Proofgold Signed Transaction

Param ordsucc^ordsucc : ι → ι
Definition u1 := 1
Definition u2 := ordsucc u1
Definition u3 := ordsucc u2
Definition u4 := ordsucc u3
Definition u5 := ordsucc u4
Definition u6 := ordsucc u5
Definition u7 := ordsucc u6
Definition u8 := ordsucc u7
Definition u9 := ordsucc u8
Definition u10 := ordsucc u9
Definition u11 := ordsucc u10
Definition u12 := ordsucc u11
Param Church17_to_u17 : CT17 ι
Definition Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0 x2 x4 x1 x3 x6 x8 x5 x7 x11 x9 x12 x10 x14 x15 x16 x13
Param u17_to_Church17 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι
Definition u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 := λ x0 . Church17_to_u17 (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_to_Church17 x0))
Known 866c8.. : ∀ x0 . x0 ∈ u12 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 u1 ⟶ x1 u2 ⟶ x1 u3 ⟶ x1 u4 ⟶ x1 u5 ⟶ x1 u6 ⟶ x1 u7 ⟶ x1 u8 ⟶ x1 u9 ⟶ x1 u10 ⟶ x1 u11 ⟶ x1 x0
Known 428fd.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 0 = u1
Known 2b77d.. : 1 ∈ 12
Known 6eb3e.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u1 = u3
Known 2f583.. : 3 ∈ 12
Known 00076.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u2 = 0
Known 46814.. : 0 ∈ 12
Known 737c8.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u3 = u2
Known 7c2ac.. : 2 ∈ 12
Known b5b60.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u4 = u5
Known 04716.. : 5 ∈ 12
Known d3a23.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u5 = u7
Known 35d73.. : 7 ∈ 12
Known 9e037.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u6 = u4
Known e4fc0.. : 4 ∈ 12
Known af667.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u7 = u6
Known fbe39.. : 6 ∈ 12
Known 86df1.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u8 = u10
Known 42552.. : 10 ∈ 12
Known 1f384.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u9 = u8
Known 5196c.. : 8 ∈ 12
Known f964e.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u10 = u11
Known fee2e.. : 11 ∈ 12
Known 1f07b.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u11 = u9
Known 4fa36.. : 9 ∈ 12
Theorem bb2bc.. : ∀ x0 . x0 ∈ u12 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 ∈ u12 (proof)
Definition u13 := ordsucc u12
Definition u14 := ordsucc u13
Definition u15 := ordsucc u14
Definition u16 := ordsucc u15
Known f2c34.. : ∀ x0 . x0 ∈ u16 ⟶ ∀ x1 . x1 ∈ u16 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 = u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1 ⟶ x0 = x1
Definition Subq^Subq := λ x0 x1 . ∀ x2 . x2 ∈ x0 ⟶ x2 ∈ x1
Known ordsuccI1^ordsuccI1 : ∀ x0 . x0 ⊆ ordsucc x0
Theorem 90895.. : ∀ x0 . x0 ∈ u12 ⟶ ∀ x1 . x1 ∈ u12 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 = u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1 ⟶ x0 = x1 (proof)
Definition u17 := ordsucc u16
