TSTP Solution File: NUM858+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n007.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 : Mon Jul 18 14:46:52 EDT 2022
% Result : Theorem 9.55s 9.76s
% Output : Proof 9.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM858+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n007.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 14:06:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.55/9.76 % SZS status Theorem
% 9.55/9.76 (* PROOF-FOUND *)
% 9.55/9.76 (* BEGIN-PROOF *)
% 9.55/9.76 % SZS output start Proof
% 9.55/9.76 1. ((max T_0 T_1) != (max T_0 T_1)) ### Refl(=)
% 9.55/9.76 2. (-. (model_max T_0 T_1 (max T_0 T_1))) ### Definition-Pseudo(model_max) 1
% 9.55/9.76 3. (T_0 != T_0) ### Refl(=)
% 9.55/9.76 4. (-. (lesseq T_0 T_0)) ### Refl(lesseq)
% 9.55/9.76 5. (T_0 != T_0) ### Refl(=)
% 9.55/9.76 6. (T_2 != T_2) ### Refl(=)
% 9.55/9.76 7. (T_0 != (max T_0 T_1)) ((max T_0 T_1) = T_0) ### Sym(=)
% 9.55/9.76 8. ((max T_0 T_1) != T_1) ((max T_0 T_1) = T_1) ### Axiom
% 9.55/9.76 9. (lesseq T_0 T_1) (-. (lesseq T_0 T_1)) ### Axiom
% 9.55/9.76 10. (((max T_0 T_1) = T_1) \/ (-. (lesseq T_0 T_1))) (lesseq T_0 T_1) ((max T_0 T_1) != T_1) ### Or 8 9
% 9.55/9.76 11. (All Y, (((max T_0 Y) = Y) \/ (-. (lesseq T_0 Y)))) ((max T_0 T_1) != T_1) (lesseq T_0 T_1) ### All 10
% 9.55/9.76 12. (-. (lesseq T_1 T_0)) (lesseq T_1 T_0) ### Axiom
% 9.55/9.76 13. ((lesseq T_0 T_1) \/ (lesseq T_1 T_0)) (-. (lesseq T_1 T_0)) ((max T_0 T_1) != T_1) (All Y, (((max T_0 Y) = Y) \/ (-. (lesseq T_0 Y)))) ### Or 11 12
% 9.55/9.76 14. (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (All Y, (((max T_0 Y) = Y) \/ (-. (lesseq T_0 Y)))) ((max T_0 T_1) != T_1) (-. (lesseq T_1 T_0)) ### All 13
% 9.55/9.76 15. (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (-. (lesseq T_1 T_0)) ((max T_0 T_1) != T_1) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) ### All 14
% 9.55/9.76 16. (((max T_0 T_1) = T_0) \/ (-. (lesseq T_1 T_0))) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) ((max T_0 T_1) != T_1) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) ### Or 7 15
% 9.55/9.76 17. (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ((max T_0 T_1) != T_1) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) ### All 16
% 9.55/9.76 18. (-. (lesseq T_2 T_1)) (lesseq T_2 (max T_0 T_1)) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) ### Trans 6 17
% 9.55/9.76 19. (T_1 != T_1) ### Refl(=)
% 9.55/9.76 20. (-. (lesseq T_1 T_1)) ### Refl(lesseq)
% 9.55/9.76 21. (T_2 != T_2) ### Refl(=)
% 9.55/9.76 22. (T_1 != (max T_0 T_1)) ((max T_0 T_1) = T_1) ### Sym(=)
% 9.55/9.76 23. (lesseq T_0 T_1) (-. (lesseq T_0 T_1)) ### Axiom
% 9.55/9.76 24. (((max T_0 T_1) = T_1) \/ (-. (lesseq T_0 T_1))) (lesseq T_0 T_1) (T_1 != (max T_0 T_1)) ### Or 22 23
% 9.55/9.76 25. (All Y, (((max T_0 Y) = Y) \/ (-. (lesseq T_0 Y)))) (T_1 != (max T_0 T_1)) (lesseq T_0 T_1) ### All 24
% 9.55/9.76 26. (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_0 T_1) (T_1 != (max T_0 T_1)) ### All 25
% 9.55/9.76 27. (-. (lesseq T_1 T_0)) (lesseq T_1 T_0) ### Axiom
% 9.55/9.76 28. ((lesseq T_0 T_1) \/ (lesseq T_1 T_0)) (-. (lesseq T_1 T_0)) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### Or 26 27
% 9.55/9.76 29. (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (-. (lesseq T_1 T_0)) ### All 28
% 9.55/9.76 30. (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (-. (lesseq T_1 T_0)) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### All 29
% 9.55/9.76 31. ((max T_0 T_1) != T_0) ((max T_0 T_1) = T_0) ### Axiom
% 9.55/9.76 32. (lesseq T_1 T_0) (-. (lesseq T_1 T_0)) ### Axiom
% 9.55/9.76 33. (((max T_0 T_1) = T_0) \/ (-. (lesseq T_1 T_0))) (lesseq T_1 T_0) ((max T_0 T_1) != T_0) ### Or 31 32
