TSTP Solution File: NUN067+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n024.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 16:39:09 EDT 2022
% Result : Theorem 29.05s 29.25s
% Output : Proof 29.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUN067+1 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 08:06:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 29.05/29.25 % SZS status Theorem
% 29.05/29.25 (* PROOF-FOUND *)
% 29.05/29.25 (* BEGIN-PROOF *)
% 29.05/29.25 % SZS output start Proof
% 29.05/29.25 1. (-. (id T_0 T_0)) ### Refl(id)
% 29.05/29.25 2. (-. (id T_0 T_0)) ### Refl(id)
% 29.05/29.25 3. (-. (r2 T_0 T_0)) (r2 T_0 T_0) ### Axiom
% 29.05/29.25 4. ((id T_0 T_1) /\ (r2 T_0 T_0)) (-. (r2 T_0 T_0)) ### And 3
% 29.05/29.25 5. (T_2 != T_2) ### Refl(=)
% 29.05/29.25 6. (T_2 != T_2) ### Refl(=)
% 29.05/29.25 7. (T_3 != T_3) ### Refl(=)
% 29.05/29.25 8. (zenon_X4 != zenon_X4) ### Refl(=)
% 29.05/29.25 9. (T_2 != T_2) ### Refl(=)
% 29.05/29.25 10. (T_5 != T_5) ### Refl(=)
% 29.05/29.25 11. (T_3 != T_3) ### Refl(=)
% 29.05/29.25 12. (zenon_X4 != zenon_X4) ### Refl(=)
% 29.05/29.25 13. (T_6 != T_6) ### Refl(=)
% 29.05/29.25 14. (T_2 != T_2) ### Refl(=)
% 29.05/29.25 15. (T_7 != T_7) ### Refl(=)
% 29.05/29.25 16. (T_2 != T_2) ### Refl(=)
% 29.05/29.25 17. (T_5 != T_5) ### Refl(=)
% 29.05/29.25 18. (T_1 != T_1) ### Refl(=)
% 29.05/29.25 19. (T_7 != T_7) ### Refl(=)
% 29.05/29.25 20. (T_8 != T_8) ### Refl(=)
% 29.05/29.25 21. (T_9 != T_9) ### Refl(=)
% 29.05/29.25 22. (id T_10 T_0) (-. (id T_10 T_0)) ### Axiom
% 29.05/29.25 23. (-. (id T_0 T_9)) (id T_9 T_10) (id T_10 T_0) ### Trans-sym 21 22
% 29.05/29.25 24. (-. (id T_8 T_9)) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) ### Trans 20 23
% 29.05/29.25 25. (T_10 != T_10) ### Refl(=)
% 29.05/29.25 26. (-. (id T_8 T_10)) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) ### Trans 24 25
% 29.05/29.25 27. (-. (id T_10 T_7)) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) ### Trans-sym 19 26
% 29.05/29.25 28. (-. (id T_1 T_7)) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) ### Trans 18 27
% 29.05/29.25 29. (T_8 != T_8) ### Refl(=)
% 29.05/29.25 30. (-. (id T_1 T_8)) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) ### Trans 28 29
% 29.05/29.25 31. (-. (id T_5 T_8)) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) ### Trans 17 30
% 29.05/29.25 32. (-. (id T_8 T_2)) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) ### Trans-sym 16 31
% 29.05/29.25 33. (T_11 != T_11) ### Refl(=)
% 29.05/29.25 34. (-. (id T_8 T_11)) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) ### Trans 32 33
% 29.05/29.25 35. (-. (id T_11 T_7)) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) ### Trans-sym 15 34
% 29.05/29.25 36. (-. (id T_7 T_2)) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) ### Trans-sym 14 35
% 29.05/29.25 37. (T_5 != T_5) ### Refl(=)
% 29.05/29.25 38. (-. (id T_7 T_5)) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) ### Trans 36 37
% 29.05/29.25 39. (T_12 != T_12) ### Refl(=)
% 29.05/29.25 40. (-. (id T_12 T_7)) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) ### Trans-sym 38 39
% 29.05/29.25 41. (T_8 != T_8) ### Refl(=)
% 29.05/29.25 42. (-. (id T_12 T_8)) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) ### Trans 40 41
% 29.05/29.25 43. (T_0 != T_0) ### Refl(=)
% 29.05/29.25 44. (-. (id T_0 T_12)) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) ### Trans-sym 42 43
% 29.05/29.25 45. (-. (id T_6 T_12)) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) ### Trans 13 44
% 29.05/29.25 46. (-. (id zenon_X4 T_12)) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) ### Trans 12 45
% 29.05/29.25 47. (-. (id T_3 T_12)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) ### Trans 11 46
% 29.05/29.25 48. (T_1 != T_1) ### Refl(=)
% 29.05/29.25 49. (-. (id T_1 T_3)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans-sym 47 48
% 29.05/29.25 50. (zenon_X4 != zenon_X4) ### Refl(=)
% 29.05/29.25 51. (-. (id T_1 zenon_X4)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans 49 50
% 29.05/29.25 52. (T_6 != T_6) ### Refl(=)
% 29.05/29.25 53. (-. (id T_1 T_6)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans 51 52
