%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : CAT032+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Fri Jul 15 00:07:50 EDT 2022 % Result : Theorem 2.64s 2.86s % Output : Proof 3.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : CAT032+1 : TPTP v8.1.0. Released v3.4.0. % 0.00/0.09 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.07/0.27 % Computer : n032.cluster.edu % 0.07/0.27 % Model : x86_64 x86_64 % 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.27 % Memory : 8042.1875MB % 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.28 % CPULimit : 300 % 0.07/0.28 % WCLimit : 600 % 0.07/0.28 % DateTime : Sun May 29 21:56:11 EDT 2022 % 0.07/0.28 % CPUTime : % 2.64/2.86 % SZS status Theorem % 2.64/2.86 (* PROOF-FOUND *) % 2.64/2.86 (* BEGIN-PROOF *) % 2.64/2.86 % SZS output start Proof % 2.64/2.86 1. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.64/2.86 2. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.64/2.86 3. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.64/2.86 4. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.64/2.86 5. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.64/2.86 6. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.64/2.86 7. (-. (v2_cat_1 (k11_cat_2 T_1 T_2))) (v2_cat_1 (k11_cat_2 T_1 T_2)) ### Axiom % 2.64/2.86 8. ((v2_cat_1 (k11_cat_2 T_1 T_2)) /\ (l1_cat_1 (k11_cat_2 T_1 T_2))) (-. (v2_cat_1 (k11_cat_2 T_1 T_2))) ### And 7 % 2.64/2.86 9. (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v2_cat_1 (k11_cat_2 T_1 T_2)) /\ (l1_cat_1 (k11_cat_2 T_1 T_2)))) (-. (v2_cat_1 (k11_cat_2 T_1 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### DisjTree 3 4 5 6 8 % 2.64/2.86 10. (All B, (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 T_1 B)) /\ (l1_cat_1 (k11_cat_2 T_1 B))))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (v2_cat_1 (k11_cat_2 T_1 T_2))) ### All 9 % 2.64/2.86 11. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (-. (v2_cat_1 (k11_cat_2 T_1 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### All 10 % 2.64/2.86 12. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.64/2.86 13. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.64/2.86 14. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.64/2.86 15. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.64/2.86 16. (-. (l1_cat_1 (k11_cat_2 T_1 T_2))) (l1_cat_1 (k11_cat_2 T_1 T_2)) ### Axiom % 2.64/2.86 17. ((v2_cat_1 (k11_cat_2 T_1 T_2)) /\ (l1_cat_1 (k11_cat_2 T_1 T_2))) (-. (l1_cat_1 (k11_cat_2 T_1 T_2))) ### And 16 % 2.64/2.86 18. (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v2_cat_1 (k11_cat_2 T_1 T_2)) /\ (l1_cat_1 (k11_cat_2 T_1 T_2)))) (-. (l1_cat_1 (k11_cat_2 T_1 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### DisjTree 12 13 14 15 17 % 2.64/2.86 19. (All B, (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 T_1 B)) /\ (l1_cat_1 (k11_cat_2 T_1 B))))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (l1_cat_1 (k11_cat_2 T_1 T_2))) ### All 18 % 2.64/2.86 20. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (-. (l1_cat_1 (k11_cat_2 T_1 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### All 19 % 2.64/2.86 21. (-. (v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) (v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) ### Axiom % 2.64/2.86 22. ((v1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))))) (-. (v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) ### ConjTree 21 % 2.64/2.86 23. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 (k11_cat_2 T_1 T_2)) /\ (l1_cat_1 (k11_cat_2 T_1 T_2))))) => ((v1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))))) (-. (v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 1 2 11 20 22 % 2.64/2.86 24. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_0 B)) /\ ((v2_cat_1 (k12_nattra_1 T_0 B)) /\ (l1_cat_1 (k12_nattra_1 T_0 B)))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (-. (v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) ### All 23 % 2.64/2.86 25. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (-. (v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 24 % 2.64/2.86 26. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.64/2.86 27. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.64/2.86 28. (-. (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) ### Axiom % 2.64/2.86 29. ((v1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))))) (-. (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) ### ConjTree 28 % 2.64/2.86 30. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 (k11_cat_2 T_1 T_2)) /\ (l1_cat_1 (k11_cat_2 T_1 T_2))))) => ((v1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))))) (-. (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 26 27 11 20 29 % 2.64/2.86 31. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_0 B)) /\ ((v2_cat_1 (k12_nattra_1 T_0 B)) /\ (l1_cat_1 (k12_nattra_1 T_0 B)))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (-. (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) ### All 30 % 2.64/2.86 32. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (-. (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 31 % 2.64/2.86 33. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.64/2.86 34. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.64/2.86 35. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.64/2.86 36. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.64/2.86 37. (-. (v2_cat_1 (k12_nattra_1 T_0 T_1))) (v2_cat_1 (k12_nattra_1 T_0 T_1)) ### Axiom % 2.64/2.86 38. ((v1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_1)))) (-. (v2_cat_1 (k12_nattra_1 T_0 T_1))) ### ConjTree 37 % 2.64/2.86 39. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_1) /\ (l1_cat_1 T_1)))) => ((v1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_1))))) (-. (v2_cat_1 (k12_nattra_1 T_0 T_1))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 33 34 35 36 38 % 2.64/2.86 40. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_0 B)) /\ ((v2_cat_1 (k12_nattra_1 T_0 B)) /\ (l1_cat_1 (k12_nattra_1 T_0 B)))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (-. (v2_cat_1 (k12_nattra_1 T_0 T_1))) ### All 39 % 2.64/2.86 41. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (-. (v2_cat_1 (k12_nattra_1 T_0 T_1))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 40 % 2.64/2.86 42. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.64/2.86 43. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.64/2.86 44. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.64/2.86 45. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.73/2.94 46. (-. (l1_cat_1 (k12_nattra_1 T_0 T_1))) (l1_cat_1 (k12_nattra_1 T_0 T_1)) ### Axiom % 2.73/2.94 47. ((v1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_1)))) (-. (l1_cat_1 (k12_nattra_1 T_0 T_1))) ### ConjTree 46 % 2.73/2.94 48. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_1) /\ (l1_cat_1 T_1)))) => ((v1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_1))))) (-. (l1_cat_1 (k12_nattra_1 T_0 T_1))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 42 43 44 45 47 % 2.73/2.94 49. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_0 B)) /\ ((v2_cat_1 (k12_nattra_1 T_0 B)) /\ (l1_cat_1 (k12_nattra_1 T_0 B)))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (-. (l1_cat_1 (k12_nattra_1 T_0 T_1))) ### All 48 % 2.73/2.94 50. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (-. (l1_cat_1 (k12_nattra_1 T_0 T_1))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 49 % 2.73/2.94 51. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.73/2.94 52. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.73/2.94 53. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.73/2.94 54. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.73/2.94 55. (-. (v2_cat_1 (k12_nattra_1 T_0 T_2))) (v2_cat_1 (k12_nattra_1 T_0 T_2)) ### Axiom % 2.73/2.94 56. ((v1_cat_1 (k12_nattra_1 T_0 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_2)))) (-. (v2_cat_1 (k12_nattra_1 T_0 T_2))) ### ConjTree 55 % 2.73/2.94 57. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v1_cat_1 (k12_nattra_1 T_0 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_2))))) (-. (v2_cat_1 (k12_nattra_1 T_0 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 51 52 53 54 56 % 2.73/2.94 58. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_0 B)) /\ ((v2_cat_1 (k12_nattra_1 T_0 B)) /\ (l1_cat_1 (k12_nattra_1 T_0 B)))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (v2_cat_1 (k12_nattra_1 T_0 T_2))) ### All 57 % 2.73/2.94 59. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (-. (v2_cat_1 (k12_nattra_1 T_0 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 58 % 2.73/2.94 60. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.73/2.94 61. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.73/2.94 62. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.73/2.94 63. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.73/2.94 64. (-. (l1_cat_1 (k12_nattra_1 T_0 T_2))) (l1_cat_1 (k12_nattra_1 T_0 T_2)) ### Axiom % 2.73/2.94 65. ((v1_cat_1 (k12_nattra_1 T_0 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_2)))) (-. (l1_cat_1 (k12_nattra_1 T_0 T_2))) ### ConjTree 64 % 2.73/2.94 66. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v1_cat_1 (k12_nattra_1 T_0 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_2))))) (-. (l1_cat_1 (k12_nattra_1 T_0 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 60 61 62 63 65 % 2.73/2.94 67. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_0 B)) /\ ((v2_cat_1 (k12_nattra_1 T_0 B)) /\ (l1_cat_1 (k12_nattra_1 T_0 B)))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (l1_cat_1 (k12_nattra_1 T_0 T_2))) ### All 66 % 2.73/2.94 68. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (-. (l1_cat_1 (k12_nattra_1 T_0 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 67 % 2.73/2.94 69. (-. (v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) ### Axiom % 2.73/2.94 70. ((v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (-. (v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) ### And 69 % 2.73/2.94 71. (((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((l1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_2))))) => ((v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))))) (-. (v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (v2_cat_1 T_2) (l1_cat_1 T_2) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) ### DisjTree 41 50 59 68 70 % 2.73/2.94 72. (All B, (((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((l1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) B)) /\ (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) B))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (l1_cat_1 T_2) (v2_cat_1 T_2) (-. (v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) ### All 71 % 2.73/2.94 73. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (-. (v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (v2_cat_1 T_2) (l1_cat_1 T_2) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) ### All 72 % 2.73/2.94 74. (-. (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) ### Axiom % 2.73/2.94 75. ((v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (-. (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) ### And 74 % 2.73/2.94 76. (((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((l1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 (k12_nattra_1 T_0 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_0 T_2))))) => ((v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))))) (-. (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (v2_cat_1 T_2) (l1_cat_1 T_2) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) ### DisjTree 41 50 59 68 75 % 2.73/2.94 77. (All B, (((v2_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((l1_cat_1 (k12_nattra_1 T_0 T_1)) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) B)) /\ (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) B))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (l1_cat_1 T_2) (v2_cat_1 T_2) (-. (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) ### All 76 % 2.73/2.94 78. (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (-. (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (v2_cat_1 T_2) (l1_cat_1 T_2) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) ### All 77 % 3.02/3.21 79. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 3.02/3.21 80. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 3.02/3.21 81. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 3.02/3.21 82. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 3.02/3.21 83. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 3.02/3.21 84. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 3.02/3.21 85. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 3.02/3.21 86. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 3.02/3.21 87. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 3.02/3.21 88. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 3.02/3.21 89. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 3.02/3.21 90. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 3.02/3.21 91. (-. (m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) ### Axiom % 3.02/3.21 92. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))))) => (m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (-. (m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 85 86 87 88 89 90 91 % 3.02/3.21 93. (All C, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 T_0 T_1 C) (k12_nattra_1 T_0 (k11_cat_2 T_1 C)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 C))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) ### All 92 % 3.02/3.21 94. (All B, (All C, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 T_0 B C) (k12_nattra_1 T_0 (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 T_0 B) (k12_nattra_1 T_0 C)))))) (-. (m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 93 % 3.02/3.21 95. (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) ### All 94 % 3.02/3.21 96. (v8_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) (-. (v8_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) ### Axiom % 3.02/3.21 97. (-. ((m2_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))))) (v8_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) ### NotAnd 95 96 % 3.02/3.21 98. (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (v8_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) ### NotExists 97 % 3.02/3.21 99. (((v2_cat_1 T_2) /\ (l1_cat_1 T_2)) => (v8_cat_1 (k17_isocat_2 T_0 T_1 T_2) (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (l1_cat_1 T_2) (v2_cat_1 T_2) ### DisjTree 83 84 98 % 3.02/3.21 100. (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 T_0 T_1 C) (k12_nattra_1 T_0 (k11_cat_2 T_1 C)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 C))))) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) ### All 99 % 3.02/3.21 101. (((v2_cat_1 T_1) /\ (l1_cat_1 T_1)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 T_0 T_1 C) (k12_nattra_1 T_0 (k11_cat_2 T_1 C)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 C)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### DisjTree 81 82 100 % 3.02/3.21 102. (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 T_0 B C) (k12_nattra_1 T_0 (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 T_0 