TSTP Solution File: SYN917+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SYN917+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n008.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 : Thu Jul 21 12:47:15 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SYN917+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 11 16:28:23 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 (* PROOF-FOUND *)
% 0.21/0.44 (* BEGIN-PROOF *)
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 1. (f zenon_X0) (-. (f zenon_X0)) ### Axiom
% 0.21/0.44 2. (g zenon_X0) (-. (g zenon_X0)) ### Axiom
% 0.21/0.44 3. (-. (h zenon_X0)) (h zenon_X0) ### Axiom
% 0.21/0.44 4. (-. ((f zenon_X0) /\ ((g zenon_X0) /\ (-. (h zenon_X0))))) (-. (h zenon_X0)) (g zenon_X0) (f zenon_X0) ### DisjTree 1 2 3
% 0.21/0.44 5. (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) (f zenon_X0) (g zenon_X0) (-. (h zenon_X0)) ### NotExists 4
% 0.21/0.44 6. (-. (((f zenon_X0) /\ (g zenon_X0)) => (h zenon_X0))) (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) ### ConjTree 5
% 0.21/0.44 7. (f T_1) (-. (f T_1)) ### Axiom
% 0.21/0.44 8. (-. (g T_1)) (g T_1) ### Axiom
% 0.21/0.44 9. ((f T_1) => (g T_1)) (-. (g T_1)) (f T_1) ### Imply 7 8
% 0.21/0.44 10. (All W, ((f W) => (g W))) (f T_1) (-. (g T_1)) ### All 9
% 0.21/0.44 11. (f T_1) (-. (f T_1)) ### Axiom
% 0.21/0.44 12. (f T_1) (-. (f T_1)) ### Axiom
% 0.21/0.44 13. (-. (h T_1)) (h T_1) ### Axiom
% 0.21/0.44 14. ((f T_1) => (h T_1)) (-. (h T_1)) (f T_1) ### Imply 12 13
% 0.21/0.44 15. (All Z, ((f Z) => (h Z))) (f T_1) (-. (h T_1)) ### All 14
% 0.21/0.44 16. (-. (g T_1)) (g T_1) ### Axiom
% 0.21/0.44 17. (((f T_1) /\ (h T_1)) => (g T_1)) (-. (g T_1)) (All Z, ((f Z) => (h Z))) (f T_1) ### DisjTree 11 15 16
% 0.21/0.44 18. (All R, (((f R) /\ (h R)) => (g R))) (f T_1) (All Z, ((f Z) => (h Z))) (-. (g T_1)) ### All 17
% 0.21/0.44 19. ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z)))) (All R, (((f R) /\ (h R)) => (g R))) (-. (g T_1)) (f T_1) ### Or 10 18
% 0.21/0.44 20. ((f T_1) /\ (-. (g T_1))) (All R, (((f R) /\ (h R)) => (g R))) ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z)))) ### And 19
% 0.21/0.44 21. (Ex Y, ((f Y) /\ (-. (g Y)))) ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z)))) (All R, (((f R) /\ (h R)) => (g R))) ### Exists 20
