TSTP Solution File: LAT337+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LAT337+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 : n017.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 : Sun Jul 17 06:57:30 EDT 2022
% Result : Theorem 2.76s 2.98s
% Output : Proof 3.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT337+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 01:43:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.76/2.98 % SZS status Theorem
% 2.76/2.98 (* PROOF-FOUND *)
% 2.76/2.98 (* BEGIN-PROOF *)
% 2.76/2.98 % SZS output start Proof
% 2.76/2.98 1. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/2.98 2. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 2.76/2.98 3. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/2.98 4. (m1_subset_1 T_1 (u1_struct_0 T_0)) (-. (m1_subset_1 T_1 (u1_struct_0 T_0))) ### Axiom
% 2.76/2.98 5. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.76/2.98 6. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/2.98 7. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 2.76/2.98 8. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/2.98 9. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/2.98 10. (v17_lattices T_0) (-. (v17_lattices T_0)) ### Axiom
% 2.76/2.98 11. (-. (v15_lattices T_0)) (v15_lattices T_0) ### Axiom
% 2.76/2.98 12. ((-. (v3_struct_0 T_0)) /\ ((v11_lattices T_0) /\ ((v13_lattices T_0) /\ ((v14_lattices T_0) /\ ((v15_lattices T_0) /\ (v16_lattices T_0)))))) (-. (v15_lattices T_0)) ### ConjTree 11
% 2.76/2.98 13. ((l3_lattices T_0) => (((-. (v3_struct_0 T_0)) /\ (v17_lattices T_0)) => ((-. (v3_struct_0 T_0)) /\ ((v11_lattices T_0) /\ ((v13_lattices T_0) /\ ((v14_lattices T_0) /\ ((v15_lattices T_0) /\ (v16_lattices T_0)))))))) (-. (v15_lattices T_0)) (v17_lattices T_0) (-. (v3_struct_0 T_0)) (l3_lattices T_0) ### DisjTree 8 9 10 12
% 2.76/2.98 14. (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (-. (v3_struct_0 T_0)) (v17_lattices T_0) (-. (v15_lattices T_0)) ### All 13
% 2.76/2.98 15. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/2.98 16. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/2.98 17. (v17_lattices T_0) (-. (v17_lattices T_0)) ### Axiom
% 2.76/2.98 18. (-. (v16_lattices T_0)) (v16_lattices T_0) ### Axiom
% 2.76/2.98 19. ((-. (v3_struct_0 T_0)) /\ ((v11_lattices T_0) /\ ((v13_lattices T_0) /\ ((v14_lattices T_0) /\ ((v15_lattices T_0) /\ (v16_lattices T_0)))))) (-. (v16_lattices T_0)) ### ConjTree 18
% 2.76/2.98 20. ((l3_lattices T_0) => (((-. (v3_struct_0 T_0)) /\ (v17_lattices T_0)) => ((-. (v3_struct_0 T_0)) /\ ((v11_lattices T_0) /\ ((v13_lattices T_0) /\ ((v14_lattices T_0) /\ ((v15_lattices T_0) /\ (v16_lattices T_0)))))))) (-. (v16_lattices T_0)) (v17_lattices T_0) (-. (v3_struct_0 T_0)) (l3_lattices T_0) ### DisjTree 15 16 17 19
% 2.76/2.98 21. (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (-. (v3_struct_0 T_0)) (v17_lattices T_0) (-. (v16_lattices T_0)) ### All 20
% 2.76/2.98 22. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/2.98 23. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/2.98 24. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/2.98 25. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 2.76/2.98 26. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/2.98 27. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/2.98 28. (v17_lattices T_0) (-. (v17_lattices T_0)) ### Axiom
% 2.76/2.98 29. (-. (v11_lattices T_0)) (v11_lattices T_0) ### Axiom
% 2.76/2.98 30. ((-. (v3_struct_0 T_0)) /\ ((v11_lattices T_0) /\ ((v13_lattices T_0) /\ ((v14_lattices T_0) /\ ((v15_lattices T_0) /\ (v16_lattices T_0)))))) (-. (v11_lattices T_0)) ### ConjTree 29
% 2.76/2.98 31. ((l3_lattices T_0) => (((-. (v3_struct_0 T_0)) /\ (v17_lattices T_0)) => ((-. (v3_struct_0 T_0)) /\ ((v11_lattices T_0) /\ ((v13_lattices T_0) /\ ((v14_lattices T_0) /\ ((v15_lattices T_0) /\ (v16_lattices T_0)))))))) (-. (v11_lattices T_0)) (v17_lattices T_0) (-. (v3_struct_0 T_0)) (l3_lattices T_0) ### DisjTree 26 27 28 30
% 2.76/2.98 32. (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (-. (v3_struct_0 T_0)) (v17_lattices T_0) (-. (v11_lattices T_0)) ### All 31
% 2.76/2.98 33. (-. (v12_lattices T_0)) (v12_lattices T_0) ### Axiom
% 2.76/2.98 34. ((-. (v3_struct_0 T_0)) /\ ((v4_lattices T_0) /\ ((v5_lattices T_0) /\ ((v6_lattices T_0) /\ ((v7_lattices T_0) /\ ((v8_lattices T_0) /\ ((v9_lattices T_0) /\ ((v10_lattices T_0) /\ (v12_lattices T_0))))))))) (-. (v12_lattices T_0)) ### ConjTree 33
% 2.76/2.98 35. ((l3_lattices T_0) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (v11_lattices T_0))) => ((-. (v3_struct_0 T_0)) /\ ((v4_lattices T_0) /\ ((v5_lattices T_0) /\ ((v6_lattices T_0) /\ ((v7_lattices T_0) /\ ((v8_lattices T_0) /\ ((v9_lattices T_0) /\ ((v10_lattices T_0) /\ (v12_lattices T_0))))))))))) (-. (v12_lattices T_0)) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (l3_lattices T_0) ### DisjTree 23 24 25 32 34