% 9.55/9.76 34. (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) ((max T_0 T_1) != T_0) (lesseq T_1 T_0) ### All 33
% 9.55/9.76 35. ((lesseq T_1 T_0) <=> (lesseq (summation T_1) (summation T_0))) ((max T_0 T_1) != T_0) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### Equiv 30 34
% 9.55/9.76 36. (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) ((max T_0 T_1) != T_0) ### All 35
% 9.55/9.76 37. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ((max T_0 T_1) != T_0) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) ### All 36
% 9.55/9.76 38. (T_2 != T_0) (T_2 = (max T_0 T_1)) (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Trans 21 37
% 9.55/9.76 39. (T_1 != T_1) ### Refl(=)
% 9.55/9.76 40. ((max T_2 T_1) != (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) (T_2 = (max T_0 T_1)) ### NotEqual 38 39
% 9.55/9.76 41. (-. (lesseq T_1 (max T_0 T_1))) ((max T_2 T_1) = T_1) (T_2 = (max T_0 T_1)) (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### TransEq2 19 20 40
% 9.55/9.76 42. (lesseq T_2 T_1) (-. (lesseq T_2 T_1)) ### Axiom
% 9.55/9.76 43. (((max T_2 T_1) = T_1) \/ (-. (lesseq T_2 T_1))) (lesseq T_2 T_1) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) (T_2 = (max T_0 T_1)) (-. (lesseq T_1 (max T_0 T_1))) ### Or 41 42
% 9.55/9.76 44. (All Y, (((max T_2 Y) = Y) \/ (-. (lesseq T_2 Y)))) (-. (lesseq T_1 (max T_0 T_1))) (T_2 = (max T_0 T_1)) (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_2 T_1) ### All 43
% 9.55/9.76 45. (lesseq T_2 T_1) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All Y, ((lesseq T_1 Y) <=> (lesseq (summation T_1) (summation Y)))) (T_2 = (max T_0 T_1)) (-. (lesseq T_1 (max T_0 T_1))) ### All 44
% 9.55/9.76 46. (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (-. (lesseq T_1 (max T_0 T_1))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_2 T_1) ### All 45
% 9.55/9.76 47. (-. (lesseq T_1 T_2)) (lesseq T_1 T_2) ### Axiom
% 9.55/9.76 48. ((lesseq T_2 T_1) \/ (lesseq T_1 T_2)) (-. (lesseq T_1 T_2)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (-. (lesseq T_1 (max T_0 T_1))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) ### Or 46 47
% 9.55/9.76 49. (All Y, ((lesseq T_2 Y) \/ (lesseq Y T_2))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (-. (lesseq T_1 (max T_0 T_1))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (-. (lesseq T_1 T_2)) ### All 48
% 9.55/9.76 50. (-. (lesseq T_1 T_2)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (-. (lesseq T_1 (max T_0 T_1))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) ### All 49
% 9.55/9.76 51. (-. (lesseq T_2 T_2)) ### Refl(lesseq)
% 9.55/9.76 52. (T_2 != T_2) ### Refl(=)
% 9.55/9.76 53. (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (-. (lesseq T_1 T_2)) ### TransEq2 50 51 52
% 9.64/9.81 54. (T_2 != T_1) (T_2 = T_1) ### Axiom
% 9.64/9.81 55. (((lesseq T_2 T_1) /\ (lesseq T_1 T_2)) => (T_2 = T_1)) (T_2 != T_1) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (lesseq T_2 (max T_0 T_1)) ### DisjTree 18 53 54
% 9.64/9.81 56. (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (lesseq T_2 (max T_0 T_1)) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 != T_1) ### All 55
% 9.64/9.81 57. ((max T_0 T_2) != (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (lesseq T_2 (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) ### NotEqual 5 56
% 9.64/9.81 58. (-. (lesseq T_0 (max T_0 T_1))) ((max T_0 T_2) = T_0) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (lesseq T_2 (max T_0 T_1)) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### TransEq2 3 4 57
% 9.64/9.81 59. (lesseq T_2 T_0) (-. (lesseq T_2 T_0)) ### Axiom
