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Proofgold Proof

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Claim L0: ...
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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.
Let x2 of type ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → 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 be given.
Assume H1: Church17_lt6 x0.
Assume H2: Church17_lt6 x1.
Assume H3: Church17_lt6 x2.
Assume H4: Church17_lt6 x3.
Apply H1 with λ x4 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_3_6_Church17 x4 x1 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x4 x2 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x4 x3 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x1 x2 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x1 x3 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x2 x3 = λ x5 x6 . x6) ⟶ False leaving 6 subgoals.
Apply H2 with λ x4 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) x4 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) x2 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) x3 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x4 x2 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x4 x3 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x2 x3 = λ x5 x6 . x6) ⟶ False leaving 6 subgoals.
Assume H5: TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) = λ x4 x5 . x5.
Apply FalseE with (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x2 x3 = λ x4 x5 . x5) ⟶ False.
Apply L0.
The subproof is completed by applying H5.
Assume H5: TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x5) = λ x4 x5 . x5.
Apply FalseE with (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x5) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x5) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x2 x3 = λ x4 x5 . x5) ⟶ False.
Apply L0.
The subproof is completed by applying H5.
Assume H5: TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x6) = λ x4 x5 . x5.
Apply FalseE with (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x4) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x6) x2 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . x6) x3 = λ x4 x5 . x5) ⟶ (TwoRamseyGraph_3_6_Church17 x2 x3 = λ x4 x5 . x5) ⟶ False.
Apply L0.
The subproof is completed by applying H5.
Apply H3 with λ x4 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x8) = ... ⟶ (TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) x4 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x5) x3 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x8) x4 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x8) x3 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x4 x3 = λ x5 x6 . x6) ⟶ False leaving 6 subgoals.
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