TSTP Solution File: KRS162+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : KRS162+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 03:32:04 EDT 2022
% Result : Theorem 8.05s 8.24s
% Output : Proof 8.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KRS162+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 7 20:20:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 8.05/8.24 % SZS status Theorem
% 8.05/8.24 (* PROOF-FOUND *)
% 8.05/8.24 (* BEGIN-PROOF *)
% 8.05/8.24 % SZS output start Proof
% 8.05/8.24 1. (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (-. (All X, ((cowlThing X) /\ (-. (cowlNothing X))))) ### Axiom
% 8.05/8.24 2. (-. (xsd_integer T_0)) (xsd_integer T_0) ### Axiom
% 8.05/8.24 3. (-. (-. (xsd_integer T_0))) (-. (xsd_integer T_0)) ### NotNot 2
% 8.05/8.24 4. (-. (xsd_string T_0)) (-. (xsd_integer T_0)) ### Definition-Pseudo(xsd_string) 3
% 8.05/8.24 5. (-. (-. (xsd_integer T_0))) (-. (xsd_integer T_0)) ### Axiom
% 8.05/8.24 6. (xsd_string T_0) (-. (-. (xsd_integer T_0))) ### Definition-Pseudo(xsd_string) 5
% 8.05/8.24 7. (-. ((xsd_string T_0) <=> (-. (xsd_integer T_0)))) ### NotEquiv 4 6
% 8.05/8.24 8. (-. (All X, ((xsd_string X) <=> (-. (xsd_integer X))))) ### NotAllEx 7
% 8.05/8.24 9. (rq T_1 T_2) (-. (rq T_1 T_2)) ### Axiom
% 8.05/8.24 10. (-. (rr T_1 T_2)) (rr T_1 T_2) ### Axiom
% 8.05/8.24 11. ((rq T_1 T_2) => (rr T_1 T_2)) (-. (rr T_1 T_2)) (rq T_1 T_2) ### Imply 9 10
% 8.05/8.24 12. (All Y, ((rq T_1 Y) => (rr T_1 Y))) (rq T_1 T_2) (-. (rr T_1 T_2)) ### All 11
% 8.05/8.24 13. (All X, (All Y, ((rq X Y) => (rr X Y)))) (-. (rr T_1 T_2)) (rq T_1 T_2) ### All 12
% 8.05/8.24 14. (rp T_1 T_3) (-. (rp T_1 T_3)) ### Axiom
% 8.05/8.24 15. (-. (rr T_1 T_3)) (rr T_1 T_3) ### Axiom
% 8.05/8.24 16. ((rp T_1 T_3) => (rr T_1 T_3)) (-. (rr T_1 T_3)) (rp T_1 T_3) ### Imply 14 15
% 8.05/8.24 17. (All Y, ((rp T_1 Y) => (rr T_1 Y))) (rp T_1 T_3) (-. (rr T_1 T_3)) ### All 16
% 8.05/8.24 18. (All X, (All Y, ((rp X Y) => (rr X Y)))) (-. (rr T_1 T_3)) (rp T_1 T_3) ### All 17
% 8.05/8.24 19. (rp T_1 T_4) (-. (rp T_1 T_4)) ### Axiom
% 8.05/8.24 20. (-. (rr T_1 T_4)) (rr T_1 T_4) ### Axiom
% 8.05/8.24 21. ((rp T_1 T_4) => (rr T_1 T_4)) (-. (rr T_1 T_4)) (rp T_1 T_4) ### Imply 19 20
% 8.05/8.24 22. (All Y, ((rp T_1 Y) => (rr T_1 Y))) (rp T_1 T_4) (-. (rr T_1 T_4)) ### All 21
% 8.05/8.24 23. (All X, (All Y, ((rp X Y) => (rr X Y)))) (-. (rr T_1 T_4)) (rp T_1 T_4) ### All 22
% 8.05/8.24 24. (rq T_1 T_5) (-. (rq T_1 T_5)) ### Axiom
% 8.05/8.24 25. (-. (rr T_1 T_5)) (rr T_1 T_5) ### Axiom
% 8.05/8.24 26. ((rq T_1 T_5) => (rr T_1 T_5)) (-. (rr T_1 T_5)) (rq T_1 T_5) ### Imply 24 25
% 8.05/8.24 27. (All Y, ((rq T_1 Y) => (rr T_1 Y))) (rq T_1 T_5) (-. (rr T_1 T_5)) ### All 26
% 8.05/8.24 28. (All X, (All Y, ((rq X Y) => (rr X Y)))) (-. (rr T_1 T_5)) (rq T_1 T_5) ### All 27
% 8.05/8.24 29. (rq T_1 T_6) (-. (rq T_1 T_6)) ### Axiom
% 8.05/8.24 30. (-. (rr T_1 T_6)) (rr T_1 T_6) ### Axiom
% 8.05/8.24 31. ((rq T_1 T_6) => (rr T_1 T_6)) (-. (rr T_1 T_6)) (rq T_1 T_6) ### Imply 29 30