% 9.64/9.81 60. (((max T_0 T_2) = T_0) \/ (-. (lesseq T_2 T_0))) (lesseq T_2 T_0) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (lesseq T_2 (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (-. (lesseq T_0 (max T_0 T_1))) ### Or 58 59
% 9.64/9.81 61. (-. (lesseq T_0 (max T_0 T_1))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (lesseq T_2 (max T_0 T_1)) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_2 T_0) ### All 60
% 9.64/9.81 62. (lesseq T_2 T_0) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All Y, (((max T_0 Y) = T_0) \/ (-. (lesseq Y T_0)))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_2 (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (-. (lesseq T_0 (max T_0 T_1))) ### All 61
% 9.64/9.81 63. (-. (lesseq T_0 (max T_0 T_1))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (lesseq T_2 (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_2 T_0) ### All 62
% 9.64/9.81 64. ((model_max T_0 T_1 (max T_0 T_1)) => (lesseq T_2 (max T_0 T_1))) (lesseq T_2 T_0) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (-. (lesseq T_0 (max T_0 T_1))) ### Imply 2 63
% 9.64/9.81 65. (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 (max T_0 T_1))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_2 T_0) ### All 64
% 9.64/9.81 66. (-. (lesseq T_0 T_2)) (lesseq T_0 T_2) ### Axiom
% 9.64/9.81 67. ((lesseq T_2 T_0) \/ (lesseq T_0 T_2)) (-. (lesseq T_0 T_2)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (-. (lesseq T_0 (max T_0 T_1))) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) ### Or 65 66
% 9.64/9.81 68. (All Y, ((lesseq T_2 Y) \/ (lesseq Y T_2))) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 (max T_0 T_1))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (-. (lesseq T_0 T_2)) ### All 67
% 9.64/9.81 69. (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (-. (lesseq T_0 T_2)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_0 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (-. (lesseq T_0 (max T_0 T_1))) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) (All Y, ((lesseq T_2 Y) \/ (lesseq Y T_2))) ### All 68
% 9.64/9.81 70. (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 (max T_0 T_1))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_0 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (-. (lesseq T_0 T_2)) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### All 69
% 9.64/9.81 71. (-. (lesseq T_2 T_2)) ### Refl(lesseq)
% 9.64/9.81 72. (T_2 != T_2) ### Refl(=)
% 9.64/9.81 73. (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (-. (lesseq T_0 T_2)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) ### TransEq2 70 71 72
% 9.64/9.81 74. (-. ((lesseq T_0 T_2) /\ (lesseq T_1 T_2))) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### NotAnd 73 53
% 9.73/9.91 75. (-. (ub T_0 T_1 T_2)) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) ### Definition-Pseudo(ub) 74
% 9.73/9.91 76. (-. (model_ub T_0 T_1 T_2)) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### Definition-Pseudo(model_ub) 75
% 9.73/9.91 77. (T_2 != T_2) ### Refl(=)
% 9.73/9.91 78. (-. (lesseq T_2 T_2)) ### Refl(lesseq)
% 9.73/9.91 79. (T_2 != T_2) ### Refl(=)
% 9.73/9.91 80. (-. (lesseq T_2 T_2)) ### Refl(lesseq)
% 9.73/9.91 81. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_1 T_0) ((max T_0 T_1) != T_0) ### All 34
% 9.73/9.91 82. (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_0 T_1) ((max T_0 T_1) != T_1) ### All 11
% 9.73/9.91 83. ((lesseq T_1 T_0) \/ (lesseq T_0 T_1)) ((max T_0 T_1) != T_1) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ((max T_0 T_1) != T_0) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Or 81 82
% 9.73/9.91 84. (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ((max T_0 T_1) != T_0) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ((max T_0 T_1) != T_1) ### All 83
