TSTP Solution File: SET775+4 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n003.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 : Tue Jul 19 05:43:53 EDT 2022
% Result : Theorem 0.49s 0.68s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET775+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.32 % Computer : n003.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 : Sun Jul 10 02:10:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.68 % SZS status Theorem
% 0.49/0.68 (* PROOF-FOUND *)
% 0.49/0.68 (* BEGIN-PROOF *)
% 0.49/0.68 % SZS output start Proof
% 0.49/0.68 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.49/0.68 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.49/0.68 3. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.49/0.68 4. (apply T_2 T_0 T_0) (-. (apply T_2 T_0 T_0)) ### Axiom
% 0.49/0.68 5. (apply T_2 T_0 T_0) (-. (apply T_2 T_0 T_0)) ### Axiom
% 0.49/0.68 6. (-. ((apply T_2 T_0 T_0) /\ (apply T_2 T_0 T_0))) (apply T_2 T_0 T_0) ### NotAnd 4 5
% 0.49/0.68 7. (-. (apply T_3 T_0 T_0)) (apply T_3 T_0 T_0) ### Axiom
% 0.49/0.68 8. ((apply T_3 T_0 T_0) <=> ((apply T_2 T_0 T_0) /\ (apply T_2 T_0 T_0))) (-. (apply T_3 T_0 T_0)) (apply T_2 T_0 T_0) ### Equiv 6 7
% 0.49/0.68 9. (((member T_0 T_1) /\ (member T_0 T_1)) => ((apply T_3 T_0 T_0) <=> ((apply T_2 T_0 T_0) /\ (apply T_2 T_0 T_0)))) (apply T_2 T_0 T_0) (-. (apply T_3 T_0 T_0)) (member T_0 T_1) ### DisjTree 2 3 8
% 0.49/0.68 10. (All B, (((member T_0 T_1) /\ (member B T_1)) => ((apply T_3 T_0 B) <=> ((apply T_2 T_0 B) /\ (apply T_2 B T_0))))) (member T_0 T_1) (-. (apply T_3 T_0 T_0)) (apply T_2 T_0 T_0) ### All 9
% 0.49/0.68 11. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_2 T_0 T_0) (-. (apply T_3 T_0 T_0)) (member T_0 T_1) ### All 10
% 0.49/0.68 12. ((member T_0 T_1) => (apply T_2 T_0 T_0)) (-. (apply T_3 T_0 T_0)) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (member T_0 T_1) ### Imply 1 11
% 0.49/0.68 13. (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (-. (apply T_3 T_0 T_0)) ### All 12
% 0.49/0.68 14. (-. ((member T_0 T_1) => (apply T_3 T_0 T_0))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (All X, ((member X T_1) => (apply T_2 X X))) ### NotImply 13
% 0.49/0.68 15. (-. (All X, ((member X T_1) => (apply T_3 X X)))) (All X, ((member X T_1) => (apply T_2 X X))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### NotAllEx 14
% 0.49/0.68 16. (member T_4 T_1) (-. (member T_4 T_1)) ### Axiom
% 0.49/0.68 17. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.49/0.68 18. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.49/0.68 19. (member T_4 T_1) (-. (member T_4 T_1)) ### Axiom
% 0.49/0.68 20. (apply T_3 T_5 T_4) (-. (apply T_3 T_5 T_4)) ### Axiom
% 0.49/0.68 21. (-. (apply T_2 T_4 T_5)) (apply T_2 T_4 T_5) ### Axiom
% 0.49/0.68 22. ((apply T_2 T_5 T_4) /\ (apply T_2 T_4 T_5)) (-. (apply T_2 T_4 T_5)) ### And 21
% 0.49/0.68 23. ((apply T_3 T_5 T_4) <=> ((apply T_2 T_5 T_4) /\ (apply T_2 T_4 T_5))) (-. (apply T_2 T_4 T_5)) (apply T_3 T_5 T_4) ### Equiv 20 22
% 0.49/0.68 24. (((member T_5 T_1) /\ (member T_4 T_1)) => ((apply T_3 T_5 T_4) <=> ((apply T_2 T_5 T_4) /\ (apply T_2 T_4 T_5)))) (apply T_3 T_5 T_4) (-. (apply T_2 T_4 T_5)) (member T_4 T_1) (member T_5 T_1) ### DisjTree 18 19 23
% 0.49/0.68 25. (All B, (((member T_5 T_1) /\ (member B T_1)) => ((apply T_3 T_5 B) <=> ((apply T_2 T_5 B) /\ (apply T_2 B T_5))))) (member T_5 T_1) (member T_4 T_1) (-. (apply T_2 T_4 T_5)) (apply T_3 T_5 T_4) ### All 24
% 0.49/0.68 26. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_5 T_4) (-. (apply T_2 T_4 T_5)) (member T_4 T_1) (member T_5 T_1) ### All 25
