TSTP Solution File: PUZ078+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : PUZ078+1 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n022.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 18:27:53 EDT 2022
% Result : Theorem 4.61s 4.80s
% Output : Proof 4.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ078+1 : TPTP v8.1.0. Released v3.5.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat May 28 21:38:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 4.61/4.80 % SZS status Theorem
% 4.61/4.80 (* PROOF-FOUND *)
% 4.61/4.80 (* BEGIN-PROOF *)
% 4.61/4.80 % SZS output start Proof
% 4.61/4.80 1. (day3 T_0) (-. (day3 T_0)) ### Axiom
% 4.61/4.80 2. (day3 (consecutive T_1)) (-. (day3 (consecutive T_1))) ### Axiom
% 4.61/4.80 3. (-. (day2 T_1)) (day3 (consecutive T_1)) ### Definition-Pseudo(day2) 2
% 4.61/4.80 4. (day3 (consecutive (consecutive T_2))) (-. (day3 (consecutive (consecutive T_2)))) ### Axiom
% 4.61/4.80 5. (-. (day2 (consecutive T_2))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 4
% 4.61/4.80 6. (-. (day1 T_2)) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day1) 5
% 4.61/4.80 7. (truthday (monday)) (-. (truthday (monday))) ### Axiom
% 4.61/4.80 8. (truthday (wednesday)) (-. (truthday (wednesday))) ### Axiom
% 4.61/4.80 9. ((monday) != (wednesday)) ((monday) = (wednesday)) ### Axiom
% 4.61/4.80 10. (((truthday (monday)) /\ (truthday (wednesday))) => ((monday) = (wednesday))) ((monday) != (wednesday)) (truthday (wednesday)) (truthday (monday)) ### DisjTree 7 8 9
% 4.61/4.80 11. (All Y, (((truthday (monday)) /\ (truthday Y)) => ((monday) = Y))) (truthday (monday)) (truthday (wednesday)) ((monday) != (wednesday)) ### All 10
% 4.61/4.80 12. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) (truthday (monday)) ### All 11
% 4.61/4.80 13. (-. (-. (truthday (monday)))) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### NotNot 12
% 4.61/4.80 14. (-. (truthday (tuesday))) (truthday (tuesday)) ### Axiom
% 4.61/4.80 15. (-. (-. (truthday (tuesday)))) (-. (truthday (tuesday))) ### NotNot 14
% 4.61/4.80 16. (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ### NotAnd 13 15
% 4.61/4.80 17. ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) ### Axiom
% 4.61/4.80 18. (-. (truthday T_2)) (truthday T_2) ### Axiom
% 4.61/4.80 19. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday T_2)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### Equiv 17 18
% 4.61/4.80 20. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. (truthday T_2)) (day3 (consecutive (consecutive T_2))) ### Imply 6 19
% 4.61/4.80 21. (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) (-. (truthday T_2)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### All 20
% 4.61/4.80 22. (truthday (wednesday)) (-. (truthday (wednesday))) ### Axiom
% 4.61/4.80 23. (T_2 != (wednesday)) (T_2 = (wednesday)) ### Axiom
% 4.61/4.80 24. (((truthday T_2) /\ (truthday (wednesday))) => (T_2 = (wednesday))) (T_2 != (wednesday)) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### DisjTree 21 22 23
% 4.61/4.80 25. (All Y, (((truthday T_2) /\ (truthday Y)) => (T_2 = Y))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (truthday (wednesday)) (T_2 != (wednesday)) ### All 24
% 4.61/4.80 26. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (T_2 != (wednesday)) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### All 25
% 4.61/4.80 27. ((consecutive T_2) != (consecutive (wednesday))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (truthday (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### NotEqual 26
% 4.61/4.80 28. ((thursday) != (thursday)) ### NotEqual
% 4.61/4.80 29. ((consecutive T_2) != (thursday)) ((consecutive (wednesday)) = (thursday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### Trans 27 28
% 4.61/4.80 30. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (wednesday)) = (thursday)) ((consecutive T_2) != (thursday)) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### Equiv 16 29
% 4.61/4.80 31. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ((consecutive T_2) != (thursday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Imply 6 30
% 4.61/4.80 32. (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive T_2) != (thursday)) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### All 31
% 4.61/4.80 33. ((consecutive (consecutive T_2)) != (consecutive (thursday))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### NotEqual 32
% 4.61/4.80 34. (-. (day3 (consecutive (thursday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### P-NotP 33
% 4.61/4.80 35. (-. (day2 (thursday))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 34
% 4.61/4.80 36. (-. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### ConjTree 35
% 4.61/4.80 37. (truthday T_3) (-. (truthday T_3)) ### Axiom
% 4.61/4.80 38. (truthday (wednesday)) (-. (truthday (wednesday))) ### Axiom
% 4.61/4.80 39. (truthday T_3) (-. (truthday T_3)) ### Axiom
% 4.61/4.80 40. (day3 (consecutive (thursday))) (-. (day3 (consecutive (thursday)))) ### Axiom
% 4.61/4.80 41. (-. (day2 (thursday))) (day3 (consecutive (thursday))) ### Definition-Pseudo(day2) 40
% 4.61/4.80 42. (-. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (day3 (consecutive (thursday))) ### ConjTree 41
% 4.61/4.80 43. (-. (truthday T_1)) (truthday T_1) ### Axiom
% 4.61/4.80 44. ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (-. (truthday T_1)) (day3 (consecutive (thursday))) ### Equiv 42 43
% 4.61/4.80 45. ((day2 T_1) => ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))))) (day3 (consecutive (thursday))) (-. (truthday T_1)) (day3 (consecutive T_1)) ### Imply 3 44
% 4.61/4.80 46. (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (-. (truthday T_1)) (day3 (consecutive (thursday))) ### All 45
% 4.61/4.80 47. (T_1 != T_3) (T_3 = T_1) ### Sym(=)
% 4.61/4.80 48. (((truthday T_3) /\ (truthday T_1)) => (T_3 = T_1)) (T_1 != T_3) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) ### DisjTree 39 46 47
% 4.61/4.80 49. (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) (T_1 != T_3) ### All 48
% 4.61/4.80 50. ((consecutive T_1) != (consecutive T_3)) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### NotEqual 49
% 4.61/4.80 51. (-. (day3 (consecutive T_3))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ### P-NotP 50
% 4.61/4.80 52. (-. (day2 T_3)) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### Definition-Pseudo(day2) 51
% 4.61/4.80 53. (T_3 = T_1) (T_1 != T_3) ### Sym(=)
% 4.61/4.80 54. ((consecutive T_1) != (consecutive T_3)) (T_3 = T_1) ### NotEqual 53
% 4.61/4.80 55. (-. (day3 (consecutive T_3))) (day3 (consecutive T_1)) (T_3 = T_1) ### P-NotP 54
% 4.61/4.80 56. (-. (day2 T_3)) (T_3 = T_1) (day3 (consecutive T_1)) ### Definition-Pseudo(day2) 55
% 4.61/4.80 57. ((thursday) != T_3) (T_3 = (thursday)) ### Sym(=)
% 4.61/4.80 58. (((day2 T_3) /\ (day2 (thursday))) => (T_3 = (thursday))) ((thursday) != T_3) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (T_3 = T_1) ### DisjTree 56 41 57
% 4.61/4.80 59. (All Y, (((day2 T_3) /\ (day2 Y)) => (T_3 = Y))) (T_3 = T_1) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ((thursday) != T_3) ### All 58
% 4.61/4.80 60. (((day2 T_3) /\ (day2 T_1)) => (T_3 = T_1)) ((thursday) != T_3) (All Y, (((day2 T_3) /\ (day2 Y)) => (T_3 = Y))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ### DisjTree 52 3 59
% 4.61/4.80 61. (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All Y, (((day2 T_3) /\ (day2 Y)) => (T_3 = Y))) ((thursday) != T_3) ### All 60
% 4.61/4.80 62. (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((thursday) != T_3) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ### All 61
% 4.61/4.80 63. ((wednesday) != (wednesday)) ### NotEqual
% 4.61/4.80 64. ((wednesday) != (thursday)) (T_3 = (wednesday)) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ### TransEq-sym 62 63 63
% 4.61/4.80 65. (((truthday T_3) /\ (truthday (wednesday))) => (T_3 = (wednesday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ((wednesday) != (thursday)) (truthday (wednesday)) (truthday T_3) ### DisjTree 37 38 64
% 4.61/4.80 66. (truthday T_3) (truthday (wednesday)) ((wednesday) != (thursday)) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ### All 65
% 4.61/4.80 67. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ((wednesday) != (thursday)) (truthday (wednesday)) (truthday T_3) ### All 66
% 4.61/4.80 68. (day2 (thursday)) (truthday T_3) (truthday (wednesday)) ((wednesday) != (thursday)) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Definition-Pseudo(day2) 67
% 4.61/4.80 69. ((consecutive (consecutive T_2)) != (consecutive (consecutive (wednesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### NotEqual 27
% 4.61/4.80 70. (-. (day3 (consecutive (consecutive (wednesday))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (truthday (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### P-NotP 69
% 4.61/4.80 71. (-. (day2 (consecutive (wednesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### Definition-Pseudo(day2) 70
% 4.61/4.80 72. (-. (day1 (wednesday))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (truthday (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Definition-Pseudo(day1) 71
% 4.61/4.80 73. ((wednesday) = T_2) (T_2 != (wednesday)) ### Sym(=)
% 4.61/4.80 74. ((consecutive T_2) != (consecutive (wednesday))) ((wednesday) = T_2) ### NotEqual 73
% 4.61/4.80 75. ((consecutive (consecutive T_2)) != (consecutive (consecutive (wednesday)))) ((wednesday) = T_2) ### NotEqual 74
% 4.61/4.80 76. (-. (day3 (consecutive (consecutive (wednesday))))) (day3 (consecutive (consecutive T_2))) ((wednesday) = T_2) ### P-NotP 75
% 4.61/4.80 77. (-. (day2 (consecutive (wednesday)))) ((wednesday) = T_2) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 76
% 4.61/4.80 78. ((consecutive (wednesday)) = T_1) (T_1 != (consecutive (wednesday))) ### Sym(=)
% 4.61/4.80 79. ((consecutive T_1) != (consecutive (consecutive (wednesday)))) ((consecutive (wednesday)) = T_1) ### NotEqual 78