% 0.21/0.44 22. ((((f zenon_X0) /\ (g zenon_X0)) => (h zenon_X0)) => (Ex Y, ((f Y) /\ (-. (g Y))))) (All R, (((f R) /\ (h R)) => (g R))) ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z)))) (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) ### Imply 6 21
% 0.21/0.44 23. (All X, ((((f X) /\ (g X)) => (h X)) => (Ex Y, ((f Y) /\ (-. (g Y)))))) (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z)))) (All R, (((f R) /\ (h R)) => (g R))) ### All 22
% 0.21/0.44 24. (-. (((All X, ((((f X) /\ (g X)) => (h X)) => (Ex Y, ((f Y) /\ (-. (g Y)))))) /\ ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z))))) => ((All R, (((f R) /\ (h R)) => (g R))) => (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))))) ### ConjTree 23
% 0.21/0.44 25. (r T_2 T_3) (-. (r T_2 T_3)) ### Axiom
% 0.21/0.44 26. (r T_2 T_3) (-. (r T_2 T_3)) ### Axiom
% 0.21/0.44 27. (r T_3 T_2) (-. (r T_3 T_2)) ### Axiom
% 0.21/0.44 28. (-. (r T_2 T_2)) (r T_2 T_2) ### Axiom
% 0.21/0.44 29. (((r T_2 T_3) /\ (r T_3 T_2)) => (r T_2 T_2)) (-. (r T_2 T_2)) (r T_3 T_2) (r T_2 T_3) ### DisjTree 26 27 28
% 0.21/0.44 30. (All Z, (((r T_2 T_3) /\ (r T_3 Z)) => (r T_2 Z))) (r T_2 T_3) (r T_3 T_2) (-. (r T_2 T_2)) ### All 29
% 0.21/0.44 31. (All Y, (All Z, (((r T_2 Y) /\ (r Y Z)) => (r T_2 Z)))) (-. (r T_2 T_2)) (r T_3 T_2) (r T_2 T_3) ### All 30
% 0.21/0.44 32. ((r T_2 T_3) => (r T_3 T_2)) (-. (r T_2 T_2)) (All Y, (All Z, (((r T_2 Y) /\ (r Y Z)) => (r T_2 Z)))) (r T_2 T_3) ### Imply 25 31
% 0.21/0.44 33. (All Y, ((r T_2 Y) => (r Y T_2))) (r T_2 T_3) (All Y, (All Z, (((r T_2 Y) /\ (r Y Z)) => (r T_2 Z)))) (-. (r T_2 T_2)) ### All 32
% 0.21/0.44 34. (All X, (All Y, ((r X Y) => (r Y X)))) (-. (r T_2 T_2)) (All Y, (All Z, (((r T_2 Y) /\ (r Y Z)) => (r T_2 Z)))) (r T_2 T_3) ### All 33
% 0.21/0.44 35. (All X, (All Y, (All Z, (((r X Y) /\ (r Y Z)) => (r X Z))))) (r T_2 T_3) (-. (r T_2 T_2)) (All X, (All Y, ((r X Y) => (r Y X)))) ### All 34
% 0.21/0.44 36. (-. ((r T_2 T_3) => (r T_2 T_2))) (All X, (All Y, ((r X Y) => (r Y X)))) (All X, (All Y, (All Z, (((r X Y) /\ (r Y Z)) => (r X Z))))) ### NotImply 35
% 0.21/0.44 37. (-. (All Y, ((r T_2 Y) => (r T_2 T_2)))) (All X, (All Y, (All Z, (((r X Y) /\ (r Y Z)) => (r X Z))))) (All X, (All Y, ((r X Y) => (r Y X)))) ### NotAllEx 36
% 0.21/0.44 38. (-. (All X, (All Y, ((r X Y) => (r X X))))) (All X, (All Y, ((r X Y) => (r Y X)))) (All X, (All Y, (All Z, (((r X Y) /\ (r Y Z)) => (r X Z))))) ### NotAllEx 37