B) (k12_nattra_1 T_0 C))))))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) ### All 101 % 3.02/3.21 103. (((v2_cat_1 T_0) /\ (l1_cat_1 T_0)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 T_0 B C) (k12_nattra_1 T_0 (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 T_0 B) (k12_nattra_1 T_0 C)))))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### DisjTree 79 80 102 % 3.02/3.23 104. (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) ### All 103 % 3.02/3.23 105. (-. (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) ### Axiom % 3.02/3.23 106. ((r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))))) (-. (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) ### Equiv 104 105 % 3.02/3.23 107. (((v2_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (l1_cat_1 (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) => ((r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (-. (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (l1_cat_1 T_2) (v2_cat_1 T_2) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) ### DisjTree 73 78 106 % 3.02/3.23 108. (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) B) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) B) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) B)))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (v2_cat_1 T_2) (l1_cat_1 T_2) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (-. (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) ### All 107 % 3.02/3.23 109. (((v2_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)))) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) B) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) B) /\ (v8_cat_1 C (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) B))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (-. (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (v2_cat_1 T_0) (l1_cat_1 T_0) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) ### DisjTree 25 32 108 % 3.02/3.23 110. (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 A B) <=> (Ex C, ((m2_cat_1 C A B) /\ (v8_cat_1 C A B)))))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (v2_cat_1 T_1) (l1_cat_1 T_1) (v2_cat_1 T_2) (l1_cat_1 T_2) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) (-. (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2)))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) ### All 109 % 3.02/3.24 111. (-. (((v2_cat_1 T_2) /\ (l1_cat_1 T_2)) => (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 T_2)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 T_2))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_1) (v2_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 A B) <=> (Ex C, ((m2_cat_1 C A B) /\ (v8_cat_1 C A B)))))))) ### ConjTree 110 % 3.02/3.24 112. (-. (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 C)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 C)))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 A B) <=> (Ex C, ((m2_cat_1 C A B) /\ (v8_cat_1 C A B)))))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (v2_cat_1 T_1) (l1_cat_1 T_1) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) ### NotAllEx 111 % 3.02/3.24 113. (-. (((v2_cat_1 T_1) /\ (l1_cat_1 T_1)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 T_1 C)) (k11_cat_2 (k12_nattra_1 T_0 T_1) (k12_nattra_1 T_0 C))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 A B) <=> (Ex C, ((m2_cat_1 C A B) /\ (v8_cat_1 C A B)))))))) ### ConjTree 112 % 3.02/3.24 114. (-. (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 T_0 B) (k12_nattra_1 T_0 C)))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 A B) <=> (Ex C, ((m2_cat_1 C A B) /\ (v8_cat_1 C A B)))))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) ### NotAllEx 113 % 3.02/3.24 115. (-. (((v2_cat_1 T_0) /\ (l1_cat_1 T_0)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (r1_isocat_1 (k12_nattra_1 T_0 (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 T_0 B) (k12_nattra_1 T_0 C))))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 A B) <=> (Ex C, ((m2_cat_1 C A B) /\ (v8_cat_1 C A B)))))))) ### ConjTree 114 % 3.02/3.24 116. (-. (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (r1_isocat_1 (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C)))))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 A B) <=> (Ex C, ((m2_cat_1 C A B) /\ (v8_cat_1 C A B)))))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 A B)) /\ ((v2_cat_1 (k12_nattra_1 A B)) /\ (l1_cat_1 (k12_nattra_1 A B))))))) (All A, (All B, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (All A, (All B, (All C, (((v2_cat_1 A) /\ ((l1_cat_1 A) /\ ((v2_cat_1 B) /\ ((l1_cat_1 B) /\ ((v2_cat_1 C) /\ (l1_cat_1 C)))))) => (m2_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))) (All A, (((v2_cat_1 A) /\ (l1_cat_1 A)) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k17_isocat_2 A B C) (k12_nattra_1 A (k11_cat_2 B C)) (k11_cat_2 (k12_nattra_1 A B) (k12_nattra_1 A C))))))))) ### NotAllEx 115 % 3.02/3.24 % SZS output end Proof % 3.02/3.24 (* END-PROOF *) %------------------------------------------------------------------------------