% 8.05/8.24 32. (All Y, ((rq T_1 Y) => (rr T_1 Y))) (rq T_1 T_6) (-. (rr T_1 T_6)) ### All 31
% 8.05/8.24 33. (All X, (All Y, ((rq X Y) => (rr X Y)))) (-. (rr T_1 T_6)) (rq T_1 T_6) ### All 32
% 8.05/8.24 34. (rq T_1 T_2) (-. (rq T_1 T_2)) ### Axiom
% 8.05/8.24 35. (T_2 = T_3) (T_2 != T_3) ### Axiom
% 8.05/8.24 36. (cB T_2) (-. (cB T_2)) ### Axiom
% 8.05/8.24 37. (-. (cB T_3)) (cB T_3) ### Axiom
% 8.05/8.24 38. (((T_2 = T_3) /\ (cB T_2)) => (cB T_3)) (-. (cB T_3)) (cB T_2) (T_2 = T_3) ### DisjTree 35 36 37
% 8.05/8.24 39. (All B, (((T_2 = B) /\ (cB T_2)) => (cB B))) (T_2 = T_3) (cB T_2) (-. (cB T_3)) ### All 38
% 8.05/8.24 40. (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_3)) (cB T_2) (T_2 = T_3) ### All 39
% 8.05/8.24 41. ((rq T_1 T_2) => (cB T_2)) (T_2 = T_3) (-. (cB T_3)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (rq T_1 T_2) ### Imply 34 40
% 8.05/8.24 42. (All Y, ((rq T_1 Y) => (cB Y))) (rq T_1 T_2) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_3)) (T_2 = T_3) ### All 41
% 8.05/8.24 43. (All X, (All Y, ((rq X Y) => (cB Y)))) (T_2 = T_3) (-. (cB T_3)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (rq T_1 T_2) ### All 42
% 8.05/8.24 44. (rq T_1 T_2) (-. (rq T_1 T_2)) ### Axiom
% 8.05/8.24 45. (T_2 = T_4) (T_2 != T_4) ### Axiom
% 8.05/8.24 46. (cB T_2) (-. (cB T_2)) ### Axiom
% 8.05/8.24 47. (-. (cB T_4)) (cB T_4) ### Axiom
% 8.05/8.24 48. (((T_2 = T_4) /\ (cB T_2)) => (cB T_4)) (-. (cB T_4)) (cB T_2) (T_2 = T_4) ### DisjTree 45 46 47
% 8.05/8.24 49. (All B, (((T_2 = B) /\ (cB T_2)) => (cB B))) (T_2 = T_4) (cB T_2) (-. (cB T_4)) ### All 48
% 8.05/8.24 50. (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (cB T_2) (T_2 = T_4) ### All 49
% 8.05/8.24 51. ((rq T_1 T_2) => (cB T_2)) (T_2 = T_4) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (rq T_1 T_2) ### Imply 44 50
% 8.05/8.24 52. (All Y, ((rq T_1 Y) => (cB Y))) (rq T_1 T_2) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (T_2 = T_4) ### All 51
% 8.05/8.24 53. (All X, (All Y, ((rq X Y) => (cB Y)))) (T_2 = T_4) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (rq T_1 T_2) ### All 52
% 8.05/8.24 54. (T_2 != T_5) (T_2 = T_5) ### Axiom
% 8.05/8.24 55. (T_2 != T_6) (T_2 = T_6) ### Axiom
% 8.05/8.24 56. (T_4 != T_3) (T_3 = T_4) ### Sym(=)
% 8.05/8.24 57. (T_3 = T_5) (T_5 != T_3) ### Sym(=)
% 8.05/8.24 58. (rq T_1 T_5) (-. (rq T_1 T_5)) ### Axiom
% 8.05/8.24 59. (-. (rq T_1 T_3)) (rq T_1 T_3) ### Axiom
% 8.05/8.24 60. (((T_5 = T_3) /\ (rq T_1 T_5)) => (rq T_1 T_3)) (-. (rq T_1 T_3)) (rq T_1 T_5) (T_3 = T_5) ### DisjTree 57 58 59
% 8.05/8.24 61. (All C, (((T_5 = T_3) /\ (rq C T_5)) => (rq C T_3))) (T_3 = T_5) (rq T_1 T_5) (-. (rq T_1 T_3)) ### All 60
% 8.05/8.24 62. (-. (cB T_3)) (cB T_3) ### Axiom
% 8.05/8.24 63. ((rq T_1 T_3) => (cB T_3)) (-. (cB T_3)) (rq T_1 T_5) (T_3 = T_5) (All C, (((T_5 = T_3) /\ (rq C T_5)) => (rq C T_3))) ### Imply 61 62
% 8.05/8.24 64. (All Y, ((rq T_1 Y) => (cB Y))) (All C, (((T_5 = T_3) /\ (rq C T_5)) => (rq C T_3))) (T_3 = T_5) (rq T_1 T_5) (-. (cB T_3)) ### All 63
