TSTP Solution File: LCL893+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL893+1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n004.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 : Sun Jul 17 14:54:45 EDT 2022
% Result : Theorem 11.86s 12.10s
% Output : Proof 11.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL893+1 : TPTP v8.1.0. Released v5.5.0.
% 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n004.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 Jul 3 02:32:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 11.86/12.10 % SZS status Theorem
% 11.86/12.10 (* PROOF-FOUND *)
% 11.86/12.10 (* BEGIN-PROOF *)
% 11.86/12.10 % SZS output start Proof
% 11.86/12.10 1. (((0) + T_0) != (T_0 + (0))) (((0) + T_0) = (T_0 + (0))) ### Axiom
% 11.86/12.10 2. (All B, (((0) + B) = (B + (0)))) (((0) + T_0) != (T_0 + (0))) ### All 1
% 11.86/12.10 3. (-. (T_0 >= T_0)) ### Refl(>=)
% 11.86/12.10 4. (T_0 != T_0) ### Refl(=)
% 11.86/12.10 5. (-. (((0) + T_0) >= T_0)) ((T_0 + (0)) = T_0) (All B, (((0) + B) = (B + (0)))) ### TransEq 2 3 4
% 11.86/12.10 6. (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (-. (((0) + T_0) >= T_0)) ### All 5
% 11.86/12.10 7. ((T_0 + (0)) = T_0) ((T_0 + (0)) != T_0) ### Axiom
% 11.86/12.10 8. (-. ((T_0 + (0)) >= T_0)) ((T_0 + (0)) = T_0) ### Refl(>=) 7
% 11.86/12.10 9. (-. ((0) >= (T_0 ==> T_0))) ((0) >= (T_0 ==> T_0)) ### Axiom
% 11.86/12.10 10. (((T_0 + (0)) >= T_0) <=> ((0) >= (T_0 ==> T_0))) (-. ((0) >= (T_0 ==> T_0))) ((T_0 + (0)) = T_0) ### Equiv 8 9
% 11.86/12.10 11. ((0) != (0)) ### NotEqual
% 11.86/12.10 12. ((h T_0) = T_0) (T_0 != (h T_0)) ### Sym(=)
% 11.86/12.10 13. (T_0 != T_0) ### Refl(=)
% 11.86/12.10 14. ((T_0 ==> T_0) != ((h T_0) ==> T_0)) ((h T_0) = T_0) ### NotEqual 12 13
% 11.86/12.10 15. (-. ((0) >= ((h T_0) ==> T_0))) ((0) >= (T_0 ==> T_0)) ((h T_0) = T_0) ### P-NotP 11 14
% 11.86/12.10 16. ((h T_0) = T_0) (-. ((0) >= ((h T_0) ==> T_0))) ((T_0 + (0)) = T_0) (((T_0 + (0)) >= T_0) <=> ((0) >= (T_0 ==> T_0))) ### Equiv 10 15
% 11.86/12.10 17. (All X7, (((T_0 + (0)) >= X7) <=> ((0) >= (T_0 ==> X7)))) ((T_0 + (0)) = T_0) (-. ((0) >= ((h T_0) ==> T_0))) ((h T_0) = T_0) ### All 16
% 11.86/12.10 18. (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) ((h T_0) = T_0) (-. ((0) >= ((h T_0) ==> T_0))) ((T_0 + (0)) = T_0) ### All 17
% 11.86/12.10 19. (-. ((h T_0) >= (h T_0))) ### Refl(>=)
% 11.86/12.10 20. ((h T_0) != (h T_0)) ### Refl(=)
% 11.86/12.10 21. (-. ((0) >= (h T_0))) ((h T_0) = ((h T_0) ==> T_0)) ((T_0 + (0)) = T_0) ((h T_0) = T_0) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) ### TransEq2 18 19 20
% 11.86/12.10 22. (All A, ((h A) = ((h A) ==> A))) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) ((h T_0) = T_0) ((T_0 + (0)) = T_0) (-. ((0) >= (h T_0))) ### All 21
% 11.86/12.10 23. (-. (T_0 >= T_0)) ### Refl(>=)
% 11.86/12.10 24. (T_0 != T_0) ### Refl(=)
% 11.86/12.10 25. (-. ((0) >= T_0)) ((T_0 + (0)) = T_0) ((h T_0) = T_0) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) (All A, ((h A) = ((h A) ==> A))) ### TransEq 22 23 24
% 11.86/12.10 26. (((0) + T_0) = (T_0 + (0))) ((T_0 + (0)) != ((0) + T_0)) ### Sym(=)
% 11.86/12.10 27. (-. ((0) >= ((0) + T_0))) (((0) + T_0) = (T_0 + (0))) (All A, ((h A) = ((h A) ==> A))) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) ((h T_0) = T_0) ((T_0 + (0)) = T_0) ### TransEq2 25 25 26
% 11.86/12.10 28. (All A, ((A + (0)) = A)) ((h T_0) = T_0) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) (All A, ((h A) = ((h A) ==> A))) (((0) + T_0) = (T_0 + (0))) (-. ((0) >= ((0) + T_0))) ### All 27
% 11.86/12.10 29. (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (-. ((0) >= ((0) + T_0))) (((0) + T_0) = (T_0 + (0))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) (All A, ((A + (0)) = A)) ### All 28