% 9.73/9.91 85. (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ((max T_0 T_1) != T_1) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ((max T_0 T_1) != T_0) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### All 84
% 9.73/9.91 86. (-. (lesseq T_2 T_0)) (T_2 = (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ((max T_0 T_1) != T_1) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### TransEq 79 80 85
% 9.73/9.91 87. (-. (lesseq T_2 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 = (max T_0 T_1)) (-. (lesseq T_2 T_0)) ### TransEq 77 78 86
% 9.73/9.91 88. (T_3 != T_3) ### Refl(=)
% 9.73/9.91 89. (-. (lesseq T_2 T_3)) (lesseq T_1 T_3) (-. (lesseq T_2 T_0)) (T_2 = (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### Trans 87 88
% 9.73/9.91 90. (T_3 != T_3) ### Refl(=)
% 9.73/9.91 91. (lesseq T_0 T_3) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 = (max T_0 T_1)) (lesseq T_1 T_3) (-. (lesseq T_2 T_3)) ### Trans 89 90
% 9.73/9.91 92. ((lesseq T_0 T_3) /\ (lesseq T_1 T_3)) (-. (lesseq T_2 T_3)) (T_2 = (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### And 91
% 9.73/9.91 93. (ub T_0 T_1 T_3) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 = (max T_0 T_1)) (-. (lesseq T_2 T_3)) ### Definition-Pseudo(ub) 92
% 9.73/9.91 94. (model_ub T_0 T_1 T_3) (-. (lesseq T_2 T_3)) (T_2 = (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### Definition-Pseudo(model_ub) 93
% 9.73/9.91 95. (-. ((model_ub T_0 T_1 T_3) => (lesseq T_2 T_3))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 = (max T_0 T_1)) ### NotImply 94
% 9.73/9.91 96. (-. (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z)))) (T_2 = (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### NotAllEx 95
% 9.73/9.91 97. (-. ((model_ub T_0 T_1 T_2) /\ (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) ### NotAnd 76 96
% 9.73/9.91 98. (model_max T_0 T_1 T_2) (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (-. ((model_ub T_0 T_1 T_2) /\ (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))))) ### Definition-Pseudo(model_max) 97
% 9.73/9.91 99. ((model_max T_0 T_1 T_2) /\ (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z)))) (-. ((model_ub T_0 T_1 T_2) /\ (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### And 98
% 9.73/9.91 100. (minsol_model_max T_0 T_1 T_2) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (-. ((model_ub T_0 T_1 T_2) /\ (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))))) ### Definition-Pseudo(minsol_model_max) 99
% 9.73/9.91 101. (-. (minsol_model_ub T_0 T_1 T_2)) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (minsol_model_max T_0 T_1 T_2) ### Definition-Pseudo(minsol_model_ub) 100
% 9.73/9.91 102. (-. (lesseq T_0 T_0)) ### Refl(lesseq)
% 9.73/9.91 103. (lesseq T_1 T_0) (-. (lesseq T_1 T_0)) ### Axiom
% 9.73/9.91 104. (-. ((lesseq T_0 T_0) /\ (lesseq T_1 T_0))) (lesseq T_1 T_0) ### NotAnd 102 103
% 9.73/9.91 105. (-. (ub T_0 T_1 T_0)) (lesseq T_1 T_0) ### Definition-Pseudo(ub) 104
% 9.73/9.91 106. (-. (model_ub T_0 T_1 T_0)) (lesseq T_1 T_0) ### Definition-Pseudo(model_ub) 105
% 9.73/9.91 107. (-. (lesseq T_2 T_0)) (lesseq T_2 T_0) ### Axiom
% 9.73/9.91 108. ((model_ub T_0 T_1 T_0) => (lesseq T_2 T_0)) (-. (lesseq T_2 T_0)) (lesseq T_1 T_0) ### Imply 106 107
% 9.73/9.91 109. (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_1 T_0) (-. (lesseq T_2 T_0)) ### All 108
% 9.73/9.91 110. (-. (lesseq T_0 T_1)) (lesseq T_0 T_1) ### Axiom
% 9.73/9.91 111. ((lesseq T_1 T_0) \/ (lesseq T_0 T_1)) (-. (lesseq T_0 T_1)) (-. (lesseq T_2 T_0)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) ### Or 109 110
% 9.73/9.91 112. (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_2 T_0)) (-. (lesseq T_0 T_1)) ### All 111
