TSTP Solution File: LAT356+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LAT356+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 : n020.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 06:57:48 EDT 2022
% Result : Theorem 2.92s 3.18s
% Output : Proof 3.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT356+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n020.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 : Thu Jun 30 09:35:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.92/3.18 % SZS status Theorem
% 2.92/3.18 (* PROOF-FOUND *)
% 2.92/3.18 (* BEGIN-PROOF *)
% 2.92/3.18 % SZS output start Proof
% 2.92/3.18 1. (v2_orders_2 T_0) (-. (v2_orders_2 T_0)) ### Axiom
% 2.92/3.18 2. (v3_orders_2 T_0) (-. (v3_orders_2 T_0)) ### Axiom
% 2.92/3.18 3. (v4_orders_2 T_0) (-. (v4_orders_2 T_0)) ### Axiom
% 2.92/3.18 4. (v1_lattice3 T_0) (-. (v1_lattice3 T_0)) ### Axiom
% 2.92/3.18 5. (v2_lattice3 T_0) (-. (v2_lattice3 T_0)) ### Axiom
% 2.92/3.18 6. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 2.92/3.18 7. (v2_orders_2 T_0) (-. (v2_orders_2 T_0)) ### Axiom
% 2.92/3.18 8. (v3_orders_2 T_0) (-. (v3_orders_2 T_0)) ### Axiom
% 2.92/3.18 9. (v4_orders_2 T_0) (-. (v4_orders_2 T_0)) ### Axiom
% 2.92/3.18 10. (v1_lattice3 T_0) (-. (v1_lattice3 T_0)) ### Axiom
% 2.92/3.18 11. (v2_lattice3 T_0) (-. (v2_lattice3 T_0)) ### Axiom
% 2.92/3.18 12. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 2.92/3.18 13. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 2.92/3.18 14. (-. (v1_funct_1 (k7_grcat_1 T_0))) (v1_funct_1 (k7_grcat_1 T_0)) ### Axiom
% 2.92/3.18 15. ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (v23_waybel_0 (k7_grcat_1 T_0) T_0 T_0)))) (-. (v1_funct_1 (k7_grcat_1 T_0))) ### ConjTree 14
% 2.92/3.18 16. ((l1_orders_2 T_0) => ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (v23_waybel_0 (k7_grcat_1 T_0) T_0 T_0))))) (-. (v1_funct_1 (k7_grcat_1 T_0))) (l1_orders_2 T_0) ### Imply 13 15
% 2.92/3.18 17. (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (-. (v1_funct_1 (k7_grcat_1 T_0))) ### All 16
% 2.92/3.18 18. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 2.92/3.18 19. (-. (l1_struct_0 T_0)) (l1_struct_0 T_0) ### Axiom
% 2.92/3.18 20. ((l1_orders_2 T_0) => (l1_struct_0 T_0)) (-. (l1_struct_0 T_0)) (l1_orders_2 T_0) ### Imply 18 19
% 2.92/3.18 21. (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (l1_orders_2 T_0) (-. (l1_struct_0 T_0)) ### All 20
% 2.92/3.18 22. (-. (v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) (v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) ### Axiom
% 2.92/3.18 23. ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v2_funct_1 (k7_grcat_1 T_0)) /\ (v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))))) (-. (v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) ### ConjTree 22
% 2.92/3.18 24. ((l1_struct_0 T_0) => ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v2_funct_1 (k7_grcat_1 T_0)) /\ (v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)))))) (-. (v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) ### Imply 21 23
% 2.92/3.18 25. (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (l1_orders_2 T_0) (-. (v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) ### All 24
% 2.92/3.18 26. (-. (m1_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) (m1_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) ### Axiom
% 2.92/3.18 27. (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) (-. (m1_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) ### Definition-Pseudo(m2_relset_1) 26
% 2.92/3.18 28. ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)))) (-. (m1_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) ### ConjTree 27
% 2.92/3.18 29. ((l1_struct_0 T_0) => ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))))) (-. (m1_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) ### Imply 21 28
% 2.92/3.18 30. (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (l1_orders_2 T_0) (-. (m1_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) ### All 29
% 2.92/3.18 31. (-. (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) ### Definition-Pseudo(m2_relset_1) 30
% 2.92/3.18 32. (v3_lattice3 T_0) (-. (v3_lattice3 T_0)) ### Axiom
% 2.92/3.18 33. (v3_lattice3 T_0) (-. (v3_lattice3 T_0)) ### Axiom
