TSTP Solution File: SET773+4 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET773+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 : n009.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 05:43:52 EDT 2022
% Result : Theorem 0.82s 0.97s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET773+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 16:25:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.82/0.97 % SZS status Theorem
% 0.82/0.97 (* PROOF-FOUND *)
% 0.82/0.97 (* BEGIN-PROOF *)
% 0.82/0.97 % SZS output start Proof
% 0.82/0.97 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.82/0.97 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.82/0.97 3. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.82/0.97 4. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.82/0.97 5. (-. (apply T_2 T_0 T_0)) (apply T_2 T_0 T_0) ### Axiom
% 0.82/0.97 6. ((member T_0 T_1) => (apply T_2 T_0 T_0)) (-. (apply T_2 T_0 T_0)) (member T_0 T_1) ### Imply 4 5
% 0.82/0.97 7. (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (-. (apply T_2 T_0 T_0)) ### All 6
% 0.82/0.97 8. (apply T_3 T_0 T_0) (-. (apply T_3 T_0 T_0)) ### Axiom
% 0.82/0.97 9. (-. ((apply T_2 T_0 T_0) /\ (apply T_3 T_0 T_0))) (apply T_3 T_0 T_0) (member T_0 T_1) (All X, ((member X T_1) => (apply T_2 X X))) ### NotAnd 7 8
% 0.82/0.97 10. (-. (apply T_4 T_0 T_0)) (apply T_4 T_0 T_0) ### Axiom
% 0.82/0.97 11. ((apply T_4 T_0 T_0) <=> ((apply T_2 T_0 T_0) /\ (apply T_3 T_0 T_0))) (-. (apply T_4 T_0 T_0)) (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (apply T_3 T_0 T_0) ### Equiv 9 10
% 0.82/0.97 12. (((member T_0 T_1) /\ (member T_0 T_1)) => ((apply T_4 T_0 T_0) <=> ((apply T_2 T_0 T_0) /\ (apply T_3 T_0 T_0)))) (apply T_3 T_0 T_0) (All X, ((member X T_1) => (apply T_2 X X))) (-. (apply T_4 T_0 T_0)) (member T_0 T_1) ### DisjTree 2 3 11
% 0.82/0.97 13. (All B, (((member T_0 T_1) /\ (member B T_1)) => ((apply T_4 T_0 B) <=> ((apply T_2 T_0 B) /\ (apply T_3 T_0 B))))) (member T_0 T_1) (-. (apply T_4 T_0 T_0)) (All X, ((member X T_1) => (apply T_2 X X))) (apply T_3 T_0 T_0) ### All 12
% 0.82/0.97 14. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_3 T_0 T_0) (All X, ((member X T_1) => (apply T_2 X X))) (-. (apply T_4 T_0 T_0)) (member T_0 T_1) ### All 13
% 0.82/0.97 15. ((member T_0 T_1) => (apply T_3 T_0 T_0)) (-. (apply T_4 T_0 T_0)) (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (member T_0 T_1) ### Imply 1 14
% 0.82/0.97 16. (All X, ((member X T_1) => (apply T_3 X X))) (member T_0 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, ((member X T_1) => (apply T_2 X X))) (-. (apply T_4 T_0 T_0)) ### All 15
% 0.82/0.97 17. (-. ((member T_0 T_1) => (apply T_4 T_0 T_0))) (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, ((member X T_1) => (apply T_3 X X))) ### NotImply 16
% 0.82/0.97 18. (-. (All X, ((member X T_1) => (apply T_4 X X)))) (All X, ((member X T_1) => (apply T_3 X X))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, ((member X T_1) => (apply T_2 X X))) ### NotAllEx 17
% 0.82/0.97 19. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.82/0.97 20. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.82/0.97 21. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.82/0.97 22. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.82/0.97 23. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.82/0.97 24. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.82/0.97 25. (apply T_4 T_6 T_5) (-. (apply T_4 T_6 T_5)) ### Axiom