% 9.73/9.91 113. (lesseq T_0 T_2) (-. (lesseq T_0 T_2)) ### Axiom
% 9.73/9.91 114. (T_0 != T_2) (T_2 = T_0) ### Sym(=)
% 9.73/9.91 115. (((lesseq T_2 T_0) /\ (lesseq T_0 T_2)) => (T_2 = T_0)) (T_0 != T_2) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) ### DisjTree 112 113 114
% 9.73/9.91 116. (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 T_1)) (lesseq T_0 T_2) (T_0 != T_2) ### All 115
% 9.73/9.93 117. (T_1 != T_1) ### Refl(=)
% 9.73/9.93 118. ((max T_0 T_1) != (max T_2 T_1)) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) ### NotEqual 116 117
% 9.73/9.93 119. (T_2 != T_2) ### Refl(=)
% 9.73/9.93 120. (T_2 != T_2) ### Refl(=)
% 9.73/9.93 121. (T_2 != (max T_0 T_1)) ((max T_2 T_1) = T_2) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 T_1)) (lesseq T_0 T_2) ### TransEq-sym 118 119 120
% 9.73/9.93 122. (lesseq T_1 T_2) (-. (lesseq T_1 T_2)) ### Axiom
% 9.73/9.93 123. (((max T_2 T_1) = T_2) \/ (-. (lesseq T_1 T_2))) (lesseq T_1 T_2) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (T_2 != (max T_0 T_1)) ### Or 121 122
% 9.73/9.93 124. (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (T_2 != (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 T_1)) (lesseq T_0 T_2) (lesseq T_1 T_2) ### All 123
% 9.73/9.93 125. (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (T_2 != (max T_0 T_1)) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) ### All 124
% 9.73/9.93 126. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 != (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 T_1)) (lesseq T_0 T_2) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### All 125
% 9.73/9.93 127. (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (T_2 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### All 126
% 9.73/9.93 128. (-. (lesseq T_1 T_1)) ### Refl(lesseq)
% 9.73/9.93 129. (-. ((lesseq T_0 T_1) /\ (lesseq T_1 T_1))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 != (max T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### NotAnd 127 128
% 9.73/9.93 130. (-. (ub T_0 T_1 T_1)) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (T_2 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Definition-Pseudo(ub) 129
% 9.73/9.93 131. (-. (model_ub T_0 T_1 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 != (max T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### Definition-Pseudo(model_ub) 130
% 9.73/9.93 132. (lesseq T_2 T_1) (-. (lesseq T_2 T_1)) ### Axiom
% 9.73/9.93 133. (lesseq T_1 T_2) (-. (lesseq T_1 T_2)) ### Axiom
% 9.73/9.93 134. (T_2 != T_2) ### Refl(=)
% 9.73/9.93 135. (T_2 != T_2) ### Refl(=)
% 9.73/9.93 136. (T_2 != T_2) ### Refl(=)
% 9.73/9.93 137. (-. (lesseq T_2 T_0)) (lesseq T_2 T_1) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### Trans 136 30
% 9.73/9.93 138. (lesseq T_0 T_2) (-. (lesseq T_0 T_2)) ### Axiom
% 9.73/9.93 139. (T_2 = T_1) (T_1 != T_2) ### Sym(=)
% 9.73/9.93 140. (T_0 != T_0) ### Refl(=)
% 9.73/9.93 141. (T_0 != T_1) (T_2 = T_0) (T_2 = T_1) ### Trans-sym 139 140
% 9.73/9.93 142. (T_2 = T_0) (T_0 != T_2) ### Sym(=)
% 9.73/9.93 143. (T_1 != T_1) ### Refl(=)
% 9.73/9.93 144. (T_1 != T_0) (T_2 = T_1) (T_2 = T_0) ### Trans-sym 142 143
% 9.73/9.93 145. ((max T_0 T_1) != (max T_1 T_0)) (T_2 = T_1) (T_2 = T_0) ### NotEqual 141 144
% 9.73/9.93 146. (T_1 != T_1) ### Refl(=)
% 9.73/9.93 147. (T_1 != T_1) ### Refl(=)
% 9.73/9.93 148. (T_1 != (max T_0 T_1)) ((max T_1 T_0) = T_1) (T_2 = T_0) (T_2 = T_1) ### TransEq-sym 145 146 147
% 9.73/9.93 149. (T_2 = T_0) (T_0 != T_2) ### Sym(=)
% 9.73/9.93 150. (T_1 != T_1) ### Refl(=)
% 9.73/9.93 151. (-. (lesseq T_0 T_1)) (lesseq T_2 T_1) (T_2 = T_0) ### Trans 149 150