% 2.76/2.98 36. (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (l3_lattices T_0) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (-. (v12_lattices T_0)) ### All 35
% 2.76/2.98 37. (r3_lattices T_0 T_1 T_2) (-. (r3_lattices T_0 T_1 T_2)) ### Axiom
% 2.76/2.98 38. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) (-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### Axiom
% 2.76/2.98 39. ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))) (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### ConjTree 38
% 2.76/2.98 40. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 T_2))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))))) (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### DisjTree 5 6 7 14 21 22 36 37 39
% 2.76/2.98 41. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### All 40
% 2.76/3.02 42. ((m1_subset_1 T_1 (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))))))))))) (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) ### Imply 4 41
% 2.76/3.02 43. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))))))))))) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### All 42
% 2.76/3.02 44. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (l3_lattices T_0))) => (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))))))))))))) (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 1 2 3 43
% 2.76/3.02 45. (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### All 44
% 2.76/3.02 46. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/3.02 47. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 2.76/3.02 48. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/3.02 49. (m1_subset_1 T_1 (u1_struct_0 T_0)) (-. (m1_subset_1 T_1 (u1_struct_0 T_0))) ### Axiom
% 2.76/3.02 50. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.76/3.02 51. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.76/3.02 52. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 2.76/3.02 53. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.76/3.02 54. (r3_lattices T_0 T_1 T_2) (-. (r3_lattices T_0 T_1 T_2)) ### Axiom
% 2.76/3.02 55. (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### Axiom
% 2.76/3.02 56. ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))) (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### ConjTree 55
% 2.76/3.02 57. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 T_2))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))))) (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### DisjTree 50 51 52 14 21 53 36 54 56
% 2.92/3.09 58. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 57
% 2.92/3.09 59. ((m1_subset_1 T_1 (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))))))))))) (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) ### Imply 49 58
% 2.92/3.09 60. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))))))))))) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 59
% 2.92/3.09 61. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (l3_lattices T_0))) => (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))))))))))))) (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 46 47 48 60
% 2.92/3.09 62. (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 61
% 2.92/3.09 63. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.92/3.09 64. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 2.92/3.09 65. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.92/3.09 66. (m1_subset_1 T_1 (u1_struct_0 T_0)) (-. (m1_subset_1 T_1 (u1_struct_0 T_0))) ### Axiom
% 2.92/3.09 67. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.92/3.09 68. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.92/3.09 69. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 2.92/3.09 70. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 2.92/3.09 71. (r3_lattices T_0 T_1 T_2) (-. (r3_lattices T_0 T_1 T_2)) ### Axiom
% 2.92/3.09 72. (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### Axiom
% 2.92/3.09 73. ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))) (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### ConjTree 72
% 3.06/3.33 74. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 T_2))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))))) (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### DisjTree 67 68 69 14 21 70 36 71 73
% 3.06/3.33 75. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 74
% 3.06/3.33 76. ((m1_subset_1 T_1 (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))))))))))) (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) ### Imply 66 75
% 3.06/3.33 77. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))))))))))) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 76
