TSTP Solution File: TOP023+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : TOP023+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 : n032.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 : Thu Jul 21 21:35:22 EDT 2022
% Result : Theorem 5.09s 5.32s
% Output : Proof 5.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : TOP023+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.08 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Sun May 29 08:01:56 EDT 2022
% 0.07/0.27 % CPUTime :
% 5.09/5.32 % SZS status Theorem
% 5.09/5.32 (* PROOF-FOUND *)
% 5.09/5.32 (* BEGIN-PROOF *)
% 5.09/5.32 % SZS output start Proof
% 5.09/5.32 1. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 5.09/5.32 2. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 5.09/5.32 3. (T_1 != T_1) ### Refl(=)
% 5.09/5.32 4. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 5.09/5.32 5. (-. (m1_subset_1 (u1_pre_topc T_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0))))) (m1_subset_1 (u1_pre_topc T_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0)))) ### Axiom
% 5.09/5.32 6. ((l1_pre_topc T_0) => (m1_subset_1 (u1_pre_topc T_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0))))) (-. (m1_subset_1 (u1_pre_topc T_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0))))) (l1_pre_topc T_0) ### Imply 4 5
% 5.09/5.32 7. (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) (-. (m1_subset_1 (u1_pre_topc T_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0))))) ### All 6
% 5.09/5.32 8. ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) != (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) ### Sym(=)
% 5.09/5.32 9. ((u1_struct_0 T_2) != (u1_struct_0 T_0)) ((u1_struct_0 T_0) = (u1_struct_0 T_2)) ### Sym(=)
% 5.09/5.32 10. (((u1_struct_0 T_0) = (u1_struct_0 T_2)) /\ ((u1_pre_topc T_0) = (u1_pre_topc T_2))) ((u1_struct_0 T_2) != (u1_struct_0 T_0)) ### And 9
% 5.09/5.32 11. (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) => (((u1_struct_0 T_0) = (u1_struct_0 T_2)) /\ ((u1_pre_topc T_0) = (u1_pre_topc T_2)))) ((u1_struct_0 T_2) != (u1_struct_0 T_0)) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ### Imply 8 10
% 5.09/5.32 12. (All D, (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) D)) => (((u1_struct_0 T_0) = (u1_struct_0 T_2)) /\ ((u1_pre_topc T_0) = D)))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((u1_struct_0 T_2) != (u1_struct_0 T_0)) ### All 11
% 5.09/5.32 13. (All C, (All D, (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc C D)) => (((u1_struct_0 T_0) = C) /\ ((u1_pre_topc T_0) = D))))) ((u1_struct_0 T_2) != (u1_struct_0 T_0)) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ### All 12
% 5.09/5.32 14. ((m1_subset_1 (u1_pre_topc T_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0)))) => (All C, (All D, (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc C D)) => (((u1_struct_0 T_0) = C) /\ ((u1_pre_topc T_0) = D)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((u1_struct_0 T_2) != (u1_struct_0 T_0)) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ### Imply 7 13
% 5.09/5.32 15. (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0)))) => (All C, (All D, (((g1_pre_topc (u1_struct_0 T_0) B) = (g1_pre_topc C D)) => (((u1_struct_0 T_0) = C) /\ (B = D))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((u1_struct_0 T_2) != (u1_struct_0 T_0)) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ### All 14
% 5.09/5.32 16. (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((u1_struct_0 T_2) != (u1_struct_0 T_0)) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ### All 15
% 5.09/5.32 17. ((k1_zfmisc_1 (u1_struct_0 T_2)) != (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ### NotEqual 16
% 5.09/5.32 18. (-. (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0)))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ### P-NotP 3 17
% 5.09/5.32 19. (l1_pre_topc T_2) (-. (l1_pre_topc T_2)) ### Axiom
% 5.09/5.32 20. (l1_pre_topc T_2) (-. (l1_pre_topc T_2)) ### Axiom
% 5.09/5.32 21. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 5.09/5.32 22. (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (-. (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2)))) ### Axiom