% 2.92/3.18 34. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 2.92/3.18 35. (v2_lattice3 T_0) (-. (v2_lattice3 T_0)) ### Axiom
% 2.92/3.18 36. (v3_struct_0 T_0) (-. (v3_struct_0 T_0)) ### Axiom
% 2.92/3.18 37. ((l1_orders_2 T_0) => ((v2_lattice3 T_0) => (-. (v3_struct_0 T_0)))) (v3_struct_0 T_0) (v2_lattice3 T_0) (l1_orders_2 T_0) ### DisjTree 34 35 36
% 2.92/3.18 38. (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v3_struct_0 T_0) ### All 37
% 2.92/3.18 39. (v2_orders_2 T_0) (-. (v2_orders_2 T_0)) ### Axiom
% 2.92/3.18 40. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 2.92/3.18 41. (-. (v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) (v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0) ### Axiom
% 2.92/3.18 42. ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v2_funct_1 (k7_grcat_1 T_0)) /\ ((-. (v1_xboole_0 (k7_grcat_1 T_0))) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v1_partfun1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v11_quantal1 (k7_grcat_1 T_0)) /\ ((v5_orders_3 (k7_grcat_1 T_0) T_0 T_0) /\ ((v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v19_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v20_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v21_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v22_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v23_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v6_waybel_1 (k7_grcat_1 T_0) T_0) /\ ((v7_waybel_1 (k7_grcat_1 T_0) T_0) /\ (v8_waybel_1 (k7_grcat_1 T_0) T_0)))))))))))))))))) (-. (v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) ### ConjTree 41
% 2.92/3.18 43. (((-. (v3_struct_0 T_0)) /\ ((v2_orders_2 T_0) /\ (l1_orders_2 T_0))) => ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v2_funct_1 (k7_grcat_1 T_0)) /\ ((-. (v1_xboole_0 (k7_grcat_1 T_0))) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v1_partfun1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v11_quantal1 (k7_grcat_1 T_0)) /\ ((v5_orders_3 (k7_grcat_1 T_0) T_0 T_0) /\ ((v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v19_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v20_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v21_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v22_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v23_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v6_waybel_1 (k7_grcat_1 T_0) T_0) /\ ((v7_waybel_1 (k7_grcat_1 T_0) T_0) /\ (v8_waybel_1 (k7_grcat_1 T_0) T_0))))))))))))))))))) (-. (v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) (v2_orders_2 T_0) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) ### DisjTree 38 39 40 42
% 2.92/3.18 44. (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v2_orders_2 T_0) (-. (v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) ### All 43
% 3.04/3.26 45. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 3.04/3.26 46. (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) (-. (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0)) ### Axiom
% 3.04/3.26 47. ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ((k7_grcat_1 T_0) = (k1_waybel34 T_0 T_0 (k7_grcat_1 T_0))) ### Sym(=)
% 3.04/3.26 48. (((k7_grcat_1 T_0) = (k1_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0)) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) ### Equiv 46 47
% 3.04/3.26 49. (((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((k7_grcat_1 T_0) = (k1_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0))) (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) ### DisjTree 17 25 31 48
% 3.04/3.26 50. (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) D) T_0 T_0)))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) ### All 49
% 3.04/3.26 51. (((-. (v3_struct_0 T_0)) /\ (l1_orders_2 T_0)) => (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0)) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) D) T_0 T_0)))) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) ### DisjTree 38 45 50
% 3.04/3.26 52. (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) D) T_0 T_0)))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 51
