ι) → ι) → ι) → ι . ∀ x2 : (((((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → ι) → (ι → ι) → ι . ∀ x3 : ((ι → ι) → ι) → ((((ι → ι) → ι) → ι) → (ι → ι → ι) → ι → ι → ι) → ι . (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x7 : ι → ι → ι . x3 (λ x9 : ι → ι . x7 (x7 (x5 (λ x10 . x1 (λ x11 . 0) (λ x11 : ι → (ι → ι) → ι . 0)) (x6 (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0 0 0) (λ x10 . x1 (λ x11 . 0) (λ x11 : ι → (ι → ι) → ι . 0))) (x6 (λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0) 0 (x6 (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0 0 0) (setsum 0 0))) (setsum (setsum (x5 (λ x10 . 0) 0 (λ x10 . 0)) 0) 0)) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . 0) = x7 (x2 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . setsum (Inj0 (x7 0 0)) (Inj1 (x7 0 0))) (λ x9 . 0)) (x3 (λ x9 : ι → ι . x3 (λ x10 : ι → ι . x2 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x2 (λ x12 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 . 0)) (λ x11 . x11)) (λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . x11 (x2 (λ x14 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . 0) (λ x14 . 0)) (Inj1 0))) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . x9 (Inj1 (x0 (λ x10 . x1 (λ x11 . 0) (λ x11 : ι → (ι → ι) → ι . 0)) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . Inj1 0) (x3 (λ x10 : ι → ι . 0) (λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . 0))))) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 . x12) (λ x13 : ι → (ι → ι) → ι . x3 (λ x14 : ι → ι . x14 (x1 (λ x15 . 0) (λ x15 : ι → (ι → ι) → ι . 0))) (λ x14 : ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . λ x16 x17 . x15 0 0))) = Inj1 (x2 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x7) (λ x9 . 0))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x6) (λ x9 . setsum 0 x6) = Inj0 0) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x2 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . x1 (λ x10 . 0) (λ x10 : ι → (ι → ι) → ι . x9 (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum x12 (x3 (λ x13 : ι → ι . 0) (λ x13 : ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0))) (λ x11 . 0) (λ x11 . 0) (x7 (λ x11 : ι → ι → ι . x0 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) 0)))) (λ x9 . 0) = setsum (x6 (λ x9 . 0)) x4) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 x7 . x1 (λ x9 . Inj1 x5) (λ x9 : ι → (ι → ι) → ι . x7) = Inj0 x6) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x1 Inj0 (λ x9 : ι → (ι → ι) → ι . setsum (x7 0 (x5 0 (λ x10 : ι → ι . Inj0 0) (Inj0 0)) (λ x10 . x9 (x7 0 0 (λ x11 . 0) 0) (λ x11 . x9 0 (λ x12 . 0))) (x3 (λ x10 : ι → ι . setsum 0 0) (λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . x0 (λ x14 . 0) (λ x14 : ι → ι . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0) 0))) 0) = x6) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 . setsum 0 x6) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x10 (λ x12 . setsum 0 0) (x0 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . Inj0 (Inj1 0)) (Inj1 0))) 0 = setsum (setsum 0 0) (Inj0 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 . x0 (λ x9 . x7) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . Inj0 (x0 (λ x12 . Inj1 (x9 0)) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x0 (λ x15 . x14 0) (λ x15 : ι → ι . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . x17 0) (setsum 0 0)) (setsum (Inj1 0) (x10 (λ x12 . 0) 0)))) (setsum (x6 (λ x9 . λ x10 : ι → ι . x9)) 0) = Inj1 (Inj1 (x5 x4 (λ x9 . 0) (λ x9 . x0 (λ x10 . 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x12 0) 0)))) ⟶ False (proof)
Theorem 47e4a.. : ∀ x0 : (ι → ((ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x1 : ((ι → ι) → (ι → ι → ι) → ι → ι) → ((((ι → ι) → ι → ι) → ι → ι) → ι) → ι . ∀ x2 : (ι → ι) → (ι → ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x3 : ((ι → ι) → (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι) → ι → ι . (∀ x4 : ι → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . x7 (λ x12 : ι → ι . λ x13 x14 . Inj1 0)) (Inj0 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . x2 (λ x12 . x11 0 0) (λ x12 x13 x14 . 0) (λ x12 x13 . x10 (λ x14 : ι → ι . 0)) (x10 (λ x12 : ι → ι . 0)) (Inj1 0)) (x4 0 (λ x9 . x1 (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0)) (x5 (λ x9 . 0))))) = x7 (λ x9 : ι → ι . λ x10 x11 . Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . 0) (setsum (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . x11 (setsum 0 0) (x7 0 0)) x5) (x7 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . 0) x5) (Inj1 (x7 0 0)))) = x6) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 . 0) (λ x9 x10 x11 . x7) (λ x9 x10 . setsum (Inj0 x10) (x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . x13 0 0) (x2 (λ x11 . x0 (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . 0) 0 0 0) (λ x11 x12 x13 . 0) (λ x11 x12 . x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . 0) 0) (setsum 0 0) (setsum 0 0)))) 0 x5 = setsum x6 x7) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 . x7) (λ x9 x10 x11 . x2 (λ x12 . x0 (λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι → ι . λ x16 : ι → ι . λ x17 . 0) (Inj1 x11) x12 (Inj1 x11)) (λ x12 x13 x14 . Inj1 x12) (λ x12 x13 . x3 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι → ι . x16 0 (Inj0 0)) x10) x9 (setsum 0 (Inj0 x11))) (λ x9 x10 . Inj1 (setsum (x0 (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . setsum 0 0) x6 (setsum 0 0) (Inj0 0)) (x0 (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . setsum 0 0) 0 (Inj0 0) 0))) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . x9 (x2 (λ x12 . x2 (λ x13 . 0) (λ x13 x14 x15 . 0) (λ x13 x14 . 0) 0 0) (λ x12 x13 x14 . 