% 0.21/0.44 39. (-. (((All X, (All Y, ((r X Y) => (r Y X)))) /\ (All X, (All Y, (All Z, (((r X Y) /\ (r Y Z)) => (r X Z)))))) => (All X, (All Y, ((r X Y) => (r X X)))))) ### ConjTree 38
% 0.21/0.44 40. (f T_4) (-. (f T_4)) ### Axiom
% 0.21/0.44 41. (g T_4) (-. (g T_4)) ### Axiom
% 0.21/0.44 42. (-. (h T_4)) (h T_4) ### Axiom
% 0.21/0.44 43. (-. ((f T_4) /\ ((g T_4) /\ (-. (h T_4))))) (-. (h T_4)) (g T_4) (f T_4) ### DisjTree 40 41 42
% 0.21/0.44 44. (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) (f T_4) (g T_4) (-. (h T_4)) ### NotExists 43
% 0.21/0.44 45. (-. (((f T_4) /\ (g T_4)) => (h T_4))) (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) ### ConjTree 44
% 0.21/0.44 46. (-. (All X, (((f X) /\ (g X)) => (h X)))) (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) ### NotAllEx 45
% 0.21/0.44 47. ((All X, (((f X) /\ (g X)) => (h X))) => (Ex Y, ((f Y) /\ (-. (g Y))))) (All R, (((f R) /\ (h R)) => (g R))) ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z)))) (-. (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))) ### Imply 46 21
% 0.21/0.44 48. (-. ((((All X, (((f X) /\ (g X)) => (h X))) => (Ex Y, ((f Y) /\ (-. (g Y))))) /\ ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z))))) => ((All R, (((f R) /\ (h R)) => (g R))) => (Ex V, ((f V) /\ ((g V) /\ (-. (h V)))))))) ### ConjTree 47
% 0.21/0.44 49. (-. (p T_5)) (p T_5) ### Axiom
% 0.21/0.44 50. (-. (((p T_6) => (q T_5)) => ((p T_5) => (q T_5)))) (-. (p T_5)) ### ConjTree 49
% 0.21/0.44 51. (-. (All Y, (((p Y) => (q T_5)) => ((p T_5) => (q T_5))))) (-. (p T_5)) ### NotAllEx 50
% 0.21/0.44 52. (-. (Ex X, (All Y, (((p Y) => (q X)) => ((p X) => (q X)))))) (-. (p T_5)) ### NotExists 51
% 0.21/0.44 53. (-. (q zenon_X7)) (q zenon_X7) ### Axiom
% 0.21/0.44 54. ((p T_5) => (q zenon_X7)) (-. (q zenon_X7)) (-. (Ex X, (All Y, (((p Y) => (q X)) => ((p X) => (q X)))))) ### Imply 52 53
% 0.21/0.44 55. (-. (((p T_5) => (q zenon_X7)) => ((p zenon_X7) => (q zenon_X7)))) (-. (Ex X, (All Y, (((p Y) => (q X)) => ((p X) => (q X)))))) ### ConjTree 54
% 0.21/0.44 56. (-. (All Y, (((p Y) => (q zenon_X7)) => ((p zenon_X7) => (q zenon_X7))))) (-. (Ex X, (All Y, (((p Y) => (q X)) => ((p X) => (q X)))))) ### NotAllEx 55
% 0.21/0.44 57. (-. (Ex X, (All Y, (((p Y) => (q X)) => ((p X) => (q X)))))) ### NotExists 56
% 0.21/0.44 58. (-. (p T_8)) (p T_8) ### Axiom
% 0.21/0.44 59. (All X, (p X)) (-. (p T_8)) ### All 58
% 0.21/0.44 60. (-. (q T_8)) (q T_8) ### Axiom