% 3.04/3.26 53. (((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 T_0) /\ (v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) D) T_0 T_0)))))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (v2_orders_2 T_0) (v2_lattice3 T_0) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (v3_lattice3 T_0) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) ### DisjTree 17 25 31 32 33 44 52
% 3.04/3.26 54. (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 C (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 T_0) /\ (v17_waybel_0 C T_0 T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 T_0 C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 C D) T_0 T_0))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (v3_lattice3 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (v2_lattice3 T_0) (v2_orders_2 T_0) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 53
% 3.04/3.28 55. (((v2_orders_2 T_0) /\ ((v3_orders_2 T_0) /\ ((v4_orders_2 T_0) /\ ((v1_lattice3 T_0) /\ ((v2_lattice3 T_0) /\ (l1_orders_2 T_0)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 C (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 T_0) /\ (v17_waybel_0 C T_0 T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 T_0 C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 C D) T_0 T_0)))))))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (v3_lattice3 T_0) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v1_lattice3 T_0) (v4_orders_2 T_0) (v3_orders_2 T_0) (v2_orders_2 T_0) ### DisjTree 7 8 9 10 11 12 54
% 3.04/3.28 56. (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 T_0) (u1_struct_0 B)) /\ (m2_relset_1 C (u1_struct_0 T_0) (u1_struct_0 B)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 B) /\ (v17_waybel_0 C T_0 B))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 B) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 B C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 B C D) T_0 B))))))))) (v2_orders_2 T_0) (v3_orders_2 T_0) (v4_orders_2 T_0) (v1_lattice3 T_0) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (v3_lattice3 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 55
% 3.04/3.28 57. (((v2_orders_2 T_0) /\ ((v3_orders_2 T_0) /\ ((v4_orders_2 T_0) /\ ((v1_lattice3 T_0) /\ ((v2_lattice3 T_0) /\ (l1_orders_2 T_0)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 T_0) (u1_struct_0 B)) /\ (m2_relset_1 C (u1_struct_0 T_0) (u1_struct_0 B)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 B) /\ (v17_waybel_0 C T_0 B))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 B) (u1_struct_0 T_0)))) => ((D = (k1_waybel34 T_0 B C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 B C D) T_0 B)))))))))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (v3_lattice3 T_0) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v1_lattice3 T_0) (v4_orders_2 T_0) (v3_orders_2 T_0) (v2_orders_2 T_0) ### DisjTree 1 2 3 4 5 6 56
% 3.36/3.56 58. (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 C (u1_struct_0 A) (u1_struct_0 B)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v17_waybel_0 C A B))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 D (u1_struct_0 B) (u1_struct_0 A)))) => ((D = (k1_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B C D) A B))))))))))) (v2_orders_2 T_0) (v3_orders_2 T_0) (v4_orders_2 T_0) (v1_lattice3 T_0) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (v3_lattice3 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) ((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 57
% 3.36/3.56 59. (v2_orders_2 T_0) (-. (v2_orders_2 T_0)) ### Axiom
% 3.36/3.56 60. (v3_orders_2 T_0) (-. (v3_orders_2 T_0)) ### Axiom
% 3.36/3.56 61. (v4_orders_2 T_0) (-. (v4_orders_2 T_0)) ### Axiom
% 3.36/3.56 62. (v1_lattice3 T_0) (-. (v1_lattice3 T_0)) ### Axiom
% 3.36/3.56 63. (v2_lattice3 T_0) (-. (v2_lattice3 T_0)) ### Axiom
% 3.36/3.56 64. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 3.36/3.56 65. (v2_orders_2 T_0) (-. (v2_orders_2 T_0)) ### Axiom
% 3.36/3.56 66. (v3_orders_2 T_0) (-. (v3_orders_2 T_0)) ### Axiom
% 3.36/3.56 67. (v4_orders_2 T_0) (-. (v4_orders_2 T_0)) ### Axiom
% 3.36/3.56 68. (v1_lattice3 T_0) (-. (v1_lattice3 T_0)) ### Axiom
% 3.36/3.56 69. (v2_lattice3 T_0) (-. (v2_lattice3 T_0)) ### Axiom
% 3.36/3.56 70. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 3.36/3.56 71. (v3_lattice3 T_0) (-. (v3_lattice3 T_0)) ### Axiom
% 3.36/3.56 72. (v3_lattice3 T_0) (-. (v3_lattice3 T_0)) ### Axiom
