TSTP Solution File: TOP025+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : TOP025+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 : n028.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 10.63s 10.82s
% Output : Proof 10.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : TOP025+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 04:12:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 10.63/10.82 % SZS status Theorem
% 10.63/10.82 (* PROOF-FOUND *)
% 10.63/10.82 (* BEGIN-PROOF *)
% 10.63/10.82 % SZS output start Proof
% 10.63/10.82 1. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 10.63/10.82 2. (v2_pre_topc T_0) (-. (v2_pre_topc T_0)) ### Axiom
% 10.63/10.82 3. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 10.63/10.82 4. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 10.63/10.82 5. (v2_pre_topc T_0) (-. (v2_pre_topc T_0)) ### Axiom
% 10.63/10.82 6. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 10.63/10.82 7. (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_0)))) ### Axiom
% 10.63/10.82 8. (v3_pre_topc T_1 T_0) (-. (v3_pre_topc T_1 T_0)) ### Axiom
% 10.63/10.82 9. (-. (r1_tarski T_1 T_1)) ### Refl(r1_tarski)
% 10.63/10.82 10. (-. (m1_subset_1 T_1 (k1_zfmisc_1 T_1))) (m1_subset_1 T_1 (k1_zfmisc_1 T_1)) ### Axiom
% 10.63/10.82 11. ((m1_subset_1 T_1 (k1_zfmisc_1 T_1)) <=> (r1_tarski T_1 T_1)) (-. (m1_subset_1 T_1 (k1_zfmisc_1 T_1))) ### Equiv 9 10
% 10.63/10.82 12. (All B, ((m1_subset_1 T_1 (k1_zfmisc_1 B)) <=> (r1_tarski T_1 B))) (-. (m1_subset_1 T_1 (k1_zfmisc_1 T_1))) ### All 11
% 10.63/10.82 13. (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (-. (m1_subset_1 T_1 (k1_zfmisc_1 T_1))) ### All 12
% 10.63/10.82 14. (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_0)))) ### Axiom
% 10.63/10.82 15. (v1_tsp_2 T_1 T_0) (-. (v1_tsp_2 T_1 T_0)) ### Axiom
% 10.63/10.82 16. (-. (T_1 != T_1)) (T_1 != T_1) ### Axiom
% 10.63/10.82 17. ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) ((u1_struct_0 T_0) != (k3_tex_4 T_0 T_1)) ### Sym(=)
% 10.63/10.82 18. ((k1_zfmisc_1 (u1_struct_0 T_0)) != (k1_zfmisc_1 (k3_tex_4 T_0 T_1))) ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) ### NotEqual 17
% 10.63/10.82 19. (-. (m1_subset_1 T_1 (k1_zfmisc_1 (k3_tex_4 T_0 T_1)))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) (-. (T_1 != T_1)) ### P-NotP 16 18
% 10.63/10.82 20. (-. (T_1 != T_1)) (T_1 != T_1) ### Axiom
% 10.63/10.82 21. (-. (v1_tex_2 T_1 (k1_zfmisc_1 (k3_tex_4 T_0 T_1)))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) (-. (T_1 != T_1)) ### P-NotP 20 18
% 10.63/10.82 22. ((k3_tex_4 T_0 T_1) = T_1) (T_1 != (k3_tex_4 T_0 T_1)) ### Sym(=)
% 10.63/10.82 23. ((v1_tex_2 T_1 (k1_zfmisc_1 (k3_tex_4 T_0 T_1))) <=> (T_1 != (k3_tex_4 T_0 T_1))) ((k3_tex_4 T_0 T_1) = T_1) (-. (T_1 != T_1)) ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ### Equiv 21 22
% 10.63/10.82 24. ((m1_subset_1 T_1 (k1_zfmisc_1 (k3_tex_4 T_0 T_1))) => ((v1_tex_2 T_1 (k1_zfmisc_1 (k3_tex_4 T_0 T_1))) <=> (T_1 != (k3_tex_4 T_0 T_1)))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = T_1) (-. (T_1 != T_1)) ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ### Imply 19 23
% 10.63/10.82 25. (All B, ((m1_subset_1 B (k1_zfmisc_1 (k3_tex_4 T_0 T_1))) => ((v1_tex_2 B (k1_zfmisc_1 (k3_tex_4 T_0 T_1))) <=> (B != (k3_tex_4 T_0 T_1))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) (-. (T_1 != T_1)) ((k3_tex_4 T_0 T_1) = T_1) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ### All 24
% 10.63/10.82 26. (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = T_1) (-. (T_1 != T_1)) ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ### All 25
% 10.63/10.82 27. ((v1_tsp_1 T_1 T_0) /\ ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (-. (T_1 != T_1)) ((k3_tex_4 T_0 T_1) = T_1) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) ### And 26
% 10.63/10.82 28. ((v1_tsp_2 T_1 T_0) <=> ((v1_tsp_1 T_1 T_0) /\ ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0)))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = T_1) (-. (T_1 != T_1)) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v1_tsp_2 T_1 T_0) ### Equiv 15 27
% 10.63/10.82 29. ((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) /\ ((k3_tex_4 T_0 T_1) = (u1_struct_0 T_0))))) (v1_tsp_2 T_1 T_0) (-. (T_1 != T_1)) ((k3_tex_4 T_0 T_1) = T_1) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ### Imply 14 28