% 29.05/29.25 54. (-. (id T_5 T_6)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans 10 53
% 29.05/29.25 55. (-. (id T_6 T_2)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans-sym 9 54
% 29.05/29.25 56. (-. (id zenon_X4 T_2)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans 8 55
% 29.05/29.25 57. (T_5 != T_5) ### Refl(=)
% 29.05/29.25 58. (-. (id zenon_X4 T_5)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans 56 57
% 29.05/29.25 59. (-. (id T_5 T_3)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans-sym 7 58
% 29.05/29.25 60. (-. (id T_3 T_2)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans-sym 6 59
% 29.05/29.25 61. (T_11 != T_11) ### Refl(=)
% 29.05/29.25 62. (-. (id T_11 T_3)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans-sym 60 61
% 29.05/29.25 63. (zenon_X4 != zenon_X4) ### Refl(=)
% 29.05/29.25 64. (-. (id T_11 zenon_X4)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans 62 63
% 29.05/29.25 65. (T_6 != T_6) ### Refl(=)
% 29.05/29.25 66. (-. (id T_11 T_6)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans 64 65
% 29.05/29.25 67. (T_0 != T_0) ### Refl(=)
% 29.05/29.25 68. (-. (id T_11 T_0)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans 66 67
% 29.05/29.25 69. (-. (id T_0 T_2)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans-sym 5 68
% 29.05/29.25 70. (T_5 != T_5) ### Refl(=)
% 29.05/29.25 71. (-. (id T_0 T_5)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Trans 69 70
% 29.05/29.25 72. (T_1 != T_1) ### Refl(=)
% 29.05/29.25 73. (-. (id T_0 T_1)) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) ### Trans 71 72
% 29.05/29.25 74. ((-. (r2 T_0 T_0)) /\ (-. (id T_0 T_1))) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### And 73
% 29.05/29.25 75. (((id T_0 T_1) /\ (r2 T_0 T_0)) \/ ((-. (r2 T_0 T_0)) /\ (-. (id T_0 T_1)))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_9 T_10) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) (-. (r2 T_0 T_0)) ### Or 4 74
% 29.05/29.25 76. (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_9 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### All 75
% 29.12/29.30 77. ((id T_9 T_10) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_10 Y16 T_9)))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### And 76
% 29.12/29.30 78. (Ex Y9, ((id Y9 T_10) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_10 Y16 Y9))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_2 T_11) (id T_5 T_1) (id T_1 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) ### Exists 77
% 29.12/29.30 79. (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_1 T_10) (id T_5 T_1) (id T_2 T_11) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### All 78
% 29.12/29.30 80. (-. (-. (id T_2 T_11))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) ### NotNot 79
% 29.12/29.30 81. (-. ((-. (id T_2 T_11)) \/ (-. (r1 T_11)))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### NotOr 80
% 29.12/29.30 82. (-. (All Y2, ((-. (id T_2 Y2)) \/ (-. (r1 Y2))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id T_12 T_1) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) ### NotAllEx 81
% 29.12/29.30 83. (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (id T_12 T_1) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### NotExists 82
% 29.12/29.30 84. ((id T_12 T_1) /\ (r2 T_0 T_12)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### And 83
% 29.12/29.30 85. (id T_5 T_12) (-. (id T_12 T_5)) ### Sym(id)
% 29.12/29.30 86. (T_1 != T_1) ### Refl(=)
% 29.12/29.30 87. (-. (id T_12 T_1)) (id T_5 T_1) (id T_5 T_12) ### Trans 85 86
% 29.12/29.30 88. ((-. (r2 T_0 T_12)) /\ (-. (id T_12 T_1))) (id T_5 T_12) (id T_5 T_1) ### And 87
% 29.12/29.30 89. (((id T_12 T_1) /\ (r2 T_0 T_12)) \/ ((-. (r2 T_0 T_12)) /\ (-. (id T_12 T_1)))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_7 T_8) (id T_8 T_0) (id T_10 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### Or 84 88
% 29.12/29.30 90. (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_10 T_0) (id T_8 T_0) (id T_7 T_8) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### All 89
% 29.12/29.30 91. ((id T_7 T_8) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_8 Y16 T_7)))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_8 T_0) (id T_10 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### And 90
