TSTP Solution File: GRP642+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n024.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 : Sat Jul 16 11:55:23 EDT 2022
% Result : Theorem 79.06s 79.26s
% Output : Proof 79.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% 0.13/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 16:25:48 EDT 2022
% 0.14/0.36 % CPUTime :
% 79.06/79.26 % SZS status Theorem
% 79.06/79.26 (* PROOF-FOUND *)
% 79.06/79.26 (* BEGIN-PROOF *)
% 79.06/79.26 % SZS output start Proof
% 79.06/79.26 1. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 79.06/79.26 2. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 79.06/79.26 3. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 79.06/79.26 4. (m1_group_2 T_1 T_0) (-. (m1_group_2 T_1 T_0)) ### Axiom
% 79.06/79.26 5. (v3_struct_0 T_1) (-. (v3_struct_0 T_1)) ### Axiom
% 79.06/79.26 6. ((-. (v3_struct_0 T_1)) /\ ((v3_group_1 T_1) /\ (l1_group_1 T_1))) (v3_struct_0 T_1) ### ConjTree 5
% 79.06/79.26 7. ((m1_group_2 T_1 T_0) => ((-. (v3_struct_0 T_1)) /\ ((v3_group_1 T_1) /\ (l1_group_1 T_1)))) (v3_struct_0 T_1) (m1_group_2 T_1 T_0) ### Imply 4 6
% 79.06/79.26 8. (All B, ((m1_group_2 B T_0) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))) (m1_group_2 T_1 T_0) (v3_struct_0 T_1) ### All 7
% 79.06/79.26 9. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ (l1_group_1 T_0))) => (All B, ((m1_group_2 B T_0) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B)))))) (v3_struct_0 T_1) (m1_group_2 T_1 T_0) (l1_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 1 2 3 8
% 79.06/79.26 10. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (l1_group_1 T_0) (m1_group_2 T_1 T_0) (v3_struct_0 T_1) ### All 9
% 79.06/79.26 11. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 79.06/79.26 12. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 79.06/79.26 13. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 79.06/79.26 14. (m1_group_2 T_1 T_0) (-. (m1_group_2 T_1 T_0)) ### Axiom
% 79.06/79.26 15. (-. (l1_group_1 T_1)) (l1_group_1 T_1) ### Axiom
% 79.06/79.26 16. ((-. (v3_struct_0 T_1)) /\ ((v3_group_1 T_1) /\ (l1_group_1 T_1))) (-. (l1_group_1 T_1)) ### ConjTree 15
% 79.06/79.26 17. ((m1_group_2 T_1 T_0) => ((-. (v3_struct_0 T_1)) /\ ((v3_group_1 T_1) /\ (l1_group_1 T_1)))) (-. (l1_group_1 T_1)) (m1_group_2 T_1 T_0) ### Imply 14 16
% 79.06/79.26 18. (All B, ((m1_group_2 B T_0) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))) (m1_group_2 T_1 T_0) (-. (l1_group_1 T_1)) ### All 17
% 79.06/79.26 19. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ (l1_group_1 T_0))) => (All B, ((m1_group_2 B T_0) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B)))))) (-. (l1_group_1 T_1)) (m1_group_2 T_1 T_0) (l1_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 11 12 13 18
% 79.06/79.26 20. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (l1_group_1 T_0) (m1_group_2 T_1 T_0) (-. (l1_group_1 T_1)) ### All 19
% 79.06/79.26 21. (-. (l1_struct_0 T_1)) (l1_struct_0 T_1) ### Axiom
% 79.06/79.26 22. ((l1_group_1 T_1) => (l1_struct_0 T_1)) (-. (l1_struct_0 T_1)) (m1_group_2 T_1 T_0) (l1_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) ### Imply 20 21
% 79.06/79.26 23. (All A, ((l1_group_1 A) => (l1_struct_0 A))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (l1_group_1 T_0) (m1_group_2 T_1 T_0) (-. (l1_struct_0 T_1)) ### All 22
% 79.06/79.26 24. (v1_xboole_0 T_2) (-. (v1_xboole_0 T_2)) ### Axiom
% 79.06/79.26 25. (T_2 != T_2) ### Refl(=)
% 79.06/79.26 26. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 79.06/79.26 27. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 79.06/79.26 28. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 79.06/79.26 29. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 79.06/79.26 30. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 79.06/79.26 31. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 79.06/79.26 32. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 79.06/79.26 33. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 79.06/79.26 34. (-. (v1_funct_1 (k1_latsubgr T_0))) (v1_funct_1 (k1_latsubgr T_0)) ### Axiom
% 79.06/79.26 35. ((v1_funct_1 (k1_latsubgr T_0)) /\ ((v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))))) (-. (v1_funct_1 (k1_latsubgr T_0))) ### ConjTree 34
% 79.06/79.26 36. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => ((v1_funct_1 (k1_latsubgr T_0)) /\ ((v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))))) (-. (v1_funct_1 (k1_latsubgr T_0))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 30 31 32 33 35
% 79.06/79.26 37. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (-. (v1_funct_1 (k1_latsubgr T_0))) ### All 36
% 79.06/79.26 38. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 79.06/79.26 39. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 79.06/79.26 40. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 79.06/79.26 41. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 79.06/79.26 42. (-. (v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) (v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) ### Axiom