% 5.09/5.32 23. (v1_tsp_2 T_1 T_2) (-. (v1_tsp_2 T_1 T_2)) ### Axiom
% 5.09/5.32 24. (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (-. (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2)))) ### Axiom
% 5.09/5.32 25. ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) != (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ### Axiom
% 5.09/5.32 26. (T_1 != T_1) ### Refl(=)
% 5.09/5.32 27. (v1_tsp_1 T_1 T_2) (-. (v1_tsp_1 T_1 T_2)) ### Axiom
% 5.09/5.32 28. (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_1 T_1 T_0) ### Axiom
% 5.09/5.32 29. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((T_1 = T_1) /\ (v1_tsp_1 T_1 T_2))) => (v1_tsp_1 T_1 T_0))) (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_1 T_1 T_2) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) ### DisjTree 18 25 26 27 28
% 5.09/5.32 30. (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((T_1 = D) /\ (v1_tsp_1 T_1 T_2))) => (v1_tsp_1 D T_0)))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (v1_tsp_1 T_1 T_2) (-. (v1_tsp_1 T_1 T_0)) ### All 29
% 5.09/5.32 31. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((T_1 = D) /\ (v1_tsp_1 T_1 T_2))) => (v1_tsp_1 D T_0))))) (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_1 T_1 T_2) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) ### Imply 24 30
% 5.09/5.32 32. (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D T_0)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (v1_tsp_1 T_1 T_2) (-. (v1_tsp_1 T_1 T_0)) ### All 31
% 5.18/5.36 33. ((v1_tsp_1 T_1 T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski T_1 C)) => (T_1 = C))))) (-. (v1_tsp_1 T_1 T_0)) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D T_0)))))) ### And 32
% 5.18/5.36 34. ((v1_tsp_2 T_1 T_2) <=> ((v1_tsp_1 T_1 T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski T_1 C)) => (T_1 = C)))))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D T_0)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_2 T_1 T_2) ### Equiv 23 33
% 5.18/5.36 35. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 T_1 T_2) <=> ((v1_tsp_1 T_1 T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski T_1 C)) => (T_1 = C))))))) (v1_tsp_2 T_1 T_2) (-. (v1_tsp_1 T_1 T_0)) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D T_0)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) ### Imply 22 34
% 5.18/5.36 36. (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D T_0)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_2 T_1 T_2) ### All 35
% 5.18/5.36 37. ((l1_pre_topc T_0) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D T_0))))))) (v1_tsp_2 T_1 T_2) (-. (v1_tsp_1 T_1 T_0)) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C)))))))) (l1_pre_topc T_0) ### Imply 21 36
% 5.18/5.36 38. (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D B)))))))) (l1_pre_topc T_0) (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_2 T_1 T_2) ### All 37
% 5.18/5.36 39. ((l1_pre_topc T_2) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_2))) => (v1_tsp_1 D B))))))))) (v1_tsp_2 T_1 T_2) (-. (v1_tsp_1 T_1 T_0)) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C)))))))) (l1_pre_topc T_0) (l1_pre_topc T_2) ### Imply 20 38
% 5.18/5.36 40. (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (l1_pre_topc T_0) (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_2 T_1 T_2) ### All 39
% 5.18/5.38 41. ((l1_pre_topc T_2) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C))))))))) (v1_tsp_2 T_1 T_2) (-. (v1_tsp_1 T_1 T_0)) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) ### Imply 19 40
% 5.18/5.38 42. (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (-. (v1_tsp_1 T_1 T_0)) (v1_tsp_2 T_1 T_2) ### All 41
% 5.18/5.38 43. (l1_pre_topc T_2) (-. (l1_pre_topc T_2)) ### Axiom
% 5.18/5.38 44. (l1_pre_topc T_2) (-. (l1_pre_topc T_2)) ### Axiom
% 5.18/5.38 45. (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (-. (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2)))) ### Axiom
% 5.18/5.38 46. (v1_tsp_2 T_1 T_2) (-. (v1_tsp_2 T_1 T_2)) ### Axiom
% 5.18/5.38 47. (T_3 != T_3) ### Refl(=)
% 5.18/5.38 48. ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) != (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) ### Sym(=)
% 5.18/5.38 49. ((u1_struct_0 T_0) != (u1_struct_0 T_2)) ((u1_struct_0 T_0) = (u1_struct_0 T_2)) ### Axiom