% 4.61/4.80 80. (-. (day3 (consecutive (consecutive (wednesday))))) (day3 (consecutive T_1)) ((consecutive (wednesday)) = T_1) ### P-NotP 79
% 4.61/4.80 81. (-. (day2 (consecutive (wednesday)))) ((consecutive (wednesday)) = T_1) (day3 (consecutive T_1)) ### Definition-Pseudo(day2) 80
% 4.61/4.80 82. (day3 (consecutive (saturday))) (-. (day3 (consecutive (saturday)))) ### Axiom
% 4.61/4.80 83. (-. (day2 (saturday))) (day3 (consecutive (saturday))) ### Definition-Pseudo(day2) 82
% 4.61/4.80 84. ((saturday) != (consecutive (wednesday))) ((consecutive (wednesday)) = (saturday)) ### Sym(=)
% 4.61/4.80 85. (((day2 (consecutive (wednesday))) /\ (day2 (saturday))) => ((consecutive (wednesday)) = (saturday))) ((saturday) != (consecutive (wednesday))) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) ((consecutive (wednesday)) = T_1) ### DisjTree 81 83 84
% 4.61/4.80 86. (All Y, (((day2 (consecutive (wednesday))) /\ (day2 Y)) => ((consecutive (wednesday)) = Y))) ((consecutive (wednesday)) = T_1) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) ((saturday) != (consecutive (wednesday))) ### All 85
% 4.61/4.80 87. (((day2 (consecutive (wednesday))) /\ (day2 T_1)) => ((consecutive (wednesday)) = T_1)) ((saturday) != (consecutive (wednesday))) (day3 (consecutive (saturday))) (All Y, (((day2 (consecutive (wednesday))) /\ (day2 Y)) => ((consecutive (wednesday)) = Y))) (day3 (consecutive T_1)) (day3 (consecutive (consecutive T_2))) ((wednesday) = T_2) ### DisjTree 77 3 86
% 4.61/4.80 88. ((wednesday) = T_2) (day3 (consecutive (consecutive T_2))) (day3 (consecutive T_1)) (All Y, (((day2 (consecutive (wednesday))) /\ (day2 Y)) => ((consecutive (wednesday)) = Y))) (day3 (consecutive (saturday))) ((saturday) != (consecutive (wednesday))) ### All 87
% 4.61/4.80 89. (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((saturday) != (consecutive (wednesday))) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (day3 (consecutive (consecutive T_2))) ((wednesday) = T_2) ### All 88
% 4.61/4.80 90. (((day1 (wednesday)) /\ (day1 T_2)) => ((wednesday) = T_2)) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) ((saturday) != (consecutive (wednesday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### DisjTree 72 6 89
% 4.61/4.80 91. (All Y, (((day1 (wednesday)) /\ (day1 Y)) => ((wednesday) = Y))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (truthday (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((saturday) != (consecutive (wednesday))) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) ### All 90
% 4.61/4.80 92. (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) ((saturday) != (consecutive (wednesday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### All 91
% 4.61/4.80 93. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((saturday) != (consecutive (wednesday))) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### Equiv 16 92
% 4.61/4.80 94. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) ((saturday) != (consecutive (wednesday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Imply 6 93
% 4.61/4.80 95. (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((saturday) != (consecutive (wednesday))) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### All 94
% 4.61/4.80 96. ((thursday) != (saturday)) ((consecutive (wednesday)) = (thursday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Trans-sym 95 28
% 4.61/4.80 97. (day2 (saturday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive T_1)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((consecutive (wednesday)) = (thursday)) ((thursday) != (saturday)) ### Definition-Pseudo(day2) 96
% 4.61/4.80 98. (day3 (consecutive (sunday))) (-. (day3 (consecutive (sunday)))) ### Axiom
% 4.61/4.80 99. (-. (day2 (sunday))) (day3 (consecutive (sunday))) ### Definition-Pseudo(day2) 98
% 4.61/4.80 100. ((sunday) != (consecutive (wednesday))) ((consecutive (wednesday)) = (sunday)) ### Sym(=)
% 4.61/4.80 101. (((day2 (consecutive (wednesday))) /\ (day2 (sunday))) => ((consecutive (wednesday)) = (sunday))) ((sunday) != (consecutive (wednesday))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) ((consecutive (wednesday)) = T_1) ### DisjTree 81 99 100
% 4.61/4.80 102. (All Y, (((day2 (consecutive (wednesday))) /\ (day2 Y)) => ((consecutive (wednesday)) = Y))) ((consecutive (wednesday)) = T_1) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) ((sunday) != (consecutive (wednesday))) ### All 101
% 4.61/4.80 103. (((day2 (consecutive (wednesday))) /\ (day2 T_1)) => ((consecutive (wednesday)) = T_1)) ((sunday) != (consecutive (wednesday))) (day3 (consecutive (sunday))) (All Y, (((day2 (consecutive (wednesday))) /\ (day2 Y)) => ((consecutive (wednesday)) = Y))) (day3 (consecutive T_1)) (day3 (consecutive (consecutive T_2))) ((wednesday) = T_2) ### DisjTree 77 3 102
% 4.61/4.80 104. ((wednesday) = T_2) (day3 (consecutive (consecutive T_2))) (day3 (consecutive T_1)) (All Y, (((day2 (consecutive (wednesday))) /\ (day2 Y)) => ((consecutive (wednesday)) = Y))) (day3 (consecutive (sunday))) ((sunday) != (consecutive (wednesday))) ### All 103
% 4.61/4.80 105. (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((sunday) != (consecutive (wednesday))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (day3 (consecutive (consecutive T_2))) ((wednesday) = T_2) ### All 104
% 4.61/4.80 106. (((day1 (wednesday)) /\ (day1 T_2)) => ((wednesday) = T_2)) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) ((sunday) != (consecutive (wednesday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### DisjTree 72 6 105
% 4.61/4.80 107. (All Y, (((day1 (wednesday)) /\ (day1 Y)) => ((wednesday) = Y))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (truthday (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((sunday) != (consecutive (wednesday))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) ### All 106
% 4.61/4.80 108. (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) ((sunday) != (consecutive (wednesday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (wednesday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### All 107
% 4.61/4.81 109. ((thursday) != (sunday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (truthday (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ### Trans-sym 108 28
% 4.61/4.81 110. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((thursday) != (sunday)) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### Equiv 16 109
% 4.61/4.81 111. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ((thursday) != (sunday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive (consecutive T_2))) ### Imply 6 110
% 4.61/4.81 112. (day3 (consecutive (consecutive T_2))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((thursday) != (sunday)) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### All 111
% 4.61/4.81 113. (day2 (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ((thursday) != (sunday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive T_1)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 112
% 4.61/4.81 114. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))) ((thursday) != (sunday)) ((thursday) != (saturday)) ((consecutive (wednesday)) = (thursday)) (-. (truthday (tuesday))) ((monday) != (wednesday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) ((wednesday) != (thursday)) (truthday (wednesday)) (truthday T_3) ### DisjTree 68 97 113
% 4.61/4.81 115. ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (truthday T_3) ((wednesday) != (thursday)) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Equiv 36 114
% 4.61/4.81 116. ((day2 T_1) => ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (truthday (wednesday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ### Imply 3 115
% 4.61/4.81 117. (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) (truthday (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### All 116
% 4.61/4.81 118. (-. (-. (truthday (wednesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ### NotNot 117
% 4.61/4.81 119. (truthday (monday)) (-. (truthday (monday))) ### Axiom
% 4.61/4.81 120. (truthday (friday)) (-. (truthday (friday))) ### Axiom
% 4.61/4.81 121. ((monday) != (friday)) ((monday) = (friday)) ### Axiom
% 4.61/4.81 122. (((truthday (monday)) /\ (truthday (friday))) => ((monday) = (friday))) ((monday) != (friday)) (truthday (friday)) (truthday (monday)) ### DisjTree 119 120 121
% 4.61/4.81 123. (All Y, (((truthday (monday)) /\ (truthday Y)) => ((monday) = Y))) (truthday (monday)) (truthday (friday)) ((monday) != (friday)) ### All 122
% 4.61/4.81 124. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) (truthday (monday)) ### All 123
% 4.61/4.81 125. (-. (-. (truthday (monday)))) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### NotNot 124
% 4.61/4.81 126. (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ### NotAnd 125 15
% 4.61/4.81 127. (truthday (friday)) (-. (truthday (friday))) ### Axiom
% 4.61/4.81 128. (T_2 != (friday)) ((friday) = T_2) ### Sym(=)
% 4.61/4.81 129. (((truthday (friday)) /\ (truthday T_2)) => ((friday) = T_2)) (T_2 != (friday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) ### DisjTree 127 21 128
% 4.61/4.81 130. (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (T_2 != (friday)) ### All 129
% 4.61/4.81 131. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (T_2 != (friday)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) ### All 130
% 4.61/4.81 132. ((consecutive T_2) != (consecutive (friday))) (truthday (friday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### NotEqual 131
% 4.61/4.81 133. ((saturday) != (saturday)) ### NotEqual
% 4.61/4.81 134. ((consecutive T_2) != (saturday)) ((consecutive (friday)) = (saturday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) ### Trans 132 133
% 4.61/4.81 135. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (friday)) = (saturday)) ((consecutive T_2) != (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### Equiv 126 134