% 8.05/8.24 65. (All X, (All Y, ((rq X Y) => (cB Y)))) (-. (cB T_3)) (rq T_1 T_5) (T_3 = T_5) (All C, (((T_5 = T_3) /\ (rq C T_5)) => (rq C T_3))) ### All 64
% 8.05/8.25 66. (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_3 = T_5) (rq T_1 T_5) (-. (cB T_3)) (All X, (All Y, ((rq X Y) => (cB Y)))) ### All 65
% 8.05/8.25 67. (T_3 = T_6) (T_6 != T_3) ### Sym(=)
% 8.05/8.25 68. (rq T_1 T_6) (-. (rq T_1 T_6)) ### Axiom
% 8.05/8.25 69. (-. (rq T_1 T_3)) (rq T_1 T_3) ### Axiom
% 8.05/8.25 70. (((T_6 = T_3) /\ (rq T_1 T_6)) => (rq T_1 T_3)) (-. (rq T_1 T_3)) (rq T_1 T_6) (T_3 = T_6) ### DisjTree 67 68 69
% 8.05/8.25 71. (All C, (((T_6 = T_3) /\ (rq C T_6)) => (rq C T_3))) (T_3 = T_6) (rq T_1 T_6) (-. (rq T_1 T_3)) ### All 70
% 8.05/8.25 72. (-. (cB T_3)) (cB T_3) ### Axiom
% 8.05/8.25 73. ((rq T_1 T_3) => (cB T_3)) (-. (cB T_3)) (rq T_1 T_6) (T_3 = T_6) (All C, (((T_6 = T_3) /\ (rq C T_6)) => (rq C T_3))) ### Imply 71 72
% 8.05/8.25 74. (All Y, ((rq T_1 Y) => (cB Y))) (All C, (((T_6 = T_3) /\ (rq C T_6)) => (rq C T_3))) (T_3 = T_6) (rq T_1 T_6) (-. (cB T_3)) ### All 73
% 8.05/8.25 75. (All X, (All Y, ((rq X Y) => (cB Y)))) (-. (cB T_3)) (rq T_1 T_6) (T_3 = T_6) (All C, (((T_6 = T_3) /\ (rq C T_6)) => (rq C T_3))) ### All 74
% 8.05/8.25 76. (rq T_1 T_5) (-. (rq T_1 T_5)) ### Axiom
% 8.05/8.25 77. (T_4 = T_5) (T_5 != T_4) ### Sym(=)
% 8.05/8.25 78. (cB T_5) (-. (cB T_5)) ### Axiom
% 8.05/8.25 79. (-. (cB T_4)) (cB T_4) ### Axiom
% 8.05/8.25 80. (((T_5 = T_4) /\ (cB T_5)) => (cB T_4)) (-. (cB T_4)) (cB T_5) (T_4 = T_5) ### DisjTree 77 78 79
% 8.05/8.25 81. (All B, (((T_5 = B) /\ (cB T_5)) => (cB B))) (T_4 = T_5) (cB T_5) (-. (cB T_4)) ### All 80
% 8.05/8.25 82. (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (cB T_5) (T_4 = T_5) ### All 81
% 8.05/8.25 83. ((rq T_1 T_5) => (cB T_5)) (T_4 = T_5) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (rq T_1 T_5) ### Imply 76 82
% 8.05/8.25 84. (All Y, ((rq T_1 Y) => (cB Y))) (rq T_1 T_5) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (T_4 = T_5) ### All 83
% 8.05/8.25 85. (All X, (All Y, ((rq X Y) => (cB Y)))) (T_4 = T_5) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (rq T_1 T_5) ### All 84
% 8.05/8.25 86. (T_4 = T_6) (T_6 != T_4) ### Sym(=)
% 8.05/8.25 87. (rq T_1 T_6) (-. (rq T_1 T_6)) ### Axiom
% 8.05/8.25 88. (-. (rq T_1 T_4)) (rq T_1 T_4) ### Axiom
% 8.05/8.25 89. (((T_6 = T_4) /\ (rq T_1 T_6)) => (rq T_1 T_4)) (-. (rq T_1 T_4)) (rq T_1 T_6) (T_4 = T_6) ### DisjTree 86 87 88
% 8.05/8.25 90. (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) (T_4 = T_6) (rq T_1 T_6) (-. (rq T_1 T_4)) ### All 89
% 8.05/8.25 91. (-. (cB T_4)) (cB T_4) ### Axiom
% 8.05/8.25 92. ((rq T_1 T_4) => (cB T_4)) (-. (cB T_4)) (rq T_1 T_6) (T_4 = T_6) (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) ### Imply 90 91
% 8.05/8.25 93. (All Y, ((rq T_1 Y) => (cB Y))) (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) (T_4 = T_6) (rq T_1 T_6) (-. (cB T_4)) ### All 92
% 8.05/8.25 94. (All X, (All Y, ((rq X Y) => (cB Y)))) (-. (cB T_4)) (rq T_1 T_6) (T_4 = T_6) (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) ### All 93
% 8.05/8.25 95. (T_6 != T_5) (T_5 = T_6) ### Sym(=)