% 5.18/5.38 50. (((u1_struct_0 T_0) = (u1_struct_0 T_2)) /\ ((u1_pre_topc T_0) = (u1_pre_topc T_2))) ((u1_struct_0 T_0) != (u1_struct_0 T_2)) ### And 49
% 5.18/5.38 51. (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) => (((u1_struct_0 T_0) = (u1_struct_0 T_2)) /\ ((u1_pre_topc T_0) = (u1_pre_topc T_2)))) ((u1_struct_0 T_0) != (u1_struct_0 T_2)) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ### Imply 48 50
% 5.18/5.38 52. (All D, (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) D)) => (((u1_struct_0 T_0) = (u1_struct_0 T_2)) /\ ((u1_pre_topc T_0) = D)))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((u1_struct_0 T_0) != (u1_struct_0 T_2)) ### All 51
% 5.18/5.38 53. (All C, (All D, (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc C D)) => (((u1_struct_0 T_0) = C) /\ ((u1_pre_topc T_0) = D))))) ((u1_struct_0 T_0) != (u1_struct_0 T_2)) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ### All 52
% 5.18/5.38 54. ((m1_subset_1 (u1_pre_topc T_0) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0)))) => (All C, (All D, (((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc C D)) => (((u1_struct_0 T_0) = C) /\ ((u1_pre_topc T_0) = D)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((u1_struct_0 T_0) != (u1_struct_0 T_2)) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ### Imply 7 53
% 5.18/5.38 55. (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 T_0)))) => (All C, (All D, (((g1_pre_topc (u1_struct_0 T_0) B) = (g1_pre_topc C D)) => (((u1_struct_0 T_0) = C) /\ (B = D))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((u1_struct_0 T_0) != (u1_struct_0 T_2)) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ### All 54
% 5.18/5.38 56. (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((u1_struct_0 T_0) != (u1_struct_0 T_2)) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ### All 55
% 5.18/5.38 57. ((k1_zfmisc_1 (u1_struct_0 T_0)) != (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ### NotEqual 56
% 5.18/5.38 58. (-. (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_2)))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ### P-NotP 47 57
% 5.18/5.38 59. (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (-. (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0)))) ### Axiom
% 5.18/5.38 60. ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) ((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) != (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) ### Sym(=)
% 5.18/5.38 61. (T_3 != T_3) ### Refl(=)
% 5.18/5.38 62. (v1_tsp_1 T_3 T_0) (-. (v1_tsp_1 T_3 T_0)) ### Axiom
% 5.18/5.38 63. (-. (v1_tsp_1 T_3 T_2)) (v1_tsp_1 T_3 T_2) ### Axiom
% 5.18/5.38 64. ((m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((T_3 = T_3) /\ (v1_tsp_1 T_3 T_0))) => (v1_tsp_1 T_3 T_2))) (-. (v1_tsp_1 T_3 T_2)) (v1_tsp_1 T_3 T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) ### DisjTree 58 60 61 62 63
% 5.18/5.38 65. (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((T_3 = D) /\ (v1_tsp_1 T_3 T_0))) => (v1_tsp_1 D T_2)))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (v1_tsp_1 T_3 T_0) (-. (v1_tsp_1 T_3 T_2)) ### All 64
% 5.21/5.41 66. ((m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((T_3 = D) /\ (v1_tsp_1 T_3 T_0))) => (v1_tsp_1 D T_2))))) (-. (v1_tsp_1 T_3 T_2)) (v1_tsp_1 T_3 T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) ### Imply 59 65
% 5.21/5.41 67. (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (v1_tsp_1 T_3 T_0) (-. (v1_tsp_1 T_3 T_2)) ### All 66
% 5.21/5.41 68. (r1_tarski T_1 T_3) (-. (r1_tarski T_1 T_3)) ### Axiom
% 5.21/5.41 69. (T_1 != T_3) (T_1 = T_3) ### Axiom
% 5.21/5.41 70. ((m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 T_3 T_2) /\ (r1_tarski T_1 T_3)) => (T_1 = T_3))) (T_1 != T_3) (r1_tarski T_1 T_3) (v1_tsp_1 T_3 T_0) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) ### DisjTree 58 67 68 69
% 5.21/5.41 71. (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski T_1 C)) => (T_1 = C)))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (v1_tsp_1 T_3 T_0) (r1_tarski T_1 T_3) (T_1 != T_3) ### All 70