% 0.82/0.97 26. (-. (apply T_2 T_6 T_5)) (apply T_2 T_6 T_5) ### Axiom
% 0.82/0.97 27. ((apply T_2 T_6 T_5) /\ (apply T_3 T_6 T_5)) (-. (apply T_2 T_6 T_5)) ### And 26
% 0.82/0.97 28. ((apply T_4 T_6 T_5) <=> ((apply T_2 T_6 T_5) /\ (apply T_3 T_6 T_5))) (-. (apply T_2 T_6 T_5)) (apply T_4 T_6 T_5) ### Equiv 25 27
% 0.82/0.97 29. (((member T_6 T_1) /\ (member T_5 T_1)) => ((apply T_4 T_6 T_5) <=> ((apply T_2 T_6 T_5) /\ (apply T_3 T_6 T_5)))) (apply T_4 T_6 T_5) (-. (apply T_2 T_6 T_5)) (member T_5 T_1) (member T_6 T_1) ### DisjTree 23 24 28
% 0.82/0.97 30. (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_4 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_3 T_6 B))))) (member T_6 T_1) (member T_5 T_1) (-. (apply T_2 T_6 T_5)) (apply T_4 T_6 T_5) ### All 29
% 0.82/0.97 31. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_6 T_5) (-. (apply T_2 T_6 T_5)) (member T_5 T_1) (member T_6 T_1) ### All 30
% 0.82/0.97 32. (-. (apply T_2 T_5 T_6)) (apply T_2 T_5 T_6) ### Axiom
% 0.82/0.97 33. (((member T_6 T_1) /\ (member T_5 T_1)) => ((apply T_2 T_6 T_5) => (apply T_2 T_5 T_6))) (-. (apply T_2 T_5 T_6)) (apply T_4 T_6 T_5) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (member T_5 T_1) (member T_6 T_1) ### DisjTree 21 22 31 32
% 0.82/0.97 34. (All Y, (((member T_6 T_1) /\ (member Y T_1)) => ((apply T_2 T_6 Y) => (apply T_2 Y T_6)))) (member T_6 T_1) (member T_5 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_6 T_5) (-. (apply T_2 T_5 T_6)) ### All 33
% 0.82/0.97 35. (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) (-. (apply T_2 T_5 T_6)) (apply T_4 T_6 T_5) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (member T_5 T_1) (member T_6 T_1) ### All 34
% 0.82/0.97 36. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.82/0.97 37. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.82/0.97 38. (member T_6 T_1) (-. (member T_6 T_1)) ### Axiom
% 0.82/0.97 39. (member T_5 T_1) (-. (member T_5 T_1)) ### Axiom
% 0.82/0.97 40. (apply T_4 T_6 T_5) (-. (apply T_4 T_6 T_5)) ### Axiom
% 0.82/0.97 41. (-. (apply T_3 T_6 T_5)) (apply T_3 T_6 T_5) ### Axiom
% 0.82/0.97 42. ((apply T_2 T_6 T_5) /\ (apply T_3 T_6 T_5)) (-. (apply T_3 T_6 T_5)) ### And 41
% 0.82/0.97 43. ((apply T_4 T_6 T_5) <=> ((apply T_2 T_6 T_5) /\ (apply T_3 T_6 T_5))) (-. (apply T_3 T_6 T_5)) (apply T_4 T_6 T_5) ### Equiv 40 42
% 0.82/0.97 44. (((member T_6 T_1) /\ (member T_5 T_1)) => ((apply T_4 T_6 T_5) <=> ((apply T_2 T_6 T_5) /\ (apply T_3 T_6 T_5)))) (apply T_4 T_6 T_5) (-. (apply T_3 T_6 T_5)) (member T_5 T_1) (member T_6 T_1) ### DisjTree 38 39 43
% 0.82/0.97 45. (All B, (((member T_6 T_1) /\ (member B T_1)) => ((apply T_4 T_6 B) <=> ((apply T_2 T_6 B) /\ (apply T_3 T_6 B))))) (member T_6 T_1) (member T_5 T_1) (-. (apply T_3 T_6 T_5)) (apply T_4 T_6 T_5) ### All 44
% 0.82/0.97 46. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_6 T_5) (-. (apply T_3 T_6 T_5)) (member T_5 T_1) (member T_6 T_1) ### All 45
% 0.82/0.97 47. (-. (apply T_3 T_5 T_6)) (apply T_3 T_5 T_6) ### Axiom