% 9.73/9.93 152. (((max T_1 T_0) = T_1) \/ (-. (lesseq T_0 T_1))) (lesseq T_2 T_1) (T_2 = T_1) (T_2 = T_0) (T_1 != (max T_0 T_1)) ### Or 148 151
% 9.73/9.93 153. (All Y, (((max T_1 Y) = T_1) \/ (-. (lesseq Y T_1)))) (T_1 != (max T_0 T_1)) (T_2 = T_0) (T_2 = T_1) (lesseq T_2 T_1) ### All 152
% 9.73/9.93 154. (((lesseq T_2 T_0) /\ (lesseq T_0 T_2)) => (T_2 = T_0)) (T_2 = T_1) (All Y, (((max T_1 Y) = T_1) \/ (-. (lesseq Y T_1)))) (lesseq T_0 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_2 T_1) ### DisjTree 137 138 153
% 9.73/9.93 155. (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (lesseq T_2 T_1) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_0 T_2) (All Y, (((max T_1 Y) = T_1) \/ (-. (lesseq Y T_1)))) (T_2 = T_1) ### All 154
% 9.73/9.93 156. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 = T_1) (lesseq T_0 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_2 T_1) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) ### All 155
% 9.73/9.93 157. (T_2 != (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (lesseq T_2 T_1) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_0 T_2) (T_2 = T_1) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### TransEq 134 135 156
% 9.73/9.93 158. (((lesseq T_2 T_1) /\ (lesseq T_1 T_2)) => (T_2 = T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_0 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (T_2 != (max T_0 T_1)) (lesseq T_1 T_2) (lesseq T_2 T_1) ### DisjTree 132 133 157
% 9.73/9.93 159. (lesseq T_2 T_1) (lesseq T_1 T_2) (T_2 != (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_0 T_2) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### All 158
% 9.73/9.93 160. (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (lesseq T_0 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_2 != (max T_0 T_1)) (lesseq T_1 T_2) (lesseq T_2 T_1) ### All 159
% 9.73/9.93 161. ((model_ub T_0 T_1 T_1) => (lesseq T_2 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (T_2 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Imply 131 160
% 9.73/9.93 162. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (T_2 != (max T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### All 161
% 9.73/9.93 163. (-. (model_max T_0 T_1 T_2)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Definition-Pseudo(model_max) 162
% 9.73/9.94 164. (lesseq T_0 T_2) (-. (lesseq T_0 T_2)) ### Axiom
% 9.73/9.94 165. (T_2 != T_2) ### Refl(=)
% 9.73/9.94 166. (-. (lesseq T_2 T_2)) ### Refl(lesseq)
% 9.73/9.94 167. (T_2 = T_0) (T_2 != T_0) ### Axiom
% 9.73/9.94 168. (T_1 != T_1) ### Refl(=)
% 9.73/9.94 169. ((max T_2 T_1) != (max T_0 T_1)) (T_2 = T_0) ### NotEqual 167 168
% 9.73/9.94 170. (-. (lesseq T_2 (max T_0 T_1))) ((max T_2 T_1) = T_2) (T_2 = T_0) ### TransEq2 165 166 169
% 9.73/9.94 171. (lesseq T_1 T_2) (-. (lesseq T_1 T_2)) ### Axiom
% 9.73/9.94 172. (((max T_2 T_1) = T_2) \/ (-. (lesseq T_1 T_2))) (lesseq T_1 T_2) (T_2 = T_0) (-. (lesseq T_2 (max T_0 T_1))) ### Or 170 171
% 9.73/9.94 173. (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (-. (lesseq T_2 (max T_0 T_1))) (T_2 = T_0) (lesseq T_1 T_2) ### All 172
% 9.73/9.94 174. (((lesseq T_2 T_0) /\ (lesseq T_0 T_2)) => (T_2 = T_0)) (lesseq T_1 T_2) (-. (lesseq T_2 (max T_0 T_1))) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) ### DisjTree 112 164 173
% 9.73/9.94 175. (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All Y, ((lesseq T_1 Y) \/ (lesseq Y T_1))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 T_1)) (lesseq T_0 T_2) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_1 T_2) ### All 174
% 9.73/9.94 176. (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (-. (lesseq T_2 (max T_0 T_1))) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) ### All 175
