Proofgold Signed Transaction

Definition a4ee9.. := λ x0 : ι → ι → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι → ι → ι → ι → ι) → ο . x1 (λ x2 x3 x4 x5 x6 x7 . x2) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x3) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x4) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x5) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x6) ⟶ x1 x0
Theorem 9367f.. : a4ee9.. (λ x0 x1 x2 x3 x4 x5 . x0) (proof)
Theorem 6b245.. : a4ee9.. (λ x0 x1 x2 x3 x4 x5 . x1) (proof)
Theorem 32eba.. : a4ee9.. (λ x0 x1 x2 x3 x4 x5 . x2) (proof)
Theorem 77b75.. : a4ee9.. (λ x0 x1 x2 x3 x4 x5 . x3) (proof)
Theorem eca3f.. : a4ee9.. (λ x0 x1 x2 x3 x4 x5 . x4) (proof)
Definition Church6_p := λ x0 : ι → ι → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι → ι → ι → ι → ι) → ο . x1 (λ x2 x3 x4 x5 x6 x7 . x2) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x3) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x4) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x5) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x6) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 . x7) ⟶ x1 x0
Definition False^False := ∀ x0 : ο . x0
Definition TwoRamseyGraph_4_6_Church6_squared_b := λ x0 x1 x2 x3 : ι → ι → ι → ι → ι → ι → ι . λ x4 x5 . x0 (x1 (x2 (x3 x5 x5 x4 x5 x4 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x5 x4 x4 x5 x4 x5) (x3 x5 x5 x4 x4 x5 x5) (x3 x4 x5 x4 x4 x5 x5)) (x2 (x3 x5 x5 x5 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x4 x5 x4) (x3 x4 x5 x5 x4 x5 x4) (x3 x5 x5 x4 x4 x5 x5) (x3 x5 x4 x4 x4 x5 x5)) (x2 (x3 x4 x5 x5 x5 x5 x4) (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x4 x5 x5 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x5) (x3 x4 x4 x4 x5 x5 x5)) (x2 (x3 x5 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x4 x4 x5 x4 x5) (x3 x4 x4 x5 x5 x5 x5) (x3 x4 x4 x5 x4 x5 x5)) (x2 (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x5 x5 x4 x4 x4) (x3 x4 x5 x5 x4 x4 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x5 x5 x5 x4 x5)) (x2 (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x4 x4 x5 x4 x4) (x3 x5 x4 x4 x5 x4 x4) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x5 x5 x5 x4 x5))) (x1 (x2 (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x5 x5 x4) (x3 x4 x5 x5 x5 x4 x5) (x3 x5 x4 x4 x4 x4 x5) (x3 x5 x4 x4 x5 x5 x4) (x3 x5 x4 x5 x5 x5 x5)) (x2 (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x5 x5 x4 x4 x5) (x3 x5 x4 x5 x5 x5 x4) (x3 x4 x5 x4 x4 x5 x4) (x3 x4 x5 x5 x4 x4 x5) (x3 x4 x5 x5 x5 x5 x5)) (x2 (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x5 x5 x5 x5 x4) (x3 x5 x5 x4 x5 x4 x5) (x3 x4 x4 x5 x4 x5 x4) (x3 x4 x5 x5 x4 x5 x4) (x3 x5 x5 x5 x4 x5 x5)) (x2 (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x4 x5 x5 x4 x5) (x3 x5 x5 x5 x4 x5 x4) (x3 x4 x4 x4 x5 x4 x5) (x3 x5 x4 x4 x5 x4 x5) (x3 x5 x5 x4 x5 x5 x5)) (x2 (x3 x4 x5 x4 x5 x5 x5) (x3 x5 x4 x5 x4 x5 x4) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x5 x4) (x3 x5 x4 x5 x4 x4 x5)) (x2 (x3 x5 x4 x5 x4 x5 x5) (x3 x4 x5 x4 x5 x4 x5) (x3 x4 x5 x4 x5 x5 x5) (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x4 x5) (x3 x4 x5 x4 x5 x4 x5))) (x1 (x2 (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x5 x5 x5 x5 x4) (x3 x5 x4 x5 x5 x4 x5) (x3 x5 x4 x4 x5 x5 