TSTP Solution File: CAT025+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% 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 *)
%------------------------------------------------------------------------------