% 0.21/0.44 61. (All X, (q X)) (-. (q T_8)) ### All 60
% 0.21/0.44 62. (-. ((p T_8) /\ (q T_8))) (All X, (q X)) (All X, (p X)) ### NotAnd 59 61
% 0.21/0.44 63. ((All X, (p X)) /\ (All X, (q X))) (-. ((p T_8) /\ (q T_8))) ### And 62
% 0.21/0.44 64. (-. (All X, ((p X) /\ (q X)))) ((All X, (p X)) /\ (All X, (q X))) ### NotAllEx 63
% 0.21/0.44 65. (-. (p T_9)) (p T_9) ### Axiom
% 0.21/0.44 66. ((p T_9) /\ (q T_9)) (-. (p T_9)) ### And 65
% 0.21/0.44 67. (All X, ((p X) /\ (q X))) (-. (p T_9)) ### All 66
% 0.21/0.44 68. (-. (All X, (p X))) (All X, ((p X) /\ (q X))) ### NotAllEx 67
% 0.21/0.44 69. (-. (q T_10)) (q T_10) ### Axiom
% 0.21/0.44 70. ((p T_10) /\ (q T_10)) (-. (q T_10)) ### And 69
% 0.21/0.44 71. (All X, ((p X) /\ (q X))) (-. (q T_10)) ### All 70
% 0.21/0.44 72. (-. (All X, (q X))) (All X, ((p X) /\ (q X))) ### NotAllEx 71
% 0.21/0.44 73. (-. ((All X, (p X)) /\ (All X, (q X)))) (All X, ((p X) /\ (q X))) ### NotAnd 68 72
% 0.21/0.44 74. (-. ((All X, ((p X) /\ (q X))) <=> ((All X, (p X)) /\ (All X, (q X))))) ### NotEquiv 64 73
% 0.21/0.44 75. (-. (p T_11)) (p T_11) ### Axiom
% 0.21/0.44 76. (All X, (p X)) (-. (p T_11)) ### All 75
% 0.21/0.44 77. (-. (q T_11)) (q T_11) ### Axiom
% 0.21/0.44 78. (All X, (q X)) (-. (q T_11)) ### All 77
% 0.21/0.44 79. ((All X, (p X)) \/ (All X, (q X))) (-. (q T_11)) (-. (p T_11)) ### Or 76 78
% 0.21/0.44 80. (-. ((p T_11) \/ (q T_11))) ((All X, (p X)) \/ (All X, (q X))) ### NotOr 79
% 0.21/0.44 81. (-. (All X, ((p X) \/ (q X)))) ((All X, (p X)) \/ (All X, (q X))) ### NotAllEx 80
% 0.21/0.44 82. (-. (((All X, (p X)) \/ (All X, (q X))) => (All X, ((p X) \/ (q X))))) ### NotImply 81
% 0.21/0.44 83. (p T_12) (-. (p T_12)) ### Axiom
% 0.21/0.44 84. (-. ((p T_12) \/ (q T_12))) (p T_12) ### NotOr 83
% 0.21/0.44 85. (-. (Ex X, ((p X) \/ (q X)))) (p T_12) ### NotExists 84
% 0.21/0.44 86. (Ex X, (p X)) (-. (Ex X, ((p X) \/ (q X)))) ### Exists 85
% 0.21/0.44 87. (q T_13) (-. (q T_13)) ### Axiom
% 0.21/0.44 88. (-. ((p T_13) \/ (q T_13))) (q T_13) ### NotOr 87
% 0.21/0.44 89. (-. (Ex X, ((p X) \/ (q X)))) (q T_13) ### NotExists 88
% 0.21/0.44 90. (Ex X, (q X)) (-. (Ex X, ((p X) \/ (q X)))) ### Exists 89
% 0.21/0.44 91. ((Ex X, (p X)) \/ (Ex X, (q X))) (-. (Ex X, ((p X) \/ (q X)))) ### Or 86 90
% 0.21/0.44 92. (p T_14) (-. (p T_14)) ### Axiom
% 0.21/0.44 93. (-. (Ex X, (p X))) (p T_14) ### NotExists 92
% 0.21/0.44 94. (q T_14) (-. (q T_14)) ### Axiom