0) (λ x12 x13 . x12) (setsum 0 0) (x11 0 0))) (setsum 0 x4)) (Inj1 (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj0 (Inj0 0)) 0 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . x0 (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . 0) 0 0 0) x5) (Inj0 (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0 0)))) = Inj1 x4) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 . setsum (x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . x3 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι) → ι . λ x17 : ι → ι → ι . 0) (x0 (λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0 0 0)) (Inj1 (x9 0))) 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . x5 (λ x10 . λ x11 : ι → ι . 0)) = x5 (λ x9 . λ x10 : ι → ι . x0 (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . setsum (setsum (setsum 0 0) (x12 (λ x16 . 0))) 0) 0 0 (x10 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 . Inj0 (x1 (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . x13 0 x11) (λ x12 : ((ι → ι) → ι → ι) → ι → ι . x10 (x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . 0) 0) (setsum 0 0)))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . setsum 0 (Inj1 x7)) = setsum (x2 (λ x9 . 0) (λ x9 x10 x11 . 0) (λ x9 x10 . Inj1 x7) x6 (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 . x13) (λ x14 x15 x16 . Inj1 0) (λ x14 x15 . Inj1 0) 0 0) (x1 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . x2 (λ x10 . 0) (λ x10 x11 x12 . 0) (λ x10 x11 . 0) 0 0)) (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x13) x6 (Inj1 0) (Inj1 0)) (Inj1 x6))) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj1 0) (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) x7 x6 (Inj1 (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) (x2 (λ x9 . 0) (λ x9 x10 x11 . 0) (λ x9 x10 . 0) 0 0) (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0 0) (x2 (λ x9 . 0) (λ x9 x10 x11 . 0) (λ x9 x10 . 0) 0 0)))) x4 0 = x4) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x5 : (ι → ι) → ι → ι → ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 . x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x13) 0 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . 0) 0) 0 = x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . Inj0 0) (setsum (Inj0 0) (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x12 (Inj0 0)) (x2 (λ x9 . 0) (λ x9 x10 x11 . setsum 0 0) (λ x9 x10 . Inj1 0) 0 (x4 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0))) (x4 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x1 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι . 0))) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . x1 (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι . 0)) (x0 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0 0))))) ⟶ False (proof)
Theorem ba301.. : ∀ x0 : (ι → ι → (ι → ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x1 : ((ι → ι) → ι) → ι → (ι → (ι → ι) → ι) → ι . ∀ x2 : (ι → ι) → (ι → (ι → ι → ι) → ι) → ι . ∀ x3 : (((ι → ι → ι) → ι → ι → ι → ι) → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 x7 . x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . 0) (x1 (λ x9 : ι → ι . 0) (Inj0 (x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . x1 (λ x10 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0)) 0)) (λ x9 . λ x10 : ι → ι . Inj0 0)) = setsum (Inj1 (Inj1 0)) (x5 x6 (Inj1 (setsum (x1 (λ x9 : ι → ι . 0) 0 (λ x9 . λ x10 : ι → ι . 0)) (setsum 0 0))) (x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . setsum x7 (x2 (λ x10 . 0) (λ x10 . λ x11 : ι → ι → ι . 0))) (Inj0 (x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x9 x10 . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . x2 (λ x10 . 0) (λ x10 . λ x11 : ι → ι → ι . setsum (x11 0 0) (setsum (x11 0 0) (x9 (λ x12 x13 . 0) 0 0 0)))) x7 = Inj0 (Inj1 0)) ⟶ (∀ x4 : (ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x2 (λ x9 . x9) (λ x9 . λ x10 : ι → ι → ι . 0) = x7) ⟶ (∀ x4 : (ι → ι) → ι → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 . setsum (setsum (x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 : ι → ι . x12 0 0) (λ x10 x11 . 0)) 0) (x2 (λ x10 . x7) (λ x10 . λ x11 : ι → ι → ι . Inj0 x10))) (λ x9 . λ x10 : ι → ι → ι . x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . x14 (Inj0 (x1 (λ x15 : ι → ι . 0) 0 (λ x15 . λ x16 : ι → ι . 0)))) (λ x11 x12 . x9)) = x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . x3 (λ x13 : (ι → ι → ι) → ι → ι → ι → ι . x2 (λ x14 . setsum (x0 (λ x15 x16 . λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) (λ x15 x16 . 0)) (x0 (λ x15 x16 . λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) (λ x15 x16 . 0))) (λ x14 . λ x15 : ι → ι → ι . x14)) (x12 x10)) (λ x9 x10 . setsum (setsum (x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . x11) (λ x11 x12 . setsum 0 0)) (Inj1 (setsum 0 0))) (x3 (λ x11 : (ι → ι → ι) → ι → ι → ι → ι . 0) 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . x1 (λ x9 : ι → ι . 0) 0 (λ x9 . λ x10 : ι → ι . x6 (x10 0)) = x6 (x6 (x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . setsum (setsum 0 0) (Inj1 0)) (λ x9 x10 . x7 (λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0) (setsum 0 0) (λ x11 . 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι → ι . x1 (λ x9 : ι → ι . 0) 0 (λ x9 . λ x10 : ι → ι . Inj1 (x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . x14 (x0 (λ x15 x16 . λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) (λ x15 x16 . 0))) (λ x11 x12 . Inj0 (x3 (λ x13 : (ι → ι → ι) → ι → ι → ι → ι . 0) 0)))) = setsum 0 (Inj1 (x5 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . setsum 0 (Inj1 (Inj1 (x11 0 0)))) (λ x9 x10 . 0) = x7 (λ x9 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . x12 (Inj1 (x11 x10 (x12 0)))) (λ x9 x10 . 0) = setsum (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 : (ι → ι → ι) → ι → ι → ι → ι . x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) (λ x13 x14 . Inj0 0)) 0)) (setsum (x3 (λ x9 : (ι → ι → ι) → ι → ι → ι → ι . x2 (λ x10 . x9 (λ x11 x12 . 0) 0 0 0) (λ x10 . λ x11 : ι → ι → ι . x2 (λ x12 . 0) (λ x12 . λ x13 : ι → ι → ι . 0))) (x2 (λ x9 . x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) (λ x10 x11 . 0)) (λ x9 . λ x10 : ι → ι → ι . x7 0 (λ x11 x12 . 0) 0))) (Inj0 (x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . x12 0) (λ x9 x10 . 0))))) ⟶ False (proof)