x4) (x3 x5 x5 x4 x4 x5 x5) (x3 x5 x5 x4 x5 x4 x5)) (x2 (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x4 x5 x5 x4 x5) (x3 x4 x5 x5 x5 x5 x4) (x3 x4 x5 x5 x4 x4 x5) (x3 x5 x5 x4 x4 x5 x5) (x3 x5 x5 x5 x4 x4 x5)) (x2 (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x5 x5 x4) (x3 x5 x5 x5 x4 x4 x5) (x3 x4 x5 x5 x4 x4 x5) (x3 x4 x4 x5 x5 x5 x5) (x3 x4 x5 x5 x5 x4 x5)) (x2 (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x5 x5 x4 x4 x5) (x3 x5 x5 x4 x5 x5 x4) (x3 x5 x4 x4 x5 x5 x4) (x3 x4 x4 x5 x5 x5 x5) (x3 x5 x4 x5 x5 x4 x5)) (x2 (x3 x4 x5 x4 x5 x4 x4) (x3 x4 x5 x4 x5 x5 x5) (x3 x4 x5 x4 x5 x5 x4) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x5 x5 x5 x5 x5)) (x2 (x3 x5 x4 x5 x4 x4 x4) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x4 x5 x4 x4 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x4 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x5))) (x1 (x2 (x3 x5 x4 x4 x5 x4 x5) (x3 x5 x4 x4 x4 x5 x5) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x5 x5 x4) (x3 x4 x4 x5 x5 x4 x5)) (x2 (x3 x4 x5 x5 x4 x5 x4) (x3 x4 x5 x4 x4 x5 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x4 x5 x5 x5 x5 x4) (x3 x5 x5 x5 x4 x4 x5) (x3 x4 x4 x5 x5 x4 x5)) (x2 (x3 x4 x5 x5 x4 x5 x4) (x3 x4 x4 x5 x4 x5 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x5 x5 x4 x5 x4) (x3 x4 x5 x5 x5 x5 x4) (x3 x5 x5 x4 x4 x4 x5)) (x2 (x3 x5 x4 x4 x5 x4 x5) (x3 x4 x4 x4 x5 x5 x5) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x5 x4 x5 x4 x5) (x3 x5 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x4 x4 x5)) (x2 (x3 x4 x5 x5 x4 x4 x4) (x3 x4 x5 x5 x4 x4 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x4 x5 x5 x5)) (x2 (x3 x5 x4 x4 x5 x4 x4) (x3 x5 x4 x4 x5 x4 x4) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x5 x4 x5 x5))) (x1 (x2 (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x5 x4 x5 x5 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x5)) (x2 (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x5 x5 x5 x4 x5 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x4 x5 x5 x5 x5)) (x2 (x3 x4 x4 x5 x5 x4 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x4 x4 x5 x5 x5 x4) (x3 x4 x5 x5 x5 x5 x5) (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x4 x5 x5)) (x2 (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x4 x5 x5 x5 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x4 x5 x5)) (x2 (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x5 x4 x5 x4) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x4 x5 x4 x5 x5) (x3 x4 x4 x4 x4 x4 x5)) (x2 (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x4 x5 x4 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x4 x5 x5 x5) (x3 x4 x5 x4 x5 x5 x5) (x3 x4 x4 x4 x4 x4 x5))) (x1 (x2 (x3 x4 x5 x4 x4 x5 x5) (x3 x5 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x5 x5 x5) (x3 x4 x4 x5 x5 x5 x4) (x3 x4 x4 x5 x5 x4 x4) (x3 x5 x5 x5 x4 x5 x5)) (x2 (x3 x5 x4 x4 x4 x5 x5) (x3 x4 x5 x5 x5 x4 x5) (x3 x5 x5 x5 x4 x5 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x4 x4 x5 x5 x4 x4) (x3 x5 x5 x4 x5 x5 x5)) (x2 (x3 x4 x4 x4 x5 x5 x5) (x3 x5 x5 x5 x4 x5 x4) (x3 x4 x5 x5 x5 x5 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x5 x5 x4 x4 x4 x4) (x3 x5 x4 x5 x5 x5 x5)) (x2 (x3 x4 x4 x5 x4 x5 x5) (x3 x5 x5 x4 x5 x4 x5) (x3 x5 x4 x5 x5 x5 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x5 x4 x4 x4 x4) (x3 x4 x5 x5 x5 x5 x5)) (x2 (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x4 x4) (x3 x4 x4 x4 x4 x5 x5) (x3 x4 x4 x4 x4 x5 x5) (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x5 x5)) (x2 (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x5)))