% 0.49/0.68 27. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.49/0.68 28. (member T_4 T_1) (-. (member T_4 T_1)) ### Axiom
% 0.49/0.68 29. (apply T_3 T_5 T_4) (-. (apply T_3 T_5 T_4)) ### Axiom
% 0.49/0.68 30. (-. (apply T_2 T_5 T_4)) (apply T_2 T_5 T_4) ### Axiom
% 0.49/0.68 31. ((apply T_2 T_5 T_4) /\ (apply T_2 T_4 T_5)) (-. (apply T_2 T_5 T_4)) ### And 30
% 0.49/0.68 32. ((apply T_3 T_5 T_4) <=> ((apply T_2 T_5 T_4) /\ (apply T_2 T_4 T_5))) (-. (apply T_2 T_5 T_4)) (apply T_3 T_5 T_4) ### Equiv 29 31
% 0.49/0.68 33. (((member T_5 T_1) /\ (member T_4 T_1)) => ((apply T_3 T_5 T_4) <=> ((apply T_2 T_5 T_4) /\ (apply T_2 T_4 T_5)))) (apply T_3 T_5 T_4) (-. (apply T_2 T_5 T_4)) (member T_4 T_1) (member T_5 T_1) ### DisjTree 27 28 32
% 0.49/0.68 34. (All B, (((member T_5 T_1) /\ (member B T_1)) => ((apply T_3 T_5 B) <=> ((apply T_2 T_5 B) /\ (apply T_2 B T_5))))) (member T_5 T_1) (member T_4 T_1) (-. (apply T_2 T_5 T_4)) (apply T_3 T_5 T_4) ### All 33
% 0.49/0.68 35. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_5 T_4) (-. (apply T_2 T_5 T_4)) (member T_4 T_1) (member T_5 T_1) ### All 34
% 0.49/0.68 36. (-. ((apply T_2 T_4 T_5) /\ (apply T_2 T_5 T_4))) (member T_5 T_1) (member T_4 T_1) (apply T_3 T_5 T_4) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### NotAnd 26 35
% 0.49/0.68 37. (-. (apply T_3 T_4 T_5)) (apply T_3 T_4 T_5) ### Axiom
% 0.49/0.68 38. ((apply T_3 T_4 T_5) <=> ((apply T_2 T_4 T_5) /\ (apply T_2 T_5 T_4))) (-. (apply T_3 T_4 T_5)) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_5 T_4) (member T_4 T_1) (member T_5 T_1) ### Equiv 36 37
% 0.49/0.68 39. (((member T_4 T_1) /\ (member T_5 T_1)) => ((apply T_3 T_4 T_5) <=> ((apply T_2 T_4 T_5) /\ (apply T_2 T_5 T_4)))) (apply T_3 T_5 T_4) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (-. (apply T_3 T_4 T_5)) (member T_5 T_1) (member T_4 T_1) ### DisjTree 16 17 38
% 0.49/0.68 40. (All B, (((member T_4 T_1) /\ (member B T_1)) => ((apply T_3 T_4 B) <=> ((apply T_2 T_4 B) /\ (apply T_2 B T_4))))) (member T_4 T_1) (member T_5 T_1) (-. (apply T_3 T_4 T_5)) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_5 T_4) ### All 39
% 0.49/0.68 41. (apply T_3 T_5 T_4) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (-. (apply T_3 T_4 T_5)) (member T_5 T_1) (member T_4 T_1) ### All 40
% 0.49/0.68 42. (-. (((member T_5 T_1) /\ (member T_4 T_1)) => ((apply T_3 T_5 T_4) => (apply T_3 T_4 T_5)))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### ConjTree 41
% 0.49/0.68 43. (-. (All Y, (((member T_5 T_1) /\ (member Y T_1)) => ((apply T_3 T_5 Y) => (apply T_3 Y T_5))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### NotAllEx 42
% 0.49/0.68 44. (-. (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X)))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### NotAllEx 43
% 0.49/0.68 45. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.49/0.68 46. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.49/0.68 47. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.49/0.68 48. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.49/0.68 49. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.49/0.68 50. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.49/0.68 51. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.49/0.68 52. (apply T_3 T_6 T_8) (-. (apply T_3 T_6 T_8)) ### Axiom
% 0.49/0.68 53. (-. (apply T_2 T_6 T_8)) (apply T_2 T_6 T_8) ### Axiom
% 0.49/0.68 54. ((apply T_2 T_6 T_8) /\ (apply T_2 T_8 T_6)) (-. (apply T_2 T_6 T_8)) ### And 53
% 0.49/0.68 55. ((apply T_3 T_6 T_8) <=> ((apply T_2 T_6 T_8) /\ (apply T_2 T_8 T_6))) (-. (apply T_2 T_6 T_8)) (apply T_3 T_6 T_8) ### Equiv 52 54