% 10.63/10.82 30. (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = T_1) (-. (T_1 != T_1)) (v1_tsp_2 T_1 T_0) ### All 29
% 10.63/10.82 31. (T_1 != T_1) ### Refl(=)
% 10.63/10.82 32. ((v1_tex_2 T_1 (k1_zfmisc_1 T_1)) <=> (T_1 != T_1)) (v1_tsp_2 T_1 T_0) ((k3_tex_4 T_0 T_1) = T_1) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) ### Equiv 30 31
% 10.63/10.82 33. ((m1_subset_1 T_1 (k1_zfmisc_1 T_1)) => ((v1_tex_2 T_1 (k1_zfmisc_1 T_1)) <=> (T_1 != T_1))) (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = T_1) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### Imply 13 32
% 10.63/10.82 34. (All B, ((m1_subset_1 B (k1_zfmisc_1 T_1)) => ((v1_tex_2 B (k1_zfmisc_1 T_1)) <=> (B != T_1)))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) ((k3_tex_4 T_0 T_1) = T_1) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) ### All 33
% 10.63/10.82 35. (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ((k3_tex_4 T_0 T_1) = T_1) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### All 34
% 10.63/10.82 36. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v3_pre_topc T_1 T_0) => ((k3_tex_4 T_0 T_1) = T_1))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (v3_pre_topc T_1 T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ### DisjTree 7 8 35
% 10.63/10.82 37. (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v3_pre_topc B T_0) => ((k3_tex_4 T_0 B) = B)))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v3_pre_topc T_1 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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### All 36
% 10.63/10.82 38. (((-. (v3_struct_0 T_0)) /\ ((v2_pre_topc T_0) /\ (l1_pre_topc T_0))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v3_pre_topc B T_0) => ((k3_tex_4 T_0 B) = B))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (v3_pre_topc T_1 T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (l1_pre_topc T_0) (v2_pre_topc T_0) (-. (v3_struct_0 T_0)) ### DisjTree 4 5 6 37
% 10.63/10.85 39. (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (-. (v3_struct_0 T_0)) (v2_pre_topc T_0) (l1_pre_topc T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v3_pre_topc T_1 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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### All 38
% 10.63/10.85 40. (((-. (v3_struct_0 T_0)) /\ ((v2_pre_topc T_0) /\ (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0))))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v3_pre_topc T_1 T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (l1_pre_topc T_0) (v2_pre_topc T_0) (-. (v3_struct_0 T_0)) ### DisjTree 1 2 3 39
% 10.63/10.85 41. (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc 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) /\ ((k3_tex_4 A B) = (u1_struct_0 A)))))))) (-. (v3_struct_0 T_0)) (v2_pre_topc T_0) (l1_pre_topc T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v3_pre_topc T_1 T_0) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### All 40
% 10.63/10.85 42. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 10.63/10.85 43. (v2_pre_topc T_0) (-. (v2_pre_topc T_0)) ### Axiom
% 10.63/10.85 44. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 10.63/10.85 45. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 10.63/10.85 46. (v2_pre_topc T_0) (-. (v2_pre_topc T_0)) ### Axiom
% 10.63/10.85 47. (l1_pre_topc T_0) (-. (l1_pre_topc T_0)) ### Axiom
% 10.63/10.85 48. (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_0)))) ### Axiom
% 10.63/10.85 49. (v4_pre_topc T_1 T_0) (-. (v4_pre_topc T_1 T_0)) ### Axiom
% 10.63/10.85 50. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v4_pre_topc T_1 T_0) => ((k3_tex_4 T_0 T_1) = T_1))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (v4_pre_topc T_1 T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) ### DisjTree 48 49 35
% 10.63/10.85 51. (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v4_pre_topc B T_0) => ((k3_tex_4 T_0 B) = B)))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v4_pre_topc T_1 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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### All 50