% 0.82/0.97 48. (((member T_6 T_1) /\ (member T_5 T_1)) => ((apply T_3 T_6 T_5) => (apply T_3 T_5 T_6))) (-. (apply T_3 T_5 T_6)) (apply T_4 T_6 T_5) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (member T_5 T_1) (member T_6 T_1) ### DisjTree 36 37 46 47
% 0.82/0.97 49. (All Y, (((member T_6 T_1) /\ (member Y T_1)) => ((apply T_3 T_6 Y) => (apply T_3 Y T_6)))) (member T_6 T_1) (member T_5 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_6 T_5) (-. (apply T_3 T_5 T_6)) ### All 48
% 0.82/0.97 50. (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) (-. (apply T_3 T_5 T_6)) (apply T_4 T_6 T_5) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (member T_5 T_1) (member T_6 T_1) ### All 49
% 0.82/0.97 51. (-. ((apply T_2 T_5 T_6) /\ (apply T_3 T_5 T_6))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) (member T_6 T_1) (member T_5 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_6 T_5) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) ### NotAnd 35 50
% 0.82/0.97 52. (-. (apply T_4 T_5 T_6)) (apply T_4 T_5 T_6) ### Axiom
% 0.82/0.97 53. ((apply T_4 T_5 T_6) <=> ((apply T_2 T_5 T_6) /\ (apply T_3 T_5 T_6))) (-. (apply T_4 T_5 T_6)) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) (apply T_4 T_6 T_5) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (member T_5 T_1) (member T_6 T_1) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) ### Equiv 51 52
% 0.82/0.99 54. (((member T_5 T_1) /\ (member T_6 T_1)) => ((apply T_4 T_5 T_6) <=> ((apply T_2 T_5 T_6) /\ (apply T_3 T_5 T_6)))) (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_6 T_5) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) (-. (apply T_4 T_5 T_6)) (member T_6 T_1) (member T_5 T_1) ### DisjTree 19 20 53
% 0.82/0.99 55. (All B, (((member T_5 T_1) /\ (member B T_1)) => ((apply T_4 T_5 B) <=> ((apply T_2 T_5 B) /\ (apply T_3 T_5 B))))) (member T_5 T_1) (member T_6 T_1) (-. (apply T_4 T_5 T_6)) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) (apply T_4 T_6 T_5) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) ### All 54
% 0.82/0.99 56. (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_6 T_5) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) (-. (apply T_4 T_5 T_6)) (member T_6 T_1) (member T_5 T_1) ### All 55
% 0.82/0.99 57. (-. (((member T_6 T_1) /\ (member T_5 T_1)) => ((apply T_4 T_6 T_5) => (apply T_4 T_5 T_6)))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) ### ConjTree 56
% 0.82/0.99 58. (-. (All Y, (((member T_6 T_1) /\ (member Y T_1)) => ((apply T_4 T_6 Y) => (apply T_4 Y T_6))))) (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) ### NotAllEx 57
% 0.82/0.99 59. (-. (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_4 X Y) => (apply T_4 Y X)))))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) ### NotAllEx 58
% 0.82/0.99 60. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.82/0.99 61. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.82/0.99 62. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.82/0.99 63. (member T_9 T_1) (-. (member T_9 T_1)) ### Axiom
% 0.82/0.99 64. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.82/0.99 65. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.82/0.99 66. (member T_9 T_1) (-. (member T_9 T_1)) ### Axiom
% 0.82/0.99 67. (apply T_4 T_7 T_9) (-. (apply T_4 T_7 T_9)) ### Axiom
% 0.82/0.99 68. (-. (apply T_2 T_7 T_9)) (apply T_2 T_7 T_9) ### Axiom