% 3.36/3.56 73. (v2_orders_2 T_0) (-. (v2_orders_2 T_0)) ### Axiom
% 3.36/3.56 74. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 3.36/3.56 75. (-. (v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) (v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0) ### Axiom
% 3.36/3.56 76. ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v2_funct_1 (k7_grcat_1 T_0)) /\ ((-. (v1_xboole_0 (k7_grcat_1 T_0))) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v1_partfun1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v11_quantal1 (k7_grcat_1 T_0)) /\ ((v5_orders_3 (k7_grcat_1 T_0) T_0 T_0) /\ ((v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v19_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v20_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v21_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v22_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v23_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v6_waybel_1 (k7_grcat_1 T_0) T_0) /\ ((v7_waybel_1 (k7_grcat_1 T_0) T_0) /\ (v8_waybel_1 (k7_grcat_1 T_0) T_0)))))))))))))))))) (-. (v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) ### ConjTree 75
% 3.36/3.56 77. (((-. (v3_struct_0 T_0)) /\ ((v2_orders_2 T_0) /\ (l1_orders_2 T_0))) => ((v1_relat_1 (k7_grcat_1 T_0)) /\ ((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v2_funct_1 (k7_grcat_1 T_0)) /\ ((-. (v1_xboole_0 (k7_grcat_1 T_0))) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v1_partfun1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ ((v11_quantal1 (k7_grcat_1 T_0)) /\ ((v5_orders_3 (k7_grcat_1 T_0) T_0 T_0) /\ ((v17_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v19_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v20_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v21_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v22_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v23_waybel_0 (k7_grcat_1 T_0) T_0 T_0) /\ ((v6_waybel_1 (k7_grcat_1 T_0) T_0) /\ ((v7_waybel_1 (k7_grcat_1 T_0) T_0) /\ (v8_waybel_1 (k7_grcat_1 T_0) T_0))))))))))))))))))) (-. (v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) (v2_orders_2 T_0) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) ### DisjTree 38 73 74 76
% 3.36/3.56 78. (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v2_orders_2 T_0) (-. (v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0)) ### All 77
% 3.36/3.56 79. (l1_orders_2 T_0) (-. (l1_orders_2 T_0)) ### Axiom
% 3.36/3.56 80. (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) (-. (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0)) ### Axiom
% 3.36/3.56 81. ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ((k7_grcat_1 T_0) = (k2_waybel34 T_0 T_0 (k7_grcat_1 T_0))) ### Sym(=)
% 3.36/3.56 82. (((k7_grcat_1 T_0) = (k2_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0)) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) ### Equiv 80 81
% 3.36/3.56 83. (((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((k7_grcat_1 T_0) = (k2_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0))) (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) ### DisjTree 17 25 31 82
% 3.36/3.57 84. (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k2_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 D (k7_grcat_1 T_0)) T_0 T_0)))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0) ### All 83
% 3.36/3.57 85. (((-. (v3_struct_0 T_0)) /\ (l1_orders_2 T_0)) => (v3_waybel_1 (k1_waybel_1 T_0 T_0 (k7_grcat_1 T_0) (k7_grcat_1 T_0)) T_0 T_0)) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k2_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 D (k7_grcat_1 T_0)) T_0 T_0)))) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) ### DisjTree 38 79 84
% 3.36/3.57 86. (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k2_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 D (k7_grcat_1 T_0)) T_0 T_0)))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 85
% 3.36/3.57 87. (((v1_funct_1 (k7_grcat_1 T_0)) /\ ((v1_funct_2 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 (k7_grcat_1 T_0) (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 T_0) /\ (v18_waybel_0 (k7_grcat_1 T_0) T_0 T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k2_waybel34 T_0 T_0 (k7_grcat_1 T_0))) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 D (k7_grcat_1 T_0)) T_0 T_0)))))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (v2_orders_2 T_0) (v2_lattice3 T_0) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (v3_lattice3 T_0) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) ### DisjTree 17 25 31 71 72 78 86