Theorem 27c51.. : ∀ x0 : (ι → ι) → ι → ι → ((ι → ι) → ι → ι) → ι . ∀ x1 : ((ι → ι) → ((ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι) → ((((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x2 : ((((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι → ((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x3 : ((ι → ι) → (((ι → ι) → ι → ι) → ι → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) (Inj1 (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 . x12) (setsum 0 0) (Inj0 0) (λ x12 : ι → ι . λ x13 . setsum 0 0)) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x0 (λ x11 . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0)) (x6 0) (setsum 0 0)))) (x6 0) = x6 (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . setsum 0 (Inj0 0)) (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . Inj1 (setsum 0 0)) (setsum (Inj0 0) x4) 0)) (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) 0) = x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . setsum (x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι → ι . x12 (x13 (λ x14 : ι → ι . λ x15 . 0) 0)) (setsum (x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0) x7) x7) (Inj1 (x1 (λ x12 : ι → ι . λ x13 : (ι → ι) → (ι → ι) → ι . λ x14 x15 x16 . x15) (λ x12 : ((ι → ι) → ι) → ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)))) (setsum (x5 0 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . Inj1 0) x4 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0)) (setsum (Inj0 0) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0))) 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : ι → ι . λ x13 : (ι → ι) → (ι → ι) → ι . λ x14 x15 x16 . setsum 0 (setsum 0 0)) (λ x12 : ((ι → ι) → ι) → ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (Inj0 (x1 (λ x9 : ι → ι . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 x13 . setsum (setsum 0 0) (x3 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0)) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0))) = x1 (λ x9 : ι → ι . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 x13 . setsum (Inj1 (setsum 0 (Inj1 0))) (Inj0 (Inj0 0))) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . Inj0 (x10 (λ x12 . setsum (x1 (λ x13 : ι → ι . λ x14 : (ι → ι) → (ι → ι) → ι . λ x15 x16 x17 . 0) (λ x13 : ((ι → ι) → ι) → ι → ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι . x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x9 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . setsum (x1 (λ x15 : ι → ι . λ x16 : (ι → ι) → (ι → ι) → ι . λ x17 x18 x19 . 0) (λ x15 : ((ι → ι) → ι) → ι → ι → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . Inj0 0)) (Inj1 (setsum 0 0))) (λ x12 : ι → ι . λ x13 . 0)) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x10 (x0 (λ x11 . 0) (x7 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0) (x1 (λ x11 : ι → ι . λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 x14 x15 . 0) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (λ x11 : ι → ι . λ x12 . setsum 0 0))) (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (x4 (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0) (λ x9 : ι → ι . λ x10 . setsum 0 0)))) = x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . Inj0 (setsum (setsum (setsum 0 0) 0) 0)) (setsum (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (setsum (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) 0) 0)) 0)) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : ι → ι . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 x13 . x11) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) = x5 (Inj0 (x5 (x5 0 (λ x9 : ι → ι . x1 (λ x10 : ι → ι . λ x11 : (ι → ι) → (ι → ι) → ι . λ x12 x13 x14 . 0) (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0))) (λ x9 : ι → ι . x6 (λ x10 . x2 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0)))) (λ x9 : ι → ι . setsum (setsum (x0 (λ x10 . x2 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0) 0 0 (λ x10 : ι → ι . λ x11 . x10 0)) (x2 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . 0) 0) (Inj1 0))) (x1 (λ x10 : ι → ι . λ x11 : (ι → ι) → (ι → ι) → ι . λ x12 x13 x14 . x3 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → ι → ι . x13) (x2 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . 0) 0) (setsum 0 0)) (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x0 (λ x13 . x0 (λ x14 . 0) 0 0 (λ x14 : ι → ι . λ x15 . 0)) 0 (x12 0) (λ x13 : ι → ι . λ x14 . x2 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι → ι . x1 (λ x9 : ι → ι . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x9 (λ x12 : ι → ι . Inj0 (x10 (λ x13 . 0))) 0 (x1 (λ x12 : ι → ι . λ x13 : (ι → ι) → (ι → ι) → ι . λ x14 x15 x16 . 0) (λ x12 : ((ι → ι) → ι) → ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x14 (x13 (λ x15 . 0))))) = setsum (setsum (x1 (λ x9 : ι → ι . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 x13 . x1 (λ x14 : ι → ι . λ x15 : (ι → ι) → (ι → ι) → ι . λ x16 x17 x18 . setsum 0 0) (λ x14 : ((ι → ι) → ι) → ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0)) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x0 (λ x12 . x3 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0) (x7 (λ x12 : (ι → ι) → ι . 