% 0.82/0.99 69. ((apply T_2 T_7 T_9) /\ (apply T_3 T_7 T_9)) (-. (apply T_2 T_7 T_9)) ### And 68
% 0.82/0.99 70. ((apply T_4 T_7 T_9) <=> ((apply T_2 T_7 T_9) /\ (apply T_3 T_7 T_9))) (-. (apply T_2 T_7 T_9)) (apply T_4 T_7 T_9) ### Equiv 67 69
% 0.82/0.99 71. (((member T_7 T_1) /\ (member T_9 T_1)) => ((apply T_4 T_7 T_9) <=> ((apply T_2 T_7 T_9) /\ (apply T_3 T_7 T_9)))) (apply T_4 T_7 T_9) (-. (apply T_2 T_7 T_9)) (member T_9 T_1) (member T_7 T_1) ### DisjTree 65 66 70
% 0.82/0.99 72. (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_7 T_1) (member T_9 T_1) (-. (apply T_2 T_7 T_9)) (apply T_4 T_7 T_9) ### All 71
% 0.82/0.99 73. (member T_9 T_1) (-. (member T_9 T_1)) ### Axiom
% 0.82/0.99 74. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.82/0.99 75. (apply T_4 T_9 T_8) (-. (apply T_4 T_9 T_8)) ### Axiom
% 0.82/0.99 76. (-. (apply T_2 T_9 T_8)) (apply T_2 T_9 T_8) ### Axiom
% 0.82/0.99 77. ((apply T_2 T_9 T_8) /\ (apply T_3 T_9 T_8)) (-. (apply T_2 T_9 T_8)) ### And 76
% 0.82/0.99 78. ((apply T_4 T_9 T_8) <=> ((apply T_2 T_9 T_8) /\ (apply T_3 T_9 T_8))) (-. (apply T_2 T_9 T_8)) (apply T_4 T_9 T_8) ### Equiv 75 77
% 0.82/0.99 79. (((member T_9 T_1) /\ (member T_8 T_1)) => ((apply T_4 T_9 T_8) <=> ((apply T_2 T_9 T_8) /\ (apply T_3 T_9 T_8)))) (apply T_4 T_9 T_8) (-. (apply T_2 T_9 T_8)) (member T_8 T_1) (member T_9 T_1) ### DisjTree 73 74 78
% 0.82/0.99 80. (All B, (((member T_9 T_1) /\ (member B T_1)) => ((apply T_4 T_9 B) <=> ((apply T_2 T_9 B) /\ (apply T_3 T_9 B))))) (member T_9 T_1) (member T_8 T_1) (-. (apply T_2 T_9 T_8)) (apply T_4 T_9 T_8) ### All 79
% 0.82/0.99 81. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (-. (apply T_2 T_9 T_8)) (member T_8 T_1) (member T_9 T_1) ### All 80
% 0.82/0.99 82. (-. (apply T_2 T_7 T_8)) (apply T_2 T_7 T_8) ### Axiom
% 0.82/0.99 83. (((member T_7 T_1) /\ ((member T_9 T_1) /\ (member T_8 T_1))) => (((apply T_2 T_7 T_9) /\ (apply T_2 T_9 T_8)) => (apply T_2 T_7 T_8))) (-. (apply T_2 T_7 T_8)) (apply T_4 T_9 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_7 T_9) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_8 T_1) (member T_9 T_1) (member T_7 T_1) ### DisjTree 62 63 64 72 81 82
% 0.82/0.99 84. (All Z, (((member T_7 T_1) /\ ((member T_9 T_1) /\ (member Z T_1))) => (((apply T_2 T_7 T_9) /\ (apply T_2 T_9 Z)) => (apply T_2 T_7 Z)))) (member T_7 T_1) (member T_9 T_1) (member T_8 T_1) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (apply T_4 T_7 T_9) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (-. (apply T_2 T_7 T_8)) ### All 83
% 0.82/0.99 85. (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_8)) (apply T_4 T_9 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_7 T_9) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_8 T_1) (member T_9 T_1) (member T_7 T_1) ### All 84
% 0.82/0.99 86. (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_9 T_1) (member T_8 T_1) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (apply T_4 T_7 T_9) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (-. (apply T_2 T_7 T_8)) ### All 85
% 0.82/0.99 87. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.82/0.99 88. (member T_9 T_1) (-. (member T_9 T_1)) ### Axiom
% 0.82/0.99 89. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.82/0.99 90. (member T_7 T_1) (-. (member T_7 T_1)) ### Axiom