% 0.21/0.44 95. (-. (Ex X, (q X))) (q T_14) ### NotExists 94
% 0.21/0.44 96. ((p T_14) \/ (q T_14)) (-. (Ex X, (q X))) (-. (Ex X, (p X))) ### Or 93 95
% 0.21/0.44 97. (-. ((Ex X, (p X)) \/ (Ex X, (q X)))) ((p T_14) \/ (q T_14)) ### NotOr 96
% 0.21/0.44 98. (Ex X, ((p X) \/ (q X))) (-. ((Ex X, (p X)) \/ (Ex X, (q X)))) ### Exists 97
% 0.21/0.44 99. (-. ((Ex X, ((p X) \/ (q X))) <=> ((Ex X, (p X)) \/ (Ex X, (q X))))) ### NotEquiv 91 98
% 0.21/0.44 100. (-. (p T_9)) (p T_9) ### Axiom
% 0.21/0.44 101. (-. ((p T_9) => (All X, (p X)))) (-. (p T_9)) ### NotImply 100
% 0.21/0.44 102. (-. (Ex Y, ((p Y) => (All X, (p X))))) (-. (p T_9)) ### NotExists 101
% 0.21/0.44 103. (-. (All X, (p X))) (-. (Ex Y, ((p Y) => (All X, (p X))))) ### NotAllEx 102
% 0.21/0.44 104. (-. ((p zenon_X15) => (All X, (p X)))) (-. (Ex Y, ((p Y) => (All X, (p X))))) ### NotImply 103
% 0.21/0.44 105. (-. (Ex Y, ((p Y) => (All X, (p X))))) ### NotExists 104
% 0.21/0.44 106. (p T_16) (-. (p T_16)) ### Axiom
% 0.21/0.44 107. (-. (Ex X, (p X))) (p T_16) ### NotExists 106
% 0.21/0.44 108. (q T_16) (-. (q T_16)) ### Axiom
% 0.21/0.44 109. (-. (Ex X, (q X))) (q T_16) ### NotExists 108
% 0.21/0.44 110. (-. ((Ex X, (p X)) /\ (Ex X, (q X)))) (q T_16) (p T_16) ### NotAnd 107 109
% 0.21/0.44 111. ((p T_16) /\ (q T_16)) (-. ((Ex X, (p X)) /\ (Ex X, (q X)))) ### And 110
% 0.21/0.44 112. (Ex X, ((p X) /\ (q X))) (-. ((Ex X, (p X)) /\ (Ex X, (q X)))) ### Exists 111
% 0.21/0.44 113. (-. ((Ex X, ((p X) /\ (q X))) => ((Ex X, (p X)) /\ (Ex X, (q X))))) ### NotImply 112
% 0.21/0.44 114. (-. (p T_17)) (p T_17) ### Axiom
% 0.21/0.44 115. (All X, (p X)) (-. (p T_17)) ### All 114
% 0.21/0.44 116. (-. ((All X, (p X)) => (p T_17))) ### NotImply 115
% 0.21/0.44 117. (-. (All Y, ((All X, (p X)) => (p Y)))) ### NotAllEx 116
% 0.21/0.44 118. (p zenon_X18) (-. (p zenon_X18)) ### Axiom
% 0.21/0.44 119. (-. (Ex X, (p X))) (p zenon_X18) ### NotExists 118
% 0.21/0.44 120. (All X, (p X)) (-. (Ex X, (p X))) ### All 119
% 0.21/0.44 121. (-. ((All X, (p X)) => (Ex X, (p X)))) ### NotImply 120
% 0.21/0.44 122. (-. (Ex X, (p X))) (Ex X, (p X)) ### Axiom
% 0.21/0.44 123. (-. ((Ex X, (p X)) => (p T_19))) (-. (Ex X, (p X))) ### NotImply 122
% 0.21/0.44 124. (-. (All Y, ((Ex X, (p X)) => (p Y)))) (-. (Ex X, (p X))) ### NotAllEx 123
% 0.21/0.44 125. (-. ((-. (Ex X, (p X))) => (All Y, ((Ex X, (p X)) => (p Y))))) ### NotImply 124
% 0.21/0.44 126. (-. (p T_20)) (p T_20) ### Axiom