% 29.12/29.30 92. (Ex Y9, ((id Y9 T_8) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_8 Y16 Y9))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_10 T_0) (id T_8 T_0) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### Exists 91
% 29.12/29.30 93. (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_8 T_0) (id T_10 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### All 92
% 29.12/29.30 94. ((id T_10 T_0) /\ (r1 T_10)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_8 T_0) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### And 93
% 29.12/29.30 95. (r1 T_10) (-. (r1 T_10)) ### Axiom
% 29.12/29.30 96. ((-. (r1 T_10)) /\ (-. (id T_10 T_0))) (r1 T_10) ### And 95
% 29.12/29.30 97. (((id T_10 T_0) /\ (r1 T_10)) \/ ((-. (r1 T_10)) /\ (-. (id T_10 T_0)))) (r1 T_10) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_2 T_5) (id T_8 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) ### Or 94 96
% 29.12/29.30 98. (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_8 T_0) (id T_2 T_5) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_10) ### All 97
% 29.12/29.30 99. ((id T_2 T_5) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_5 Y16 T_2)))) (r1 T_10) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_8 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### And 98
% 29.12/29.30 100. (Ex Y9, ((id Y9 T_5) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_5 Y16 Y9))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_12) (id T_5 T_1) (id T_1 T_10) (id T_8 T_0) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_10) ### Exists 99
% 29.12/29.30 101. (r1 T_10) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_8 T_0) (id T_1 T_10) (id T_5 T_1) (id T_5 T_12) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### All 100
% 29.12/29.34 102. (-. (-. (id T_5 T_12))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_1) (id T_1 T_10) (id T_8 T_0) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_10) ### NotNot 101
% 29.12/29.34 103. (-. ((-. (id T_5 T_12)) \/ (-. (r1 T_12)))) (r1 T_10) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_8 T_0) (id T_1 T_10) (id T_5 T_1) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### NotOr 102
% 29.12/29.34 104. (-. (All Y2, ((-. (id T_5 Y2)) \/ (-. (r1 Y2))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_1) (id T_1 T_10) (id T_8 T_0) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_10) ### NotAllEx 103
% 29.12/29.34 105. (r1 T_10) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_8 T_0) (id T_1 T_10) (id T_5 T_1) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### NotExists 104
% 29.12/29.34 106. ((id T_8 T_0) /\ (r1 T_8)) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_1) (id T_1 T_10) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_10) ### And 105
% 29.12/29.34 107. (r1 T_8) (-. (r1 T_8)) ### Axiom
% 29.12/29.34 108. ((-. (r1 T_8)) /\ (-. (id T_8 T_0))) (r1 T_8) ### And 107
% 29.12/29.34 109. (((id T_8 T_0) /\ (r1 T_8)) \/ ((-. (r1 T_8)) /\ (-. (id T_8 T_0)))) (r1 T_8) (r1 T_10) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_1 T_10) (id T_5 T_1) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### Or 106 108
% 29.12/29.34 110. (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_1) (id T_1 T_10) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_10) (r1 T_8) ### All 109
% 29.12/29.34 111. (-. (-. (r1 T_10))) (r1 T_8) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_1 T_10) (id T_5 T_1) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### NotNot 110
% 29.12/29.34 112. (-. (-. (id T_1 T_10))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_1) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_8) (-. (-. (r1 T_10))) ### NotNot 111
% 29.12/29.34 113. (-. ((-. (id T_1 T_10)) \/ (-. (r1 T_10)))) (r1 T_8) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_5 T_1) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### NotOr 112
% 29.12/29.34 114. (-. (All Y2, ((-. (id T_1 Y2)) \/ (-. (r1 Y2))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_1) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (r1 T_8) ### NotAllEx 113
% 29.12/29.34 115. (r1 T_8) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_5 T_1) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### NotExists 114
