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Proofgold Proof

pf
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.
Assume H0: Church17_p x0.
Assume H1: Church17_p x1.
Apply H0 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 x2 x1 = TwoRamseyGraph_4_4_Church17 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 x2) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 x1) leaving 17 subgoals.
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 x2) 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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x4))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x5))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x6))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x7))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x8))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x9))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x10))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x11))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x12))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x13))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x14))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x15))).
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 (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x3)) (Church17_perm_3_4_5_6_7_8_9_10_11_12_13_14_15_16_0_1_2 (λ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . x16))).
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)) ....
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