% 11.86/12.10 30. (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (-. ((0) >= ((0) + T_0))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) ### All 29
% 11.86/12.10 31. (T_0 != T_0) ### Refl(=)
% 11.86/12.10 32. (-. ((0) >= T_0)) (((0) + T_0) >= T_0) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) ### Trans 30 31
% 11.86/12.10 33. ((((0) + T_0) >= T_0) <=> (T_0 >= ((0) ==> T_0))) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (-. ((0) >= T_0)) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) ### Equiv 6 32
% 11.86/12.10 34. (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (-. ((0) >= T_0)) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) ### All 33
% 11.86/12.10 35. (-. ((h T_0) >= (h T_0))) ### Refl(>=)
% 11.86/12.10 36. ((h T_0) != (h T_0)) ### Refl(=)
% 11.86/12.10 37. (-. ((0) >= (h T_0))) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) ### TransEq2 34 35 36
% 11.86/12.10 38. (((h T_0) ==> T_0) != ((h T_0) ==> T_0)) ### Refl(=)
% 11.86/12.10 39. (-. (((h T_0) ==> T_0) >= ((h T_0) ==> T_0))) ### Refl(>=)
% 11.86/12.10 40. ((h T_0) != (h T_0)) ### Refl(=)
% 11.86/12.10 41. (-. ((h T_0) >= (h T_0))) ### Refl(>=)
% 11.86/12.10 42. (-. (((0) + T_0) >= (0))) (T_0 >= (0)) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) ### Trans 6 11
% 11.86/12.10 43. (-. (T_0 >= ((0) ==> (0)))) (T_0 >= ((0) ==> (0))) ### Axiom
% 11.86/12.10 44. ((((0) + T_0) >= (0)) <=> (T_0 >= ((0) ==> (0)))) (-. (T_0 >= ((0) ==> (0)))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (T_0 >= (0)) ### Equiv 42 43
% 11.86/12.10 45. (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) (T_0 >= (0)) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (-. (T_0 >= ((0) ==> (0)))) ### All 44
% 11.86/12.10 46. (All A, (A >= (0))) (-. (T_0 >= ((0) ==> (0)))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) ### All 45
% 11.86/12.10 47. (-. ((h T_0) >= ((0) ==> (0)))) ((h T_0) = T_0) (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (All A, (A >= (0))) ### TransEq 40 41 46
% 11.86/12.10 48. (-. (((h T_0) ==> T_0) >= ((0) ==> (0)))) ((h T_0) = ((h T_0) ==> T_0)) (All A, (A >= (0))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) ((h T_0) = T_0) ### TransEq2 38 39 47
% 11.86/12.10 49. (-. ((0) >= ((0) ==> (0)))) (All A, (A >= (0))) ((h T_0) = ((h T_0) ==> T_0)) (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) ### TransEq 37 48 48
% 11.86/12.10 50. ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) (All A, (A >= (0))) (-. ((0) >= ((0) ==> (0)))) ### All 49
% 11.86/12.10 51. (All X6, (All X7, ((((0) + X6) >= X7) <=> (X6 >= ((0) ==> X7))))) (-. ((0) >= ((0) ==> (0)))) (All A, (A >= (0))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) ### All 50
% 11.86/12.10 52. (-. (T_0 >= (0))) (T_0 >= (0)) ### Axiom
% 11.86/12.10 53. (All A, (A >= (0))) (-. (T_0 >= (0))) ### All 52
% 11.86/12.10 54. (((0) ==> (0)) != ((0) ==> (0))) ### Refl(=)
% 11.86/12.10 55. (-. (T_0 >= ((0) ==> (0)))) ((0) >= ((0) ==> (0))) (All A, (A >= (0))) ### Trans 53 54
% 11.86/12.10 56. (T_0 != (T_0 + (0))) ((T_0 + (0)) = T_0) ### Sym(=)
% 11.86/12.10 57. (All A, ((A + (0)) = A)) (T_0 != (T_0 + (0))) ### All 56
% 11.86/12.10 58. (-. (T_0 >= (T_0 + (0)))) (All A, ((A + (0)) = A)) ### Refl(>=) 57
% 11.86/12.10 59. (-. (((0) + T_0) >= ((0) + T_0))) ### Refl(>=)
% 11.86/12.10 60. (((0) + T_0) != ((0) + T_0)) ### Refl(=)
% 11.86/12.10 61. (-. (T_0 >= ((0) + T_0))) (((0) + T_0) = (T_0 + (0))) (All A, ((A + (0)) = A)) ### TransEq2 58 59 60
% 11.86/12.10 62. (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (-. (T_0 >= ((0) + T_0))) ### All 61
% 11.86/12.10 63. (-. (T_0 >= (0))) (((0) + T_0) >= (0)) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) ### Trans 62 11
% 11.86/12.10 64. (T_0 != (0)) ((0) = T_0) ### Sym(=)
% 11.86/12.10 65. ((((0) >= T_0) /\ (T_0 >= (0))) => ((0) = T_0)) (T_0 != (0)) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (((0) + T_0) >= (0)) (All A, ((h A) = ((h A) ==> A))) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) ((h T_0) = T_0) ((T_0 + (0)) = T_0) ### DisjTree 25 63 64