% 0.82/0.99 91. (member T_9 T_1) (-. (member T_9 T_1)) ### Axiom
% 0.82/0.99 92. (apply T_4 T_7 T_9) (-. (apply T_4 T_7 T_9)) ### Axiom
% 0.82/0.99 93. (-. (apply T_3 T_7 T_9)) (apply T_3 T_7 T_9) ### Axiom
% 0.82/0.99 94. ((apply T_2 T_7 T_9) /\ (apply T_3 T_7 T_9)) (-. (apply T_3 T_7 T_9)) ### And 93
% 0.82/0.99 95. ((apply T_4 T_7 T_9) <=> ((apply T_2 T_7 T_9) /\ (apply T_3 T_7 T_9))) (-. (apply T_3 T_7 T_9)) (apply T_4 T_7 T_9) ### Equiv 92 94
% 0.82/0.99 96. (((member T_7 T_1) /\ (member T_9 T_1)) => ((apply T_4 T_7 T_9) <=> ((apply T_2 T_7 T_9) /\ (apply T_3 T_7 T_9)))) (apply T_4 T_7 T_9) (-. (apply T_3 T_7 T_9)) (member T_9 T_1) (member T_7 T_1) ### DisjTree 90 91 95
% 0.82/0.99 97. (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_7 T_1) (member T_9 T_1) (-. (apply T_3 T_7 T_9)) (apply T_4 T_7 T_9) ### All 96
% 0.82/1.01 98. (member T_9 T_1) (-. (member T_9 T_1)) ### Axiom
% 0.82/1.01 99. (member T_8 T_1) (-. (member T_8 T_1)) ### Axiom
% 0.82/1.01 100. (apply T_4 T_9 T_8) (-. (apply T_4 T_9 T_8)) ### Axiom
% 0.82/1.01 101. (-. (apply T_3 T_9 T_8)) (apply T_3 T_9 T_8) ### Axiom
% 0.82/1.01 102. ((apply T_2 T_9 T_8) /\ (apply T_3 T_9 T_8)) (-. (apply T_3 T_9 T_8)) ### And 101
% 0.82/1.01 103. ((apply T_4 T_9 T_8) <=> ((apply T_2 T_9 T_8) /\ (apply T_3 T_9 T_8))) (-. (apply T_3 T_9 T_8)) (apply T_4 T_9 T_8) ### Equiv 100 102
% 0.82/1.01 104. (((member T_9 T_1) /\ (member T_8 T_1)) => ((apply T_4 T_9 T_8) <=> ((apply T_2 T_9 T_8) /\ (apply T_3 T_9 T_8)))) (apply T_4 T_9 T_8) (-. (apply T_3 T_9 T_8)) (member T_8 T_1) (member T_9 T_1) ### DisjTree 98 99 103
% 0.82/1.01 105. (All B, (((member T_9 T_1) /\ (member B T_1)) => ((apply T_4 T_9 B) <=> ((apply T_2 T_9 B) /\ (apply T_3 T_9 B))))) (member T_9 T_1) (member T_8 T_1) (-. (apply T_3 T_9 T_8)) (apply T_4 T_9 T_8) ### All 104
% 0.82/1.01 106. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (-. (apply T_3 T_9 T_8)) (member T_8 T_1) (member T_9 T_1) ### All 105
% 0.82/1.01 107. (-. (apply T_3 T_7 T_8)) (apply T_3 T_7 T_8) ### Axiom
% 0.82/1.01 108. (((member T_7 T_1) /\ ((member T_9 T_1) /\ (member T_8 T_1))) => (((apply T_3 T_7 T_9) /\ (apply T_3 T_9 T_8)) => (apply T_3 T_7 T_8))) (-. (apply T_3 T_7 T_8)) (apply T_4 T_9 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_7 T_9) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_8 T_1) (member T_9 T_1) (member T_7 T_1) ### DisjTree 87 88 89 97 106 107
% 0.82/1.01 109. (All Z, (((member T_7 T_1) /\ ((member T_9 T_1) /\ (member Z T_1))) => (((apply T_3 T_7 T_9) /\ (apply T_3 T_9 Z)) => (apply T_3 T_7 Z)))) (member T_7 T_1) (member T_9 T_1) (member T_8 T_1) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (apply T_4 T_7 T_9) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (-. (apply T_3 T_7 T_8)) ### All 108
% 0.82/1.01 110. (All Y, (All Z, (((member T_7 T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_3 T_7 Y) /\ (apply T_3 Y Z)) => (apply T_3 T_7 Z))))) (-. (apply T_3 T_7 T_8)) (apply T_4 T_9 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_7 T_9) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_8 T_1) (member T_9 T_1) (member T_7 T_1) ### All 109
% 0.82/1.01 111. (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)))))) (member T_7 T_1) (member T_9 T_1) (member T_8 T_1) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (apply T_4 T_7 T_9) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (-. (apply T_3 T_7 T_8)) ### All 110
