Apply H1 with
λ x2 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) x2 = TwoRamseyGraph_4_4_Church17 x2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) leaving 17 subgoals.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x4)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x4) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x5)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x5) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x6)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x6) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x7)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x7) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x8)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x8) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x9)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x9) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x10)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x10) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x11)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x11) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x12)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x12) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x13)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x13) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x14)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x14) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x15)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x15) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x16)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x16) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x17)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x17) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x18)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x18) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).
The subproof is completed by applying H2.
Let x2 of type (ι → ι → ι) → (ι → ι → ι) → ο be given.
Assume H2:
x2 (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x19)) (TwoRamseyGraph_4_4_Church17 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x19) (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)).