0) 0) (x7 (λ x12 : (ι → ι) → ι . 0) 0) (λ x12 : ι → ι . λ x13 . x10 (λ x14 . 0)))) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . Inj0 (x1 (λ x11 : ι → ι . λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 x14 x15 . 0) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))) (Inj0 (Inj0 0)) (setsum x6 0))) (setsum (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x7 (λ x11 : (ι → ι) → ι . x10 (λ x12 : ι → ι . λ x13 . 0) 0) (setsum 0 0)) (setsum (Inj0 0) (setsum 0 0)) x6) (Inj1 (x5 (x0 (λ x9 . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0)) 0 (x5 0 0 0 0) x6)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι) → ι . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι . ∀ x7 . x0 (λ x9 . x9) (Inj0 0) x7 (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ι . λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 x14 x15 . Inj0 0) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x10)) = Inj0 (x0 (λ x9 . 0) (x0 (λ x9 . Inj1 (x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0)) 0 (x0 (λ x9 . x9) (Inj1 0) 0 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0)) (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . setsum 0 0) 0)) (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x10 (λ x11 : ι → ι . λ x12 . 0) (x2 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) 0)) 0 (setsum (x3 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0) (Inj0 0))) (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ι . λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 x14 x15 . setsum x14 (x3 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0)) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . setsum (x1 (λ x14 : ι → ι . λ x15 : (ι → ι) → (ι → ι) → ι . λ x16 x17 x18 . 0) (λ x14 : ((ι → ι) → ι) → ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0)) (x2 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 . 0) (x0 (λ x9 . x3 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 x7) x7 (x0 (λ x9 . 0) 0 0 (λ x9 : ι → ι . λ x10 . Inj1 0)) (λ x9 : ι → ι . λ x10 . Inj1 (Inj1 0))) (setsum (x1 (λ x9 : ι → ι . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 x13 . setsum x11 (Inj1 0)) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι → ι . x11 0) (x2 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) 0) 0)) (setsum (Inj0 (Inj1 0)) (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . 0) 0) 0))) (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ι . λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 x14 x15 . 0) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x2 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . x1 (λ x17 : ι → ι . λ x18 : (ι → ι) → (ι → ι) → ι . λ x19 x20 x21 . Inj0 0) (λ x17 : ((ι → ι) → ι) → ι → ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . x19 0)) 0)) = setsum (x0 (λ x9 . Inj0 (x0 (λ x10 . 0) (x1 (λ x10 : ι → ι . λ x11 : (ι → ι) → (ι → ι) → ι . λ x12 x13 x14 . 0) (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)) 0 (λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0))) (x1 (λ x9 : ι → ι . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 x13 . 0) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x10 (λ x12 . 0))) x6 (λ x9 : ι → ι . λ x10 . x9 0)) (x2 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : ι → ι . λ x13 : (ι → ι) → (ι → ι) → ι . λ x14 x15 x16 . x1 (λ x17 : ι → ι . λ x18 : (ι → ι) → (ι → ι) → ι . λ x19 x20 x21 . setsum 0 0) (λ x17 : ((ι → ι) → ι) → ι → ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . x3 (λ x20 : ι → ι . λ x21 : ((ι → ι) → ι → ι) → ι → ι . 0) 0 0)) (λ x12 : ((ι → ι) → ι) → ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) x4)) ⟶ False (proof)
Theorem b633b.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : ((ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ι) → ((ι → (ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x2 : (((ι → ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι) → ι) → (ι → ι → ι → ι → ι) → (((ι → ι) → ι → ι) → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ι → ι → ι → ι) → ι . (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 x11 x12 . x1 (λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . setsum 0 0) (λ x13 : ι → (ι → ι) → ι → ι . λ x14 x15 . x15)) = x1 (λ x9 : ι → ι → ι → ι . λ x10 x11 : ι → ι . x9 (x11 (Inj1 (Inj1 0))) (x10 (x0 (λ x12 . 0) (setsum 0 0))) 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . Inj1 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 Inj0 (λ x9 : ι → ι . λ x10 x11 x12 . x12) = setsum 0 (x4 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (setsum (x1 (λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . 0) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 . 0)) x11) (x10 (x2 (λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 x13 x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0)))) (λ x9 : ι → ι . x5 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . Inj0 (setsum 0 0)) (λ x9 x10 x11 x12 . Inj1 0) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . Inj0 (Inj0 (x12 0))) (λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 . Inj1 (x0 (λ x13 . 0) (x1 (λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . 0) (λ x13 : ι → (ι → ι) → ι → ι . λ x14 x15 . 0))))) = Inj0 0) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 x7 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . x7) (λ x9 x10 x11 x12 . x12) (λ x9 : (ι → ι) → ι → ι . 0) = x7) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : ι → ι → ι → ι . λ x10 x11 : ι → ι . x11 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . x11) = x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x10 (x10 (x0 (λ x12 . x0 (λ x13 . 0) 0) 0)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x9 : ι → ι → ι → ι . λ x10 x11 : ι → ι . 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . setsum x11 (x9 x11 (λ x12 . setsum (setsum 0 0) 0) (x0 (λ x12 . 0) x10))) = setsum 0 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 x11 x12 . Inj0 (x9 x11)))) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι → ι → ι . x0 (λ x9 . 0) 0 = x4) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 . x5 (x0 (λ x10 . x3 (λ x11 . Inj0 0) (λ x11 : ι → ι . λ x12 x13 x14 . x11 0)) (x0 (λ x10 . x9) (x0 (λ x10 . 0) 0)))) 0 = Inj1 (x3 (λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι . 0) (λ x10 x11 x12 x13 . x13) (λ x10 : (ι → ι) → ι → ι . Inj1 (Inj0 0))) (λ x9 : ι → ι . λ x10 x11 x12 . x9 (x0 (λ x13 . Inj1 0) (Inj1 0))))) ⟶ False (proof)