% 5.21/5.41 72. ((v1_tsp_1 T_1 T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski T_1 C)) => (T_1 = C))))) (T_1 != T_3) (r1_tarski T_1 T_3) (v1_tsp_1 T_3 T_0) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) ### And 71
% 5.21/5.41 73. ((v1_tsp_2 T_1 T_2) <=> ((v1_tsp_1 T_1 T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski T_1 C)) => (T_1 = C)))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (v1_tsp_1 T_3 T_0) (r1_tarski T_1 T_3) (T_1 != T_3) (v1_tsp_2 T_1 T_2) ### Equiv 46 72
% 5.21/5.41 74. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 T_1 T_2) <=> ((v1_tsp_1 T_1 T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski T_1 C)) => (T_1 = C))))))) (v1_tsp_2 T_1 T_2) (T_1 != T_3) (r1_tarski T_1 T_3) (v1_tsp_1 T_3 T_0) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) ### Imply 45 73
% 5.21/5.41 75. (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (v1_tsp_1 T_3 T_0) (r1_tarski T_1 T_3) (T_1 != T_3) (v1_tsp_2 T_1 T_2) ### All 74
% 5.21/5.41 76. ((l1_pre_topc T_2) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_2))) => ((v1_tsp_2 B T_2) <=> ((v1_tsp_1 B T_2) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (((v1_tsp_1 C T_2) /\ (r1_tarski B C)) => (B = C))))))))) (v1_tsp_2 T_1 T_2) (T_1 != T_3) (r1_tarski T_1 T_3) (v1_tsp_1 T_3 T_0) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (l1_pre_topc T_2) ### Imply 44 75
% 5.21/5.43 77. (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2)))))) (v1_tsp_1 T_3 T_0) (r1_tarski T_1 T_3) (T_1 != T_3) (v1_tsp_2 T_1 T_2) ### All 76
% 5.21/5.43 78. ((l1_pre_topc T_2) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_2))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D T_2))))))) (v1_tsp_2 T_1 T_2) (T_1 != T_3) (r1_tarski T_1 T_3) (v1_tsp_1 T_3 T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) ### Imply 43 77
% 5.21/5.43 79. (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B)))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (v1_tsp_1 T_3 T_0) (r1_tarski T_1 T_3) (T_1 != T_3) (v1_tsp_2 T_1 T_2) ### All 78
% 5.21/5.43 80. (-. ((m1_subset_1 T_3 (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 T_3 T_0) /\ (r1_tarski T_1 T_3)) => (T_1 = T_3)))) (v1_tsp_2 T_1 T_2) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B)))))))) ### ConjTree 79
% 5.21/5.43 81. (-. (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski T_1 C)) => (T_1 = C))))) (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B)))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (v1_tsp_2 T_1 T_2) ### NotAllEx 80
% 5.21/5.43 82. (-. ((v1_tsp_1 T_1 T_0) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski T_1 C)) => (T_1 = C)))))) (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B)))))))) (v1_tsp_2 T_1 T_2) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) ### NotAnd 42 81
% 5.21/5.43 83. (T_1 = T_4) (T_1 != T_4) ### Axiom
% 5.21/5.43 84. (T_0 != T_0) ### Refl(=)
% 5.21/5.43 85. (-. (v1_tsp_2 T_4 T_0)) (v1_tsp_2 T_1 T_0) (T_1 = T_4) ### P-NotP 83 84
% 5.21/5.43 86. ((v1_tsp_2 T_1 T_0) <=> ((v1_tsp_1 T_1 T_0) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski T_1 C)) => (T_1 = C)))))) (T_1 = T_4) (-. (v1_tsp_2 T_4 T_0)) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (v1_tsp_2 T_1 T_2) (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B)))))))) ### Equiv 82 85
% 5.26/5.43 87. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v1_tsp_2 T_1 T_0) <=> ((v1_tsp_1 T_1 T_0) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski T_1 C)) => (T_1 = C))))))) (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B)))))))) (v1_tsp_2 T_1 T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (-. (v1_tsp_2 T_4 T_0)) (T_1 = T_4) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (l1_pre_topc T_0) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) ### Imply 18 86
% 5.26/5.43 88. (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v1_tsp_2 B T_0) <=> ((v1_tsp_1 B T_0) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski B C)) => (B = C)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (l1_pre_topc T_0) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (T_1 = T_4) (-. (v1_tsp_2 T_4 T_0)) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (v1_tsp_2 T_1 T_2) (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B)))))))) ### All 87