% 4.61/4.81 136. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ((consecutive T_2) != (saturday)) ((consecutive (friday)) = (saturday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Imply 6 135
% 4.61/4.81 137. (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (friday)) = (saturday)) ((consecutive T_2) != (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### All 136
% 4.61/4.81 138. ((consecutive (consecutive T_2)) != (consecutive (saturday))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ((consecutive (friday)) = (saturday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### NotEqual 137
% 4.61/4.81 139. (-. (day3 (consecutive (saturday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (friday)) = (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### P-NotP 138
% 4.61/4.81 140. (-. (day2 (saturday))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ((consecutive (friday)) = (saturday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 139
% 4.61/4.81 141. (-. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (friday)) = (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### ConjTree 140
% 4.61/4.81 142. ((consecutive T_2) != (consecutive (friday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ### NotEqual 130
% 4.61/4.81 143. ((consecutive (consecutive T_2)) != (consecutive (consecutive (friday)))) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### NotEqual 142
% 4.61/4.81 144. (-. (day3 (consecutive (consecutive (friday))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ### P-NotP 143
% 4.61/4.81 145. (-. (day2 (consecutive (friday)))) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### Definition-Pseudo(day2) 144
% 4.61/4.81 146. ((consecutive (friday)) = T_1) (T_1 != (consecutive (friday))) ### Sym(=)
% 4.61/4.81 147. ((consecutive T_1) != (consecutive (consecutive (friday)))) ((consecutive (friday)) = T_1) ### NotEqual 146
% 4.61/4.81 148. (-. (day3 (consecutive (consecutive (friday))))) (day3 (consecutive T_1)) ((consecutive (friday)) = T_1) ### P-NotP 147
% 4.61/4.81 149. (-. (day2 (consecutive (friday)))) ((consecutive (friday)) = T_1) (day3 (consecutive T_1)) ### Definition-Pseudo(day2) 148
% 4.61/4.81 150. ((thursday) != (consecutive (friday))) ((consecutive (friday)) = (thursday)) ### Sym(=)
% 4.61/4.81 151. (((day2 (consecutive (friday))) /\ (day2 (thursday))) => ((consecutive (friday)) = (thursday))) ((thursday) != (consecutive (friday))) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) ((consecutive (friday)) = T_1) ### DisjTree 149 41 150
% 4.61/4.81 152. (All Y, (((day2 (consecutive (friday))) /\ (day2 Y)) => ((consecutive (friday)) = Y))) ((consecutive (friday)) = T_1) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ((thursday) != (consecutive (friday))) ### All 151
% 4.61/4.81 153. (((day2 (consecutive (friday))) /\ (day2 T_1)) => ((consecutive (friday)) = T_1)) ((thursday) != (consecutive (friday))) (day3 (consecutive (thursday))) (All Y, (((day2 (consecutive (friday))) /\ (day2 Y)) => ((consecutive (friday)) = Y))) (day3 (consecutive T_1)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ### DisjTree 145 3 152
% 4.61/4.81 154. (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive T_1)) (All Y, (((day2 (consecutive (friday))) /\ (day2 Y)) => ((consecutive (friday)) = Y))) (day3 (consecutive (thursday))) ((thursday) != (consecutive (friday))) ### All 153
% 4.61/4.81 155. (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((thursday) != (consecutive (friday))) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ### All 154
% 4.61/4.81 156. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (friday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) ((thursday) != (consecutive (friday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ### All 155
% 4.61/4.81 157. ((thursday) != (saturday)) ((consecutive (friday)) = (saturday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Trans 156 133
% 4.61/4.81 158. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((consecutive (friday)) = (saturday)) ((thursday) != (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### Equiv 126 157
% 4.61/4.81 159. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ((thursday) != (saturday)) ((consecutive (friday)) = (saturday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive (thursday))) (day3 (consecutive T_1)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Imply 6 158
% 4.61/4.81 160. (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive T_1)) (day3 (consecutive (thursday))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((consecutive (friday)) = (saturday)) ((thursday) != (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### All 159
% 4.61/4.81 161. (day2 (thursday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ((thursday) != (saturday)) ((consecutive (friday)) = (saturday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive T_1)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 160
% 4.61/4.81 162. (truthday (friday)) (-. (truthday (friday))) ### Axiom
% 4.61/4.81 163. (truthday T_3) (-. (truthday T_3)) ### Axiom
% 4.61/4.81 164. ((friday) != (friday)) ### NotEqual
% 4.61/4.81 165. (truthday T_3) (-. (truthday T_3)) ### Axiom
% 4.61/4.81 166. (-. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (day3 (consecutive (saturday))) ### ConjTree 83
% 4.61/4.81 167. (-. (truthday T_1)) (truthday T_1) ### Axiom
% 4.61/4.81 168. ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (-. (truthday T_1)) (day3 (consecutive (saturday))) ### Equiv 166 167
% 4.61/4.81 169. ((day2 T_1) => ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))))) (day3 (consecutive (saturday))) (-. (truthday T_1)) (day3 (consecutive T_1)) ### Imply 3 168
% 4.61/4.81 170. (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (-. (truthday T_1)) (day3 (consecutive (saturday))) ### All 169
% 4.61/4.81 171. (T_3 != T_1) (T_3 = T_1) ### Axiom
% 4.61/4.81 172. (((truthday T_3) /\ (truthday T_1)) => (T_3 = T_1)) (T_3 != T_1) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) ### DisjTree 165 170 171
% 4.61/4.81 173. (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (T_3 != T_1) ### All 172
% 4.61/4.81 174. (T_1 != (friday)) ((friday) = T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### TransEq-sym 164 164 173
% 4.61/4.81 175. (((truthday (friday)) /\ (truthday T_3)) => ((friday) = T_3)) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (T_1 != (friday)) (truthday T_3) (truthday (friday)) ### DisjTree 162 163 174
% 4.61/4.81 176. (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (truthday T_3) (T_1 != (friday)) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### All 175
% 4.61/4.81 177. ((consecutive T_1) != (consecutive (friday))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ### NotEqual 176
% 4.61/4.81 178. (-. (day3 (consecutive (friday)))) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### P-NotP 177
% 4.61/4.81 179. (-. (day2 (friday))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ### Definition-Pseudo(day2) 178
% 4.61/4.81 180. ((friday) != (saturday)) ((friday) = (saturday)) ### Axiom
% 4.61/4.81 181. (((day2 (friday)) /\ (day2 (saturday))) => ((friday) = (saturday))) ((friday) != (saturday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### DisjTree 179 83 180
% 4.61/4.81 182. (All Y, (((day2 (friday)) /\ (day2 Y)) => ((friday) = Y))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ((friday) != (saturday)) ### All 181
% 4.61/4.81 183. (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((friday) != (saturday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) (truthday (friday)) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### All 182
% 4.61/4.81 184. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (truthday (friday)) (All Y, (((truthday (friday)) /\ (truthday Y)) => ((friday) = Y))) ((friday) != (saturday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ### All 183
% 4.61/4.81 185. (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((friday) != (saturday)) (truthday (friday)) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### All 184
% 4.61/4.81 186. (day2 (saturday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (truthday T_3) (truthday (friday)) ((friday) != (saturday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ### Definition-Pseudo(day2) 185
% 4.61/4.81 187. (-. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (day3 (consecutive (sunday))) ### ConjTree 99
% 4.61/4.81 188. (-. (truthday T_1)) (truthday T_1) ### Axiom
% 4.61/4.81 189. ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (-. (truthday T_1)) (day3 (consecutive (sunday))) ### Equiv 187 188
% 4.61/4.81 190. ((day2 T_1) => ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))))) (day3 (consecutive (sunday))) (-. (truthday T_1)) (day3 (consecutive T_1)) ### Imply 3 189
% 4.61/4.81 191. (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (-. (truthday T_1)) (day3 (consecutive (sunday))) ### All 190
% 4.61/4.81 192. (truthday (friday)) (-. (truthday (friday))) ### Axiom
% 4.61/4.81 193. (T_1 != (friday)) (T_1 = (friday)) ### Axiom
% 4.61/4.81 194. (((truthday T_1) /\ (truthday (friday))) => (T_1 = (friday))) (T_1 != (friday)) (truthday (friday)) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ### DisjTree 191 192 193
% 4.61/4.81 195. (All Y, (((truthday T_1) /\ (truthday Y)) => (T_1 = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (truthday (friday)) (T_1 != (friday)) ### All 194
% 4.61/4.81 196. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (T_1 != (friday)) (truthday (friday)) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ### All 195
% 4.61/4.81 197. ((consecutive T_1) != (consecutive (friday))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (truthday (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### NotEqual 196
% 4.61/4.81 198. (-. (day3 (consecutive (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (friday)) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ### P-NotP 197