% 0.49/0.68 56. (((member T_6 T_1) /\ (member T_8 T_1)) => ((apply T_3 T_6 T_8) <=> ((apply T_2 T_6 T_8) /\ (apply T_2 T_8 T_6)))) (apply T_3 T_6 T_8) (-. (apply T_2 T_6 T_8)) (member T_8 T_1) (member T_6 T_1) ### DisjTree 50 51 55
% 0.49/0.68 57. (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (member T_6 T_1) (member T_8 T_1) (-. (apply T_2 T_6 T_8)) (apply T_3 T_6 T_8) ### All 56
% 0.49/0.68 58. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.49/0.68 59. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.49/0.68 60. (apply T_3 T_8 T_7) (-. (apply T_3 T_8 T_7)) ### Axiom
% 0.49/0.68 61. (-. (apply T_2 T_8 T_7)) (apply T_2 T_8 T_7) ### Axiom
% 0.49/0.68 62. ((apply T_2 T_8 T_7) /\ (apply T_2 T_7 T_8)) (-. (apply T_2 T_8 T_7)) ### And 61
% 0.49/0.68 63. ((apply T_3 T_8 T_7) <=> ((apply T_2 T_8 T_7) /\ (apply T_2 T_7 T_8))) (-. (apply T_2 T_8 T_7)) (apply T_3 T_8 T_7) ### Equiv 60 62
% 0.49/0.70 64. (((member T_8 T_1) /\ (member T_7 T_1)) => ((apply T_3 T_8 T_7) <=> ((apply T_2 T_8 T_7) /\ (apply T_2 T_7 T_8)))) (apply T_3 T_8 T_7) (-. (apply T_2 T_8 T_7)) (member T_7 T_1) (member T_8 T_1) ### DisjTree 58 59 63
% 0.49/0.70 65. (All B, (((member T_8 T_1) /\ (member B T_1)) => ((apply T_3 T_8 B) <=> ((apply T_2 T_8 B) /\ (apply T_2 B T_8))))) (member T_8 T_1) (member T_7 T_1) (-. (apply T_2 T_8 T_7)) (apply T_3 T_8 T_7) ### All 64
% 0.49/0.70 66. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) (-. (apply T_2 T_8 T_7)) (member T_7 T_1) (member T_8 T_1) ### All 65
% 0.49/0.70 67. (-. (apply T_2 T_6 T_7)) (apply T_2 T_6 T_7) ### Axiom
% 0.49/0.70 68. (((member T_6 T_1) /\ ((member T_8 T_1) /\ (member T_7 T_1))) => (((apply T_2 T_6 T_8) /\ (apply T_2 T_8 T_7)) => (apply T_2 T_6 T_7))) (-. (apply T_2 T_6 T_7)) (apply T_3 T_8 T_7) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_6 T_8) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (member T_7 T_1) (member T_8 T_1) (member T_6 T_1) ### DisjTree 47 48 49 57 66 67
% 0.49/0.70 69. (All Z, (((member T_6 T_1) /\ ((member T_8 T_1) /\ (member Z T_1))) => (((apply T_2 T_6 T_8) /\ (apply T_2 T_8 Z)) => (apply T_2 T_6 Z)))) (member T_6 T_1) (member T_8 T_1) (member T_7 T_1) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_6 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) (-. (apply T_2 T_6 T_7)) ### All 68
% 0.49/0.70 70. (All Y, (All Z, (((member T_6 T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 T_6 Y) /\ (apply T_2 Y Z)) => (apply T_2 T_6 Z))))) (-. (apply T_2 T_6 T_7)) (apply T_3 T_8 T_7) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_6 T_8) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (member T_7 T_1) (member T_8 T_1) (member T_6 T_1) ### All 69
% 0.49/0.70 71. (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (member T_6 T_1) (member T_8 T_1) (member T_7 T_1) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_6 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) (-. (apply T_2 T_6 T_7)) ### All 70
% 0.49/0.70 72. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.49/0.70 73. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.49/0.70 74. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.49/0.70 75. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.49/0.70 76. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.49/0.70 77. (apply T_3 T_8 T_7) (-. (apply T_3 T_8 T_7)) ### Axiom
% 0.49/0.70 78. (-. (apply T_2 T_7 T_8)) (apply T_2 T_7 T_8) ### Axiom
% 0.49/0.70 79. ((apply T_2 T_8 T_7) /\ (apply T_2 T_7 T_8)) (-. (apply T_2 T_7 T_8)) ### And 78
% 0.49/0.70 80. ((apply T_3 T_8 T_7) <=> ((apply T_2 T_8 T_7) /\ (apply T_2 T_7 T_8))) (-. (apply T_2 T_7 T_8)) (apply T_3 T_8 T_7) ### Equiv 77 79