Definition TwoRamseyGraph_3_6_Church17 := λ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . λ x2 x3 . x0 (x1 x2 x2 x2 x3 x3 x3 x3 x2 x3 x3 x2 x3 x3 x3 x3 x2 x3) (x1 x2 x2 x3 x2 x3 x3 x2 x3 x3 x3 x3 x2 x2 x3 x3 x3 x3) (x1 x2 x3 x2 x2 x3 x2 x3 x3 x2 x3 x3 x3 x3 x3 x2 x3 x3) (x1 x3 x2 x2 x2 x2 x3 x3 x3 x3 x2 x3 x3 x3 x2 x3 x3 x3) (x1 x3 x3 x3 x2 x2 x2 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x3) (x1 x3 x3 x2 x3 x2 x2 x3 x2 x3 x3 x3 x2 x2 x3 x3 x3 x3) (x1 x3 x2 x3 x3 x2 x3 x2 x2 x2 x3 x3 x3 x3 x3 x2 x3 x3) (x1 x2 x3 x3 x3 x3 x2 x2 x2 x3 x2 x3 x3 x3 x2 x3 x3 x3) (x1 x3 x3 x2 x3 x3 x3 x2 x3 x2 x3 x3 x2 x2 x2 x3 x3 x3) (x1 x3 x3 x3 x2 x3 x3 x3 x2 x3 x2 x2 x3 x2 x3 x3 x2 x3) (x1 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x2 x3 x3 x2 x2 x3 x3) (x1 x3 x2 x3 x3 x3 x2 x3 x3 x2 x3 x3 x2 x3 x3 x2 x2 x3) (x1 x3 x2 x3 x3 x3 x2 x3 x3 x2 x2 x3 x3 x2 x3 x3 x3 x2) (x1 x3 x3 x3 x2 x3 x3 x3 x2 x2 x3 x2 x3 x3 x2 x3 x3 x2) (x1 x3 x3 x2 x3 x3 x3 x2 x3 x3 x3 x2 x2 x3 x3 x2 x3 x2) (x1 x2 x3 x3 x3 x2 x3 x3 x3 x3 x2 x3 x2 x3 x3 x3 x2 x2) (x1 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x3 x2 x2 x2 x2 x2)
Definition TwoRamseyGraph_3_6_17 := λ x0 x1 . x0 ∈ u17 ⟶ x1 ∈ u17 ⟶ TwoRamseyGraph_3_6_Church17 (u17_to_Church17 x0) (u17_to_Church17 x1) = λ x3 x4 . x3
Known 36aae.. : ∀ x0 . x0 ∈ u16 ⟶ ∀ x1 . x1 ∈ u16 ⟶ TwoRamseyGraph_3_6_17 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0) (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1) ⟶ TwoRamseyGraph_3_6_17 x0 x1
Theorem 619e7.. : ∀ x0 . x0 ∈ u12 ⟶ ∀ x1 . x1 ∈ u12 ⟶ TwoRamseyGraph_3_6_17 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0) (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1) ⟶ TwoRamseyGraph_3_6_17 x0 x1 (proof)
Known cases_8^cases_8 : ∀ x0 . x0 ∈ 8 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 4 ⟶ x1 5 ⟶ x1 6 ⟶ x1 7 ⟶ x1 x0
Known In_1_8^In_1_8 : 1 ∈ 8
Known In_3_8^In_3_8 : 3 ∈ 8
Known In_0_8^In_0_8 : 0 ∈ 8
Known In_2_8^In_2_8 : 2 ∈ 8
Known In_5_8^In_5_8 : 5 ∈ 8
Known In_7_8^In_7_8 : 7 ∈ 8
Known In_4_8^In_4_8 : 4 ∈ 8
Known In_6_8^In_6_8 : 6 ∈ 8
Theorem fe49a.. : ∀ x0 . x0 ∈ u8 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 ∈ u8 (proof)
Theorem 902b5.. : ∀ x0 . x0 ∈ u8 ⟶ ∀ x1 . x1 ∈ u8 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 = u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1 ⟶ x0 = x1 (proof)
Theorem 6ac2d.. : ∀ x0 . x0 ∈ u8 ⟶ ∀ x1 . x1 ∈ u8 ⟶ TwoRamseyGraph_3_6_17 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0) (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x1) ⟶ TwoRamseyGraph_3_6_17 x0 x1 (proof)