% 4.61/4.81 199. (-. (day2 (friday))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (truthday (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Definition-Pseudo(day2) 198
% 4.61/4.81 200. ((friday) != (sunday)) ((friday) = (sunday)) ### Axiom
% 4.61/4.81 201. (((day2 (friday)) /\ (day2 (sunday))) => ((friday) = (sunday))) ((friday) != (sunday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (friday)) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ### DisjTree 199 99 200
% 4.61/4.81 202. (All Y, (((day2 (friday)) /\ (day2 Y)) => ((friday) = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (truthday (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((friday) != (sunday)) ### All 201
% 4.61/4.81 203. (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((friday) != (sunday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (friday)) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ### All 202
% 4.61/4.81 204. (day2 (sunday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (truthday (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((friday) != (sunday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ### Definition-Pseudo(day2) 203
% 4.61/4.81 205. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))) ((friday) != (sunday)) ((friday) != (saturday)) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive T_1)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((consecutive (friday)) = (saturday)) ((thursday) != (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ### DisjTree 161 186 204
% 4.61/4.81 206. ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) ((thursday) != (saturday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) ((friday) != (saturday)) ((friday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ((consecutive (friday)) = (saturday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Equiv 141 205
% 4.61/4.81 207. ((day2 T_1) => ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (friday)) = (saturday)) (truthday (friday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((friday) != (sunday)) ((friday) != (saturday)) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((thursday) != (saturday)) (day3 (consecutive T_1)) ### Imply 3 206
% 4.61/4.81 208. (day3 (consecutive T_1)) ((thursday) != (saturday)) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) ((friday) != (saturday)) ((friday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (friday)) (truthday (friday)) ((consecutive (friday)) = (saturday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### All 207
% 4.61/4.81 209. (-. (-. (truthday (friday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((friday) != (sunday)) ((friday) != (saturday)) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) ((thursday) != (saturday)) (day3 (consecutive T_1)) ### NotNot 208
% 4.61/4.81 210. (-. ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### NotAnd 118 209
% 4.61/4.81 211. (day3 T_0) (-. (day3 T_0)) ### Axiom
% 4.61/4.81 212. ((consecutive (sunday)) != (consecutive (sunday))) ### Refl(=)
% 4.61/4.81 213. (truthday (monday)) (-. (truthday (monday))) ### Axiom
% 4.61/4.81 214. (day3 (consecutive T_1)) (-. (day3 (consecutive T_1))) ### Axiom
% 4.61/4.81 215. ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ### Axiom
% 4.61/4.81 216. (-. (truthday (consecutive T_1))) (truthday (consecutive T_1)) ### Axiom
% 4.61/4.81 217. ((truthday (consecutive T_1)) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) (-. (truthday (consecutive T_1))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### Equiv 215 216
% 4.61/4.81 218. ((day3 (consecutive T_1)) => ((truthday (consecutive T_1)) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. (truthday (consecutive T_1))) (day3 (consecutive T_1)) ### Imply 214 217
% 4.61/4.81 219. (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive T_1)) (-. (truthday (consecutive T_1))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### All 218
% 4.61/4.81 220. ((monday) != (consecutive T_1)) ((monday) = (consecutive T_1)) ### Axiom
% 4.61/4.81 221. (((truthday (monday)) /\ (truthday (consecutive T_1))) => ((monday) = (consecutive T_1))) ((monday) != (consecutive T_1)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (day3 (consecutive T_1)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (truthday (monday)) ### DisjTree 213 219 220
% 4.61/4.81 222. (All Y, (((truthday (monday)) /\ (truthday Y)) => ((monday) = Y))) (truthday (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive T_1)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((monday) != (consecutive T_1)) ### All 221
% 4.61/4.81 223. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (consecutive T_1)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (day3 (consecutive T_1)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (truthday (monday)) ### All 222
% 4.61/4.81 224. ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (truthday (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive T_1)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Trans-sym 212 223
% 4.61/4.81 225. (-. (-. (truthday (monday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (day3 (consecutive T_1)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ### NotNot 224
% 4.61/4.81 226. (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (tuesday))) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive T_1)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### NotAnd 225 15
% 4.61/4.81 227. ((consecutive (saturday)) != (consecutive (saturday))) ### Refl(=)
% 4.61/4.81 228. ((consecutive (thursday)) != (consecutive (thursday))) ### Refl(=)
% 4.61/4.81 229. ((consecutive (tuesday)) = (wednesday)) ((consecutive (tuesday)) != (wednesday)) ### Axiom
% 4.61/4.81 230. ((consecutive (consecutive (tuesday))) != (consecutive (wednesday))) ((consecutive (tuesday)) = (wednesday)) ### NotEqual 229
% 4.61/4.81 231. ((consecutive (monday)) != (consecutive (monday))) ### Refl(=)
% 4.61/4.81 232. ((consecutive (sunday)) != (consecutive (sunday))) ### Refl(=)
% 4.61/4.81 233. ((monday) != (consecutive T_1)) ((consecutive T_1) = (monday)) ### Sym(=)
% 4.61/4.81 234. ((tuesday) != (consecutive T_1)) ((consecutive T_1) = (tuesday)) ### Sym(=)
% 4.61/4.81 235. ((consecutive (monday)) = (tuesday)) ((consecutive (monday)) != (tuesday)) ### Axiom
% 4.61/4.81 236. ((consecutive (consecutive (monday))) != (consecutive (tuesday))) ((consecutive (monday)) = (tuesday)) ### NotEqual 235
% 4.61/4.81 237. ((consecutive T_1) = (wednesday)) ((wednesday) != (consecutive T_1)) ### Sym(=)
% 4.61/4.81 238. ((consecutive T_1) != (consecutive (consecutive (monday)))) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) = (wednesday)) ((consecutive (monday)) = (tuesday)) ### Trans-sym 236 237
% 4.61/4.81 239. ((thursday) != (consecutive T_1)) ((consecutive T_1) = (thursday)) ### Sym(=)
% 4.61/4.81 240. ((friday) != (consecutive T_1)) ((consecutive T_1) = (friday)) ### Sym(=)
% 4.61/4.81 241. ((consecutive (thursday)) = (friday)) ((consecutive (thursday)) != (friday)) ### Axiom
% 4.61/4.81 242. ((consecutive (consecutive (thursday))) != (consecutive (friday))) ((consecutive (thursday)) = (friday)) ### NotEqual 241
% 4.61/4.81 243. ((consecutive T_1) = (saturday)) ((saturday) != (consecutive T_1)) ### Sym(=)
% 4.61/4.81 244. ((consecutive T_1) != (consecutive (consecutive (thursday)))) ((consecutive (friday)) = (saturday)) ((consecutive T_1) = (saturday)) ((consecutive (thursday)) = (friday)) ### Trans-sym 242 243
% 4.61/4.81 245. ((sunday) != (consecutive T_1)) ((consecutive T_1) = (sunday)) ### Sym(=)
% 4.61/4.81 246. (((consecutive T_1) = (monday)) \/ (((consecutive T_1) = (tuesday)) \/ (((consecutive T_1) = (wednesday)) \/ (((consecutive T_1) = (thursday)) \/ (((consecutive T_1) = (friday)) \/ (((consecutive T_1) = (saturday)) \/ ((consecutive T_1) = (sunday)))))))) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive T_1) != (consecutive (consecutive (thursday)))) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((tuesday) != (consecutive T_1)) ((monday) != (consecutive T_1)) ### DisjTree 233 234 238 239 240 244 245
% 4.61/4.81 247. (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((monday) != (consecutive T_1)) ((tuesday) != (consecutive T_1)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (monday)) = (tuesday)) ((thursday) != (consecutive T_1)) ((friday) != (consecutive T_1)) ((consecutive T_1) != (consecutive (consecutive (thursday)))) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) ### All 246
% 4.61/4.81 248. (-. (day3 (consecutive (consecutive (thursday))))) (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((tuesday) != (consecutive T_1)) ((monday) != (consecutive T_1)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ### P-NotP 247
% 4.61/4.81 249. (-. (day2 (consecutive (thursday)))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((monday) != (consecutive T_1)) ((tuesday) != (consecutive T_1)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (monday)) = (tuesday)) ((thursday) != (consecutive T_1)) ((friday) != (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) (day3 (consecutive T_1)) ### Definition-Pseudo(day2) 248
% 4.61/4.82 250. (-. (day1 (thursday))) (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((tuesday) != (consecutive T_1)) ((monday) != (consecutive T_1)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ### Definition-Pseudo(day1) 249
% 4.61/4.82 251. (day3 (consecutive (consecutive T_2))) (-. (day3 (consecutive (consecutive T_2)))) ### Axiom
% 4.61/4.82 252. ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ### Axiom
% 4.61/4.82 253. (-. (truthday (consecutive (consecutive T_2)))) (truthday (consecutive (consecutive T_2))) ### Axiom
% 4.61/4.82 254. ((truthday (consecutive (consecutive T_2))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) (-. (truthday (consecutive (consecutive T_2)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### Equiv 252 253