% 11.86/12.10 66. (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) ((T_0 + (0)) = T_0) ((h T_0) = T_0) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) (All A, ((h A) = ((h A) ==> A))) (((0) + T_0) >= (0)) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (T_0 != (0)) ### All 65
% 11.86/12.11 67. (T_0 != (0)) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (((0) + T_0) >= (0)) (All A, ((h A) = ((h A) ==> A))) (All X6, (All X7, (((T_0 + X6) >= X7) <=> (X6 >= (T_0 ==> X7))))) ((h T_0) = T_0) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) ### All 66
% 11.86/12.11 68. (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (((0) + T_0) >= (0)) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (T_0 != (0)) ### All 67
% 11.86/12.11 69. ((((0) + T_0) >= (0)) <=> (T_0 >= ((0) ==> (0)))) (T_0 != (0)) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, (A >= (0))) ((0) >= ((0) ==> (0))) ### Equiv 55 68
% 11.86/12.11 70. (All X7, ((((0) + T_0) >= X7) <=> (T_0 >= ((0) ==> X7)))) ((0) >= ((0) ==> (0))) (All A, (A >= (0))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (T_0 != (0)) ### All 69
% 11.86/12.11 71. (All X6, (All X7, ((((0) + X6) >= X7) <=> (X6 >= ((0) ==> X7))))) (T_0 != (0)) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, (A >= (0))) ((0) >= ((0) ==> (0))) ### All 70
% 11.86/12.11 72. ((((0) + (0)) >= (0)) <=> ((0) >= ((0) ==> (0)))) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) (T_0 != (0)) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (All A, (A >= (0))) (All X6, (All X7, ((((0) + X6) >= X7) <=> (X6 >= ((0) ==> X7))))) ### Equiv 51 71
% 11.86/12.11 73. (All X7, ((((0) + (0)) >= X7) <=> ((0) >= ((0) ==> X7)))) (All X6, (All X7, ((((0) + X6) >= X7) <=> (X6 >= ((0) ==> X7))))) (All A, (A >= (0))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) (T_0 != (0)) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) ### All 72
% 11.86/12.11 74. (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) (T_0 != (0)) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All B, (((0) + B) = (B + (0)))) (All A, ((A + (0)) = A)) (All A, (A >= (0))) (All X6, (All X7, ((((0) + X6) >= X7) <=> (X6 >= ((0) ==> X7))))) ### All 73
% 11.86/12.11 75. (All A, (A >= (0))) (All A, ((A + (0)) = A)) (All B, (((0) + B) = (B + (0)))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) (T_0 != (0)) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) ### All 74
% 11.86/12.11 76. (All A, (All B, ((A + B) = (B + A)))) (All X4, ((((0) >= X4) /\ (X4 >= (0))) => ((0) = X4))) (T_0 != (0)) ((h T_0) = T_0) (All A, ((h A) = ((h A) ==> A))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((A + (0)) = A)) (All A, (A >= (0))) ### All 75
% 11.86/12.11 77. (All X3, (All X4, (((X3 >= X4) /\ (X4 >= X3)) => (X3 = X4)))) (All A, (A >= (0))) (All A, ((A + (0)) = A)) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) ((h T_0) = T_0) (T_0 != (0)) (All A, (All B, ((A + B) = (B + A)))) ### All 76
% 11.86/12.11 78. (-. (((h T_0) = T_0) => (T_0 = (0)))) (All A, (All B, ((A + B) = (B + A)))) (All A, ((h A) = ((h A) ==> A))) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((A + (0)) = A)) (All A, (A >= (0))) (All X3, (All X4, (((X3 >= X4) /\ (X4 >= X3)) => (X3 = X4)))) ### NotImply 77
% 11.86/12.11 79. (-. (All X17, (((h X17) = X17) => (X17 = (0))))) (All X3, (All X4, (((X3 >= X4) /\ (X4 >= X3)) => (X3 = X4)))) (All A, (A >= (0))) (All A, ((A + (0)) = A)) (All X5, (All X6, (All X7, (((X5 + X6) >= X7) <=> (X6 >= (X5 ==> X7)))))) (All A, ((h A) = ((h A) ==> A))) (All A, (All B, ((A + B) = (B + A)))) ### NotAllEx 78
% 11.86/12.11 % SZS output end Proof
% 11.86/12.11 (* END-PROOF *)
%------------------------------------------------------------------------------