Definition Church17_p := λ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι) → ο . x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x2) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x3) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x4) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x5) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x6) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x7) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x8) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x9) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x10) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x11) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x12) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x13) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x15) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) ⟶ x1 (λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x18) ⟶ x1 x0
Known 1b7f9.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x1)
Known 9e7eb.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x3)
Known e70c8.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x0)
Known 25b64.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x2)
Known e224e.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x5)
Known 3b0d1.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x7)
Known 51a81.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x4)
Known 5d397.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x6)
Known 4f699.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x10)
Known e7def.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x8)
Known 712d3.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x11)
Known a8b9a.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x9)
Known 51598.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x13)
Known 15dad.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x14)
Known 7e8b2.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x15)
Known d5e0f.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x12)
Known 02267.. : Church17_p (λ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . x16)
Theorem 0504f.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p (Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0) (proof)
Known d0cff.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ u17_to_Church17 (Church17_to_u17 x0) = x0
Known 495f5.. : ∀ x0 . x0 ∈ u17 ⟶ Church17_to_u17 (u17_to_Church17 x0) = x0
Known db165.. : ∀ x0 . x0 ∈ u17 ⟶ Church17_p (u17_to_Church17 x0)
Theorem 01145.. : ∀ x0 . x0 ∈ u16 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 (u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0))) = x0 (proof)
Definition and^and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Definition inj^inj := λ x0 x1 . λ x2 : ι → ι . and (∀ x3 . x3 ∈ x0 ⟶ x2 x3 ∈ x1) (∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x2 x3 = x2 x4 ⟶ x3 = x4)
Definition atleastp^atleastp := λ x0 x1 . ∀ x2 : ο . (∀ x3 : ι → ι . inj x0 x1 x3 ⟶ x2) ⟶ x2
Definition False^False := ∀ x0 : ο . x0
Definition not^not := λ x0 : ο . x0 ⟶ False
Param setminus^setminus : ι → ι → ι