% 4.61/4.82 255. ((day3 (consecutive (consecutive T_2))) => ((truthday (consecutive (consecutive T_2))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. (truthday (consecutive (consecutive T_2)))) (day3 (consecutive (consecutive T_2))) ### Imply 251 254
% 4.61/4.82 256. (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (consecutive T_2))) (-. (truthday (consecutive (consecutive T_2)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### All 255
% 4.61/4.82 257. (T_2 = (consecutive (consecutive T_2))) (T_2 != (consecutive (consecutive T_2))) ### Axiom
% 4.61/4.82 258. ((thursday) != (consecutive (consecutive T_2))) ((thursday) = T_2) (T_2 = (consecutive (consecutive T_2))) ### TransEq 28 28 257
% 4.61/4.82 259. (((truthday T_2) /\ (truthday (consecutive (consecutive T_2)))) => (T_2 = (consecutive (consecutive T_2)))) ((thursday) = T_2) ((thursday) != (consecutive (consecutive T_2))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### DisjTree 21 256 258
% 4.61/4.82 260. (All Y, (((truthday T_2) /\ (truthday Y)) => (T_2 = Y))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((thursday) != (consecutive (consecutive T_2))) ((thursday) = T_2) ### All 259
% 4.61/4.82 261. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((thursday) = T_2) ((thursday) != (consecutive (consecutive T_2))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### All 260
% 4.61/4.82 262. ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((thursday) = T_2) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((consecutive (tuesday)) = (wednesday)) ### Trans-sym 230 261
% 4.61/4.82 263. (((day1 (thursday)) /\ (day1 T_2)) => ((thursday) = T_2)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((monday) != (consecutive T_1)) ((tuesday) != (consecutive T_1)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (monday)) = (tuesday)) ((thursday) != (consecutive T_1)) ((friday) != (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) (day3 (consecutive T_1)) ### DisjTree 250 6 262
% 4.61/4.82 264. (All Y, (((day1 (thursday)) /\ (day1 Y)) => ((thursday) = Y))) (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((tuesday) != (consecutive T_1)) ((monday) != (consecutive T_1)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### All 263
% 4.61/4.82 265. (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((monday) != (consecutive T_1)) ((tuesday) != (consecutive T_1)) ((consecutive T_1) != (consecutive (consecutive (monday)))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (monday)) = (tuesday)) ((thursday) != (consecutive T_1)) ((friday) != (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) (day3 (consecutive T_1)) ### All 264
% 4.61/4.82 266. (-. (day3 (consecutive (consecutive (monday))))) (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) ((tuesday) != (consecutive T_1)) ((monday) != (consecutive T_1)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ### P-NotP 265
% 4.61/4.82 267. (-. (day2 (consecutive (monday)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((monday) != (consecutive T_1)) ((tuesday) != (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive (monday)) = (tuesday)) ((thursday) != (consecutive T_1)) ((friday) != (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) (day3 (consecutive T_1)) ### Definition-Pseudo(day2) 266
% 4.61/4.82 268. (-. (day1 (monday))) (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) ((tuesday) != (consecutive T_1)) ((monday) != (consecutive T_1)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ### Definition-Pseudo(day1) 267
% 4.61/4.82 269. ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) ### Axiom
% 4.61/4.82 270. (-. (truthday (monday))) (truthday (monday)) ### Axiom
% 4.61/4.82 271. ((truthday (monday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (monday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### Equiv 269 270
% 4.61/4.82 272. ((day1 (monday)) => ((truthday (monday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((monday) != (consecutive T_1)) ((tuesday) != (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive (monday)) = (tuesday)) ((thursday) != (consecutive T_1)) ((friday) != (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) (day3 (consecutive T_1)) ### Imply 268 271
% 4.61/4.82 273. (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) ((tuesday) != (consecutive T_1)) ((monday) != (consecutive T_1)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ### All 272
% 4.61/4.82 274. ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((tuesday) != (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive (monday)) = (tuesday)) ((thursday) != (consecutive T_1)) ((friday) != (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) (day3 (consecutive T_1)) ### Trans-sym 232 273
% 4.61/4.82 275. ((consecutive T_1) != (consecutive (monday))) (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((friday) != (consecutive T_1)) ((thursday) != (consecutive T_1)) ((consecutive (monday)) = (tuesday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ### Trans-sym 231 274
% 4.61/4.82 276. ((consecutive T_1) != (consecutive (consecutive (tuesday)))) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((friday) != (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((sunday) != (consecutive T_1)) (day3 (consecutive T_1)) ((consecutive T_1) != (consecutive (monday))) ((consecutive (tuesday)) = (wednesday)) ### Trans-sym 230 275
% 4.61/4.82 277. ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (monday))) (day3 (consecutive T_1)) ((sunday) != (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive T_1) != (consecutive (consecutive (tuesday)))) ### Trans-sym 228 276
% 4.61/4.82 278. ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (consecutive (tuesday)))) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) (day3 (consecutive T_1)) ((consecutive T_1) != (consecutive (monday))) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) ### Trans-sym 227 277
% 4.61/4.82 279. (-. (day3 (consecutive (monday)))) ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) (day3 (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive T_1) != (consecutive (consecutive (tuesday)))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) ### P-NotP 278
% 4.61/4.82 280. ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ### Axiom
% 4.61/4.82 281. (truthday (consecutive (monday))) (-. (truthday (consecutive (monday)))) ### Axiom
% 4.61/4.82 282. (truthday T_3) (-. (truthday T_3)) ### Axiom
% 4.61/4.82 283. (T_3 != (consecutive (monday))) ((consecutive (monday)) = T_3) ### Sym(=)
% 4.61/4.82 284. (((truthday (consecutive (monday))) /\ (truthday T_3)) => ((consecutive (monday)) = T_3)) (T_3 != (consecutive (monday))) (truthday T_3) (truthday (consecutive (monday))) ### DisjTree 281 282 283
% 4.61/4.82 285. (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) (truthday (consecutive (monday))) (truthday T_3) (T_3 != (consecutive (monday))) ### All 284
% 4.61/4.82 286. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (T_3 != (consecutive (monday))) (truthday T_3) (truthday (consecutive (monday))) ### All 285
% 4.61/4.82 287. ((tuesday) != (tuesday)) ### NotEqual
% 4.61/4.82 288. (T_3 != (tuesday)) ((consecutive (monday)) = (tuesday)) (truthday (consecutive (monday))) (truthday T_3) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Trans 286 287
% 4.61/4.82 289. ((truthday (consecutive (monday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday T_3) ((consecutive (monday)) = (tuesday)) (T_3 != (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### Equiv 280 288
% 4.61/4.82 290. ((day3 (consecutive (monday))) => ((truthday (consecutive (monday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) (T_3 != (tuesday)) (truthday T_3) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (consecutive (tuesday)))) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) (day3 (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) ### Imply 279 289
% 4.61/4.82 291. ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) (day3 (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (consecutive T_2)) != (consecutive (consecutive (tuesday)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive T_1) != (consecutive (consecutive (tuesday)))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (truthday T_3) (T_3 != (tuesday)) ### All 290
% 4.61/4.82 292. (-. (day3 (consecutive (consecutive (tuesday))))) (T_3 != (tuesday)) (truthday T_3) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (consecutive (tuesday)))) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) (day3 (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) ### P-NotP 291
% 4.61/4.82 293. ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) (day3 (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (truthday T_3) (T_3 != (tuesday)) (-. (day3 (consecutive (consecutive (tuesday))))) ### P-NotP 292
% 4.61/4.82 294. (-. (day2 (consecutive (tuesday)))) (T_3 != (tuesday)) (truthday T_3) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) (day3 (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) ### Definition-Pseudo(day2) 293
% 4.61/4.82 295. (-. (day1 (tuesday))) ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) (day3 (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (truthday T_3) (T_3 != (tuesday)) ### Definition-Pseudo(day1) 294
% 4.61/4.82 296. ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) ### Axiom
% 4.61/4.82 297. (-. (truthday (tuesday))) (truthday (tuesday)) ### Axiom
% 4.61/4.82 298. ((truthday (tuesday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (tuesday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### Equiv 296 297
% 4.61/4.82 299. ((day1 (tuesday)) => ((truthday (tuesday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) (T_3 != (tuesday)) (truthday T_3) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) (day3 (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) ### Imply 295 298