% 8.05/8.25 96. (-. ((rr T_1 T_2) /\ ((rr T_1 T_3) /\ ((rr T_1 T_4) /\ ((rr T_1 T_5) /\ ((rr T_1 T_6) /\ ((T_2 != T_3) /\ ((T_2 != T_4) /\ ((T_2 != T_5) /\ ((T_2 != T_6) /\ ((T_3 != T_4) /\ ((T_3 != T_5) /\ ((T_3 != T_6) /\ ((T_4 != T_5) /\ ((T_4 != T_6) /\ (T_5 != T_6)))))))))))))))) (T_6 != T_5) (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) (All C, (((T_6 = T_3) /\ (rq C T_6)) => (rq C T_3))) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_4 != T_3) (T_2 != T_6) (T_2 != T_5) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_3)) (All X, (All Y, ((rq X Y) => (cB Y)))) (rq T_1 T_6) (rq T_1 T_5) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rq X Y) => (rr X Y)))) ### DisjTree 13 18 23 28 33 43 53 54 55 56 66 75 85 94 95
% 8.05/8.27 97. (-. (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 T_3) /\ ((rr T_1 T_4) /\ ((rr T_1 T_5) /\ ((rr T_1 Y4) /\ ((T_2 != T_3) /\ ((T_2 != T_4) /\ ((T_2 != T_5) /\ ((T_2 != Y4) /\ ((T_3 != T_4) /\ ((T_3 != T_5) /\ ((T_3 != Y4) /\ ((T_4 != T_5) /\ ((T_4 != Y4) /\ (T_5 != Y4))))))))))))))))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (rq T_1 T_5) (rq T_1 T_6) (All X, (All Y, ((rq X Y) => (cB Y)))) (-. (cB T_3)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (T_2 != T_5) (T_2 != T_6) (T_4 != T_3) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (All C, (((T_6 = T_3) /\ (rq C T_6)) => (rq C T_3))) (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) (T_6 != T_5) ### NotExists 96
% 8.05/8.27 98. (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (T_6 != T_5) (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_4 != T_3) (T_2 != T_6) (T_2 != T_5) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_3)) (All X, (All Y, ((rq X Y) => (cB Y)))) (rq T_1 T_6) (rq T_1 T_5) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rq X Y) => (rr X Y)))) (-. (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 T_3) /\ ((rr T_1 T_4) /\ ((rr T_1 T_5) /\ ((rr T_1 Y4) /\ ((T_2 != T_3) /\ ((T_2 != T_4) /\ ((T_2 != T_5) /\ ((T_2 != Y4) /\ ((T_3 != T_4) /\ ((T_3 != T_5) /\ ((T_3 != Y4) /\ ((T_4 != T_5) /\ ((T_4 != Y4) /\ (T_5 != Y4))))))))))))))))) ### All 97
% 8.05/8.27 99. (-. (Ex Y3, (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 T_3) /\ ((rr T_1 T_4) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((T_2 != T_3) /\ ((T_2 != T_4) /\ ((T_2 != Y3) /\ ((T_2 != Y4) /\ ((T_3 != T_4) /\ ((T_3 != Y3) /\ ((T_3 != Y4) /\ ((T_4 != Y3) /\ ((T_4 != Y4) /\ (Y3 != Y4)))))))))))))))))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (rq T_1 T_5) (rq T_1 T_6) (All X, (All Y, ((rq X Y) => (cB Y)))) (-. (cB T_3)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (T_2 != T_5) (T_2 != T_6) (T_4 != T_3) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (All C, (((T_6 = T_4) /\ (rq C T_6)) => (rq C T_4))) (T_6 != T_5) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) ### NotExists 98