Theorem c0927.. : ∀ x0 : (((ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι) → ι) → ι → ι . ∀ x1 : ((((ι → ι) → ι) → ι → ι) → (((ι → ι) → ι) → ι) → ι → ι) → ι → ι → ι . ∀ x2 : (ι → ι → ι) → ι → ι . ∀ x3 : ((ι → ι → ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι) → (((ι → ι) → ι) → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 : ι → ι → ι → ι . setsum (x9 x7 (x2 (λ x10 x11 . 0) (Inj1 0)) 0) 0) (λ x9 : ι → (ι → ι) → ι . x7) (λ x9 : (ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x7) (Inj0 (x2 (λ x10 x11 . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0) (x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 . 0) 0 0)))) = Inj1 (x3 (λ x9 : ι → ι → ι → ι . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 . x11 (λ x13 : ι → ι . x3 (λ x14 : ι → ι → ι → ι . 0) (λ x14 : ι → (ι → ι) → ι . 0) (λ x14 : (ι → ι) → ι . 0))) (x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 . setsum 0 0) (x3 (λ x10 : ι → ι → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . 0)) 0) (Inj0 0)) (λ x9 : ι → (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . x9 (λ x10 . x10)))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x3 (λ x9 : ι → ι → ι → ι . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 . x3 (λ x13 : ι → ι → ι → ι . x11 (λ x14 : ι → ι . x11 (λ x15 : ι → ι . 0))) (λ x13 : ι → (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . x3 (λ x14 : ι → ι → ι → ι . x14 0 0 0) (λ x14 : ι → (ι → ι) → ι . 0) (λ x14 : (ι → ι) → ι . Inj0 0))) 0 x7) (λ x9 : ι → (ι → ι) → ι . setsum (Inj1 (setsum (x2 (λ x10 x11 . 0) 0) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0))) 0) (λ x9 : (ι → ι) → ι . 0) = Inj0 (x4 0 (setsum (x4 (x5 0) x7 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0) (x3 (λ x9 : ι → ι → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . 0))) (x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . 0) 0 (setsum 0 0))) 0 (Inj1 0))) ⟶ (∀ x4 : ((ι → ι) → ι) → ι → ι → ι . ∀ x5 x6 x7 . x2 (λ x9 x10 . x9) (Inj0 (x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . x2 (λ x12 x13 . 0) (setsum 0 0)) (setsum x7 x5) x7)) = x4 (λ x9 : ι → ι . x5) (Inj1 (x4 (λ x9 : ι → ι . setsum x5 0) (Inj0 (x3 (λ x9 : ι → ι → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . 0))) (x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . 0) (setsum 0 0) (x2 (λ x9 x10 . 0) 0)))) (x3 (λ x9 : ι → ι → ι → ι . Inj0 (x9 0 (setsum 0 0) (x9 0 0 0))) (λ x9 : ι → (ι → ι) → ι . Inj1 (x9 (x2 (λ x10 x11 . 0) 0) (λ x10 . 0))) (λ x9 : (ι → ι) → ι . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . setsum (Inj1 0)) 0 (setsum 0 x7)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x2 (λ x9 x10 . x2 (λ x11 x12 . 0) 0) (x3 (λ x9 : ι → ι → ι → ι . x1 (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 . x9 (x11 (λ x13 : ι → ι . 0)) (x3 (λ x13 : ι → ι → ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0)) 0) (x5 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 x11 . x9 0 0 0)) (Inj0 (x6 (λ x10 . 0)))) (λ x9 : ι → (ι → ι) → ι . x3 (λ x10 : ι → ι → ι → ι . x3 (λ x11 : ι → ι → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0) (λ x11 : (ι → ι) → ι . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0)) (λ x10 : ι → (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . x9 0 (λ x11 . x9 0 (λ x12 . 0)))) (λ x9 : (ι → ι) → ι . setsum (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . setsum 0 0) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0)) 0)) = Inj0 (Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → ι . x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . x3 (λ x12 : ι → ι → ι → ι . x12 0 x11 (setsum 0 (x10 (λ x13 : ι → ι . 0)))) (λ x12 : ι → (ι → ι) → ι . setsum (Inj0 (Inj0 0)) (setsum 0 x11)) (λ x12 : (ι → ι) → ι . x10 (λ x13 : ι → ι . Inj0 0))) 0 0 = x3 (λ x9 : ι → ι → ι → ι . setsum (x3 (λ x10 : ι → ι → ι → ι . x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0) 0) (λ x10 : ι → (ι → ι) → ι . Inj1 (x2 (λ x11 x12 . 0) 0)) (λ x10 : (ι → ι) → ι . 0)) (Inj0 (x9 (setsum 0 0) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0) (setsum 0 0)))) (λ x9 : ι → (ι → ι) → ι . x2 (λ x10 x11 . setsum (x3 (λ x12 : ι → ι → ι → ι . 0) (λ x12 : ι → (ι → ι) → ι . Inj0 0) (λ x12 : (ι → ι) → ι . x11)) (x1 (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : ((ι → ι) → ι) → ι . λ x14 . Inj1 0) (Inj0 0) (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0))) 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : ι → ι → ι → ι . Inj0 0) (λ x10 : ι → (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι . 0))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . 0) 0 0 = Inj0 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x3 (λ x10 : ι → ι → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . x10 (x7 (x10 0 (λ x11 . 0))) (λ x11 . x2 (λ x12 x13 . Inj0 0) (x3 (λ x12 : ι → ι → ι → ι . 0) (λ x12 : ι → (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0)))) (λ x10 : (ι → ι) → ι . x6 (x6 (setsum 0 0) (Inj0 0)) (setsum (Inj0 0) (Inj0 0)))) 0 = Inj0 (Inj1 (Inj0 (x2 (λ x9 x10 . x9) 0)))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . Inj1 (x5 (x3 (λ x10 : ι → ι → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . x1 (λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 . 0) 0 0) (λ x10 : (ι → ι) → ι . x10 (λ x11 . 0))) (λ x10 . x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0)) (λ x10 . x6 (x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0)) (x3 (λ x10 : ι → ι → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . x3 (λ x11 : ι → ι → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . 0)) (λ x10 : (ι → ι) → ι . x7)))) 0 = x6 (setsum (x2 (λ x9 x10 . 0) (setsum (x6 0) (Inj0 0))) (Inj0 (Inj1 (Inj0 0))))) ⟶ False (proof)
