Let x0 of type ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι be given.
Let x1 of type ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι be given.
Let x2 of type ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι be given.
Apply H1 with
λ x3 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) ⟶ ∀ x4 : ο . x4) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = x3 ⟶ ∀ x4 : ο . x4) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = x1 ⟶ ∀ x4 : ο . x4) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) = x2 ⟶ ∀ x4 : ο . x4) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) = x3 ⟶ ∀ x4 : ο . x4) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) = x1 ⟶ ∀ x4 : ο . x4) ⟶ ((λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) = x2 ⟶ ∀ x4 : ο . x4) ⟶ (x3 = x1 ⟶ ∀ x4 : ο . x4) ⟶ (x3 = x2 ⟶ ∀ x4 : ο . x4) ⟶ (x1 = x2 ⟶ ∀ x4 : ο . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 x3 x1 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 x3 x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_5_Church13 x1 x2 = λ x4 x5 . x5) ⟶ False leaving 13 subgoals.
Assume H4: ((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) = λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) ⟶ ∀ x3 : ο . x3.
Assume H5: ((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) = λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) ⟶ ∀ x3 : ο . x3.
Apply FalseE with
(... ⟶ ∀ x3 : ο . x3) ⟶ ((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) = x2 ⟶ ∀ x3 : ο . x3) ⟶ (((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) = λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) ⟶ ∀ x3 : ο . x3) ⟶ ((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) = x1 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) = x2 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) = x1 ⟶ ∀ x3 : ο . x3) ⟶ ((λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) = x2 ⟶ ∀ x3 : ο . x3) ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) x1 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) x2 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) x1 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x5) x2 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) x1 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . x3) x2 = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_5_Church13 x1 x2 = λ x3 x4 . x4) ⟶ False.