% 3.36/3.57 88. (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 C (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 T_0) /\ (v18_waybel_0 C T_0 T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k2_waybel34 T_0 T_0 C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 D C) T_0 T_0))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (v3_lattice3 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (v2_lattice3 T_0) (v2_orders_2 T_0) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 87
% 3.36/3.58 89. (((v2_orders_2 T_0) /\ ((v3_orders_2 T_0) /\ ((v4_orders_2 T_0) /\ ((v1_lattice3 T_0) /\ ((v2_lattice3 T_0) /\ (l1_orders_2 T_0)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 C (u1_struct_0 T_0) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 T_0) /\ (v18_waybel_0 C T_0 T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 T_0)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 T_0)))) => ((D = (k2_waybel34 T_0 T_0 C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 T_0 D C) T_0 T_0)))))))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (v3_lattice3 T_0) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v1_lattice3 T_0) (v4_orders_2 T_0) (v3_orders_2 T_0) (v2_orders_2 T_0) ### DisjTree 65 66 67 68 69 70 88
% 3.36/3.58 90. (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 T_0)) /\ (m2_relset_1 C (u1_struct_0 B) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 B) /\ (v18_waybel_0 C B T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 B)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 B)))) => ((D = (k2_waybel34 T_0 B C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 B D C) T_0 B))))))))) (v2_orders_2 T_0) (v3_orders_2 T_0) (v4_orders_2 T_0) (v1_lattice3 T_0) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (v3_lattice3 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 89
% 3.36/3.58 91. (((v2_orders_2 T_0) /\ ((v3_orders_2 T_0) /\ ((v4_orders_2 T_0) /\ ((v1_lattice3 T_0) /\ ((v2_lattice3 T_0) /\ (l1_orders_2 T_0)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 T_0)) /\ (m2_relset_1 C (u1_struct_0 B) (u1_struct_0 T_0)))) => (((v3_lattice3 T_0) /\ ((v3_lattice3 B) /\ (v18_waybel_0 C B T_0))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 T_0) (u1_struct_0 B)) /\ (m2_relset_1 D (u1_struct_0 T_0) (u1_struct_0 B)))) => ((D = (k2_waybel34 T_0 B C)) <=> (v3_waybel_1 (k1_waybel_1 T_0 B D C) T_0 B)))))))))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (v3_lattice3 T_0) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v1_lattice3 T_0) (v4_orders_2 T_0) (v3_orders_2 T_0) (v2_orders_2 T_0) ### DisjTree 59 60 61 62 63 64 90
% 3.36/3.58 92. (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 C (u1_struct_0 B) (u1_struct_0 A)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v18_waybel_0 C B A))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 D (u1_struct_0 A) (u1_struct_0 B)))) => ((D = (k2_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B D C) A B))))))))))) (v2_orders_2 T_0) (v3_orders_2 T_0) (v4_orders_2 T_0) (v1_lattice3 T_0) (v2_lattice3 T_0) (l1_orders_2 T_0) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (v3_lattice3 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) != (k7_grcat_1 T_0)) ### All 91
% 3.36/3.58 93. (-. (((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) = (k7_grcat_1 T_0)) /\ ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) = (k7_grcat_1 T_0)))) (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 C (u1_struct_0 B) (u1_struct_0 A)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v18_waybel_0 C B A))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 D (u1_struct_0 A) (u1_struct_0 B)))) => ((D = (k2_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B D C) A B))))))))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (v3_lattice3 T_0) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (l1_orders_2 T_0) (v2_lattice3 T_0) (v1_lattice3 T_0) (v4_orders_2 T_0) (v3_orders_2 T_0) (v2_orders_2 T_0) (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 C (u1_struct_0 A) (u1_struct_0 B)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v17_waybel_0 C A B))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 D (u1_struct_0 B) (u1_struct_0 A)))) => ((D = (k1_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B C D) A B))))))))))) ### NotAnd 58 92
