%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : CAT025+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 : n026.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 00:07:48 EDT 2022 % Result : Theorem 2.87s 3.06s % Output : Proof 3.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : CAT025+1 : TPTP v8.1.0. Released v3.4.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n026.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 : Sun May 29 22:50:24 EDT 2022 % 0.12/0.33 % CPUTime : % 2.87/3.06 % SZS status Theorem % 2.87/3.06 (* PROOF-FOUND *) % 2.87/3.06 (* BEGIN-PROOF *) % 2.87/3.06 % SZS output start Proof % 2.87/3.06 1. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.87/3.06 2. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.87/3.06 3. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.87/3.06 4. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.87/3.06 5. (-. (v2_cat_1 (k11_cat_2 T_0 T_1))) (v2_cat_1 (k11_cat_2 T_0 T_1)) ### Axiom % 2.87/3.06 6. ((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ (l1_cat_1 (k11_cat_2 T_0 T_1))) (-. (v2_cat_1 (k11_cat_2 T_0 T_1))) ### And 5 % 2.87/3.06 7. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_1) /\ (l1_cat_1 T_1)))) => ((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ (l1_cat_1 (k11_cat_2 T_0 T_1)))) (-. (v2_cat_1 (k11_cat_2 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 1 2 3 4 6 % 2.87/3.06 8. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 T_0 B)) /\ (l1_cat_1 (k11_cat_2 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 (k11_cat_2 T_0 T_1))) ### All 7 % 2.87/3.06 9. (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_0 T_1))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 8 % 2.87/3.06 10. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.87/3.06 11. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.87/3.06 12. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.87/3.06 13. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.87/3.06 14. (-. (l1_cat_1 (k11_cat_2 T_0 T_1))) (l1_cat_1 (k11_cat_2 T_0 T_1)) ### Axiom % 2.87/3.06 15. ((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ (l1_cat_1 (k11_cat_2 T_0 T_1))) (-. (l1_cat_1 (k11_cat_2 T_0 T_1))) ### And 14 % 2.87/3.06 16. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 T_1) /\ (l1_cat_1 T_1)))) => ((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ (l1_cat_1 (k11_cat_2 T_0 T_1)))) (-. (l1_cat_1 (k11_cat_2 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 10 11 12 13 15 % 2.87/3.06 17. (All B, (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v2_cat_1 (k11_cat_2 T_0 B)) /\ (l1_cat_1 (k11_cat_2 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 (k11_cat_2 T_0 T_1))) ### All 16 % 2.87/3.06 18. (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_0 T_1))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) ### All 17 % 2.87/3.06 19. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.87/3.06 20. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.87/3.06 21. (-. (v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) (v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) ### Axiom % 2.87/3.06 22. ((v1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ ((v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)))) (-. (v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) ### ConjTree 21 % 2.87/3.06 23. (((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ ((l1_cat_1 (k11_cat_2 T_0 T_1)) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ ((v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))))) (-. (v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) (l1_cat_1 T_2) (v2_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)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) ### DisjTree 9 18 19 20 22 % 2.87/3.06 24. (All B, (((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ ((l1_cat_1 (k11_cat_2 T_0 T_1)) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) B)) /\ ((v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) B)) /\ (l1_cat_1 (k12_nattra_1 (k11_cat_2 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)))) => ((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) (l1_cat_1 T_0) (v2_cat_1 T_0) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) ### All 23 % 2.87/3.06 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 (k11_cat_2 T_0 T_1) T_2))) (l1_cat_1 T_2) (v2_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)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) ### All 24 % 2.87/3.06 26. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.87/3.06 27. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.87/3.06 28. (-. (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) ### Axiom % 2.87/3.06 29. ((v1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ ((v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)))) (-. (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) ### ConjTree 28 % 2.87/3.06 30. (((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ ((l1_cat_1 (k11_cat_2 T_0 T_1)) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ ((v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))))) (-. (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) (l1_cat_1 T_2) (v2_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)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) ### DisjTree 9 18 26 27 29 % 2.87/3.06 31. (All B, (((v2_cat_1 (k11_cat_2 T_0 T_1)) /\ ((l1_cat_1 (k11_cat_2 T_0 T_1)) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) B)) /\ ((v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) B)) /\ (l1_cat_1 (k12_nattra_1 (k11_cat_2 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)))) => ((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) (l1_cat_1 T_0) (v2_cat_1 T_0) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) ### All 30 % 2.87/3.06 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 (k11_cat_2 T_0 T_1) T_2))) (l1_cat_1 T_2) (v2_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)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) ### All 31 % 2.87/3.06 33. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.87/3.06 34. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.87/3.06 35. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.87/3.06 36. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.87/3.06 37. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.87/3.06 38. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.87/3.06 39. (-. (v2_cat_1 (k12_nattra_1 T_1 T_2))) (v2_cat_1 (k12_nattra_1 T_1 T_2)) ### Axiom % 2.87/3.06 40. ((v1_cat_1 (k12_nattra_1 T_1 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_1 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_1 T_2)))) (-. (v2_cat_1 (k12_nattra_1 T_1 T_2))) ### ConjTree 39 % 2.87/3.06 41. (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v1_cat_1 (k12_nattra_1 T_1 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_1 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_1 T_2))))) (-. (v2_cat_1 (k12_nattra_1 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 35 36 37 38 40 % 2.87/3.06 42. (All B, (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_1 B)) /\ ((v2_cat_1 (k12_nattra_1 T_1 B)) /\ (l1_cat_1 (k12_nattra_1 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 (k12_nattra_1 T_1 T_2))) ### All 41 % 2.87/3.06 43. (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_1 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### All 42 % 2.97/3.18 44. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.97/3.18 45. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.97/3.18 46. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.97/3.18 47. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.97/3.18 48. (-. (l1_cat_1 (k12_nattra_1 T_1 T_2))) (l1_cat_1 (k12_nattra_1 T_1 T_2)) ### Axiom % 2.97/3.18 49. ((v1_cat_1 (k12_nattra_1 T_1 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_1 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_1 T_2)))) (-. (l1_cat_1 (k12_nattra_1 T_1 T_2))) ### ConjTree 48 % 2.97/3.18 50. (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 T_2) /\ (l1_cat_1 T_2)))) => ((v1_cat_1 (k12_nattra_1 T_1 T_2)) /\ ((v2_cat_1 (k12_nattra_1 T_1 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_1 T_2))))) (-. (l1_cat_1 (k12_nattra_1 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 44 45 46 47 49 % 2.97/3.18 51. (All B, (((v2_cat_1 T_1) /\ ((l1_cat_1 T_1) /\ ((v2_cat_1 B) /\ (l1_cat_1 B)))) => ((v1_cat_1 (k12_nattra_1 T_1 B)) /\ ((v2_cat_1 (k12_nattra_1 T_1 B)) /\ (l1_cat_1 (k12_nattra_1 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 (k12_nattra_1 T_1 T_2))) ### All 50 % 2.97/3.18 52. (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_1 T_2))) (l1_cat_1 T_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### All 51 % 2.97/3.18 53. (-. (v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) (v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) ### Axiom % 2.97/3.18 54. ((v1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))))) (-. (v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) ### ConjTree 53 % 2.97/3.18 55. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 (k12_nattra_1 T_1 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_1 T_2))))) => ((v1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))))) (-. (v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 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)))) => ((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_0) (v2_cat_1 T_0) ### DisjTree 33 34 43 52 54 % 2.97/3.18 56. (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)))) => ((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_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (-. (v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) ### All 55 % 2.97/3.18 57. (-. (v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 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)))) => ((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_0) (v2_cat_1 T_0) ### All 56 % 2.97/3.18 58. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.97/3.18 59. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.97/3.18 60. (-. (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) ### Axiom % 2.97/3.18 61. ((v1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))))) (-. (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) ### ConjTree 60 % 2.97/3.18 62. (((v2_cat_1 T_0) /\ ((l1_cat_1 T_0) /\ ((v2_cat_1 (k12_nattra_1 T_1 T_2)) /\ (l1_cat_1 (k12_nattra_1 T_1 T_2))))) => ((v1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ ((v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))))) (-. (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 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)))) => ((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_0) (v2_cat_1 T_0) ### DisjTree 58 59 43 52 61 % 2.97/3.18 63. (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)))) => ((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_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) (-. (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) ### All 62 % 2.97/3.18 64. (-. (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 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)))) => ((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_0) (v2_cat_1 T_0) ### All 63 % 2.97/3.18 65. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.97/3.18 66. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.97/3.18 67. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.97/3.18 68. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.97/3.18 69. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.97/3.18 70. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.97/3.18 71. (v2_cat_1 T_0) (-. (v2_cat_1 T_0)) ### Axiom % 2.97/3.18 72. (l1_cat_1 T_0) (-. (l1_cat_1 T_0)) ### Axiom % 2.97/3.18 73. (v2_cat_1 T_1) (-. (v2_cat_1 T_1)) ### Axiom % 2.97/3.18 74. (l1_cat_1 T_1) (-. (l1_cat_1 T_1)) ### Axiom % 2.97/3.18 75. (v2_cat_1 T_2) (-. (v2_cat_1 T_2)) ### Axiom % 2.97/3.18 76. (l1_cat_1 T_2) (-. (l1_cat_1 T_2)) ### Axiom % 2.97/3.18 77. (-. (m2_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) (m2_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) ### Axiom % 2.97/3.18 78. (((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 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) (-. (m2_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 71 72 73 74 75 76 77 % 2.97/3.18 79. (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 (k7_isocat_2 T_0 T_1 C) (k12_nattra_1 (k11_cat_2 T_0 T_1) C) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) ### All 78 % 2.97/3.18 80. (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 (k7_isocat_2 T_0 B C) (k12_nattra_1 (k11_cat_2 T_0 