% 0.21/0.44 127. (All X, (p X)) (-. (p T_20)) ### All 126
% 0.21/0.44 128. (-. (c)) (c) ### P-NotP
% 0.21/0.44 129. ((All X, (p X)) \/ (c)) (-. (c)) (-. (p T_20)) ### Or 127 128
% 0.21/0.44 130. (-. ((p T_20) \/ (c))) ((All X, (p X)) \/ (c)) ### NotOr 129
% 0.21/0.44 131. (-. (All X, ((p X) \/ (c)))) ((All X, (p X)) \/ (c)) ### NotAllEx 130
% 0.21/0.44 132. (-. (p T_9)) (p T_9) ### Axiom
% 0.21/0.44 133. ((p T_9) \/ (c)) (-. (c)) (-. (p T_9)) ### Or 132 128
% 0.21/0.44 134. (All X, ((p X) \/ (c))) (-. (p T_9)) (-. (c)) ### All 133
% 0.21/0.44 135. (-. (All X, (p X))) (-. (c)) (All X, ((p X) \/ (c))) ### NotAllEx 134
% 0.21/0.44 136. (-. ((All X, (p X)) \/ (c))) (All X, ((p X) \/ (c))) ### NotOr 135
% 0.21/0.44 137. (-. ((All X, ((p X) \/ (c))) <=> ((All X, (p X)) \/ (c)))) ### NotEquiv 131 136
% 0.21/0.44 138. (p T_12) (-. (p T_12)) ### Axiom
% 0.21/0.44 139. (-. ((p T_12) /\ (c))) (c) (p T_12) ### NotAnd 138 128
% 0.21/0.44 140. (-. (Ex X, ((p X) /\ (c)))) (p T_12) (c) ### NotExists 139
% 0.21/0.44 141. (Ex X, (p X)) (c) (-. (Ex X, ((p X) /\ (c)))) ### Exists 140
% 0.21/0.44 142. ((Ex X, (p X)) /\ (c)) (-. (Ex X, ((p X) /\ (c)))) ### And 141
% 0.21/0.44 143. (p T_21) (-. (p T_21)) ### Axiom
% 0.21/0.44 144. (-. (Ex X, (p X))) (p T_21) ### NotExists 143
% 0.21/0.44 145. (-. ((Ex X, (p X)) /\ (c))) (c) (p T_21) ### NotAnd 144 128
% 0.21/0.44 146. ((p T_21) /\ (c)) (-. ((Ex X, (p X)) /\ (c))) ### And 145
% 0.21/0.44 147. (Ex X, ((p X) /\ (c))) (-. ((Ex X, (p X)) /\ (c))) ### Exists 146
% 0.21/0.44 148. (-. ((Ex X, ((p X) /\ (c))) <=> ((Ex X, (p X)) /\ (c)))) ### NotEquiv 142 147
% 0.21/0.44 149. (-. (Ex X, (c))) (c) ### NotExists 128
% 0.21/0.44 150. (Ex X, (c)) (-. (c)) ### Exists 128
% 0.21/0.44 151. (-. ((Ex X, (c)) <=> (c))) ### NotEquiv 149 150
% 0.21/0.44 152. (-. (All X, (c))) (c) ### NotAllEx 128
% 0.21/0.44 153. (All X, (c)) (-. (c)) ### All 128
% 0.21/0.44 154. (-. ((All X, (c)) <=> (c))) ### NotEquiv 152 153
% 0.21/0.44 155. (-. ((c) => (p zenon_X22))) (-. (c)) ### NotImply 128
% 0.21/0.44 156. (-. (Ex X, ((c) => (p X)))) (-. (c)) ### NotExists 155
% 0.21/0.44 157. (p T_12) (-. (p T_12)) ### Axiom
% 0.21/0.44 158. (-. ((c) => (p T_12))) (p T_12) ### NotImply 157
% 0.21/0.44 159. (-. (Ex X, ((c) => (p X)))) (p T_12) ### NotExists 158
% 0.21/0.44 160. (Ex X, (p X)) (-. (Ex X, ((c) => (p X)))) ### Exists 159
% 0.21/0.44 161. ((c) => (Ex X, (p X))) (-. (Ex X, ((c) => (p X)))) ### Imply 156 160
