TSTP Solution File: CAT032+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% 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 *)
%------------------------------------------------------------------------------