% 0.49/0.70 81. (((member T_8 T_1) /\ (member T_7 T_1)) => ((apply T_3 T_8 T_7) <=> ((apply T_2 T_8 T_7) /\ (apply T_2 T_7 T_8)))) (apply T_3 T_8 T_7) (-. (apply T_2 T_7 T_8)) (member T_7 T_1) (member T_8 T_1) ### DisjTree 75 76 80
% 0.49/0.70 82. (All B, (((member T_8 T_1) /\ (member B T_1)) => ((apply T_3 T_8 B) <=> ((apply T_2 T_8 B) /\ (apply T_2 B T_8))))) (member T_8 T_1) (member T_7 T_1) (-. (apply T_2 T_7 T_8)) (apply T_3 T_8 T_7) ### All 81
% 0.49/0.70 83. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) (-. (apply T_2 T_7 T_8)) (member T_7 T_1) (member T_8 T_1) ### All 82
% 0.49/0.70 84. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.49/0.70 85. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.49/0.70 86. (apply T_3 T_6 T_8) (-. (apply T_3 T_6 T_8)) ### Axiom
% 0.49/0.70 87. (-. (apply T_2 T_8 T_6)) (apply T_2 T_8 T_6) ### Axiom
% 0.49/0.70 88. ((apply T_2 T_6 T_8) /\ (apply T_2 T_8 T_6)) (-. (apply T_2 T_8 T_6)) ### And 87
% 0.49/0.70 89. ((apply T_3 T_6 T_8) <=> ((apply T_2 T_6 T_8) /\ (apply T_2 T_8 T_6))) (-. (apply T_2 T_8 T_6)) (apply T_3 T_6 T_8) ### Equiv 86 88
% 0.49/0.70 90. (((member T_6 T_1) /\ (member T_8 T_1)) => ((apply T_3 T_6 T_8) <=> ((apply T_2 T_6 T_8) /\ (apply T_2 T_8 T_6)))) (apply T_3 T_6 T_8) (-. (apply T_2 T_8 T_6)) (member T_8 T_1) (member T_6 T_1) ### DisjTree 84 85 89
% 0.49/0.70 91. (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (member T_6 T_1) (member T_8 T_1) (-. (apply T_2 T_8 T_6)) (apply T_3 T_6 T_8) ### All 90
% 0.49/0.70 92. (-. (apply T_2 T_7 T_6)) (apply T_2 T_7 T_6) ### Axiom
% 0.49/0.70 93. (((member T_7 T_1) /\ ((member T_8 T_1) /\ (member T_6 T_1))) => (((apply T_2 T_7 T_8) /\ (apply T_2 T_8 T_6)) => (apply T_2 T_7 T_6))) (-. (apply T_2 T_7 T_6)) (apply T_3 T_6 T_8) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_8 T_7) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (member T_6 T_1) (member T_8 T_1) (member T_7 T_1) ### DisjTree 72 73 74 83 91 92
% 0.49/0.70 94. (All Z, (((member T_7 T_1) /\ ((member T_8 T_1) /\ (member Z T_1))) => (((apply T_2 T_7 T_8) /\ (apply T_2 T_8 Z)) => (apply T_2 T_7 Z)))) (member T_7 T_1) (member T_8 T_1) (member T_6 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_6 T_8) (-. (apply T_2 T_7 T_6)) ### All 93
% 0.49/0.70 95. (All Y, (All Z, (((member T_7 T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 T_7 Y) /\ (apply T_2 Y Z)) => (apply T_2 T_7 Z))))) (-. (apply T_2 T_7 T_6)) (apply T_3 T_6 T_8) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_8 T_7) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (member T_6 T_1) (member T_8 T_1) (member T_7 T_1) ### All 94
% 0.49/0.70 96. (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (member T_7 T_1) (member T_8 T_1) (member T_6 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_6 T_8) (-. (apply T_2 T_7 T_6)) ### All 95
% 0.49/0.70 97. (-. ((apply T_2 T_6 T_7) /\ (apply T_2 T_7 T_6))) (apply T_3 T_8 T_7) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_6 T_8) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (member T_7 T_1) (member T_8 T_1) (member T_6 T_1) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) ### NotAnd 71 96
% 0.49/0.70 98. (-. (apply T_3 T_6 T_7)) (apply T_3 T_6 T_7) ### Axiom
% 0.49/0.70 99. ((apply T_3 T_6 T_7) <=> ((apply T_2 T_6 T_7) /\ (apply T_2 T_7 T_6))) (-. (apply T_3 T_6 T_7)) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (member T_6 T_1) (member T_8 T_1) (member T_7 T_1) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_6 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) ### Equiv 97 98