% 29.12/29.34 116. ((r1 T_8) /\ (r3 T_1 T_8 T_5)) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_5 T_1) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### And 115
% 29.12/29.34 117. (Ex Y16, ((r1 Y16) /\ (r3 T_1 Y16 T_5))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id T_5 T_1) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### Exists 116
% 29.12/29.34 118. ((id T_5 T_1) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_1 Y16 T_5)))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### And 117
% 29.12/29.34 119. (Ex Y9, ((id Y9 T_1) /\ (Ex Y16, ((r1 Y16) /\ (r3 T_1 Y16 Y9))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### Exists 118
% 29.12/29.34 120. (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### All 119
% 29.12/29.35 121. (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 Y21)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_3 zenon_X4) (id T_6 T_0) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### Exists 120
% 29.12/29.35 122. (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_6 T_0) (id T_3 zenon_X4) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### All 121
% 29.12/29.35 123. ((id T_3 zenon_X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 zenon_X4 Y16 T_3)))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_6 T_0) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### And 122
% 29.12/29.35 124. (Ex Y9, ((id Y9 zenon_X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 zenon_X4 Y16 Y9))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (-. (r2 T_0 T_0)) (id zenon_X4 T_6) (id T_6 T_0) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### Exists 123
% 29.12/29.35 125. (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_6 T_0) (id zenon_X4 T_6) (-. (r2 T_0 T_0)) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### All 124
% 29.12/29.35 126. ((-. (r2 T_0 T_0)) /\ (-. (r2 T_0 T_0))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (id zenon_X4 T_6) (id T_6 T_0) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) ### And 125
% 29.12/29.35 127. (id T_0 T_1) (-. (id T_1 T_0)) ### Sym(id)
% 29.12/29.35 128. (r1 T_1) (-. (r1 T_1)) ### Axiom
% 29.12/29.35 129. ((-. (id T_1 T_0)) \/ (-. (r1 T_1))) (r1 T_1) (id T_0 T_1) ### Or 127 128
% 29.12/29.35 130. (All Y20, ((-. (id Y20 T_0)) \/ (-. (r1 Y20)))) (id T_0 T_1) (r1 T_1) ### All 129
% 29.12/29.35 131. ((id T_1 T_0) /\ (r1 T_1)) (id T_0 T_1) (All Y20, ((-. (id Y20 T_0)) \/ (-. (r1 Y20)))) ### And 130
% 29.12/29.35 132. (id T_0 T_1) (-. (id T_1 T_0)) ### Sym(id)
% 29.12/29.35 133. ((-. (r1 T_1)) /\ (-. (id T_1 T_0))) (id T_0 T_1) ### And 132
% 29.12/29.35 134. (((id T_1 T_0) /\ (r1 T_1)) \/ ((-. (r1 T_1)) /\ (-. (id T_1 T_0)))) (All Y20, ((-. (id Y20 T_0)) \/ (-. (r1 Y20)))) (id T_0 T_1) ### Or 131 133
% 29.12/29.35 135. (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (id T_0 T_1) (All Y20, ((-. (id Y20 T_0)) \/ (-. (r1 Y20)))) ### All 134
% 29.12/29.35 136. (r2 T_0 T_0) (-. (r2 T_0 T_0)) ### Axiom
% 29.12/29.35 137. ((All Y20, ((-. (id Y20 T_0)) \/ (-. (r1 Y20)))) \/ (-. (r2 T_0 T_0))) (r2 T_0 T_0) (id T_0 T_1) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) ### Or 135 136
% 29.12/29.35 138. (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 T_0 Y10)))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (id T_0 T_1) (r2 T_0 T_0) ### All 137
% 29.12/29.35 139. ((id T_0 T_1) /\ (r2 T_0 T_0)) (r2 T_0 T_0) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 T_0 Y10)))) ### And 138
% 29.12/29.35 140. (r2 T_0 T_0) (-. (r2 T_0 T_0)) ### Axiom
% 29.12/29.35 141. ((-. (r2 T_0 T_0)) /\ (-. (id T_0 T_1))) (r2 T_0 T_0) ### And 140
% 29.12/29.35 142. (((id T_0 T_1) /\ (r2 T_0 T_0)) \/ ((-. (r2 T_0 T_0)) /\ (-. (id T_0 T_1)))) (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 T_0 Y10)))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (r2 T_0 T_0) ### Or 139 141
% 29.12/29.35 143. (All X12, (((id X12 T_1) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 T_1))))) (r2 T_0 T_0) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 T_0 Y10)))) ### All 142
% 29.12/29.35 144. (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 T_0 X12)) \/ ((-. (r2 T_0 X12)) /\ (-. (id X12 Y21)))))) (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 T_0 Y10)))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (r2 T_0 T_0) ### Exists 143