% 0.82/1.01 112. (-. ((apply T_2 T_7 T_8) /\ (apply T_3 T_7 T_8))) (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)))))) (apply T_4 T_9 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_7 T_9) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_8 T_1) (member T_9 T_1) (member T_7 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 86 111
% 0.82/1.01 113. (-. (apply T_4 T_7 T_8)) (apply T_4 T_7 T_8) ### Axiom
% 0.82/1.01 114. ((apply T_4 T_7 T_8) <=> ((apply T_2 T_7 T_8) /\ (apply T_3 T_7 T_8))) (-. (apply T_4 T_7 T_8)) (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_9 T_1) (member T_8 T_1) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (apply T_4 T_7 T_9) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (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)))))) ### Equiv 112 113
% 0.82/1.01 115. (((member T_7 T_1) /\ (member T_8 T_1)) => ((apply T_4 T_7 T_8) <=> ((apply T_2 T_7 T_8) /\ (apply T_3 T_7 T_8)))) (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)))))) (apply T_4 T_9 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_7 T_9) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (member T_9 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_4 T_7 T_8)) (member T_8 T_1) (member T_7 T_1) ### DisjTree 60 61 114
% 0.82/1.01 116. (member T_7 T_1) (member T_8 T_1) (-. (apply T_4 T_7 T_8)) (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_9 T_1) (All B, (((member T_7 T_1) /\ (member B T_1)) => ((apply T_4 T_7 B) <=> ((apply T_2 T_7 B) /\ (apply T_3 T_7 B))))) (apply T_4 T_7 T_9) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_9 T_8) (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 115
% 0.82/1.01 117. (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)))))) (apply T_4 T_9 T_8) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (apply T_4 T_7 T_9) (member T_9 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_4 T_7 T_8)) (member T_8 T_1) (member T_7 T_1) ### All 116
% 0.82/1.01 118. (-. (((member T_7 T_1) /\ ((member T_9 T_1) /\ (member T_8 T_1))) => (((apply T_4 T_7 T_9) /\ (apply T_4 T_9 T_8)) => (apply T_4 T_7 T_8)))) (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (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)))))) ### ConjTree 117
% 0.82/1.01 119. (-. (All Z, (((member T_7 T_1) /\ ((member T_9 T_1) /\ (member Z T_1))) => (((apply T_4 T_7 T_9) /\ (apply T_4 T_9 Z)) => (apply T_4 T_7 Z))))) (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (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 118
% 0.82/1.01 120. (-. (All Y, (All Z, (((member T_7 T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_4 T_7 Y) /\ (apply T_4 Y Z)) => (apply T_4 T_7 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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (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)))))) ### NotAllEx 119
% 0.82/1.01 121. (-. (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_4 X Y) /\ (apply T_4 Y Z)) => (apply T_4 X Z))))))) (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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (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 120