Known 7c829.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . (∀ x2 . x2 ∈ u12 ⟶ x1 x2 ∈ u12) ⟶ (∀ x2 . x2 ∈ u12 ⟶ ∀ x3 . x3 ∈ u12 ⟶ x1 x2 = x1 x3 ⟶ x2 = x3) ⟶ (∀ x2 . x2 ∈ u12 ⟶ ∀ x3 . x3 ∈ u12 ⟶ x0 (x1 x2) (x1 x3) ⟶ x0 x2 x3) ⟶ x1 u9 = u8 ⟶ x1 u10 = u11 ⟶ x1 u11 = u9 ⟶ x0 u8 u11 ⟶ ∀ x2 . x2 ⊆ u12 ⟶ atleastp u5 x2 ⟶ (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ not (x0 x3 x4)) ⟶ atleastp u2 (setminus x2 u8) ⟶ ∀ x3 : ο . (∀ x4 . x4 ⊆ u12 ⟶ atleastp u5 x4 ⟶ (∀ x5 . x5 ∈ x4 ⟶ ∀ x6 . x6 ∈ x4 ⟶ not (x0 x5 x6)) ⟶ u8 ∈ x4 ⟶ u9 ∈ x4 ⟶ x3) ⟶ (∀ x4 . x4 ⊆ u12 ⟶ atleastp u5 x4 ⟶ (∀ x5 . x5 ∈ x4 ⟶ ∀ x6 . x6 ∈ x4 ⟶ not (x0 x5 x6)) ⟶ u8 ∈ x4 ⟶ u10 ∈ x4 ⟶ x3) ⟶ (∀ x4 . x4 ⊆ u12 ⟶ atleastp u5 x4 ⟶ (∀ x5 . x5 ∈ x4 ⟶ ∀ x6 . x6 ∈ x4 ⟶ not (x0 x5 x6)) ⟶ u9 ∈ x4 ⟶ u10 ∈ x4 ⟶ x3) ⟶ x3
Known andI^andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Known FalseE^FalseE : False ⟶ ∀ x0 : ο . x0
Known d7087.. : u17_to_Church17 u10 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x11
Known a3fb1.. : u17_to_Church17 u9 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x10
Known 4fc31.. : u10 = u9 ⟶ ∀ x0 : ο . x0
Known b3a20.. : u11 = u8 ⟶ ∀ x0 : ο . x0
Known 48ba7.. : u17_to_Church17 u8 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x9
Known a87a3.. : u17_to_Church17 u11 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x12
Theorem d2e57.. : ∀ x0 . x0 ⊆ u12 ⟶ atleastp u5 x0 ⟶ (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ not (TwoRamseyGraph_3_6_17 x1 x2)) ⟶ atleastp u2 (setminus x0 u8) ⟶ ∀ x1 : ο . (∀ x2 . x2 ⊆ u12 ⟶ atleastp u5 x2 ⟶ (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ not (TwoRamseyGraph_3_6_17 x3 x4)) ⟶ u8 ∈ x2 ⟶ u9 ∈ x2 ⟶ x1) ⟶ (∀ x2 . x2 ⊆ u12 ⟶ atleastp u5 x2 ⟶ (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ not (TwoRamseyGraph_3_6_17 x3 x4)) ⟶ u8 ∈ x2 ⟶ u10 ∈ x2 ⟶ x1) ⟶ x1 (proof)
Known ReplE_impred^ReplE_impred : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . x2 ∈ prim5 x0 x1 ⟶ ∀ x3 : ο . (∀ x4 . x4 ∈ x0 ⟶ x2 = x1 x4 ⟶ x3) ⟶ x3
Theorem 02751.. : ∀ x0 x1 . ∀ x2 : ι → ι . (∀ x3 . x3 ∈ x0 ⟶ x2 x3 ∈ x1) ⟶ prim5 x0 x2 ⊆ x1 (proof)
Param binintersect^binintersect : ι → ι → ι
Known binintersectE^{binintersectE} : ∀ x0 x1 x2 . x2 ∈ binintersect x0 x1 ⟶ and (x2 ∈ x0) (x2 ∈ x1)
Known binintersectI^{binintersectI} : ∀ x0 x1 x2 . x2 ∈ x0 ⟶ x2 ∈ x1 ⟶ x2 ∈ binintersect x0 x1
Known ReplI^ReplI : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . x2 ∈ x0 ⟶ x1 x2 ∈ prim5 x0 x1
Theorem a08e7.. : ∀ x0 x1 . ∀ x2 : ι → ι . inj x0 x0 x2 ⟶ atleastp (binintersect x1 x0) (binintersect (prim5 x1 x2) x0) (proof)
Param nat_p^nat_p : ι → ο
Definition or^or := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x2) ⟶ (x1 ⟶ x2) ⟶ x2
Known 48e0f.. : ∀ x0 . nat_p x0 ⟶ ∀ x1 . or (atleastp x1 x0) (atleastp (ordsucc x0) x1)
Known nat_1^nat_1 : nat_p 1