Definition TwoRamseyGraph_4_6_Church6_squared_a := λ x0 x1 x2 x3 : ι → ι → ι → ι → ι → ι → ι . λ x4 x5 . x0 (x1 (x2 (x3 x4 x5 x4 x5 x4 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x5 x4 x4 x5 x4 x5) (x3 x5 x5 x4 x4 x5 x5) (x3 x4 x5 x4 x4 x5 x4)) (x2 (x3 x5 x4 x5 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x4 x5 x4) (x3 x4 x5 x5 x4 x5 x4) (x3 x5 x5 x4 x4 x5 x5) (x3 x5 x4 x4 x4 x5 x4)) (x2 (x3 x4 x5 x4 x5 x5 x4) (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x4 x5 x5 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x5) (x3 x4 x4 x4 x5 x5 x4)) (x2 (x3 x5 x4 x5 x4 x4 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x4 x4 x5 x4 x5) (x3 x4 x4 x5 x5 x5 x5) (x3 x4 x4 x5 x4 x5 x4)) (x2 (x3 x4 x5 x5 x4 x4 x5) (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x5 x5 x4 x4 x4) (x3 x4 x5 x5 x4 x4 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x5 x5 x5 x4 x4)) (x2 (x3 x5 x4 x4 x5 x5 x4) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x4 x4 x5 x4 x4) (x3 x5 x4 x4 x5 x4 x4) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x5 x5 x5 x4 x4))) (x1 (x2 (x3 x4 x4 x5 x5 x5 x4) (x3 x4 x5 x4 x5 x5 x4) (x3 x4 x5 x5 x5 x4 x5) (x3 x5 x4 x4 x4 x4 x5) (x3 x5 x4 x4 x5 x5 x4) (x3 x5 x4 x5 x5 x5 x4)) (x2 (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x4 x5 x4 x4 x5) (x3 x5 x4 x5 x5 x5 x4) (x3 x4 x5 x4 x4 x5 x4) (x3 x4 x5 x5 x4 x4 x5) (x3 x4 x5 x5 x5 x5 x4)) (x2 (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x5 x4 x5 x5 x4) (x3 x5 x5 x4 x5 x4 x5) (x3 x4 x4 x5 x4 x5 x4) (x3 x4 x5 x5 x4 x5 x4) (x3 x5 x5 x5 x4 x5 x4)) (x2 (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x4 x5 x4 x4 x5) (x3 x5 x5 x5 x4 x5 x4) (x3 x4 x4 x4 x5 x4 x5) (x3 x5 x4 x4 x5 x4 x5) (x3 x5 x5 x4 x5 x5 x4)) (x2 (x3 x4 x5 x4 x5 x5 x5) (x3 x5 x4 x5 x4 x4 x4) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x5 x4) (x3 x5 x4 x5 x4 x4 x4)) (x2 (x3 x5 x4 x5 x4 x5 x5) (x3 x4 x5 x4 x5 x4 x4) (x3 x4 x5 x4 x5 x5 x5) (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x4 x5) (x3 x4 x5 x4 x5 x4 x4))) (x1 (x2 (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x5 x5 x5 x5 x4) (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x4 x4 x5 x5 x4) (x3 x5 x5 x4 x4 x5 x5) (x3 x5 x5 x4 x5 x4 x4)) (x2 (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x4 x5 x5 x4 x5) (x3 x4 x4 x5 x5 x5 x4) (x3 x4 x5 x5 x4 x4 x5) (x3 x5 x5 x4 x4 x5 x5) (x3 x5 x5 x5 x4 x4 x4)) (x2 (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x5 x5 x4) (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x5 x5 x4 x4 x5) (x3 x4 x4 x5 x5 x5 x5) (x3 x4 x5 x5 x5 x4 x4)) (x2 (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x5 x5 x4 x4 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x4 x4 x5 x5 x4) (x3 x4 x4 x5 x5 x5 x5) (x3 x5 x4 x5 x5 x4 x4)) (x2 (x3 x4 x5 x4 x5 x4 x4) (x3 x4 x5 x4 x5 x5 x5) (x3 x4 x5 x4 x5 x4 x4) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x5 x5 x5 x5 x4)) (x2 (x3 x5 x4 x5 x4 x4 x4) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x4 x5 