% 3.36/3.58 94. (-. (((v2_orders_2 T_0) /\ ((v3_orders_2 T_0) /\ ((v4_orders_2 T_0) /\ ((v1_lattice3 T_0) /\ ((v2_lattice3 T_0) /\ ((v3_lattice3 T_0) /\ (l1_orders_2 T_0))))))) => (((k1_waybel34 T_0 T_0 (k7_grcat_1 T_0)) = (k7_grcat_1 T_0)) /\ ((k2_waybel34 T_0 T_0 (k7_grcat_1 T_0)) = (k7_grcat_1 T_0))))) (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 C (u1_struct_0 A) (u1_struct_0 B)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v17_waybel_0 C A B))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 D (u1_struct_0 B) (u1_struct_0 A)))) => ((D = (k1_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B C D) A B))))))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 C (u1_struct_0 B) (u1_struct_0 A)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v18_waybel_0 C B A))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 D (u1_struct_0 A) (u1_struct_0 B)))) => ((D = (k2_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B D C) A B))))))))))) ### ConjTree 93
% 3.36/3.58 95. (-. (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ ((v3_lattice3 A) /\ (l1_orders_2 A))))))) => (((k1_waybel34 A A (k7_grcat_1 A)) = (k7_grcat_1 A)) /\ ((k2_waybel34 A A (k7_grcat_1 A)) = (k7_grcat_1 A)))))) (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 C (u1_struct_0 B) (u1_struct_0 A)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v18_waybel_0 C B A))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 D (u1_struct_0 A) (u1_struct_0 B)))) => ((D = (k2_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B D C) A B))))))))))) (All A, (((-. (v3_struct_0 A)) /\ (l1_orders_2 A)) => (v3_waybel_1 (k1_waybel_1 A A (k7_grcat_1 A) (k7_grcat_1 A)) A A))) (All A, ((l1_orders_2 A) => ((v2_lattice3 A) => (-. (v3_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v2_orders_2 A) /\ (l1_orders_2 A))) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ ((-. (v1_xboole_0 (k7_grcat_1 A))) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v1_partfun1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ ((v11_quantal1 (k7_grcat_1 A)) /\ ((v5_orders_3 (k7_grcat_1 A) A A) /\ ((v17_waybel_0 (k7_grcat_1 A) A A) /\ ((v18_waybel_0 (k7_grcat_1 A) A A) /\ ((v19_waybel_0 (k7_grcat_1 A) A A) /\ ((v20_waybel_0 (k7_grcat_1 A) A A) /\ ((v21_waybel_0 (k7_grcat_1 A) A A) /\ ((v22_waybel_0 (k7_grcat_1 A) A A) /\ ((v23_waybel_0 (k7_grcat_1 A) A A) /\ ((v6_waybel_1 (k7_grcat_1 A) A) /\ ((v7_waybel_1 (k7_grcat_1 A) A) /\ (v8_waybel_1 (k7_grcat_1 A) A)))))))))))))))))))) (All A, ((l1_struct_0 A) => ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (m2_relset_1 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)))))) (All A, ((l1_orders_2 A) => (l1_struct_0 A))) (All A, ((l1_struct_0 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v2_funct_1 (k7_grcat_1 A)) /\ (v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A))))))) (All A, ((l1_orders_2 A) => ((v1_relat_1 (k7_grcat_1 A)) /\ ((v1_funct_1 (k7_grcat_1 A)) /\ ((v1_funct_2 (k7_grcat_1 A) (u1_struct_0 A) (u1_struct_0 A)) /\ (v23_waybel_0 (k7_grcat_1 A) A A)))))) (All A, (((v2_orders_2 A) /\ ((v3_orders_2 A) /\ ((v4_orders_2 A) /\ ((v1_lattice3 A) /\ ((v2_lattice3 A) /\ (l1_orders_2 A)))))) => (All B, (((v2_orders_2 B) /\ ((v3_orders_2 B) /\ ((v4_orders_2 B) /\ ((v1_lattice3 B) /\ ((v2_lattice3 B) /\ (l1_orders_2 B)))))) => (All C, (((v1_funct_1 C) /\ ((v1_funct_2 C (u1_struct_0 A) (u1_struct_0 B)) /\ (m2_relset_1 C (u1_struct_0 A) (u1_struct_0 B)))) => (((v3_lattice3 A) /\ ((v3_lattice3 B) /\ (v17_waybel_0 C A B))) => (All D, (((v1_funct_1 D) /\ ((v1_funct_2 D (u1_struct_0 B) (u1_struct_0 A)) /\ (m2_relset_1 D (u1_struct_0 B) (u1_struct_0 A)))) => ((D = (k1_waybel34 A B C)) <=> (v3_waybel_1 (k1_waybel_1 A B C D) A B))))))))))) ### NotAllEx 94
% 3.36/3.58 % SZS output end Proof
% 3.36/3.58 (* END-PROOF *)
%------------------------------------------------------------------------------