% 0.21/0.44 162. (p T_23) (-. (p T_23)) ### Axiom
% 0.21/0.44 163. (-. (Ex X, (p X))) (p T_23) ### NotExists 162
% 0.21/0.44 164. ((c) => (p T_23)) (-. (Ex X, (p X))) (c) ### Imply 128 163
% 0.21/0.44 165. (-. ((c) => (Ex X, (p X)))) ((c) => (p T_23)) ### NotImply 164
% 0.21/0.44 166. (Ex X, ((c) => (p X))) (-. ((c) => (Ex X, (p X)))) ### Exists 165
% 0.21/0.44 167. (-. ((Ex X, ((c) => (p X))) <=> ((c) => (Ex X, (p X))))) ### NotEquiv 161 166
% 0.21/0.44 168. (-. (p T_9)) (p T_9) ### Axiom
% 0.21/0.44 169. (-. ((p T_9) => (c))) (-. (p T_9)) ### NotImply 168
% 0.21/0.44 170. (-. (Ex X, ((p X) => (c)))) (-. (p T_9)) ### NotExists 169
% 0.21/0.44 171. (-. (All X, (p X))) (-. (Ex X, ((p X) => (c)))) ### NotAllEx 170
% 0.21/0.44 172. (-. ((p zenon_X24) => (c))) (c) ### NotImply 128
% 0.21/0.44 173. (-. (Ex X, ((p X) => (c)))) (c) ### NotExists 172
% 0.21/0.44 174. ((All X, (p X)) => (c)) (-. (Ex X, ((p X) => (c)))) ### Imply 171 173
% 0.21/0.44 175. (-. (p T_25)) (p T_25) ### Axiom
% 0.21/0.44 176. (All X, (p X)) (-. (p T_25)) ### All 175
% 0.21/0.44 177. ((p T_25) => (c)) (-. (c)) (All X, (p X)) ### Imply 176 128
% 0.21/0.44 178. (-. ((All X, (p X)) => (c))) ((p T_25) => (c)) ### NotImply 177
% 0.21/0.44 179. (Ex X, ((p X) => (c))) (-. ((All X, (p X)) => (c))) ### Exists 178
% 0.21/0.44 180. (-. ((Ex X, ((p X) => (c))) <=> ((All X, (p X)) => (c)))) ### NotEquiv 174 179
% 0.21/0.44 181. (-. (p T_26)) (p T_26) ### Axiom
% 0.21/0.44 182. (All X, (p X)) (-. (p T_26)) ### All 181
% 0.21/0.44 183. ((c) => (All X, (p X))) (-. (p T_26)) (c) ### Imply 128 182
% 0.21/0.44 184. (-. ((c) => (p T_26))) ((c) => (All X, (p X))) ### NotImply 183
% 0.21/0.44 185. (-. (All X, ((c) => (p X)))) ((c) => (All X, (p X))) ### NotAllEx 184
% 0.21/0.44 186. (-. (p T_9)) (p T_9) ### Axiom
% 0.21/0.44 187. ((c) => (p T_9)) (-. (p T_9)) (c) ### Imply 128 186
% 0.21/0.44 188. (All X, ((c) => (p X))) (c) (-. (p T_9)) ### All 187
% 0.21/0.44 189. (-. (All X, (p X))) (c) (All X, ((c) => (p X))) ### NotAllEx 188
% 0.21/0.44 190. (-. ((c) => (All X, (p X)))) (All X, ((c) => (p X))) ### NotImply 189
% 0.21/0.44 191. (-. ((All X, ((c) => (p X))) <=> ((c) => (All X, (p X))))) ### NotEquiv 185 190
% 0.21/0.44 192. (p T_27) (-. (p T_27)) ### Axiom
% 0.21/0.44 193. (-. (Ex X, (p X))) (p T_27) ### NotExists 192
% 0.21/0.44 194. ((Ex X, (p X)) => (c)) (-. (c)) (p T_27) ### Imply 193 128