% 79.06/79.26 43. ((v1_funct_1 (k1_latsubgr T_0)) /\ ((v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))))) (-. (v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) ### ConjTree 42
% 79.06/79.26 44. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => ((v1_funct_1 (k1_latsubgr T_0)) /\ ((v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))))) (-. (v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 38 39 40 41 43
% 79.06/79.26 45. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (-. (v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) ### All 44
% 79.06/79.26 46. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 79.06/79.26 47. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 79.06/79.26 48. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 79.06/79.26 49. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 79.06/79.26 50. (-. (m1_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) (m1_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) ### Axiom
% 79.06/79.26 51. (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) (-. (m1_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) ### Definition-Pseudo(m2_relset_1) 50
% 79.06/79.26 52. ((v1_funct_1 (k1_latsubgr T_0)) /\ ((v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))))) (-. (m1_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) ### ConjTree 51
% 79.06/79.26 53. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => ((v1_funct_1 (k1_latsubgr T_0)) /\ ((v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))))) (-. (m1_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 46 47 48 49 52
% 79.06/79.26 54. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (-. (m1_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) ### All 53
% 79.12/79.32 55. (-. (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0)))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) ### Definition-Pseudo(m2_relset_1) 54
% 79.12/79.32 56. ((k1_latsubgr T_0) != (k1_latsubgr T_0)) ### Refl(=)
% 79.12/79.32 57. (v1_group_1 T_1) (-. (v1_group_1 T_1)) ### Axiom
% 79.12/79.32 58. (m1_group_2 T_1 T_0) (-. (m1_group_2 T_1 T_0)) ### Axiom
% 79.12/79.32 59. ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (u1_struct_0 T_1)) ### Sym(=)
% 79.12/79.32 60. (((v1_group_1 T_1) /\ (m1_group_2 T_1 T_0)) => ((k1_funct_1 (k1_latsubgr T_0) T_1) = (u1_struct_0 T_1))) ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ### DisjTree 57 58 59
% 79.12/79.32 61. (All C, (((v1_group_1 C) /\ (m1_group_2 C T_0)) => ((k1_funct_1 (k1_latsubgr T_0) C) = (u1_struct_0 C)))) (v1_group_1 T_1) (m1_group_2 T_1 T_0) ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) ### All 60
% 79.12/79.32 62. (((k1_latsubgr T_0) = (k1_latsubgr T_0)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C T_0)) => ((k1_funct_1 (k1_latsubgr T_0) C) = (u1_struct_0 C))))) ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ### Equiv 56 61
% 79.12/79.32 63. (((v1_funct_1 (k1_latsubgr T_0)) /\ ((v1_funct_2 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 (k1_latsubgr T_0) (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))))) => (((k1_latsubgr T_0) = (k1_latsubgr T_0)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C T_0)) => ((k1_funct_1 (k1_latsubgr T_0) C) = (u1_struct_0 C)))))) (v1_group_1 T_1) (m1_group_2 T_1 T_0) ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) ### DisjTree 37 45 55 62
% 79.12/79.32 64. (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 B (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))))) => ((B = (k1_latsubgr T_0)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C T_0)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ### All 63
% 79.12/79.32 65. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))) /\ (m2_relset_1 B (k1_group_3 T_0) (k1_zfmisc_1 (u1_struct_0 T_0))))) => ((B = (k1_latsubgr T_0)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C T_0)) => ((k1_funct_1 B C) = (u1_struct_0 C)))))))) (v1_group_1 T_1) (m1_group_2 T_1 T_0) ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 26 27 28 29 64
% 79.12/79.32 66. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) ((u1_struct_0 T_1) != (k1_funct_1 (k1_latsubgr T_0) T_1)) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ### All 65
% 79.12/79.32 67. ((k1_xboole_0) != (k1_xboole_0)) ### NotEqual
% 79.12/79.32 68. ((k1_xboole_0) != (u1_struct_0 T_1)) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (k1_xboole_0)) (v1_group_1 T_1) (m1_group_2 T_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) ### Trans-sym 66 67
% 79.12/79.32 69. (T_2 != (u1_struct_0 T_1)) (T_2 = (k1_xboole_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (k1_xboole_0)) ### Trans 25 68