% 9.73/9.94 177. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (-. (lesseq T_0 T_1)) (lesseq T_0 T_2) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) ### All 176
% 9.73/9.94 178. (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_0 T_2) (-. (lesseq T_0 T_1)) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### All 177
% 9.73/9.94 179. (-. (lesseq T_1 T_1)) ### Refl(lesseq)
% 9.73/9.94 180. (-. ((lesseq T_0 T_1) /\ (lesseq T_1 T_1))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### NotAnd 178 179
% 9.73/9.94 181. (-. (ub T_0 T_1 T_1)) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Definition-Pseudo(ub) 180
% 9.73/9.94 182. (-. (model_ub T_0 T_1 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### Definition-Pseudo(model_ub) 181
% 9.73/9.94 183. (T_2 != T_2) ### Refl(=)
% 9.73/9.94 184. (lesseq T_2 T_1) (-. (lesseq T_2 T_1)) ### Axiom
% 9.73/9.94 185. (lesseq T_1 T_2) (-. (lesseq T_1 T_2)) ### Axiom
% 9.73/9.94 186. (T_2 != T_2) ### Refl(=)
% 9.73/9.94 187. (-. (lesseq T_2 T_0)) (lesseq T_2 T_1) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) ### Trans 186 29
% 9.73/9.94 188. (lesseq T_0 T_2) (-. (lesseq T_0 T_2)) ### Axiom
% 9.73/9.94 189. (T_2 != T_2) ### Refl(=)
% 9.73/9.94 190. (-. (lesseq T_2 T_2)) ### Refl(lesseq)
% 9.73/9.94 191. (T_2 = T_0) (T_2 != T_0) ### Axiom
% 9.73/9.94 192. (T_2 = T_1) (T_2 != T_1) ### Axiom
% 9.73/9.94 193. ((max T_2 T_2) != (max T_0 T_1)) (T_2 = T_1) (T_2 = T_0) ### NotEqual 191 192
% 9.73/9.94 194. (-. (lesseq T_2 (max T_0 T_1))) ((max T_2 T_2) = T_2) (T_2 = T_0) (T_2 = T_1) ### TransEq2 189 190 193
% 9.73/9.94 195. (-. (lesseq T_2 T_2)) ### Refl(lesseq)
% 9.73/9.94 196. (((max T_2 T_2) = T_2) \/ (-. (lesseq T_2 T_2))) (T_2 = T_1) (T_2 = T_0) (-. (lesseq T_2 (max T_0 T_1))) ### Or 194 195
% 9.73/9.94 197. (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (-. (lesseq T_2 (max T_0 T_1))) (T_2 = T_0) (T_2 = T_1) ### All 196
% 9.73/9.94 198. (((lesseq T_2 T_0) /\ (lesseq T_0 T_2)) => (T_2 = T_0)) (T_2 = T_1) (-. (lesseq T_2 (max T_0 T_1))) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (lesseq T_0 T_2) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (lesseq T_2 T_1) ### DisjTree 187 188 197
% 9.73/9.94 199. (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (lesseq T_2 T_1) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All Y, ((lesseq T_0 Y) \/ (lesseq Y T_0))) (lesseq T_0 T_2) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (-. (lesseq T_2 (max T_0 T_1))) (T_2 = T_1) ### All 198
% 9.73/9.94 200. (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (T_2 = T_1) (-. (lesseq T_2 (max T_0 T_1))) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (lesseq T_0 T_2) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (lesseq T_2 T_1) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) ### All 199
% 9.73/9.94 201. (((lesseq T_2 T_1) /\ (lesseq T_1 T_2)) => (T_2 = T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_0 T_2) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (-. (lesseq T_2 (max T_0 T_1))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_2 T_1) ### DisjTree 184 185 200
% 9.73/9.94 202. (lesseq T_2 T_1) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (-. (lesseq T_2 (max T_0 T_1))) (All Y, (((max T_2 Y) = T_2) \/ (-. (lesseq Y T_2)))) (lesseq T_0 T_2) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) ### All 201
% 9.73/9.94 203. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Y, (((lesseq T_2 Y) /\ (lesseq Y T_2)) => (T_2 = Y))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_0 T_2) (-. (lesseq T_2 (max T_0 T_1))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_2 T_1) ### All 202