% 8.05/8.27 100. (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_4 != T_3) (T_2 != T_6) (T_2 != T_5) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_3)) (All X, (All Y, ((rq X Y) => (cB Y)))) (rq T_1 T_6) (rq T_1 T_5) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rq X Y) => (rr X Y)))) (-. (Ex Y3, (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 T_3) /\ ((rr T_1 T_4) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((T_2 != T_3) /\ ((T_2 != T_4) /\ ((T_2 != Y3) /\ ((T_2 != Y4) /\ ((T_3 != T_4) /\ ((T_3 != Y3) /\ ((T_3 != Y4) /\ ((T_4 != Y3) /\ ((T_4 != Y4) /\ (Y3 != Y4)))))))))))))))))) ### All 99
% 8.05/8.27 101. (-. (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 T_3) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((T_2 != T_3) /\ ((T_2 != Y2) /\ ((T_2 != Y3) /\ ((T_2 != Y4) /\ ((T_3 != Y2) /\ ((T_3 != Y3) /\ ((T_3 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (rq T_1 T_5) (rq T_1 T_6) (All X, (All Y, ((rq X Y) => (cB Y)))) (-. (cB T_3)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (T_2 != T_5) (T_2 != T_6) (T_4 != T_3) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) ### NotExists 100
% 8.05/8.27 102. (-. (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((T_2 != Y1) /\ ((T_2 != Y2) /\ ((T_2 != Y3) /\ ((T_2 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4)))))))))))))))))))) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_4 != T_3) (T_2 != T_6) (T_2 != T_5) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_3)) (All X, (All Y, ((rq X Y) => (cB Y)))) (rq T_1 T_6) (rq T_1 T_5) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rq X Y) => (rr X Y)))) ### NotExists 101
% 8.05/8.27 103. (rp T_1 T_3) (-. (rp T_1 T_3)) ### Axiom
% 8.05/8.27 104. (-. (cA T_3)) (cA T_3) ### Axiom
% 8.05/8.27 105. ((rp T_1 T_3) => (cA T_3)) (-. (cA T_3)) (rp T_1 T_3) ### Imply 103 104
% 8.05/8.27 106. (All Y, ((rp T_1 Y) => (cA Y))) (rp T_1 T_3) (-. (cA T_3)) ### All 105
% 8.05/8.27 107. (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (cA T_3)) (rp T_1 T_3) ### All 106
% 8.05/8.27 108. (-. ((cB T_3) /\ (cA T_3))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (rq T_1 T_5) (rq T_1 T_6) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (T_2 != T_5) (T_2 != T_6) (T_4 != T_3) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (-. (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((T_2 != Y1) /\ ((T_2 != Y2) /\ ((T_2 != Y3) /\ ((T_2 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4)))))))))))))))))))) ### NotAnd 102 107
% 8.05/8.27 109. (All X, (-. ((cB X) /\ (cA X)))) (-. (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 T_2) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((T_2 != Y1) /\ ((T_2 != Y2) /\ ((T_2 != Y3) /\ ((T_2 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4)))))))))))))))))))) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_4 != T_3) (T_2 != T_6) (T_2 != T_5) (-. (cB T_4)) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (rq T_1 T_6) (rq T_1 T_5) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) ### All 108
% 8.05/8.27 110. (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (rq T_1 T_5) (rq T_1 T_6) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (-. (cB T_4)) (T_2 != T_5) (T_2 != T_6) (T_4 != T_3) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (All X, (-. ((cB X) /\ (cA X)))) ### NotExists 109
