Let x0 of type ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → CN (ι → ι) be given.
Let x1 of type ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → CN (ι → ι) be given.
Let x2 of type ((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) → CN (ι → ι) be given.
Let x3 of type ((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) → CN (ι → ι) be given.
Apply H1 with
λ x4 : ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . (TwoRamseyGraph_4_5_24_ChurchNums_3x8 x4 x2 x1 x3 = λ x5 x6 . x6) ⟶ ChurchNums_3x8_to_u24 x4 x2 = ChurchNums_3x8_to_u24 x1 x3 ⟶ False leaving 3 subgoals.
Apply H3 with
λ x4 : ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . (TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x2 x4 x3 = λ x5 x6 . x6) ⟶ ChurchNums_3x8_to_u24 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x2 = ChurchNums_3x8_to_u24 x4 x3 ⟶ False leaving 3 subgoals.
Apply H2 with
λ x4 : ((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 → ι) → ι → ι) → (ι → ι) → ι → ι . (TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x4 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x3 = λ x5 x6 . x6) ⟶ ChurchNums_3x8_to_u24 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x4 = ChurchNums_3x8_to_u24 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x3 ⟶ False leaving 8 subgoals.
Apply H4 with
λ x4 : ((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 → ι) → ι → ι) → (ι → ι) → ι → ι . (TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι) → ι → ι . x5) (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x4 = λ x5 x6 . x6) ⟶ ChurchNums_3x8_to_u24 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι) → ι → ι . x5) = ChurchNums_3x8_to_u24 (λ x5 x6 x7 : (ι → ι) → ι → ι . x5) x4 ⟶ False leaving 8 subgoals.
Assume H5:
TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) = λ x4 x5 . x5.
Apply FalseE with
ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) = ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) ⟶ False.
Apply L0.
The subproof is completed by applying H5.
Assume H5:
TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x5) = λ x4 x5 . x5.
Apply FalseE with
ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) = ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x5) ⟶ False.
Apply L0.
The subproof is completed by applying H5.
Assume H5:
TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x6) = λ x4 x5 . x5.
Apply FalseE with
ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) = ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x6) ⟶ False.
Apply L0.
The subproof is completed by applying H5.
Assume H5:
TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x7) = λ x4 x5 . x5.
Assume H6:
ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) = ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x7).
Apply neq_3_0.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H6 with λ x5 x6 . x4 x6 x5.
Assume H5:
TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x8) = λ x4 x5 . x5.
Apply FalseE with
ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) = ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x8) ⟶ False.
Apply L0.
The subproof is completed by applying H5.
Assume H5:
TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x9) = λ x4 x5 . x5.
Assume H6:
ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x4) = ChurchNums_3x8_to_u24 (λ x4 x5 x6 : (ι → ι) → ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι) → ι → ι . x9).
Apply neq_5_0.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H6 with λ x5 x6 . x4 x6 x5.