% 3.06/3.33 78. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (l3_lattices T_0))) => (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))))))))))))) (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 63 64 65 77
% 3.06/3.33 79. (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 78
% 3.06/3.33 80. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 3.06/3.33 81. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 3.06/3.33 82. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 3.16/3.37 83. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 3.16/3.37 84. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 3.16/3.37 85. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 3.16/3.37 86. (m1_subset_1 T_1 (u1_struct_0 T_0)) (-. (m1_subset_1 T_1 (u1_struct_0 T_0))) ### Axiom
% 3.16/3.37 87. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 3.16/3.37 88. (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2)) (-. (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2))) ### Axiom
% 3.16/3.37 89. ((-. (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2))) /\ (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2)) ### And 88
% 3.16/3.37 90. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((l3_lattices T_0) /\ ((m1_subset_1 T_1 (u1_struct_0 T_0)) /\ (m1_subset_1 T_2 (u1_struct_0 T_0)))))) => ((-. (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2))) /\ (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0))) (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 83 84 85 86 87 89
% 3.16/3.37 91. (All C, (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((l3_lattices T_0) /\ ((m1_subset_1 T_1 (u1_struct_0 T_0)) /\ (m1_subset_1 C (u1_struct_0 T_0)))))) => ((-. (v1_xboole_0 (k22_filter_2 T_0 T_1 C))) /\ (m2_lattice4 (k22_filter_2 T_0 T_1 C) T_0)))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2)) ### All 90
% 3.16/3.37 92. (All B, (All C, (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((l3_lattices T_0) /\ ((m1_subset_1 B (u1_struct_0 T_0)) /\ (m1_subset_1 C (u1_struct_0 T_0)))))) => ((-. (v1_xboole_0 (k22_filter_2 T_0 B C))) /\ (m2_lattice4 (k22_filter_2 T_0 B C) T_0))))) (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### All 91
% 3.16/3.37 93. (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2)) ### All 92
% 3.16/3.37 94. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 3.16/3.37 95. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 3.16/3.37 96. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 3.16/3.37 97. (m1_subset_1 T_1 (u1_struct_0 T_0)) (-. (m1_subset_1 T_1 (u1_struct_0 T_0))) ### Axiom
% 3.16/3.37 98. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 3.16/3.37 99. (-. (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0) ### Axiom
% 3.16/3.37 100. ((-. (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2))) /\ (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) (-. (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) ### And 99
% 3.16/3.37 101. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((l3_lattices T_0) /\ ((m1_subset_1 T_1 (u1_struct_0 T_0)) /\ (m1_subset_1 T_2 (u1_struct_0 T_0)))))) => ((-. (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2))) /\ (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0))) (-. (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 94 95 96 97 98 100
% 3.16/3.37 102. (All C, (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((l3_lattices T_0) /\ ((m1_subset_1 T_1 (u1_struct_0 T_0)) /\ (m1_subset_1 C (u1_struct_0 T_0)))))) => ((-. (v1_xboole_0 (k22_filter_2 T_0 T_1 C))) /\ (m2_lattice4 (k22_filter_2 T_0 T_1 C) T_0)))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) ### All 101
% 3.16/3.37 103. (All B, (All C, (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((l3_lattices T_0) /\ ((m1_subset_1 B (u1_struct_0 T_0)) /\ (m1_subset_1 C (u1_struct_0 T_0)))))) => ((-. (v1_xboole_0 (k22_filter_2 T_0 B C))) /\ (m2_lattice4 (k22_filter_2 T_0 B C) T_0))))) (-. (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### All 102
% 3.16/3.37 104. (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) ### All 103
% 3.16/3.37 105. (-. (v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### Axiom
% 3.16/3.37 106. (((-. (v1_xboole_0 (k22_filter_2 T_0 T_1 T_2))) /\ (m2_lattice4 (k22_filter_2 T_0 T_1 T_2) T_0)) => ((v11_lattices T_0) => (v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))) (-. (v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) ### DisjTree 93 104 32 105
% 3.16/3.37 107. (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B T_0)) => ((v11_lattices T_0) => (v11_lattices (k23_filter_2 T_0 B))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (-. (v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 106