% 29.12/29.35 145. (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (r2 T_0 T_0) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 T_0 Y10)))) ### All 144
% 29.12/29.35 146. (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (r2 T_0 T_0) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### All 145
% 29.12/29.35 147. ((r2 T_0 T_0) /\ (r2 T_0 T_0)) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) ### And 146
% 29.12/29.35 148. ((-. (id T_0 T_0)) \/ ((-. (id T_0 T_0)) \/ (((-. (r2 T_0 T_0)) /\ (-. (r2 T_0 T_0))) \/ ((r2 T_0 T_0) /\ (r2 T_0 T_0))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_6 T_0) (id zenon_X4 T_6) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### DisjTree 1 2 126 147
% 29.12/29.35 149. (All X31, ((-. (id T_0 T_0)) \/ ((-. (id T_0 X31)) \/ (((-. (r2 T_0 T_0)) /\ (-. (r2 T_0 X31))) \/ ((r2 T_0 T_0) /\ (r2 T_0 X31)))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (id zenon_X4 T_6) (id T_6 T_0) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) ### All 148
% 29.12/29.35 150. (All X30, (All X31, ((-. (id T_0 X30)) \/ ((-. (id T_0 X31)) \/ (((-. (r2 T_0 T_0)) /\ (-. (r2 X30 X31))) \/ ((r2 T_0 T_0) /\ (r2 X30 X31))))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_6 T_0) (id zenon_X4 T_6) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### All 149
% 29.12/29.35 151. (All X29, (All X30, (All X31, ((-. (id T_0 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 T_0 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 T_0 X29) /\ (r2 X30 X31)))))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (id zenon_X4 T_6) (id T_6 T_0) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) ### All 150
% 29.12/29.35 152. (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id T_6 T_0) (id zenon_X4 T_6) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### All 151
% 29.12/29.35 153. ((id T_6 T_0) /\ (r1 T_6)) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (id zenon_X4 T_6) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) ### And 152
% 29.12/29.35 154. (r1 T_6) (-. (r1 T_6)) ### Axiom
% 29.12/29.35 155. ((-. (r1 T_6)) /\ (-. (id T_6 T_0))) (r1 T_6) ### And 154
% 29.12/29.35 156. (((id T_6 T_0) /\ (r1 T_6)) \/ ((-. (r1 T_6)) /\ (-. (id T_6 T_0)))) (r1 T_6) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id zenon_X4 T_6) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### Or 153 155
% 29.12/29.35 157. (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (id zenon_X4 T_6) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) (r1 T_6) ### All 156
% 29.12/29.35 158. (-. (-. (r1 T_6))) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (id zenon_X4 T_6) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### NotNot 157
% 29.12/29.35 159. (-. (-. (id zenon_X4 T_6))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) (-. (-. (r1 T_6))) ### NotNot 158
% 29.12/29.35 160. (-. ((-. (id zenon_X4 T_6)) \/ (-. (r1 T_6)))) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### NotOr 159
% 29.12/29.35 161. (-. (All Y2, ((-. (id zenon_X4 Y2)) \/ (-. (r1 Y2))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) ### NotAllEx 160
% 29.12/29.35 162. (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (All X19, (((id X19 T_0) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 T_0))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) ### NotExists 161
% 29.12/29.35 163. (Ex Y24, (All X19, (((id X19 Y24) /\ (r1 X19)) \/ ((-. (r1 X19)) /\ (-. (id X19 Y24)))))) (All X11, (Ex Y21, (All X12, (((id X12 Y21) /\ (r2 X11 X12)) \/ ((-. (r2 X11 X12)) /\ (-. (id X12 Y21))))))) (All X4, (Ex Y9, ((id Y9 X4) /\ (Ex Y16, ((r1 Y16) /\ (r3 X4 Y16 Y9)))))) (-. (Ex Y1, (All Y2, ((-. (id Y1 Y2)) \/ (-. (r1 Y2)))))) (All X7, (All Y10, ((All Y20, ((-. (id Y20 Y10)) \/ (-. (r1 Y20)))) \/ (-. (r2 X7 Y10))))) (All X28, (All X29, (All X30, (All X31, ((-. (id X28 X30)) \/ ((-. (id X29 X31)) \/ (((-. (r2 X28 X29)) /\ (-. (r2 X30 X31))) \/ ((r2 X28 X29) /\ (r2 X30 X31))))))))) ### Exists 162
% 29.12/29.35 % SZS output end Proof
% 29.12/29.35 (* END-PROOF *)
%------------------------------------------------------------------------------