% 0.49/0.71 100. (((member T_6 T_1) /\ (member T_7 T_1)) => ((apply T_3 T_6 T_7) <=> ((apply T_2 T_6 T_7) /\ (apply T_2 T_7 T_6)))) (apply T_3 T_8 T_7) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_6 T_8) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (member T_8 T_1) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (-. (apply T_3 T_6 T_7)) (member T_7 T_1) (member T_6 T_1) ### DisjTree 45 46 99
% 0.49/0.71 101. (member T_6 T_1) (member T_7 T_1) (-. (apply T_3 T_6 T_7)) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (member T_8 T_1) (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_3 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_2 B T_6))))) (apply T_3 T_6 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_8 T_7) ### All 100
% 0.49/0.71 102. (apply T_3 T_8 T_7) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (apply T_3 T_6 T_8) (member T_8 T_1) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (-. (apply T_3 T_6 T_7)) (member T_7 T_1) (member T_6 T_1) ### All 101
% 0.49/0.71 103. (-. (((member T_6 T_1) /\ ((member T_8 T_1) /\ (member T_7 T_1))) => (((apply T_3 T_6 T_8) /\ (apply T_3 T_8 T_7)) => (apply T_3 T_6 T_7)))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### ConjTree 102
% 0.49/0.71 104. (-. (All Z, (((member T_6 T_1) /\ ((member T_8 T_1) /\ (member Z T_1))) => (((apply T_3 T_6 T_8) /\ (apply T_3 T_8 Z)) => (apply T_3 T_6 Z))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) ### NotAllEx 103
% 0.49/0.71 105. (-. (All Y, (All Z, (((member T_6 T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_3 T_6 Y) /\ (apply T_3 Y Z)) => (apply T_3 T_6 Z)))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### NotAllEx 104
% 0.49/0.71 106. (-. (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_3 X Y) /\ (apply T_3 Y Z)) => (apply T_3 X Z))))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) ### NotAllEx 105
% 0.49/0.71 107. (-. ((All X, ((member X T_1) => (apply T_3 X X))) /\ ((All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) /\ (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_3 X Y) /\ (apply T_3 Y Z)) => (apply T_3 X Z))))))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (All X, ((member X T_1) => (apply T_2 X X))) ### DisjTree 15 44 106
% 0.49/0.71 108. (-. (equivalence T_3 T_1)) (All X, ((member X T_1) => (apply T_2 X X))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))) ### Definition-Pseudo(equivalence) 107
% 0.49/0.71 109. ((All X, ((member X T_1) => (apply T_2 X X))) /\ (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z))))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) (-. (equivalence T_3 T_1)) ### And 108
% 0.49/0.71 110. (pre_order T_2 T_1) (-. (equivalence T_3 T_1)) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A)))))) ### Definition-Pseudo(pre_order) 109
% 0.49/0.71 111. (-. (((pre_order T_2 T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_3 A B) <=> ((apply T_2 A B) /\ (apply T_2 B A))))))) => (equivalence T_3 T_1))) ### ConjTree 110
% 0.49/0.71 112. (-. (All R, (((pre_order T_2 T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply R A B) <=> ((apply T_2 A B) /\ (apply T_2 B A))))))) => (equivalence R T_1)))) ### NotAllEx 111
% 0.49/0.71 113. (-. (All P, (All R, (((pre_order P T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply R A B) <=> ((apply P A B) /\ (apply P B A))))))) => (equivalence R T_1))))) ### NotAllEx 112
% 0.49/0.71 114. (-. (All E, (All P, (All R, (((pre_order P E) /\ (All A, (All B, (((member A E) /\ (member B E)) => ((apply R A B) <=> ((apply P A B) /\ (apply P B A))))))) => (equivalence R E)))))) ### NotAllEx 113
% 0.49/0.71 % SZS output end Proof
% 0.49/0.71 (* END-PROOF *)
%------------------------------------------------------------------------------