% 79.12/79.32 70. (-. (v1_xboole_0 (u1_struct_0 T_1))) (v1_xboole_0 T_2) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (k1_xboole_0)) (v1_group_1 T_1) (m1_group_2 T_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (T_2 = (k1_xboole_0)) ### P-NotP 69
% 79.12/79.32 71. ((v1_xboole_0 T_2) => (T_2 = (k1_xboole_0))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (k1_xboole_0)) (-. (v1_xboole_0 (u1_struct_0 T_1))) (v1_xboole_0 T_2) ### Imply 24 70
% 79.12/79.34 72. (((-. (v3_struct_0 T_1)) /\ (l1_struct_0 T_1)) => (-. (v1_xboole_0 (u1_struct_0 T_1)))) (v1_xboole_0 T_2) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (k1_xboole_0)) (v1_group_1 T_1) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (v4_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) ((v1_xboole_0 T_2) => (T_2 = (k1_xboole_0))) (All A, ((l1_group_1 A) => (l1_struct_0 A))) (m1_group_2 T_1 T_0) (l1_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) ### DisjTree 10 23 71
% 79.12/79.34 73. (All A, (((-. (v3_struct_0 A)) /\ (l1_struct_0 A)) => (-. (v1_xboole_0 (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (l1_group_1 T_0) (m1_group_2 T_1 T_0) (All A, ((l1_group_1 A) => (l1_struct_0 A))) ((v1_xboole_0 T_2) => (T_2 = (k1_xboole_0))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (v4_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (v1_group_1 T_1) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (k1_xboole_0)) (v1_xboole_0 T_2) ### All 72
% 79.12/79.34 74. (All A, ((v1_xboole_0 A) => (A = (k1_xboole_0)))) (v1_xboole_0 T_2) ((k1_funct_1 (k1_latsubgr T_0) T_1) = (k1_xboole_0)) (v1_group_1 T_1) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (v4_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (All A, ((l1_group_1 A) => (l1_struct_0 A))) (m1_group_2 T_1 T_0) (l1_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_struct_0 A)) => (-. (v1_xboole_0 (u1_struct_0 A))))) ### All 73
% 79.12/79.34 75. (-. (((v1_group_1 T_1) /\ (m1_group_2 T_1 T_0)) => ((k1_funct_1 (k1_latsubgr T_0) T_1) != (k1_xboole_0)))) (All A, (((-. (v3_struct_0 A)) /\ (l1_struct_0 A)) => (-. (v1_xboole_0 (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (l1_group_1 T_0) (All A, ((l1_group_1 A) => (l1_struct_0 A))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (v4_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (v1_xboole_0 T_2) (All A, ((v1_xboole_0 A) => (A = (k1_xboole_0)))) ### ConjTree 74
% 79.12/79.34 76. (-. (All B, (((v1_group_1 B) /\ (m1_group_2 B T_0)) => ((k1_funct_1 (k1_latsubgr T_0) B) != (k1_xboole_0))))) (All A, ((v1_xboole_0 A) => (A = (k1_xboole_0)))) (v1_xboole_0 T_2) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (v4_group_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (All A, ((l1_group_1 A) => (l1_struct_0 A))) (l1_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_struct_0 A)) => (-. (v1_xboole_0 (u1_struct_0 A))))) ### NotAllEx 75
% 79.12/79.34 77. (-. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B T_0)) => ((k1_funct_1 (k1_latsubgr T_0) B) != (k1_xboole_0)))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_struct_0 A)) => (-. (v1_xboole_0 (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (All A, ((l1_group_1 A) => (l1_struct_0 A))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (v1_xboole_0 T_2) (All A, ((v1_xboole_0 A) => (A = (k1_xboole_0)))) ### ConjTree 76
% 79.12/79.34 78. (-. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => ((k1_funct_1 (k1_latsubgr A) B) != (k1_xboole_0))))))) (All A, ((v1_xboole_0 A) => (A = (k1_xboole_0)))) (v1_xboole_0 T_2) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (All A, ((l1_group_1 A) => (l1_struct_0 A))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_struct_0 A)) => (-. (v1_xboole_0 (u1_struct_0 A))))) ### NotAllEx 77
% 79.12/79.34 79. (Ex A, (v1_xboole_0 A)) (All A, (((-. (v3_struct_0 A)) /\ (l1_struct_0 A)) => (-. (v1_xboole_0 (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ (l1_group_1 A))) => (All B, ((m1_group_2 B A) => ((-. (v3_struct_0 B)) /\ ((v3_group_1 B) /\ (l1_group_1 B))))))) (All A, ((l1_group_1 A) => (l1_struct_0 A))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_funct_1 B) /\ ((v1_funct_2 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 B (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))) => ((B = (k1_latsubgr A)) <=> (All C, (((v1_group_1 C) /\ (m1_group_2 C A)) => ((k1_funct_1 B C) = (u1_struct_0 C))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => ((v1_funct_1 (k1_latsubgr A)) /\ ((v1_funct_2 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))) /\ (m2_relset_1 (k1_latsubgr A) (k1_group_3 A) (k1_zfmisc_1 (u1_struct_0 A))))))) (All A, ((v1_xboole_0 A) => (A = (k1_xboole_0)))) (-. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => ((k1_funct_1 (k1_latsubgr A) B) != (k1_xboole_0))))))) ### Exists 78
% 79.12/79.34 % SZS output end Proof
% 79.12/79.34 (* END-PROOF *)
%------------------------------------------------------------------------------