Known d03c6.. : ∀ x0 . atleastp u4 x0 ⟶ ∀ x1 : ο . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ (x2 = x3 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x2 = x5 ⟶ ∀ x6 : ο . x6) ⟶ (x3 = x4 ⟶ ∀ x6 : ο . x6) ⟶ (x3 = x5 ⟶ ∀ x6 : ο . x6) ⟶ (x4 = x5 ⟶ ∀ x6 : ο . x6) ⟶ x1) ⟶ x1
Param Church17_lt8 : (ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι) → ο
Known b4903.. : ∀ x0 x1 x2 x3 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_lt8 x0 ⟶ Church17_lt8 x1 ⟶ Church17_lt8 x2 ⟶ Church17_lt8 x3 ⟶ (TwoRamseyGraph_3_6_Church17 x0 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x13) = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x1 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x13) = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x2 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x13) = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x3 (λ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . x13) = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x0 x1 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x0 x2 = λ x5 x6 . x6) ⟶ (TwoRamseyGraph_3_6_Church17 x0 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
Known 67bc1.. : ∀ x0 . x0 ∈ u8 ⟶ Church17_lt8 (u17_to_Church17 x0)
Known d8d63.. : ∀ x0 x1 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . Church17_p x0 ⟶ Church17_p x1 ⟶ or (TwoRamseyGraph_3_6_Church17 x0 x1 = λ x3 x4 . x3) (TwoRamseyGraph_3_6_Church17 x0 x1 = λ x3 x4 . x4)
Definition nIn^nIn := λ x0 x1 . not (x0 ∈ x1)
Known In_irref^In_irref : ∀ x0 . nIn x0 x0
Known xm^xm : ∀ x0 : ο . or x0 (not x0)
Known ordsuccE^ordsuccE : ∀ x0 x1 . x1 ∈ ordsucc x0 ⟶ or (x1 ∈ x0) (x1 = x0)
Known atleastp_tra^atleastp_tra : ∀ x0 x1 x2 . atleastp x0 x1 ⟶ atleastp x1 x2 ⟶ atleastp x0 x2
Known 4fb58..^{Pigeonhole_not_atleastp_ordsucc} : ∀ x0 . nat_p x0 ⟶ not (atleastp (ordsucc x0) x0)
Known nat_4^nat_4 : nat_p 4
Param setsum^setsum : ι → ι → ι
Param binunion^binunion : ι → ι → ι
Known a8a92.. : ∀ x0 x1 . x0 = binunion (setminus x0 x1) (binintersect x0 x1)
Known 385ef.. : ∀ x0 x1 x2 x3 . atleastp x0 x2 ⟶ atleastp x1 x3 ⟶ (∀ x4 . x4 ∈ x0 ⟶ nIn x4 x1) ⟶ atleastp (binunion x0 x1) (setsum x2 x3)
Known 4c104.. : ∀ x0 x1 x2 . (∀ x3 . x3 ∈ x0 ⟶ or (x3 = x1) (x3 = x2)) ⟶ atleastp x0 u2
Known setminusE1^setminusE1 : ∀ x0 x1 x2 . x2 ∈ setminus x0 x1 ⟶ x2 ∈ x0
Known orIL^orIL : ∀ x0 x1 : ο . x0 ⟶ or x0 x1
Known neq_5_4^neq_5_4 : u5 = u4 ⟶ ∀ x0 : ο . x0
Known 22977.. : u17_to_Church17 u5 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x6
Known 05513.. : u17_to_Church17 u4 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x5
Known neq_6_4^neq_6_4 : u6 = u4 ⟶ ∀ x0 : ο . x0
Known 0e32a.. : u17_to_Church17 u6 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x7
Known orIR^orIR : ∀ x0 x1 : ο . x1 ⟶ or x0 x1
Known neq_7_5^neq_7_5 : u7 = u5 ⟶ ∀ x0 : ο . x0