% 0.21/0.44 195. (-. ((p T_27) => (c))) ((Ex X, (p X)) => (c)) ### NotImply 194
% 0.21/0.44 196. (-. (All X, ((p X) => (c)))) ((Ex X, (p X)) => (c)) ### NotAllEx 195
% 0.21/0.44 197. (p T_12) (-. (p T_12)) ### Axiom
% 0.21/0.44 198. ((p T_12) => (c)) (-. (c)) (p T_12) ### Imply 197 128
% 0.21/0.44 199. (All X, ((p X) => (c))) (p T_12) (-. (c)) ### All 198
% 0.21/0.44 200. (Ex X, (p X)) (-. (c)) (All X, ((p X) => (c))) ### Exists 199
% 0.21/0.44 201. (-. ((Ex X, (p X)) => (c))) (All X, ((p X) => (c))) ### NotImply 200
% 0.21/0.44 202. (-. ((All X, ((p X) => (c))) <=> ((Ex X, (p X)) => (c)))) ### NotEquiv 196 201
% 0.21/0.44 203. (-. ((((All X, ((((f X) /\ (g X)) => (h X)) => (Ex Y, ((f Y) /\ (-. (g Y)))))) /\ ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z))))) => ((All R, (((f R) /\ (h R)) => (g R))) => (Ex V, ((f V) /\ ((g V) /\ (-. (h V))))))) /\ ((((All X, (All Y, ((r X Y) => (r Y X)))) /\ (All X, (All Y, (All Z, (((r X Y) /\ (r Y Z)) => (r X Z)))))) => (All X, (All Y, ((r X Y) => (r X X))))) /\ (((((All X, (((f X) /\ (g X)) => (h X))) => (Ex Y, ((f Y) /\ (-. (g Y))))) /\ ((All W, ((f W) => (g W))) \/ (All Z, ((f Z) => (h Z))))) => ((All R, (((f R) /\ (h R)) => (g R))) => (Ex V, ((f V) /\ ((g V) /\ (-. (h V))))))) /\ ((Ex X, (All Y, (((p Y) => (q X)) => ((p X) => (q X))))) /\ (((All X, ((p X) /\ (q X))) <=> ((All X, (p X)) /\ (All X, (q X)))) /\ ((((All X, (p X)) \/ (All X, (q X))) => (All X, ((p X) \/ (q X)))) /\ (((Ex X, ((p X) \/ (q X))) <=> ((Ex X, (p X)) \/ (Ex X, (q X)))) /\ ((Ex Y, ((p Y) => (All X, (p X)))) /\ (((Ex X, ((p X) /\ (q X))) => ((Ex X, (p X)) /\ (Ex X, (q X)))) /\ ((All Y, ((All X, (p X)) => (p Y))) /\ (((All X, (p X)) => (Ex X, (p X))) /\ (((-. (Ex X, (p X))) => (All Y, ((Ex X, (p X)) => (p Y)))) /\ (((All X, ((p X) \/ (c))) <=> ((All X, (p X)) \/ (c))) /\ (((Ex X, ((p X) /\ (c))) <=> ((Ex X, (p X)) /\ (c))) /\ (((Ex X, (c)) <=> (c)) /\ (((All X, (c)) <=> (c)) /\ (((Ex X, ((c) => (p X))) <=> ((c) => (Ex X, (p X)))) /\ (((Ex X, ((p X) => (c))) <=> ((All X, (p X)) => (c))) /\ (((All X, ((c) => (p X))) <=> ((c) => (All X, (p X)))) /\ ((All X, ((p X) => (c))) <=> ((Ex X, (p X)) => (c))))))))))))))))))))))) ### DisjTree 24 39 48 57 74 82 99 105 113 117 121 125 137 148 151 154 167 180 191 202
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44 (* END-PROOF *)
%------------------------------------------------------------------------------