% 8.05/8.27 111. (rp T_1 T_4) (-. (rp T_1 T_4)) ### Axiom
% 8.05/8.27 112. (-. (cA T_4)) (cA T_4) ### Axiom
% 8.05/8.27 113. ((rp T_1 T_4) => (cA T_4)) (-. (cA T_4)) (rp T_1 T_4) ### Imply 111 112
% 8.05/8.27 114. (All Y, ((rp T_1 Y) => (cA Y))) (rp T_1 T_4) (-. (cA T_4)) ### All 113
% 8.05/8.27 115. (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (cA T_4)) (rp T_1 T_4) ### All 114
% 8.05/8.27 116. (-. ((cB T_4) /\ (cA T_4))) (All X, (-. ((cB X) /\ (cA X)))) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_4 != T_3) (T_2 != T_6) (T_2 != T_5) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (rq T_1 T_6) (rq T_1 T_5) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) ### NotAnd 110 115
% 8.05/8.28 117. (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (rq T_1 T_5) (rq T_1 T_6) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (T_2 != T_5) (T_2 != T_6) (T_4 != T_3) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_6 != T_5) (All B, (All C, (((T_6 = B) /\ (rq C T_6)) => (rq C B)))) (All X, (-. ((cB X) /\ (cA X)))) ### All 116
% 8.05/8.28 118. (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) (All X, (-. ((cB X) /\ (cA X)))) (T_6 != T_5) (All B, (All C, (((T_5 = B) /\ (rq C T_5)) => (rq C B)))) (T_4 != T_3) (T_2 != T_6) (T_2 != T_5) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (rq T_1 T_6) (rq T_1 T_5) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) ### All 117
% 8.05/8.28 119. (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (rq T_1 T_2) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (rq T_1 T_5) (rq T_1 T_6) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (T_2 != T_5) (T_2 != T_6) (T_4 != T_3) (T_6 != T_5) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) ### All 118
% 8.05/8.28 120. ((rq T_1 T_2) /\ ((rq T_1 T_6) /\ ((rq T_1 T_5) /\ ((T_2 != T_6) /\ ((T_2 != T_5) /\ (T_6 != T_5)))))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) (All X, (-. ((cB X) /\ (cA X)))) (T_4 != T_3) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) ### ConjTree 119
% 8.05/8.28 121. (Ex Y2, ((rq T_1 T_2) /\ ((rq T_1 T_6) /\ ((rq T_1 Y2) /\ ((T_2 != T_6) /\ ((T_2 != Y2) /\ (T_6 != Y2))))))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (T_4 != T_3) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) ### Exists 120
% 8.05/8.28 122. (Ex Y1, (Ex Y2, ((rq T_1 T_2) /\ ((rq T_1 Y1) /\ ((rq T_1 Y2) /\ ((T_2 != Y1) /\ ((T_2 != Y2) /\ (Y1 != Y2)))))))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) (All X, (-. ((cB X) /\ (cA X)))) (T_4 != T_3) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (rp T_1 T_4) (rp T_1 T_3) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) ### Exists 121
% 8.05/8.28 123. (Ex Y0, (Ex Y1, (Ex Y2, ((rq T_1 Y0) /\ ((rq T_1 Y1) /\ ((rq T_1 Y2) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ (Y1 != Y2))))))))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (rp T_1 T_3) (rp T_1 T_4) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (T_4 != T_3) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) ### Exists 122