% 0.82/1.01 122. (-. ((All X, ((member X T_1) => (apply T_4 X X))) /\ ((All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_4 X Y) => (apply T_4 Y X))))) /\ (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_4 X Y) /\ (apply T_4 Y Z)) => (apply T_4 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 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, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) => (apply T_3 Y X))))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y 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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, ((member X T_1) => (apply T_3 X X))) ### DisjTree 18 59 121
% 0.82/1.01 123. (-. (equivalence T_4 T_1)) (All X, ((member X T_1) => (apply T_3 X X))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, ((member X T_1) => (apply T_2 X X))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y 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)))))) ### Definition-Pseudo(equivalence) 122
% 0.82/1.01 124. ((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 X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y 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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (-. (equivalence T_4 T_1)) ### ConjTree 123
% 0.82/1.01 125. (equivalence T_3 T_1) (-. (equivalence T_4 T_1)) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (All X, ((member X T_1) => (apply T_2 X X))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y 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)))))) ### Definition-Pseudo(equivalence) 124
% 0.82/1.01 126. ((All X, ((member X T_1) => (apply T_2 X X))) /\ ((All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y 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_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) (-. (equivalence T_4 T_1)) (equivalence T_3 T_1) ### ConjTree 125
% 0.82/1.01 127. (equivalence T_2 T_1) (equivalence T_3 T_1) (-. (equivalence T_4 T_1)) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))) ### Definition-Pseudo(equivalence) 126
% 0.82/1.01 128. (-. (((equivalence T_2 T_1) /\ ((equivalence T_3 T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_4 A B) <=> ((apply T_2 A B) /\ (apply T_3 A B)))))))) => (equivalence T_4 T_1))) ### ConjTree 127
% 0.82/1.01 129. (-. (All R, (((equivalence T_2 T_1) /\ ((equivalence T_3 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_3 A B)))))))) => (equivalence R T_1)))) ### NotAllEx 128
% 0.82/1.01 130. (-. (All R2, (All R, (((equivalence T_2 T_1) /\ ((equivalence R2 T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply R A B) <=> ((apply T_2 A B) /\ (apply R2 A B)))))))) => (equivalence R T_1))))) ### NotAllEx 129
% 0.82/1.01 131. (-. (All R1, (All R2, (All R, (((equivalence R1 T_1) /\ ((equivalence R2 T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply R A B) <=> ((apply R1 A B) /\ (apply R2 A B)))))))) => (equivalence R T_1)))))) ### NotAllEx 130
% 0.82/1.01 132. (-. (All E, (All R1, (All R2, (All R, (((equivalence R1 E) /\ ((equivalence R2 E) /\ (All A, (All B, (((member A E) /\ (member B E)) => ((apply R A B) <=> ((apply R1 A B) /\ (apply R2 A B)))))))) => (equivalence R E))))))) ### NotAllEx 131
% 0.82/1.01 % SZS output end Proof
% 0.82/1.01 (* END-PROOF *)
%------------------------------------------------------------------------------