% 10.63/10.85 52. (((-. (v3_struct_0 T_0)) /\ ((v2_pre_topc T_0) /\ (l1_pre_topc T_0))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => ((v4_pre_topc B T_0) => ((k3_tex_4 T_0 B) = B))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (v4_pre_topc T_1 T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (l1_pre_topc T_0) (v2_pre_topc T_0) (-. (v3_struct_0 T_0)) ### DisjTree 45 46 47 51
% 10.63/10.85 53. (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (-. (v3_struct_0 T_0)) (v2_pre_topc T_0) (l1_pre_topc T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v4_pre_topc T_1 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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### All 52
% 10.63/10.85 54. (((-. (v3_struct_0 T_0)) /\ ((v2_pre_topc T_0) /\ (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) /\ ((k3_tex_4 T_0 B) = (u1_struct_0 T_0))))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v4_pre_topc T_1 T_0) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (l1_pre_topc T_0) (v2_pre_topc T_0) (-. (v3_struct_0 T_0)) ### DisjTree 42 43 44 53
% 10.63/10.85 55. (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc 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) /\ ((k3_tex_4 A B) = (u1_struct_0 A)))))))) (-. (v3_struct_0 T_0)) (v2_pre_topc T_0) (l1_pre_topc T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v4_pre_topc T_1 T_0) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (v1_tsp_2 T_1 T_0) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) ### All 54
% 10.63/10.85 56. ((v3_pre_topc T_1 T_0) \/ (v4_pre_topc T_1 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (v1_tsp_2 T_1 T_0) (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (l1_pre_topc T_0) (v2_pre_topc T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc 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) /\ ((k3_tex_4 A B) = (u1_struct_0 A)))))))) ### Or 41 55
% 10.86/11.06 57. (-. ((m1_subset_1 T_1 (k1_zfmisc_1 (u1_struct_0 T_0))) => (-. (((v3_pre_topc T_1 T_0) \/ (v4_pre_topc T_1 T_0)) /\ ((v1_tsp_2 T_1 T_0) /\ (v1_tex_2 T_1 (k1_zfmisc_1 (u1_struct_0 T_0)))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc 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) /\ ((k3_tex_4 A B) = (u1_struct_0 A)))))))) (-. (v3_struct_0 T_0)) (v2_pre_topc T_0) (l1_pre_topc T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) ### ConjTree 56
% 10.86/11.06 58. (-. (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => (-. (((v3_pre_topc B T_0) \/ (v4_pre_topc B T_0)) /\ ((v1_tsp_2 B T_0) /\ (v1_tex_2 B (k1_zfmisc_1 (u1_struct_0 T_0))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (l1_pre_topc T_0) (v2_pre_topc T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc 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) /\ ((k3_tex_4 A B) = (u1_struct_0 A)))))))) ### NotAllEx 57
% 10.86/11.06 59. (-. (((-. (v3_struct_0 T_0)) /\ ((v2_pre_topc T_0) /\ (l1_pre_topc T_0))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 T_0))) => (-. (((v3_pre_topc B T_0) \/ (v4_pre_topc B T_0)) /\ ((v1_tsp_2 B T_0) /\ (v1_tex_2 B (k1_zfmisc_1 (u1_struct_0 T_0)))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc 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) /\ ((k3_tex_4 A B) = (u1_struct_0 A)))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) ### ConjTree 58
% 10.86/11.06 60. (-. (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => (-. (((v3_pre_topc B A) \/ (v4_pre_topc B A)) /\ ((v1_tsp_2 B A) /\ (v1_tex_2 B (k1_zfmisc_1 (u1_struct_0 A))))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v4_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (All A, (All B, ((m1_subset_1 A (k1_zfmisc_1 B)) <=> (r1_tarski A B)))) (All A, (All B, ((m1_subset_1 B (k1_zfmisc_1 A)) => ((v1_tex_2 B (k1_zfmisc_1 A)) <=> (B != A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc A) /\ (l1_pre_topc A))) => (All B, ((m1_subset_1 B (k1_zfmisc_1 (u1_struct_0 A))) => ((v3_pre_topc B A) => ((k3_tex_4 A B) = B)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_pre_topc 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) /\ ((k3_tex_4 A B) = (u1_struct_0 A)))))))) ### NotAllEx 59
% 10.86/11.06 % SZS output end Proof
% 10.86/11.06 (* END-PROOF *)
%------------------------------------------------------------------------------