Known b0f83.. : u17_to_Church17 u7 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x8
Known cases_4^cases_4 : ∀ x0 . x0 ∈ 4 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 2 ⟶ x1 3 ⟶ x1 x0
Known neq_1_0^neq_1_0 : u1 = 0 ⟶ ∀ x0 : ο . x0
Known b0ce1.. : u17_to_Church17 u1 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x2
Known c5926.. : u17_to_Church17 0 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x1
Known neq_2_0^neq_2_0 : u2 = 0 ⟶ ∀ x0 : ο . x0
Known e8ec5.. : u17_to_Church17 u2 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x3
Known neq_3_1^neq_3_1 : u3 = u1 ⟶ ∀ x0 : ο . x0
Known 1ef08.. : u17_to_Church17 u3 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x4
Known setminusE2^setminusE2 : ∀ x0 x1 x2 . x2 ∈ setminus x0 x1 ⟶ nIn x2 x1
Known binintersectE2^{binintersectE2} : ∀ x0 x1 x2 . x2 ∈ binintersect x0 x1 ⟶ x2 ∈ x1
Param equip^equip : ι → ι → ο
Known equip_atleastp^{equip_atleastp} : ∀ x0 x1 . equip x0 x1 ⟶ atleastp x0 x1
Known equip_sym^equip_sym : ∀ x0 x1 . equip x0 x1 ⟶ equip x1 x0
Known 5b991.. : equip 4 (setsum 2 2)
Known setminusE^setminusE : ∀ x0 x1 x2 . x2 ∈ setminus x0 x1 ⟶ and (x2 ∈ x0) (nIn x2 x1)
Known In_0_4^In_0_4 : 0 ∈ 4
Known In_1_4^In_1_4 : 1 ∈ 4
Known In_2_4^In_2_4 : 2 ∈ 4
Known In_3_4^In_3_4 : 3 ∈ 4
Known dneg^dneg : ∀ x0 : ο . not (not x0) ⟶ x0
Known nat_3^nat_3 : nat_p 3
Param If_i^If_i : ο → ι → ι → ι
Known If_i_1^If_i_1 : ∀ x0 : ο . ∀ x1 x2 . x0 ⟶ If_i x0 x1 x2 = x1
Known If_i_0^If_i_0 : ∀ x0 : ο . ∀ x1 x2 . not x0 ⟶ If_i x0 x1 x2 = x2
Known ordsuccI2^ordsuccI2 : ∀ x0 . x0 ∈ ordsucc x0
Param ap^ap : ι → ι → ι
Param lam^Sigma : ι → (ι → ι) → ι
Known cases_2^cases_2 : ∀ x0 . x0 ∈ 2 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 x0
Known tuple_2_0_eq^tuple_2_0_eq : ∀ x0 x1 . ap (lam 2 (λ x3 . If_i (x3 = 0) x0 x1)) 0 = x0
Known setminusI^setminusI : ∀ x0 x1 x2 . x2 ∈ x0 ⟶ nIn x2 x1 ⟶ x2 ∈ setminus x0 x1
Known tuple_2_1_eq^tuple_2_1_eq : ∀ x0 x1 . ap (lam 2 (λ x3 . If_i (x3 = 0) x0 x1)) 1 = x1
Known 10417.. : ∀ x0 . x0 ⊆ u12 ⟶ atleastp u5 x0 ⟶ u8 ∈ x0 ⟶ u9 ∈ x0 ⟶ (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ not (TwoRamseyGraph_3_6_17 x1 x2)) ⟶ False
Known 32ea8.. : ∀ x0 . x0 ⊆ u12 ⟶ atleastp u5 x0 ⟶ u8 ∈ x0 ⟶ u10 ∈ x0 ⟶ (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ not (TwoRamseyGraph_3_6_17 x1 x2)) ⟶ False
Param add_nat^add_nat : ι → ι → ι
Known 1521b.. : add_nat 8 8 = 16
Known 4d87b.. : ∀ x0 x1 . nat_p x1 ⟶ x0 ⊆ add_nat x0 x1
Known nat_8^nat_8 : nat_p 8
Theorem 9cadc.. : ∀ x0 . x0 ⊆ u12 ⟶ atleastp u5 x0 ⟶ not (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ not (TwoRamseyGraph_3_6_17 x1 x2)) (proof)
Theorem 40b07.. : ∀ x0 . x0 ⊆ u12 ⟶ atleastp u5 x0 ⟶ not (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ not (and (TwoRamseyGraph_3_6_17 x1 x2) (x1 = x2 ⟶ ∀ x3 : ο . x3))) (proof)