% 3.16/3.37 108. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (l3_lattices T_0))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B T_0)) => ((v11_lattices T_0) => (v11_lattices (k23_filter_2 T_0 B)))))) (-. (v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 80 81 82 107
% 3.16/3.37 109. (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (-. (v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 108
% 3.16/3.40 110. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 3.16/3.40 111. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 3.16/3.40 112. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 3.16/3.40 113. (m1_subset_1 T_1 (u1_struct_0 T_0)) (-. (m1_subset_1 T_1 (u1_struct_0 T_0))) ### Axiom
% 3.16/3.40 114. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 3.16/3.40 115. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 3.16/3.40 116. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 3.16/3.40 117. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 3.16/3.40 118. (r3_lattices T_0 T_1 T_2) (-. (r3_lattices T_0 T_1 T_2)) ### Axiom
% 3.16/3.40 119. (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### Axiom
% 3.16/3.40 120. ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))) (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### ConjTree 119
% 3.16/3.40 121. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 T_2))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))))) (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### DisjTree 114 115 116 14 21 117 36 118 120
% 3.16/3.40 122. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 121
% 3.16/3.40 123. ((m1_subset_1 T_1 (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))))))))))) (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) ### Imply 113 122
% 3.16/3.40 124. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))))))))))) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 123
% 3.16/3.40 125. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (l3_lattices T_0))) => (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))))))))))))) (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 110 111 112 124
% 3.24/3.41 126. (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 125
% 3.24/3.41 127. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 3.24/3.41 128. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 3.24/3.41 129. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 3.24/3.41 130. (m1_subset_1 T_1 (u1_struct_0 T_0)) (-. (m1_subset_1 T_1 (u1_struct_0 T_0))) ### Axiom
% 3.24/3.41 131. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 3.24/3.41 132. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 3.24/3.41 133. (v10_lattices T_0) (-. (v10_lattices T_0)) ### Axiom
% 3.24/3.41 134. (l3_lattices T_0) (-. (l3_lattices T_0)) ### Axiom
% 3.24/3.41 135. (r3_lattices T_0 T_1 T_2) (-. (r3_lattices T_0 T_1 T_2)) ### Axiom
% 3.24/3.41 136. (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### Axiom
% 3.24/3.41 137. ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))) (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### ConjTree 136
% 3.24/3.41 138. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 T_2))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))))) (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### DisjTree 131 132 133 14 21 134 36 135 137
% 3.24/3.41 139. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 138
% 3.24/3.41 140. ((m1_subset_1 T_1 (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 T_1 C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))))))))))) (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) ### Imply 130 139
% 3.24/3.41 141. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))))))))))) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 140
% 3.24/3.41 142. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (l3_lattices T_0))) => (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v15_lattices T_0) /\ ((v16_lattices T_0) /\ ((l3_lattices T_0) /\ ((v12_lattices T_0) /\ (r3_lattices T_0 B C))))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))))))))))))) (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) ### DisjTree 127 128 129 141
% 3.24/3.43 143. (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (-. (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 142
% 3.24/3.43 144. (-. (v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) ### Axiom
% 3.24/3.43 145. ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ (v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (-. (v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### And 144