% 8.05/8.28 124. ((rp T_1 T_4) /\ ((rp T_1 T_3) /\ (T_4 != T_3))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (Ex Y0, (Ex Y1, (Ex Y2, ((rq T_1 Y0) /\ ((rq T_1 Y1) /\ ((rq T_1 Y2) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ (Y1 != Y2))))))))) ### ConjTree 123
% 8.05/8.28 125. (Ex Y1, ((rp T_1 T_4) /\ ((rp T_1 Y1) /\ (T_4 != Y1)))) (Ex Y0, (Ex Y1, (Ex Y2, ((rq T_1 Y0) /\ ((rq T_1 Y1) /\ ((rq T_1 Y2) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ (Y1 != Y2))))))))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) ### Exists 124
% 8.05/8.28 126. (Ex Y0, (Ex Y1, ((rp T_1 Y0) /\ ((rp T_1 Y1) /\ (Y0 != Y1))))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) (-. (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))) (Ex Y0, (Ex Y1, (Ex Y2, ((rq T_1 Y0) /\ ((rq T_1 Y1) /\ ((rq T_1 Y2) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ (Y1 != Y2))))))))) ### Exists 125
% 8.05/8.28 127. (-. (((Ex Y0, (Ex Y1, ((rp T_1 Y0) /\ ((rp T_1 Y1) /\ (Y0 != Y1))))) /\ (Ex Y0, (Ex Y1, (Ex Y2, ((rq T_1 Y0) /\ ((rq T_1 Y1) /\ ((rq T_1 Y2) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ (Y1 != Y2)))))))))) => (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr T_1 Y0) /\ ((rr T_1 Y1) /\ ((rr T_1 Y2) /\ ((rr T_1 Y3) /\ ((rr T_1 Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4)))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) ### ConjTree 126
% 8.05/8.28 128. (-. (All X, (((Ex Y0, (Ex Y1, ((rp X Y0) /\ ((rp X Y1) /\ (Y0 != Y1))))) /\ (Ex Y0, (Ex Y1, (Ex Y2, ((rq X Y0) /\ ((rq X Y1) /\ ((rq X Y2) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ (Y1 != Y2)))))))))) => (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr X Y0) /\ ((rr X Y1) /\ ((rr X Y2) /\ ((rr X Y3) /\ ((rr X Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (cA Y)))) ### NotAllEx 127
% 8.05/8.28 129. (-. ((All X, ((cowlThing X) /\ (-. (cowlNothing X)))) /\ ((All X, ((xsd_string X) <=> (-. (xsd_integer X)))) /\ (All X, (((Ex Y0, (Ex Y1, ((rp X Y0) /\ ((rp X Y1) /\ (Y0 != Y1))))) /\ (Ex Y0, (Ex Y1, (Ex Y2, ((rq X Y0) /\ ((rq X Y1) /\ ((rq X Y2) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ (Y1 != Y2)))))))))) => (Ex Y0, (Ex Y1, (Ex Y2, (Ex Y3, (Ex Y4, ((rr X Y0) /\ ((rr X Y1) /\ ((rr X Y2) /\ ((rr X Y3) /\ ((rr X Y4) /\ ((Y0 != Y1) /\ ((Y0 != Y2) /\ ((Y0 != Y3) /\ ((Y0 != Y4) /\ ((Y1 != Y2) /\ ((Y1 != Y3) /\ ((Y1 != Y4) /\ ((Y2 != Y3) /\ ((Y2 != Y4) /\ (Y3 != Y4))))))))))))))))))))))))) (All X, (All Y, ((rp X Y) => (cA Y)))) (All X, (All Y, ((rq X Y) => (rr X Y)))) (All X, (All Y, ((rp X Y) => (rr X Y)))) (All X, (All Y, ((rq X Y) => (cB Y)))) (All A, (All B, (((A = B) /\ (cB A)) => (cB B)))) (All X, (-. ((cB X) /\ (cA X)))) (All A, (All B, (All C, (((A = B) /\ (rq C A)) => (rq C B))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) ### DisjTree 1 8 128
% 8.05/8.28 % SZS output end Proof
% 8.05/8.28 (* END-PROOF *)
%------------------------------------------------------------------------------