% 4.61/4.82 300. ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) (day3 (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (monday))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (truthday T_3) (T_3 != (tuesday)) (-. (truthday (tuesday))) ### All 299
% 4.65/4.82 301. (-. (truthday (tuesday))) (truthday T_3) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (-. (truthday (monday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) (day3 (consecutive T_1)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) ### P-NotP 300
% 4.65/4.82 302. ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) (day3 (consecutive T_1)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (truthday T_3) (-. (truthday (tuesday))) ### And 301
% 4.65/4.82 303. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (truthday T_3) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (day3 (consecutive (consecutive T_2))) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (day3 (consecutive T_1)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) (-. (truthday (tuesday))) ### Equiv 226 302
% 4.65/4.82 304. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive T_1)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (friday)) = (saturday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (truthday T_3) (day3 (consecutive (consecutive T_2))) ### Imply 6 303
% 4.65/4.82 305. (day3 (consecutive (consecutive T_2))) (truthday T_3) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (friday)) = (saturday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (day3 (consecutive T_1)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) (-. (truthday (tuesday))) ### All 304
% 4.65/4.82 306. ((truthday T_0) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) ### Equiv 210 305
% 4.65/4.82 307. ((day3 T_0) => ((truthday T_0) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) ((consecutive T_1) != (consecutive (thursday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) (day3 T_0) ### Imply 211 306
% 4.65/4.82 308. (day3 T_0) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive T_1) != (consecutive (thursday))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) ((consecutive T_1) != (consecutive (saturday))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) ### All 307
% 4.65/4.82 309. (-. (day3 (consecutive (thursday)))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive T_1) != (consecutive (saturday))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) ((consecutive T_1) != (consecutive (sunday))) (day3 T_0) ### P-NotP 308
% 4.65/4.82 310. (-. (day3 (consecutive (saturday)))) (day3 T_0) ((consecutive T_1) != (consecutive (sunday))) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) (-. (day3 (consecutive (thursday)))) ### P-NotP 309
% 4.65/4.82 311. (-. (day3 (consecutive (sunday)))) (-. (day3 (consecutive (thursday)))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) (-. (day3 (consecutive (saturday)))) ### P-NotP 310
% 4.65/4.82 312. (-. (day2 (sunday))) (-. (day3 (consecutive (saturday)))) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) (-. (day3 (consecutive (thursday)))) ### Definition-Pseudo(day2) 311
% 4.65/4.82 313. (-. (day2 (saturday))) (-. (day3 (consecutive (thursday)))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) (-. (day2 (sunday))) ### Definition-Pseudo(day2) 312
% 4.65/4.82 314. (-. (day2 (thursday))) (-. (day2 (sunday))) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) (-. (day2 (saturday))) ### Definition-Pseudo(day2) 313
% 4.65/4.82 315. (-. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) ### ConjTree 314
% 4.65/4.82 316. (day3 (consecutive (thursday))) (-. (day3 (consecutive (thursday)))) ### Axiom
% 4.65/4.82 317. ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ### Axiom
% 4.65/4.82 318. (truthday (consecutive (thursday))) (-. (truthday (consecutive (thursday)))) ### Axiom
% 4.65/4.82 319. (truthday (monday)) (-. (truthday (monday))) ### Axiom
% 4.65/4.82 320. ((monday) != (consecutive (thursday))) ((consecutive (thursday)) = (monday)) ### Sym(=)
% 4.65/4.82 321. (((truthday (consecutive (thursday))) /\ (truthday (monday))) => ((consecutive (thursday)) = (monday))) ((monday) != (consecutive (thursday))) (truthday (monday)) (truthday (consecutive (thursday))) ### DisjTree 318 319 320
% 4.65/4.82 322. (All Y, (((truthday (consecutive (thursday))) /\ (truthday Y)) => ((consecutive (thursday)) = Y))) (truthday (consecutive (thursday))) (truthday (monday)) ((monday) != (consecutive (thursday))) ### All 321
% 4.65/4.82 323. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (consecutive (thursday))) (truthday (monday)) (truthday (consecutive (thursday))) ### All 322
% 4.65/4.82 324. ((truthday (consecutive (thursday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) (truthday (monday)) ((monday) != (consecutive (thursday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### Equiv 317 323
% 4.65/4.82 325. ((day3 (consecutive (thursday))) => ((truthday (consecutive (thursday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (consecutive (thursday))) (truthday (monday)) (day3 (consecutive (thursday))) ### Imply 316 324
% 4.65/4.82 326. (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (thursday))) (truthday (monday)) ((monday) != (consecutive (thursday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### All 325
% 4.65/4.82 327. ((monday) != (friday)) ((consecutive (thursday)) = (friday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (truthday (monday)) (day3 (consecutive (thursday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### Trans 326 164
% 4.65/4.82 328. (-. (-. (truthday (monday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (thursday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (thursday)) = (friday)) ((monday) != (friday)) ### NotNot 327
% 4.65/4.82 329. (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (tuesday))) ((monday) != (friday)) ((consecutive (thursday)) = (friday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (thursday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### NotAnd 328 15
% 4.65/4.82 330. ((consecutive (wednesday)) = (thursday)) ((thursday) != (consecutive (wednesday))) ### Sym(=)
% 4.65/4.82 331. ((consecutive (thursday)) != (consecutive (consecutive (wednesday)))) ((consecutive (wednesday)) = (thursday)) ### NotEqual 330
% 4.65/4.82 332. (-. (day3 (consecutive (consecutive (wednesday))))) (day3 (consecutive (thursday))) ((consecutive (wednesday)) = (thursday)) ### P-NotP 331
% 4.65/4.82 333. (-. (day2 (consecutive (wednesday)))) ((consecutive (wednesday)) = (thursday)) (day3 (consecutive (thursday))) ### Definition-Pseudo(day2) 332
% 4.65/4.82 334. (-. (day1 (wednesday))) (day3 (consecutive (thursday))) ((consecutive (wednesday)) = (thursday)) ### Definition-Pseudo(day1) 333
% 4.65/4.82 335. ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) ### Axiom
% 4.65/4.82 336. (-. (truthday (wednesday))) (truthday (wednesday)) ### Axiom
% 4.65/4.82 337. ((truthday (wednesday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (wednesday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### Equiv 335 336
% 4.65/4.82 338. ((day1 (wednesday)) => ((truthday (wednesday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. (truthday (wednesday))) ((consecutive (wednesday)) = (thursday)) (day3 (consecutive (thursday))) ### Imply 334 337
% 4.65/4.82 339. (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (thursday))) ((consecutive (wednesday)) = (thursday)) (-. (truthday (wednesday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### All 338
% 4.65/4.83 340. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (wednesday))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (thursday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (thursday)) = (friday)) ((monday) != (friday)) (-. (truthday (tuesday))) ### Equiv 329 339
% 4.65/4.83 341. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) ((monday) != (friday)) ((consecutive (thursday)) = (friday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (thursday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (-. (truthday (wednesday))) (day3 (consecutive (consecutive T_2))) ### Imply 6 340
% 4.65/4.83 342. (day3 (consecutive (consecutive T_2))) (-. (truthday (wednesday))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (thursday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (thursday)) = (friday)) ((monday) != (friday)) (-. (truthday (tuesday))) ### All 341
% 4.65/4.83 343. (day2 (thursday)) (-. (truthday (tuesday))) ((monday) != (friday)) ((consecutive (thursday)) = (friday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (-. (truthday (wednesday))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 342
% 4.65/4.83 344. (truthday (monday)) (-. (truthday (monday))) ### Axiom
% 4.65/4.83 345. (truthday T_3) (-. (truthday T_3)) ### Axiom
% 4.65/4.83 346. ((monday) != (monday)) ### NotEqual
% 4.65/4.83 347. (T_1 != (monday)) ((monday) = T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday T_3) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### TransEq-sym 346 346 173
% 4.65/4.83 348. (((truthday (monday)) /\ (truthday T_3)) => ((monday) = T_3)) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (T_1 != (monday)) (truthday T_3) (truthday (monday)) ### DisjTree 344 345 347
% 4.65/4.83 349. (All Y, (((truthday (monday)) /\ (truthday Y)) => ((monday) = Y))) (truthday (monday)) (truthday T_3) (T_1 != (monday)) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All Y, (((truthday T_3) /\ (truthday Y)) => (T_3 = Y))) ### All 348
% 4.65/4.83 350. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (T_1 != (monday)) (truthday T_3) (truthday (monday)) (All Y, (((truthday (monday)) /\ (truthday Y)) => ((monday) = Y))) ### All 349
% 4.65/4.83 351. (truthday (monday)) (truthday T_3) (T_1 != (monday)) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### All 350