% 3.24/3.43 146. ((l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) => (((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v11_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v15_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (v16_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ (v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))))) (-. (v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) ### DisjTree 79 45 109 126 143 145
% 3.24/3.43 147. (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (r3_lattices T_0 T_1 T_2) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (-. (v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) ### All 146
% 3.24/3.43 148. (-. ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (r3_lattices T_0 T_1 T_2) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (v17_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) ### DisjTree 45 62 147 79
% 3.24/3.45 149. (-. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v17_lattices T_0) /\ ((l3_lattices T_0) /\ (r3_lattices T_0 T_1 T_2))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ ((v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 T_2))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (m1_subset_1 T_1 (u1_struct_0 T_0)) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) ### ConjTree 148
% 3.24/3.45 150. (-. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v17_lattices T_0) /\ ((l3_lattices T_0) /\ (r3_lattices T_0 T_1 C))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (m1_subset_1 T_1 (u1_struct_0 T_0)) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) ### NotAllEx 149
% 3.24/3.45 151. (-. ((m1_subset_1 T_1 (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v17_lattices T_0) /\ ((l3_lattices T_0) /\ (r3_lattices T_0 T_1 C))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ ((v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 T_1 C))))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (-. (v3_struct_0 T_0)) (v10_lattices T_0) (l3_lattices T_0) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) ### NotImply 150
% 3.24/3.45 152. (-. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v17_lattices T_0) /\ ((l3_lattices T_0) /\ (r3_lattices T_0 B C))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))))))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (l3_lattices T_0) (v10_lattices T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) ### NotAllEx 151
% 3.24/3.45 153. (-. (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ (l3_lattices T_0))) => (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (((-. (v3_struct_0 T_0)) /\ ((v10_lattices T_0) /\ ((v17_lattices T_0) /\ ((l3_lattices T_0) /\ (r3_lattices T_0 B C))))) => ((-. (v3_struct_0 (k23_filter_2 T_0 (k22_filter_2 T_0 B C)))) /\ ((v10_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ ((v17_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))) /\ (l3_lattices (k23_filter_2 T_0 (k22_filter_2 T_0 B C))))))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) ### ConjTree 152
% 3.24/3.45 154. (-. (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v17_lattices A) /\ ((l3_lattices A) /\ (r3_lattices A B C))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v17_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((l3_lattices A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A)))))) => ((-. (v1_xboole_0 (k22_filter_2 A B C))) /\ (m2_lattice4 (k22_filter_2 A B C) A)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, (((-. (v1_xboole_0 B)) /\ (m2_lattice4 B A)) => ((v11_lattices A) => (v11_lattices (k23_filter_2 A B))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A)))) => ((-. (v3_struct_0 A)) /\ (v17_lattices A))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (v11_lattices A))) => ((-. (v3_struct_0 A)) /\ ((v4_lattices A) /\ ((v5_lattices A) /\ ((v6_lattices A) /\ ((v7_lattices A) /\ ((v8_lattices A) /\ ((v9_lattices A) /\ ((v10_lattices A) /\ (v12_lattices A)))))))))))) (All A, ((l3_lattices A) => (((-. (v3_struct_0 A)) /\ (v17_lattices A)) => ((-. (v3_struct_0 A)) /\ ((v11_lattices A) /\ ((v13_lattices A) /\ ((v14_lattices A) /\ ((v15_lattices A) /\ (v16_lattices A))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ (l3_lattices A))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => (((-. (v3_struct_0 A)) /\ ((v10_lattices A) /\ ((v15_lattices A) /\ ((v16_lattices A) /\ ((l3_lattices A) /\ ((v12_lattices A) /\ (r3_lattices A B C))))))) => ((-. (v3_struct_0 (k23_filter_2 A (k22_filter_2 A B C)))) /\ ((v10_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v15_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ ((v16_lattices (k23_filter_2 A (k22_filter_2 A B C))) /\ (l3_lattices (k23_filter_2 A (k22_filter_2 A B C)))))))))))))) ### NotAllEx 153
% 3.24/3.45 % SZS output end Proof
% 3.24/3.45 (* END-PROOF *)
%------------------------------------------------------------------------------