% 5.26/5.43 89. ((l1_pre_topc T_0) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C T_0))) => (v1_tsp_1 D B))))))))) (v1_tsp_2 T_1 T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (-. (v1_tsp_2 T_4 T_0)) (T_1 = T_4) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v1_tsp_2 B T_0) <=> ((v1_tsp_1 B T_0) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski B C)) => (B = C)))))))) (l1_pre_topc T_0) ### Imply 2 88
% 5.26/5.43 90. (l1_pre_topc T_0) (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v1_tsp_2 B T_0) <=> ((v1_tsp_1 B T_0) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski B C)) => (B = C)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (T_1 = T_4) (-. (v1_tsp_2 T_4 T_0)) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (v1_tsp_2 T_1 T_2) ### All 89
% 5.26/5.43 91. ((l1_pre_topc T_0) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v1_tsp_2 B T_0) <=> ((v1_tsp_1 B T_0) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_0))) => (((v1_tsp_1 C T_0) /\ (r1_tarski B C)) => (B = C))))))))) (v1_tsp_2 T_1 T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (-. (v1_tsp_2 T_4 T_0)) (T_1 = T_4) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (l1_pre_topc T_0) ### Imply 1 90
% 5.26/5.43 92. (l1_pre_topc T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (T_1 = T_4) (-. (v1_tsp_2 T_4 T_0)) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (v1_tsp_2 T_1 T_2) ### All 91
% 5.26/5.43 93. (-. ((m1_subset_1 T_4 (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((T_1 = T_4) /\ (v1_tsp_2 T_1 T_2))) => (v1_tsp_2 T_4 T_0)))) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (l1_pre_topc T_0) ### ConjTree 92
% 5.26/5.43 94. (-. (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((T_1 = D) /\ (v1_tsp_2 T_1 T_2))) => (v1_tsp_2 D T_0))))) (l1_pre_topc T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) ### NotAllEx 93
% 5.26/5.44 95. (-. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((T_1 = D) /\ (v1_tsp_2 T_1 T_2))) => (v1_tsp_2 D T_0)))))) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (l1_pre_topc T_0) ### NotImply 94
% 5.26/5.44 96. (-. (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_2 C T_2))) => (v1_tsp_2 D T_0))))))) (l1_pre_topc T_0) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) ### NotAllEx 95
% 5.26/5.44 97. (-. ((l1_pre_topc T_0) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 T_0))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 T_0) (u1_pre_topc T_0))) /\ ((C = D) /\ (v1_tsp_2 C T_2))) => (v1_tsp_2 D T_0)))))))) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ### NotImply 96
% 5.26/5.44 98. (-. (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_2 C T_2))) => (v1_tsp_2 D B))))))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (l1_pre_topc T_2) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) ### NotAllEx 97
% 5.27/5.45 99. (-. ((l1_pre_topc T_2) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 T_2))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 T_2) (u1_pre_topc T_2)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_2 C T_2))) => (v1_tsp_2 D B)))))))))) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) ### NotImply 98
% 5.27/5.45 100. (-. (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_2 C A))) => (v1_tsp_2 D B))))))))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 (k1_zfmisc_1 A))) => (All C, (All D, (((g1_pre_topc A B) = (g1_pre_topc C D)) => ((A = C) /\ (B = D)))))))) (All A, ((l1_pre_topc A) => (m1_subset_1 (u1_pre_topc A) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 A)))))) (All A, ((l1_pre_topc A) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v1_tsp_2 B A) <=> ((v1_tsp_1 B A) /\ (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (((v1_tsp_1 C A) /\ (r1_tarski B C)) => (B = C)))))))))) (All A, ((l1_pre_topc A) => (All B, ((l1_pre_topc B) => (All C, ((m1_subset_1 C (k1_zfmisc_1 (u1_struct_0 A))) => (All D, ((m1_subset_1 D (k1_zfmisc_1 (u1_struct_0 B))) => ((((g1_pre_topc (u1_struct_0 A) (u1_pre_topc A)) = (g1_pre_topc (u1_struct_0 B) (u1_pre_topc B))) /\ ((C = D) /\ (v1_tsp_1 C A))) => (v1_tsp_1 D B)))))))))) ### NotAllEx 99
% 5.27/5.45 % SZS output end Proof
% 5.27/5.45 (* END-PROOF *)
%------------------------------------------------------------------------------