Theorem 73e8d.. : ∀ x0 : ((((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι) → ι) → ((((ι → ι) → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι . ∀ x1 : (((ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → ι → ι → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : ((ι → ι) → ι) → ι → ι . (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . x1 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . 0) 0 x7) x7 = x1 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj0 (x3 (λ x10 : ι → ι . x6 (x3 (λ x11 : ι → ι . 0) 0) 0) 0)) (λ x9 . Inj1 (setsum x7 0)) (setsum (Inj1 0) (Inj0 (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . Inj0 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . Inj1 0)))) (setsum 0 (x1 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x9 (λ x10 . λ x11 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0)) (x2 (λ x9 . x9)) (Inj1 (Inj1 0)) (setsum (x6 0 0) x5)))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 : ι → ι . Inj1 (x1 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x10 (λ x11 . λ x12 : ι → ι . x2 (λ x13 . 0) 0) (λ x11 : ι → ι . λ x12 . setsum 0 0)) (λ x10 . x10) 0 (setsum 0 (x9 0)))) (x1 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum x5 0) (λ x9 . x5) 0 (x1 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 (x3 (λ x10 : ι → ι . 0) 0)) (λ x9 . x6) (setsum 0 0) (Inj0 x5))) = x1 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x6) (λ x9 . x0 (λ x10 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . x1 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 . x10 (λ x12 : ι → ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x14 . 0) 0 0) (λ x12 x13 . 0)) 0 x9) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . x9)) (setsum 0 (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . x5) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0))) x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 . x2 (λ x9 . 0) 0 = x4) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x9) (λ x10 . Inj0 (x3 (λ x11 : ι → ι . 0) (x2 (λ x11 . 0) 0))) (x6 (λ x10 : ι → ι . Inj1 (x3 (λ x11 : ι → ι . 0) 0)) 0 (λ x10 . 0) (setsum 0 x7)) (Inj0 (x2 (λ x10 . x7) (x6 (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0)))) x5 = x5) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 . x2 (λ x10 . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . Inj1 (Inj0 0))) 0) 0 x7 = Inj0 (Inj1 (x5 (λ x9 : (ι → ι) → ι . x2 (λ x10 . x1 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 . 0) 0 0) (x2 (λ x10 . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 . 0) 0 (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . setsum (Inj1 (setsum 0 0)) (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . x9 (λ x11 : ι → ι → ι . λ x12 . 0) (λ x11 x12 . 0)) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . 0) 0))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . x7 (λ x12 : ι → ι → ι . λ x13 . x13)) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 : ι → ι . x0 (λ x14 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . 0) (λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . 0)) 0))) = setsum (setsum 0 (x6 (x6 (x2 (λ x9 . 0) 0)))) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . setsum 0 (Inj1 (x9 (λ x10 : ι → ι → ι . λ x11 . 0) (λ x10 x11 . 0)))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι → ι . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . Inj1 (setsum (setsum 0 (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . 0) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . 0))) (Inj0 0))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0) = x5 (λ x9 : ι → ι . x9 (x7 (λ x10 . λ x11 : ι → ι . setsum 0 (Inj0 0)) (x2 (λ x10 . setsum 0 0) 0) (x3 (λ x10 : ι → ι . x2 (λ x11 . 0) 0) 0))) (Inj1 (x4 (λ x9 : (ι → ι) → ι . Inj0 (x1 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . 0) 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0) = Inj1 x7) ⟶ False (proof)
Theorem 1cf83.. : ∀ x0 : (((ι → ι) → ι → (ι → ι) → ι → ι) → ι) → ι → ι . ∀ x1 : (ι → ι) → ι → ι . ∀ x2 : ((ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι . ∀ x3 : (ι → ι) → ((((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι) → ι . (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x3 (λ x9 . Inj1 (x3 (λ x10 . x3 (λ x11 . x7 (λ x12 : (ι → ι) → ι → ι . 0)) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 . Inj1 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x2 (λ x13 : ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . 0)))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x2 (λ x12 : ι → ι . x2 (λ x13 : ι → ι . x10 (λ x14 . Inj0 0)) (λ x13 : (ι → ι → ι) → ι . x11)) (λ x12 : (ι → ι → ι) → ι . 