B) C) (k12_nattra_1 T_0 (k12_nattra_1 B C)))))) (-. (m2_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 79 % 2.97/3.18 81. (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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) ### All 80 % 3.38/3.55 82. (v8_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) (-. (v8_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) ### Axiom % 3.38/3.55 83. (-. ((m2_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))))) (v8_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) ### NotAnd 81 82 % 3.38/3.55 84. (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) ### NotExists 83 % 3.38/3.55 85. (((v2_cat_1 T_2) /\ (l1_cat_1 T_2)) => (v8_cat_1 (k7_isocat_2 T_0 T_1 T_2) (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))))) (l1_cat_1 T_2) (v2_cat_1 T_2) ### DisjTree 69 70 84 % 3.38/3.55 86. (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k7_isocat_2 T_0 T_1 C) (k12_nattra_1 (k11_cat_2 T_0 T_1) C) (k12_nattra_1 T_0 (k12_nattra_1 T_1 C))))) (v2_cat_1 T_2) (l1_cat_1 T_2) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) (v2_cat_1 T_1) (l1_cat_1 T_1) ### All 85 % 3.38/3.55 87. (((v2_cat_1 T_1) /\ (l1_cat_1 T_1)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k7_isocat_2 T_0 T_1 C) (k12_nattra_1 (k11_cat_2 T_0 T_1) C) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 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 67 68 86 % 3.38/3.55 88. (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (v8_cat_1 (k7_isocat_2 T_0 B C) (k12_nattra_1 (k11_cat_2 T_0 B) C) (k12_nattra_1 T_0 (k12_nattra_1 B 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 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) (v2_cat_1 T_0) (l1_cat_1 T_0) ### All 87 % 3.38/3.55 89. (((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 (k7_isocat_2 T_0 B C) (k12_nattra_1 (k11_cat_2 T_0 B) C) (k12_nattra_1 T_0 (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) (-. (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 65 66 88 % 3.38/3.55 90. (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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) ### All 89 % 3.38/3.55 91. (-. (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) ### Axiom % 3.38/3.55 92. ((r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))))) (-. (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))))) ### Equiv 90 91 % 3.38/3.55 93. (((v2_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (l1_cat_1 (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2)))) => ((r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 T_2))) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) (-. (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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)))) => ((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_2) (v2_cat_1 T_2) (l1_cat_1 T_1) (v2_cat_1 T_1) ### DisjTree 57 64 92 % 3.38/3.59 94. (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) B) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) B) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) 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)))) => ((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_0) (v2_cat_1 T_0) (-. (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))))) ### All 93 % 3.38/3.59 95. (((v2_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2)) /\ (l1_cat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2))) => (All B, (((v2_cat_1 B) /\ (l1_cat_1 B)) => ((r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) B) <=> (Ex C, ((m2_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) B) /\ (v8_cat_1 C (k12_nattra_1 (k11_cat_2 T_0 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))) (-. (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_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_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (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)))) => ((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 94 % 3.38/3.59 96. (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))))))) (l1_cat_1 T_2) (v2_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)))) => ((v2_cat_1 (k11_cat_2 A B)) /\ (l1_cat_1 (k11_cat_2 A B)))))) (-. (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))))) ### All 95 % 3.38/3.59 97. (-. (((v2_cat_1 T_2) /\ (l1_cat_1 T_2)) => (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) T_2) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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)))))) (l1_cat_1 T_1) (v2_cat_1 T_1) (l1_cat_1 T_0) (v2_cat_1 T_0) (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 96 % 3.38/3.59 98. (-. (All C, (((v2_cat_1 C) /\ (l1_cat_1 C)) => (r1_isocat_1 (k12_nattra_1 (k11_cat_2 T_0 T_1) C) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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_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)))) => ((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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))))) ### NotAllEx 97 % 3.38/3.59 99. (-. (((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 (k11_cat_2 T_0 T_1) C) (k12_nattra_1 T_0 (k12_nattra_1 T_1 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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)))))) (l1_cat_1 T_0) (v2_cat_1 T_0) (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 98 % 3.38/3.59 100. (-. (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 (k11_cat_2 T_0 B) C) (k12_nattra_1 T_0 (k12_nattra_1 B 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_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, (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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))))) ### NotAllEx 99 % 3.38/3.59 101. (-. (((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 (k11_cat_2 T_0 B) C) (k12_nattra_1 T_0 (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 100 % 3.38/3.59 102. (-. (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 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B 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 (k7_isocat_2 A B C) (k12_nattra_1 (k11_cat_2 A B) C) (k12_nattra_1 A (k12_nattra_1 B C))))))))) ### NotAllEx 101 % 3.38/3.59 % SZS output end Proof % 3.38/3.59 (* END-PROOF *) %------------------------------------------------------------------------------