% 4.65/4.83 352. ((consecutive T_1) != (consecutive (monday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (truthday (monday)) ### NotEqual 351
% 4.65/4.83 353. (-. (day3 (consecutive (monday)))) (truthday (monday)) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### P-NotP 352
% 4.65/4.83 354. ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ### Axiom
% 4.65/4.83 355. (truthday (consecutive (monday))) (-. (truthday (consecutive (monday)))) ### Axiom
% 4.65/4.83 356. (truthday (monday)) (-. (truthday (monday))) ### Axiom
% 4.65/4.83 357. ((monday) != (consecutive (monday))) ((consecutive (monday)) = (monday)) ### Sym(=)
% 4.65/4.83 358. (((truthday (consecutive (monday))) /\ (truthday (monday))) => ((consecutive (monday)) = (monday))) ((monday) != (consecutive (monday))) (truthday (monday)) (truthday (consecutive (monday))) ### DisjTree 355 356 357
% 4.65/4.83 359. (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) (truthday (consecutive (monday))) (truthday (monday)) ((monday) != (consecutive (monday))) ### All 358
% 4.65/4.83 360. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (consecutive (monday))) (truthday (monday)) (truthday (consecutive (monday))) ### All 359
% 4.65/4.83 361. ((truthday (consecutive (monday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) (truthday (monday)) ((monday) != (consecutive (monday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### Equiv 354 360
% 4.65/4.83 362. ((day3 (consecutive (monday))) => ((truthday (consecutive (monday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((monday) != (consecutive (monday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (truthday (monday)) ### Imply 353 361
% 4.65/4.83 363. (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (truthday (monday)) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (consecutive (monday))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### All 362
% 4.65/4.83 364. ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (truthday (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### Trans 363 287
% 4.65/4.83 365. (-. (-. (truthday (monday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (monday)) = (tuesday)) ((monday) != (tuesday)) ### NotNot 364
% 4.65/4.83 366. (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (tuesday))) ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### NotAnd 365 15
% 4.65/4.83 367. ((consecutive (friday)) = (saturday)) ((saturday) != (consecutive (friday))) ### Sym(=)
% 4.65/4.83 368. ((consecutive (saturday)) != (consecutive (consecutive (friday)))) ((consecutive (friday)) = (saturday)) ### NotEqual 367
% 4.65/4.83 369. (-. (day3 (consecutive (consecutive (friday))))) (day3 (consecutive (saturday))) ((consecutive (friday)) = (saturday)) ### P-NotP 368
% 4.65/4.83 370. (-. (day2 (consecutive (friday)))) ((consecutive (friday)) = (saturday)) (day3 (consecutive (saturday))) ### Definition-Pseudo(day2) 369
% 4.65/4.83 371. (-. (day1 (friday))) (day3 (consecutive (saturday))) ((consecutive (friday)) = (saturday)) ### Definition-Pseudo(day1) 370
% 4.65/4.83 372. ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) ### Axiom
% 4.65/4.83 373. (-. (truthday (friday))) (truthday (friday)) ### Axiom
% 4.65/4.83 374. ((truthday (friday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (friday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### Equiv 372 373
% 4.65/4.83 375. ((day1 (friday)) => ((truthday (friday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. (truthday (friday))) ((consecutive (friday)) = (saturday)) (day3 (consecutive (saturday))) ### Imply 371 374
% 4.65/4.83 376. (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (saturday))) ((consecutive (friday)) = (saturday)) (-. (truthday (friday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### All 375
% 4.65/4.83 377. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (friday))) ((consecutive (friday)) = (saturday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (monday)) = (tuesday)) ((monday) != (tuesday)) (-. (truthday (tuesday))) ### Equiv 366 376
% 4.65/4.83 378. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (saturday))) (truthday T_3) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (friday)) = (saturday)) (-. (truthday (friday))) (day3 (consecutive (consecutive T_2))) ### Imply 6 377
% 4.65/4.83 379. (day3 (consecutive (consecutive T_2))) (-. (truthday (friday))) ((consecutive (friday)) = (saturday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (truthday T_3) (day3 (consecutive (saturday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (monday)) = (tuesday)) ((monday) != (tuesday)) (-. (truthday (tuesday))) ### All 378
% 4.65/4.83 380. (day2 (saturday)) (-. (truthday (tuesday))) ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (truthday T_3) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (friday)) = (saturday)) (-. (truthday (friday))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 379
% 4.65/4.83 381. (truthday (monday)) (-. (truthday (monday))) ### Axiom
% 4.65/4.83 382. (T_1 != (monday)) ((monday) = T_1) ### Sym(=)
% 4.65/4.83 383. (((truthday (monday)) /\ (truthday T_1)) => ((monday) = T_1)) (T_1 != (monday)) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (monday)) ### DisjTree 381 191 382
% 4.65/4.83 384. (All Y, (((truthday (monday)) /\ (truthday Y)) => ((monday) = Y))) (truthday (monday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (T_1 != (monday)) ### All 383
% 4.65/4.83 385. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (T_1 != (monday)) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (monday)) ### All 384
% 4.65/4.83 386. ((consecutive T_1) != (consecutive (monday))) (truthday (monday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### NotEqual 385
% 4.65/4.83 387. (-. (day3 (consecutive (monday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (monday)) ### P-NotP 386
% 4.65/4.83 388. ((day3 (consecutive (monday))) => ((truthday (consecutive (monday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((monday) != (consecutive (monday))) (truthday (monday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Imply 387 361
% 4.65/4.83 389. (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (monday)) ((monday) != (consecutive (monday))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### All 388
% 4.65/4.83 390. ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (truthday (monday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### Trans 389 287
% 4.65/4.83 391. (-. (-. (truthday (monday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (monday)) = (tuesday)) ((monday) != (tuesday)) ### NotNot 390
% 4.65/4.83 392. (-. ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (-. (truthday (tuesday))) ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### NotAnd 391 15
% 4.65/4.83 393. (day3 (consecutive (sunday))) (-. (day3 (consecutive (sunday)))) ### Axiom
% 4.65/4.83 394. ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ### Axiom
% 4.65/4.83 395. (truthday (consecutive (sunday))) (-. (truthday (consecutive (sunday)))) ### Axiom
% 4.65/4.83 396. (T_2 != (consecutive (sunday))) ((consecutive (sunday)) = T_2) ### Sym(=)
% 4.65/4.83 397. (((truthday (consecutive (sunday))) /\ (truthday T_2)) => ((consecutive (sunday)) = T_2)) (T_2 != (consecutive (sunday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (consecutive (sunday))) ### DisjTree 395 21 396
% 4.65/4.83 398. (All Y, (((truthday (consecutive (sunday))) /\ (truthday Y)) => ((consecutive (sunday)) = Y))) (truthday (consecutive (sunday))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (T_2 != (consecutive (sunday))) ### All 397
% 4.65/4.83 399. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (T_2 != (consecutive (sunday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (truthday (consecutive (sunday))) ### All 398
% 4.65/4.83 400. (T_2 != (monday)) ((consecutive (sunday)) = (monday)) (truthday (consecutive (sunday))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ### Trans 399 346
% 4.65/4.83 401. ((truthday (consecutive (sunday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (sunday)) = (monday)) (T_2 != (monday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### Equiv 394 400
% 4.65/4.83 402. ((day3 (consecutive (sunday))) => ((truthday (consecutive (sunday))) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (T_2 != (monday)) ((consecutive (sunday)) = (monday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) ### Imply 393 401
% 4.65/4.83 403. (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (sunday)) = (monday)) (T_2 != (monday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### All 402
% 4.65/4.83 404. ((consecutive T_2) != (consecutive (monday))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (sunday)) = (monday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### NotEqual 403
% 4.65/4.83 405. ((consecutive (consecutive T_2)) != (consecutive (consecutive (monday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (sunday)) = (monday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### NotEqual 404
% 4.65/4.83 406. (-. (day3 (consecutive (consecutive (monday))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (sunday)) = (monday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### P-NotP 405
% 4.65/4.83 407. (-. (day2 (consecutive (monday)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (sunday)) = (monday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ### Definition-Pseudo(day2) 406
% 4.65/4.83 408. (truthday (consecutive (monday))) (-. (truthday (consecutive (monday)))) ### Axiom
% 4.65/4.83 409. (T_1 != (consecutive (monday))) ((consecutive (monday)) = T_1) ### Sym(=)
% 4.65/4.83 410. (((truthday (consecutive (monday))) /\ (truthday T_1)) => ((consecutive (monday)) = T_1)) (T_1 != (consecutive (monday))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (consecutive (monday))) ### DisjTree 408 191 409