Known ea47f.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι . (∀ x2 . x2 ∈ u16 ⟶ x1 x2 ∈ u16) ⟶ (∀ x2 . x2 ∈ u16 ⟶ ∀ x3 . x3 ∈ u16 ⟶ x1 x2 = x1 x3 ⟶ x2 = x3) ⟶ (∀ x2 . x2 ∈ u16 ⟶ ∀ x3 . x3 ∈ u16 ⟶ x0 (x1 x2) (x1 x3) ⟶ x0 x2 x3) ⟶ (∀ x2 . x2 ∈ u16 ⟶ x1 (x1 (x1 (x1 x2))) = x2) ⟶ x1 u12 = u13 ⟶ x1 u13 = u14 ⟶ x1 u14 = u15 ⟶ x1 u15 = u12 ⟶ ∀ x2 . x2 ⊆ u16 ⟶ atleastp u6 x2 ⟶ (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ not (x0 x3 x4)) ⟶ atleastp u2 (setminus x2 u12) ⟶ ∀ x3 : ο . (∀ x4 . x4 ⊆ u16 ⟶ atleastp u6 x4 ⟶ (∀ x5 . x5 ∈ x4 ⟶ ∀ x6 . x6 ∈ x4 ⟶ not (x0 x5 x6)) ⟶ u12 ∈ x4 ⟶ u13 ∈ x4 ⟶ x3) ⟶ (∀ x4 . x4 ⊆ u16 ⟶ atleastp u6 x4 ⟶ (∀ x5 . x5 ∈ x4 ⟶ ∀ x6 . x6 ∈ x4 ⟶ not (x0 x5 x6)) ⟶ u12 ∈ x4 ⟶ u14 ∈ x4 ⟶ x3) ⟶ x3
Known f9dcb.. : ∀ x0 . x0 ∈ u16 ⟶ u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 x0 ∈ u16
Known be3a6.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u12 = u13
Known 0e84a.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u13 = u14
Known 4b6e2.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u14 = u15
Known 5681c.. : u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12 u15 = u12
Known 27d0c.. : ∀ x0 : ι → ι → ο . x0 0 u2 ⟶ x0 u4 u6 ⟶ x0 u1 u12 ⟶ x0 u5 u12 ⟶ x0 u8 u12 ⟶ x0 u9 u12 ⟶ x0 u3 u13 ⟶ x0 u7 u13 ⟶ x0 u10 u13 ⟶ x0 u2 u14 ⟶ x0 u6 u14 ⟶ x0 u11 u14 ⟶ x0 0 u15 ⟶ x0 u4 u15 ⟶ x0 0 u2 ⟶ x0 u4 u6 ⟶ x0 u11 u15 ⟶ ∀ x1 . x1 ⊆ u16 ⟶ atleastp u6 x1 ⟶ u12 ∈ x1 ⟶ u13 ∈ x1 ⟶ (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ not (x0 x2 x3)) ⟶ False
Known 6b8c1.. : ∀ x0 : ι → ι → ο . x0 0 u2 ⟶ x0 u4 u6 ⟶ x0 u1 u12 ⟶ x0 u5 u12 ⟶ x0 u8 u12 ⟶ x0 u9 u12 ⟶ x0 u3 u13 ⟶ x0 u7 u13 ⟶ x0 u10 u13 ⟶ x0 u2 u14 ⟶ x0 u6 u14 ⟶ x0 u11 u14 ⟶ x0 0 u15 ⟶ x0 u4 u15 ⟶ x0 u3 u4 ⟶ x0 0 u7 ⟶ x0 u10 u14 ⟶ ∀ x1 . x1 ⊆ u16 ⟶ atleastp u6 x1 ⟶ u12 ∈ x1 ⟶ u14 ∈ x1 ⟶ (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ not (x0 x2 x3)) ⟶ False
Known cf897.. : u17_to_Church17 u14 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x15
Known f5ab5.. : u14 = u10 ⟶ ∀ x0 : ο . x0
Known neq_7_0^neq_7_0 : u7 = 0 ⟶ ∀ x0 : ο . x0
Known neq_4_3^neq_4_3 : u4 = u3 ⟶ ∀ x0 : ο . x0
Known c424d.. : u17_to_Church17 u15 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x16
Known 9c5db.. : u15 = u11 ⟶ ∀ x0 : ο . x0
Known 4b742.. : u15 = u4 ⟶ ∀ x0 : ο . x0
Known 160ad.. : u15 = 0 ⟶ ∀ x0 : ο . x0
Known 4e1aa.. : u14 = u11 ⟶ ∀ x0 : ο . x0
Known 62d80.. : u14 = u6 ⟶ ∀ x0 : ο . x0
Known 0bb18.. : u14 = u2 ⟶ ∀ x0 : ο . x0
Known 0975c.. : u17_to_Church17 u13 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x14
Known 78358.. : u13 = u10 ⟶ ∀ x0 : ο . x0
Known d9b35.. : u13 = u7 ⟶ ∀ x0 : ο . x0
Known 19222.. : u13 = u3 ⟶ ∀ x0 : ο . x0
Known a52d8.. : u17_to_Church17 u12 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x13
Known 22885.. : u12 = u9 ⟶ ∀ x0 : ο . x0
Known a6a6c.. : u12 = u8 ⟶ ∀ x0 : ο . x0
Known 07eba.. : u12 = u5 ⟶ ∀ x0 : ο . x0
Known ce0cd.. : u12 = u1 ⟶ ∀ x0 : ο . x0