0)) = x2 (λ x9 : ι → ι . x3 (λ x10 . Inj0 (x2 (λ x11 : ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0))) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x0 (λ x13 : (ι → ι) → ι → (ι → ι) → ι → ι . Inj0 (Inj0 0)) (x2 (λ x13 : ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . Inj0 0)))) (λ x9 : (ι → ι → ι) → ι . x7 (λ x10 : (ι → ι) → ι → ι . Inj0 (setsum (Inj0 0) (x2 (λ x11 : ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x0 (λ x10 : (ι → ι) → ι → (ι → ι) → ι → ι . setsum x9 0) x9) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x1 (λ x12 . 0) (setsum (Inj0 x11) 0)) = setsum (x3 (λ x9 . Inj0 (x3 (λ x10 . x1 (λ x11 . 0) 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x11 (λ x13 . 0)))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . x0 (λ x11 : (ι → ι) → ι → (ι → ι) → ι → ι . x10 (λ x12 . Inj0 0)))) (Inj1 (x4 (Inj1 x7)))) ⟶ (∀ x4 : (ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . x5) (λ x9 : (ι → ι → ι) → ι . 0) = setsum (x3 (λ x9 . 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x1 (λ x12 . x10 (λ x13 . x11)) (Inj1 x11))) (setsum (x6 0) (x3 (λ x9 . x5) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . 0)))) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 : ι → ι . Inj1 0) (λ x9 : (ι → ι → ι) → ι . Inj0 (setsum (x3 (λ x10 . x3 (λ x11 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 . 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x2 (λ x13 : ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . 0))) (x6 (λ x10 . 0) (λ x10 : ι → ι . x10 0)))) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . x1 (λ x9 . x9) 0 = setsum 0 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x1 (λ x9 . 0) (x6 (λ x9 . Inj1 (x1 (λ x10 . x6 (λ x11 . 0) 0 (λ x11 . 0)) 0)) (setsum x7 (x2 (λ x9 : ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0))) (λ x9 . 0)) = Inj1 x7) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : (ι → ι) → ι → (ι → ι) → ι → ι . x1 (λ x10 . setsum (Inj0 0) 0) 0) (x0 (λ x9 : (ι → ι) → ι → (ι → ι) → ι → ι . x6 (setsum 0 (x3 (λ x10 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . 0)))) 0) = x1 (λ x9 . x2 (λ x10 : ι → ι . x9) (λ x10 : (ι → ι → ι) → ι . x1 (λ x11 . 0) (setsum (x3 (λ x11 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 . 0)) 0))) (setsum (setsum (Inj1 0) x7) x5)) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι → ι . x0 (λ x9 : (ι → ι) → ι → (ι → ι) → ι → ι . Inj1 x6) (Inj0 (Inj0 (x7 0 (setsum 0 0) (x3 (λ x9 . 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . 0))))) = x5 (x1 (λ x9 . x9) (x4 (λ x9 . setsum 0 0) (λ x9 . Inj0 (x5 0)) (λ x9 . 0) (Inj0 (setsum 0 0))))) ⟶ False (proof)
Theorem e46a9.. : ∀ x0 : ((ι → (ι → ι) → ι → ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → ι → ι . ∀ x2 : ((ι → ι → ι → ι) → ι) → ι → ι → ι . ∀ x3 : (ι → (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι → ((ι → ι) → ι → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x9) (λ x9 : (ι → ι → ι) → ι . x5 (λ x10 : ι → ι → ι . x6) (setsum (x0 (λ x10 : ι → (ι → ι) → ι → ι → ι . Inj0 0) (λ x10 . x10) (setsum 0 0)) (setsum (x0 (λ x10 : ι → (ι → ι) → ι → ι → ι . 0) (λ x10 . 0) 0) (Inj1 0)))) (x2 (λ x9 : ι → ι → ι → ι . 0) (setsum (x1 (λ x9 x10 . x1 (λ x11 x12 . 0) 0) (Inj1 0)) (x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . setsum 0 0) (λ x9 . x9) (x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . 0) (λ x9 . 0) 0))) 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 x12 . x10) 0) (x1 (λ x9 x10 . 0) (x2 (λ x9 : ι → ι → ι → ι . x5 (λ x10 : ι → ι → ι . Inj1 0) (x3 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 : ι → ι . λ x11 . 0) 0 0)) (Inj1 (Inj0 0)) 0)) (x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . x6) (λ x9 . Inj1 (x3 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x0 (λ x12 : ι → (ι → ι) → ι → ι → ι . 0) (λ x12 . 0) 0) (λ x10 : (ι → ι → ι) → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 : ι → ι . λ x12 . 0) 0 0) x7 (λ x10 : ι → ι . λ x11 . 0) (x1 (λ x10 x11 . 0) 0) x9)) (setsum (setsum 0 x4) 0)) = x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . x6) (λ x9 . x2 (λ x10 : ι → ι → ι → ι . Inj1 (x1 (λ x11 x12 . 0) (setsum 0 0))) 0 (x1 (λ x10 x11 . x3 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x0 (λ x14 : ι → (ι → ι) → ι → ι → ι . 0) (λ x14 . 0) 0) (λ x12 : (ι → ι → ι) → ι . x12 (λ x13 x14 . 0)) x9 (λ x12 : ι → ι . λ x13 . x13) 0 (Inj1 0)) (x2 (λ x10 : ι → ι → ι → ι . x0 (λ x11 : ι → (ι → ι) → ι → ι → ι . 0) (λ x11 . 0) 0) (setsum 0 0) (x0 (λ x10 : ι → (ι → ι) → ι → ι → ι . 0) (λ x10 . 0) 0)))) (Inj0 (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x2 (λ x11 : ι → ι → ι → ι . x0 (λ x12 : ι → (ι → ι) → ι → ι → ι . 0) (λ x12 . 0) 0) (x0 (λ x11 : ι → (ι → ι) → ι → ι → ι . 0) (λ x11 . 0) 0) 0) (λ x9 : (ι → ι → ι) → ι . Inj1 0) (x1 (λ x9 x10 . x2 (λ x11 : ι → ι → ι → ι . 0) 0 0) 0) (λ x9 : ι → ι . λ x10 . x9 (Inj0 0)) (Inj1 x4) (Inj1 0)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x7) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 x11 . x2 (λ x12 : ι → ι → ι → ι . setsum x10 x11) (Inj0 (Inj0 0)) (x2 (λ x12 : ι → ι → ι → ι . x2 (λ x13 : ι → ι → ι → ι . 0) 0 0) 0 (x3 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 : ι → ι . λ x13 . 0) 0 0))) (Inj1 (x3 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 : ι → ι . λ x11 . 0) x7 (x2 (λ x10 : ι → ι → ι → ι . 0) 0 0)))) (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 x11 . x2 (λ x12 : ι → ι → ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 (λ x13 : ι → ι . λ x14 . 0) 0 0) (x9 (λ x12 x13 . 0)) (x0 (λ x12 : ι → (ι → ι) → ι → ι → ι . 0) (λ x12 . 0) 0)) (x5 (λ x10 : (ι → ι) → ι . x6 0) x7 (Inj0 0))) 0 (λ x9 : ι → ι . λ x10 . Inj1 0) 0 (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) (x1 (λ x9 x10 . 0) (Inj1 0)) (λ x9 : ι → ι . λ x10 . setsum (x9 0) (x9 0)) 0 (x1 (λ x9 x10 . x6 0) (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 (λ x9 : ι → ι . λ x10 . 