Let x0 of type ι → ι → ι → ι → 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 → ι → ι → ι → ι be given.
Apply H0 with
λ x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_3_6_Church17 x2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x15) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 x2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x17) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 x2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x18) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x15) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x17) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x18) = λ x3 x4 . x4) ⟶ (TwoRamseyGraph_3_6_Church17 x2 x1 = λ x3 x4 . x4) ⟶ ∀ x3 : ο . (84660.. x2 ⟶ x3) ⟶ (84660.. x1 ⟶ x3) ⟶ x3 leaving 8 subgoals.
Assume H2:
TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) = λ x2 x3 . x3.
Assume H3:
TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) = λ x2 x3 . x3.
Assume H4:
TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) = λ x2 x3 . x3.
Apply FalseE with
(TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) x1 = λ x2 x3 . x3) ⟶ ∀ x2 : ο . (84660.. (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) ⟶ x2) ⟶ (84660.. x1 ⟶ x2) ⟶ x2.
Apply unknownprop_1019f796b5519c5beeeef55b1daae2de48848a97e75d217687db0a2449fd5208.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
The subproof is completed by applying H4 with λ x3 x4 : ι → ι → ι . x2 x4 x3.
Assume H2:
TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) = λ x2 x3 . x3.
Apply FalseE with
(TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) x1 = λ x2 x3 . x3) ⟶ ∀ x2 : ο . (84660.. (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x4) ⟶ x2) ⟶ (84660.. x1 ⟶ x2) ⟶ x2.
Apply unknownprop_1019f796b5519c5beeeef55b1daae2de48848a97e75d217687db0a2449fd5208.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
The subproof is completed by applying H2 with λ x3 x4 : ι → ι → ι . x2 x4 x3.
Assume H2:
TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) = λ x2 x3 . x3.
Assume H3:
TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) = λ x2 x3 . x3.
Apply FalseE with
(TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) = λ x2 x3 . x3) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) x1 = λ x2 x3 . x3) ⟶ ∀ x2 : ο . (84660.. (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x5) ⟶ x2) ⟶ (84660.. x1 ⟶ x2) ⟶ x2.
Apply unknownprop_1019f796b5519c5beeeef55b1daae2de48848a97e75d217687db0a2449fd5208.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
The subproof is completed by applying H3 with λ x3 x4 : ι → ι → ι . ....