Known a62ab.. : ∀ x0 : ι → ι → ο . (∀ x1 . x1 ⊆ u12 ⟶ atleastp u5 x1 ⟶ not (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ not (x0 x2 x3))) ⟶ ∀ x1 . x1 ⊆ u16 ⟶ atleastp u6 x1 ⟶ (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ not (x0 x2 x3)) ⟶ atleastp u2 (setminus x1 u12)
Theorem 30d6b.. : ∀ x0 . x0 ⊆ u16 ⟶ atleastp u6 x0 ⟶ not (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ not (TwoRamseyGraph_3_6_17 x1 x2)) (proof)
Known 32519.. : ∀ x0 : ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι → ι . (x0 u12 = λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x14) ⟶ (x0 u13 = λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x15) ⟶ (x0 u14 = λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x16) ⟶ (x0 u15 = λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x17) ⟶ (x0 u16 = λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . x18) ⟶ ∀ x1 : ι → ι → ο . (∀ x2 . x2 ∈ u17 ⟶ ∀ x3 . x3 ∈ u17 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ (TwoRamseyGraph_3_6_Church17 (x0 x2) (x0 x3) = λ x5 x6 . x5) ⟶ x1 x2 x3) ⟶ (∀ x2 . x2 ⊆ u12 ⟶ atleastp u5 x2 ⟶ not (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ not (x1 x3 x4))) ⟶ (∀ x2 . x2 ⊆ u16 ⟶ atleastp u6 x2 ⟶ not (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ not (x1 x3 x4))) ⟶ ∀ x2 . x2 ⊆ u17 ⟶ atleastp u6 x2 ⟶ not (∀ x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ (x3 = x4 ⟶ ∀ x5 : ο . x5) ⟶ not (x1 x3 x4))
Known 480e6.. : u17_to_Church17 u16 = λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . x17
Theorem 5922f.. : ∀ x0 . x0 ⊆ u17 ⟶ atleastp u6 x0 ⟶ not (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ not (TwoRamseyGraph_3_6_17 x1 x2)) (proof)
Param TwoRamseyProp_atleastp : ι → ι → ι → ο
Known 68ea7.. : ∀ x0 : ι → ι → ο . (∀ x1 x2 . x0 x1 x2 ⟶ x0 x2 x1) ⟶ (∀ x1 . x1 ⊆ u17 ⟶ atleastp u3 x1 ⟶ not (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ x0 x2 x3)) ⟶ (∀ x1 . x1 ⊆ u17 ⟶ atleastp u6 x1 ⟶ not (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ not (x0 x2 x3))) ⟶ not (TwoRamseyProp_atleastp 3 6 17)
Known 72dc0.. : ∀ x0 x1 . TwoRamseyGraph_3_6_17 x0 x1 ⟶ TwoRamseyGraph_3_6_17 x1 x0
Known d6d79.. : ∀ x0 . x0 ⊆ u17 ⟶ atleastp u3 x0 ⟶ not (∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ TwoRamseyGraph_3_6_17 x1 x2)
Theorem not_TwoRamseyProp_atleast_3_6_17 : not (TwoRamseyProp_atleastp 3 6 17) (proof)
Param TwoRamseyProp^{TwoRamseyProp} : ι → ι → ι → ο
Known 9e653.. : ∀ x0 : ι → ι → ο . (∀ x1 x2 . x0 x1 x2 ⟶ x0 x2 x1) ⟶ (∀ x1 . x1 ⊆ u17 ⟶ atleastp u3 x1 ⟶ not (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ x0 x2 x3)) ⟶ (∀ x1 . x1 ⊆ u17 ⟶ atleastp u6 x1 ⟶ not (∀ x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ not (x0 x2 x3))) ⟶ not (TwoRamseyProp 3 6 17)
Theorem not_TwoRamseyProp_3_6_17^{not_TwoRamseyProp_3_6_17} : not (TwoRamseyProp 3 6 17) (proof)