% 4.65/4.83 411. (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) (truthday (consecutive (monday))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (T_1 != (consecutive (monday))) ### All 410
% 4.65/4.83 412. ((consecutive T_1) != (consecutive (consecutive (monday)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (consecutive (monday))) (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) ### NotEqual 411
% 4.65/4.83 413. (-. (day3 (consecutive (consecutive (monday))))) (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) (truthday (consecutive (monday))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) ### P-NotP 412
% 4.65/4.83 414. (-. (day2 (consecutive (monday)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (consecutive (monday))) (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) ### Definition-Pseudo(day2) 413
% 4.65/4.83 415. (-. (day1 (monday))) (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) (truthday (consecutive (monday))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) ### Definition-Pseudo(day1) 414
% 4.65/4.83 416. ((day1 (monday)) => ((truthday (monday)) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. (truthday (monday))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (consecutive (monday))) (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) ### Imply 415 271
% 4.65/4.83 417. (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All Y, (((truthday (consecutive (monday))) /\ (truthday Y)) => ((consecutive (monday)) = Y))) (truthday (consecutive (monday))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (-. (truthday (monday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) ### All 416
% 4.65/4.83 418. (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (-. (truthday (monday))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (truthday (consecutive (monday))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ### All 417
% 4.65/4.83 419. ((truthday (consecutive (monday))) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (-. (truthday (monday))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) ### Equiv 187 418
% 4.65/4.83 420. ((day2 (consecutive (monday))) => ((truthday (consecutive (monday))) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))))) (-. (truthday (monday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (sunday)) = (monday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### Imply 407 419
% 4.65/4.83 421. (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (sunday)) = (monday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (-. (truthday (monday))) ### All 420
% 4.65/4.83 422. (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (sunday)) = (monday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ### And 421
% 4.65/4.83 423. ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (monday)) = (tuesday)) ((monday) != (tuesday)) (-. (truthday (tuesday))) ### Equiv 392 422
% 4.65/4.83 424. ((day1 T_2) => ((truthday T_2) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday)))))) (-. (truthday (tuesday))) ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (day3 (consecutive (sunday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Imply 6 423
% 4.65/4.83 425. (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (day3 (consecutive (sunday))) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (monday)) = (tuesday)) ((monday) != (tuesday)) (-. (truthday (tuesday))) ### All 424
% 4.65/4.83 426. (day2 (sunday)) (-. (truthday (tuesday))) ((monday) != (tuesday)) ((consecutive (monday)) = (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ### Definition-Pseudo(day2) 425
% 4.65/4.83 427. ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))) ((consecutive (sunday)) = (monday)) (-. (truthday (friday))) ((consecutive (friday)) = (saturday)) (truthday T_3) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((consecutive (monday)) = (tuesday)) ((monday) != (tuesday)) (day3 (consecutive (consecutive T_2))) (-. (truthday (wednesday))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) ((consecutive (thursday)) = (friday)) ((monday) != (friday)) (-. (truthday (tuesday))) ### DisjTree 343 380 426
% 4.65/4.83 428. ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. (truthday (wednesday))) ((monday) != (tuesday)) (-. (truthday (friday))) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) ### Equiv 315 427
% 4.65/4.83 429. ((day2 T_1) => ((truthday T_1) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday)))))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) (-. (truthday (friday))) ((monday) != (tuesday)) (-. (truthday (wednesday))) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (day3 (consecutive T_1)) ### Imply 3 428
% 4.65/4.83 430. (day3 (consecutive T_1)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (-. (truthday (wednesday))) ((monday) != (tuesday)) (-. (truthday (friday))) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) ### All 429
% 4.65/4.83 431. ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) ((monday) != (tuesday)) ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))) (day3 (consecutive T_1)) ### And 430
% 4.65/4.83 432. ((truthday T_0) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))) ((monday) != (tuesday)) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) ### Equiv 210 431
% 4.65/4.83 433. ((day3 T_0) => ((truthday T_0) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday)))))) ((friday) != (saturday)) ((friday) != (sunday)) ((monday) != (friday)) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) ((wednesday) != (thursday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) ((thursday) != (saturday)) ((thursday) != (sunday)) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((monday) != (wednesday)) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) ((monday) != (tuesday)) (day3 T_0) ### Imply 1 432
% 4.65/4.83 434. (day3 T_0) ((monday) != (tuesday)) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) ((monday) != (wednesday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) ((thursday) != (sunday)) ((thursday) != (saturday)) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((wednesday) != (thursday)) (truthday T_3) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) ((monday) != (friday)) ((friday) != (sunday)) ((friday) != (saturday)) ### All 433
% 4.65/4.83 435. (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (truthday T_3) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) (day3 (consecutive (consecutive T_2))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) ### ConjTree 434
% 4.65/4.83 436. (Ex X, (truthday X)) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (day3 (consecutive (consecutive T_2))) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) ### Exists 435
% 4.65/4.83 437. (day2 (consecutive T_2)) (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) (Ex X, (truthday X)) ### Definition-Pseudo(day2) 436
% 4.65/4.83 438. (day1 T_2) (Ex X, (truthday X)) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (day3 (consecutive T_1)) ((consecutive (friday)) = (saturday)) (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) ### Definition-Pseudo(day1) 437
% 4.65/4.83 439. (Ex X, (day1 X)) (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) ((consecutive (friday)) = (saturday)) (day3 (consecutive T_1)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) (Ex X, (truthday X)) ### Exists 438
% 4.65/4.83 440. (day2 T_1) (Ex X, (truthday X)) (day3 T_0) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((consecutive (friday)) = (saturday)) (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) (Ex X, (day1 X)) ### Definition-Pseudo(day2) 439
% 4.65/4.83 441. (Ex X, (day2 X)) (Ex X, (day1 X)) (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) ((consecutive (friday)) = (saturday)) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) ((consecutive (wednesday)) = (thursday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (saturday)) = (sunday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (monday)) = (tuesday)) ((consecutive (thursday)) = (friday)) ((consecutive (tuesday)) = (wednesday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (sunday)) = (monday)) (day3 T_0) (Ex X, (truthday X)) ### Exists 440
% 4.65/4.83 442. (Ex X, (day3 X)) (Ex X, (truthday X)) ((consecutive (sunday)) = (monday)) (All X, ((day3 X) => ((truthday X) <=> ((-. (truthday (wednesday))) /\ (-. (truthday (friday))))))) ((consecutive (tuesday)) = (wednesday)) ((consecutive (thursday)) = (friday)) ((consecutive (monday)) = (tuesday)) (All X, ((X = (monday)) \/ ((X = (tuesday)) \/ ((X = (wednesday)) \/ ((X = (thursday)) \/ ((X = (friday)) \/ ((X = (saturday)) \/ (X = (sunday))))))))) ((consecutive (saturday)) = (sunday)) (All X, ((day1 X) => ((truthday X) <=> ((-. (truthday (monday))) /\ (-. (truthday (tuesday))))))) ((consecutive (wednesday)) = (thursday)) (All X, (All Y, (((truthday X) /\ (truthday Y)) => (X = Y)))) (-. (truthday (tuesday))) (All X, (All Y, (((day1 X) /\ (day1 Y)) => (X = Y)))) (All X, (All Y, (((day2 X) /\ (day2 Y)) => (X = Y)))) (All X, ((day2 X) => ((truthday X) <=> ((day2 (thursday)) \/ ((day2 (saturday)) \/ (day2 (sunday))))))) ((consecutive (friday)) = (saturday)) (((monday) != (tuesday)) /\ (((monday) != (wednesday)) /\ (((monday) != (thursday)) /\ (((monday) != (friday)) /\ (((monday) != (saturday)) /\ (((monday) != (sunday)) /\ (((tuesday) != (wednesday)) /\ (((tuesday) != (thursday)) /\ (((tuesday) != (friday)) /\ (((tuesday) != (saturday)) /\ (((tuesday) != (sunday)) /\ (((wednesday) != (thursday)) /\ (((wednesday) != (friday)) /\ (((wednesday) != (saturday)) /\ (((wednesday) != (sunday)) /\ (((thursday) != (friday)) /\ (((thursday) != (saturday)) /\ (((thursday) != (sunday)) /\ (((friday) != (saturday)) /\ (((friday) != (sunday)) /\ ((saturday) != (sunday)))))))))))))))))))))) (Ex X, (day1 X)) (Ex X, (day2 X)) ### Exists 441
% 4.65/4.83 % SZS output end Proof
% 4.65/4.83 (* END-PROOF *)
%------------------------------------------------------------------------------