% 9.73/9.94 204. (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (lesseq T_2 T_1) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_0 T_2) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (T_1 != (max T_0 T_1)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### All 203
% 9.73/9.94 205. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (lesseq T_0 T_2) (-. (lesseq T_2 (max T_0 T_1))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_2 T_1) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### Trans 183 204
% 9.73/9.94 206. ((model_ub T_0 T_1 T_1) => (lesseq T_2 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Imply 182 205
% 9.73/9.94 207. (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (-. (lesseq T_2 (max T_0 T_1))) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### All 206
% 9.73/9.94 208. (-. (lesseq T_4 T_4)) ### Refl(lesseq)
% 9.73/9.95 209. (T_4 != T_4) ### Refl(=)
% 9.73/9.95 210. (-. (lesseq T_2 T_4)) (T_4 = (max T_0 T_1)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### TransEq2 207 208 209
% 9.73/9.95 211. (model_max T_0 T_1 T_4) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (-. (lesseq T_2 T_4)) ### Definition-Pseudo(model_max) 210
% 9.73/9.95 212. (-. ((model_max T_0 T_1 T_4) => (lesseq T_2 T_4))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### NotImply 211
% 9.73/9.95 213. (-. (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### NotAllEx 212
% 9.73/9.95 214. (-. ((model_max T_0 T_1 T_2) /\ (All Z, ((model_max T_0 T_1 Z) => (lesseq T_2 Z))))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (lesseq T_0 T_2) (lesseq T_1 T_2) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### NotAnd 163 213
% 9.73/9.95 215. (-. (minsol_model_max T_0 T_1 T_2)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (lesseq T_1 T_2) (lesseq T_0 T_2) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Definition-Pseudo(minsol_model_max) 214
% 9.73/9.95 216. ((lesseq T_0 T_2) /\ (lesseq T_1 T_2)) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (-. (minsol_model_max T_0 T_1 T_2)) ### And 215
% 9.73/9.95 217. (ub T_0 T_1 T_2) (-. (minsol_model_max T_0 T_1 T_2)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### Definition-Pseudo(ub) 216
% 9.73/9.95 218. (model_ub T_0 T_1 T_2) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (-. (minsol_model_max T_0 T_1 T_2)) ### Definition-Pseudo(model_ub) 217
% 9.73/9.95 219. ((model_ub T_0 T_1 T_2) /\ (All Z, ((model_ub T_0 T_1 Z) => (lesseq T_2 Z)))) (-. (minsol_model_max T_0 T_1 T_2)) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) ### And 218
% 9.73/9.95 220. (minsol_model_ub T_0 T_1 T_2) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (-. (minsol_model_max T_0 T_1 T_2)) ### Definition-Pseudo(minsol_model_ub) 219
% 9.73/9.95 221. (-. ((minsol_model_ub T_0 T_1 T_2) <=> (minsol_model_max T_0 T_1 T_2))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### NotEquiv 101 220
% 9.73/9.95 222. (-. (All Z, ((minsol_model_ub T_0 T_1 Z) <=> (minsol_model_max T_0 T_1 Z)))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### NotAllEx 221
% 9.73/9.95 223. (-. (All Y, (All Z, ((minsol_model_ub T_0 Y Z) <=> (minsol_model_max T_0 Y Z))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) ### NotAllEx 222
% 9.73/9.95 224. (-. (All X, (All Y, (All Z, ((minsol_model_ub X Y Z) <=> (minsol_model_max X Y Z)))))) (All X, (All Y, (((lesseq X Y) /\ (lesseq Y X)) => (X = Y)))) (All X, (All Y, (((max X Y) = X) \/ (-. (lesseq Y X))))) (All X, (All Y, ((lesseq X Y) \/ (lesseq Y X)))) (All X, (All Y, ((lesseq X Y) <=> (lesseq (summation X) (summation Y))))) (All X, (All Y, (((max X Y) = Y) \/ (-. (lesseq X Y))))) ### NotAllEx 223
% 9.73/9.95 % SZS output end Proof
% 9.73/9.95 (* END-PROOF *)
%------------------------------------------------------------------------------