x4 x4 x4) (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x4 x5 x5 x5) (x3 x5 x5 x5 x5 x5 x4))) (x1 (x2 (x3 x5 x4 x4 x5 x4 x5) (x3 x5 x4 x4 x4 x5 x5) (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x5 x5 x4) (x3 x4 x4 x5 x5 x4 x4)) (x2 (x3 x4 x5 x5 x4 x5 x4) (x3 x4 x5 x4 x4 x5 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x5 x5 x4 x4 x5) (x3 x4 x4 x5 x5 x4 x4)) (x2 (x3 x4 x5 x5 x4 x5 x4) (x3 x4 x4 x5 x4 x5 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x4 x5 x5 x5 x5 x4) (x3 x5 x5 x4 x4 x4 x4)) (x2 (x3 x5 x4 x4 x5 x4 x5) (x3 x4 x4 x4 x5 x5 x5) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x5 x4 x5 x5 x4 x5) (x3 x5 x5 x4 x4 x4 x4)) (x2 (x3 x4 x5 x5 x4 x4 x4) (x3 x4 x5 x5 x4 x4 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x5 x5 x4 x4 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x4 x5 x5 x4)) (x2 (x3 x5 x4 x4 x5 x4 x4) (x3 x5 x4 x4 x5 x4 x4) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x4 x4 x5 x5 x4) (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x5 x4 x5 x4))) (x1 (x2 (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x5 x4 x5 x5 x5) (x3 x4 x5 x4 x4 x5 x4) (x3 x4 x4 x5 x5 x5 x4)) (x2 (x3 x5 x5 x4 x4 x4 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x5 x5 x5 x4 x5 x5) (x3 x5 x4 x4 x4 x4 x5) (x3 x4 x4 x5 x5 x5 x4)) (x2 (x3 x4 x4 x5 x5 x4 x5) (x3 x4 x5 x5 x4 x5 x5) (x3 x4 x4 x5 x5 x5 x4) (x3 x4 x5 x5 x5 x5 x5) (x3 x4 x4 x4 x5 x5 x4) (x3 x5 x5 x4 x4 x5 x4)) (x2 (x3 x4 x4 x5 x5 x5 x4) (x3 x5 x4 x4 x5 x5 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x5 x4 x5 x5 x5 x5) (x3 x4 x4 x5 x4 x4 x5) (x3 x5 x5 x4 x4 x5 x4)) (x2 (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x5 x4 x5 x4) (x3 x5 x5 x5 x5 x5 x5) (x3 x5 x4 x5 x4 x5 x5) (x3 x5 x4 x5 x4 x4 x5) (x3 x4 x4 x4 x4 x4 x4)) (x2 (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x4 x5 x4 x5) (x3 x5 x5 x5 x5 x5 x5) (x3 x4 x5 x4 x5 x5 x5) (x3 x4 x5 x4 x5 x5 x4) (x3 x4 x4 x4 x4 x4 x4))) (x1 (x2 (x3 x4 x5 x4 x4 x5 x5) (x3 x5 x4 x5 x5 x5 x4) (x3 x5 x5 x4 x5 x5 x5) (x3 x4 x4 x5 x5 x5 x4) (x3 x4 x4 x5 x5 x4 x4) (x3 x4 x5 x5 x4 x5 x4)) (x2 (x3 x5 x4 x4 x4 x5 x5) (x3 x4 x5 x5 x5 x4 x5) (x3 x5 x5 x5 x4 x5 x5) (x3 x4 x4 x5 x5 x4 x5) (x3 x4 x4 x5 x5 x4 x4) (x3 x5 x4 x4 x5 x5 x4)) (x2 (x3 x4 x4 x4 x5 x5 x5) (x3 x5 x5 x5 x4 x5 x4) (x3 x4 x5 x5 x5 x5 x5) (x3 x5 x5 x4 x4 x4 x5) (x3 x5 x5 x4 x4 x4 x4) (x3 x5 x4 x4 x5 x5 x4)) (x2 (x3 x4 x4 x5 x4 x5 x5) (x3 x5 x5 x4 x5 x4 x5) (x3 x5 x4 x5 x5 x5 x5) (x3 x5 x5 x4 x4 x5 x4) (x3 x5 x5 x4 x4 x4 x4) (x3 x4 x5 x5 x4 x5 x4)) (x2 (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x4 x4) (x3 x4 x4 x4 x4 x5 x5) (x3 x4 x4 x4 x4 x5 x5) (x3 x5 x5 x5 x5 x4 x4) (x3 x5 x5 x5 x5 x4 x4)) (x2 (x3 x4 x4 x4 x4 x4 x4) (x3 x4 x4 x4 x4 x4 x4) (x3 x4 x4 x4 x4 x4 x4) (x3 x4 x4 x4 x4 x4 x4) (x3 x4 x4 x4 x4 x4 x4) (x3 x4 x4 x4 x4 x4 x4)))
Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Known 768c1.. : ((λ x1 x2 . x2) = λ x1 x2 . x1) ⟶ ∀ x0 : ο . x0
Theorem d20f9.. : ∀ x0 x1 x2 : ι → ι → ι → ι → ι → ι → ι . a4ee9.. x0 ⟶ Church6_p x1 ⟶ Church6_p x2 ⟶ ((x1 = λ x4 x5 x6 x7 x8 x9 . x9) ⟶ (x2 = λ x4 x5 x6 x7 x8 x9 . x9) ⟶ False) ⟶ (TwoRamseyGraph_4_6_Church6_squared_b (λ x4 x5 x6 x7 x8 x9 . x9) x0 x1 x2 = λ x4 x5 . x4) ⟶ TwoRamseyGraph_4_6_Church6_squared_a (λ x4 x5 x6 x7 x8 x9 . x9) x0 x1 x2 = λ x4 x5 . x4 (proof)