0) 0 0)))) (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → ι → ι → ι . x11 0 0 0) (x3 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (λ x11 : (ι → ι → ι) → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x2 (λ x14 : ι → ι → ι → ι . 0) 0 0) (λ x12 : (ι → ι → ι) → ι . x12 (λ x13 x14 . 0)) 0 (λ x12 : ι → ι . λ x13 . Inj0 0) (x1 (λ x12 x13 . 0) 0) 0) x7 (λ x11 : ι → ι . λ x12 . 0) 0 0) x7) (setsum (x2 (λ x9 : ι → ι → ι → ι . 0) 0 0) 0) (x1 (λ x9 x10 . x7) (x6 x4)) = x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 (x6 0)) (λ x9 : (ι → ι → ι) → ι . setsum (x1 (λ x10 x11 . x0 (λ x12 : ι → (ι → ι) → ι → ι → ι . Inj0 0) (λ x12 . 0) x10) (x1 (λ x10 x11 . x9 (λ x12 x13 . 0)) (x5 (λ x10 : (ι → ι) → ι . 0) 0 0))) 0) (Inj0 x7) (λ x9 : ι → ι . λ x10 . setsum (setsum 0 (Inj0 (x3 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 : ι → ι . λ x12 . 0) 0 0))) (Inj0 (x3 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x0 (λ x13 : ι → (ι → ι) → ι → ι → ι . 0) (λ x13 . 0) 0) (λ x11 : (ι → ι → ι) → ι . Inj0 0) (Inj1 0) (λ x11 : ι → ι . λ x12 . setsum 0 0) (Inj0 0) (x1 (λ x11 x12 . 0) 0)))) (x5 (λ x9 : (ι → ι) → ι . 0) x4 (setsum (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x9) (λ x9 : (ι → ι → ι) → ι . 0) (Inj0 0) (λ x9 : ι → ι . λ x10 . Inj0 0) x4 (x1 (λ x9 x10 . 0) 0)) (x2 (λ x9 : ι → ι → ι → ι . x0 (λ x10 : ι → (ι → ι) → ι → ι → ι . 0) (λ x10 . 0) 0) (setsum 0 0) (x5 (λ x9 : (ι → ι) → ι . 0) 0 0)))) (setsum (x1 (λ x9 x10 . 0) 0) x4)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ι → ι → ι → ι . 0) (Inj0 (setsum (x2 (λ x9 : ι → ι → ι → ι . Inj0 0) (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 (λ x9 : ι → ι . λ x10 . 0) 0 0) x4) (Inj0 (x3 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 (λ x9 : ι → ι . λ x10 . 0) 0 0)))) x6 = x6) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 : ι → ι → ι → ι . Inj0 0) (Inj0 (x2 (λ x9 : ι → ι → ι → ι . x0 (λ x10 : ι → (ι → ι) → ι → ι → ι . x10 0 (λ x11 . 0) 0 0) (λ x10 . x0 (λ x11 : ι → (ι → ι) → ι → ι → ι . 0) (λ x11 . 0) 0) (x1 (λ x10 x11 . 0) 0)) 0 0)) 0 = x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 x7 : ι → ι . x1 (λ x9 x10 . 0) (x4 0) = Inj1 (x4 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . Inj0 (x7 x6)) x4 = x4) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . setsum x7 (x1 (λ x10 x11 . setsum (x1 (λ x12 x13 . 0) 0) 0) x7)) (λ x9 . x6) 0 = setsum x4 0) ⟶ (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . setsum x5 (setsum (x9 0 (λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 : ι → ι . λ x12 . 0) 0 0) (Inj1 0) 0) (x3 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . x9 0 (λ x11 . 0) 0 0) 0 (λ x10 : ι → ι . λ x11 . setsum 0 0) (x9 0 (λ x10 . 0) 0 0) (Inj0 0)))) (λ x9 . x9) (Inj0 (x4 0 (λ x9 . x7 (x7 0)) (λ x9 . Inj1 0) (setsum (Inj0 0) (Inj0 0)))) = setsum (Inj0 (setsum (setsum (Inj1 0) (Inj1 0)) 0)) (setsum (setsum (setsum (x0 (λ x9 : ι → (ι → ι) → ι → ι → ι . 0) (λ x9 . 0) 0) (Inj1 0)) 0) 0)) ⟶ False (proof)
Theorem 88f1b.. : ∀ x0 x1 : (ι → ι) → ι → ι . ∀ x2 : ((((ι → ι → ι) → ι) → ι) → ι) → ι → ι → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι → ι . x3 (λ x9 . x7 (Inj1 0) x9 (x7 (x6 (setsum 0 0)) 0 0)) (Inj0 (Inj0 (setsum (x2 (λ x9 : ((ι → ι → ι) → ι) → ι . 0) 0 0) x4))) (x6 (x0 (λ x9 . 0) (x6 (setsum 0 0)))) = x6 (x7 0 x4 (Inj0 (Inj1 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x9) 0 (Inj0 0) = x5 (λ x9 . λ x10 : ι → ι . λ x11 . x9)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 : ((ι → ι → ι) → ι) → ι . 0) 0 x6 = setsum (x0 (λ x9 . setsum x9 (setsum 0 (Inj0 0))) x7) (x4 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x0 (λ x11 . 0) 0))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . x2 (λ x9 : ((ι → ι → ι) → ι) → ι . Inj1 (x6 (λ x10 : ι → ι . 0) (λ x10 x11 . x1 (λ x12 . x1 (λ x13 . 0) 0) x10) (x9 (λ x10 : ι → ι → ι . x10 0 0)))) (x1 (λ x9 . x1 (λ x10 . x7 (λ x11 : (ι → ι) → ι . λ x12 x13 . Inj1 0) (λ x11 : ι → ι . 0) 0) (x3 (λ x10 . setsum 0 0) (x7 (λ x10 : (ι → ι) → ι . λ x11 x12 . 0) (λ x10 : ι → ι . 0) 0) x9)) (x2 (λ x9 : ((ι → ι → ι) → ι) → ι . Inj1 (Inj1 0)) (x1 (λ x9 . x6 (λ x10 : ι → ι . 0) (λ x10 x11 . 0) 0) (x4 0 0 (λ x9 . 0))) 0)) (setsum 0 (x3 (λ x9 . x5 (λ x10 . Inj1 0)) (x3 (λ x9 . x3 (λ x10 . 0) 0 0) (setsum 0 0) (x4 0 0 (λ x9 . 0))) (x7 (λ x9 : (ι → ι) → ι . λ x10 x11 . 0) (λ x9 : ι → ι . x3 (λ x10 . 0) 0 0) (x3 (λ x9 . 0) 0 0)))) = x1 (λ x9 . x0 (λ x10 . x10) (x5 (λ x10 . x2 (λ x11 : ((ι → ι → ι) → ι) → ι . x7 (λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x12 : ι → ι . 0) 0) (Inj0 0) (x3 (λ x11 . 0) 0 0)))) (x7 (λ x9 : (ι → ι) → ι . λ x10 x11 . x11) (λ x9 : ι → ι . x1 (λ x10 . 0) (x7 (λ x10 : (ι → ι) → ι . λ x11 x12 . x1 (λ x13 . 0) 0) (λ x10 : ι → ι . setsum 0 0) (x6 (λ x10 : ι → ι . 0) (λ x10 x11 . 0) 0))) (x6 (λ x9 : ι → ι . x0 (λ x10 . Inj1 0) (x1 (λ x10 . 0) 0)) (λ x9 x10 . x0 (λ x11 . x1 (λ x12 . 0) 0) 0) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 . x5) (x2 (λ x9 : ((ι → ι → ι) → ι) → ι . setsum 0 (x0 (λ x10 . x10) (x0 (λ x10 . 0) 0))) (Inj0 x7) (x1 (λ x9 . setsum (setsum 0 0) x6) (setsum (x1 (λ x9 . 0) 0) 0))) = Inj1 (setsum (setsum (setsum x5 (Inj0 0)) (x2 (λ x9 : ((ι → ι → ι) → ι) → ι . setsum 0 0) 0 0)) (setsum (x1 (λ x9 . setsum 0 0) x5) (setsum x6 x5)))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . x0 (λ x10 . x9) (Inj1 (x2 (λ x10 : ((ι → ι → ι) → ι) → ι . Inj1 0) x5 (x3 (λ x10 . 0) 0 0)))) (x1 (λ x9 . x3 (λ x10 . x7) (setsum x6 x9) (setsum (Inj0 0) (Inj0 0))) (Inj0 0)) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι → ι . x0 (λ x9 . 0) x6 = Inj1 (x3 (λ x9 . 0) (setsum 0 (Inj0 (Inj1 0))) (setsum (x1 (λ x9 . 0) (Inj1 0)) (setsum (x1 (λ x9 . 0) 0) (setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 . setsum x9 0) (setsum (x0 (λ x9 . x0 (λ x10 . x9) (x3 (λ x10 . 0) 0 0)) 0) x6) = x6) ⟶ False (proof)