TSTP Solution File: SEU148+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n010.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 : 300s
% DateTime : Tue Sep 20 05:55:33 EDT 2022
% Result : Theorem 23.36s 5.39s
% Output : Proof 23.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:34:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000049s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 9
% 0.13/0.35 Launch Gotab with destructive = true
% 23.36/5.39 % SZS output start Proof for theBenchmark.p
% 23.36/5.39 [0] ALPHA_AND : (! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3))) & ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5))))) & empty(empty_set) & ! [A8_8] : (~=(singleton(A8_8), empty_set)) & ? [A11_11] : (empty(A11_11)) & ? [A12_12] : (~empty(A12_12)) & ! [A13_13, B14_14] : (subset(A13_13, A13_13)) & ~! [A15_15, B16_16] : ((subset(singleton(A15_15), singleton(B16_16)) => =(A15_15, B16_16))))
% 23.36/5.39 -> [1] ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3))), ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5))))), empty(empty_set), ! [A8_8] : (~=(singleton(A8_8), empty_set)), ? [A11_11] : (empty(A11_11)), ? [A12_12] : (~empty(A12_12)), ! [A13_13, B14_14] : (subset(A13_13, A13_13)), ~! [A15_15, B16_16] : ((subset(singleton(A15_15), singleton(B16_16)) => =(A15_15, B16_16)))
% 23.36/5.39
% 23.36/5.39 [1] DELTA_EXISTS : ? [A11_11] : (empty(A11_11))
% 23.36/5.39 -> [2] empty(skolem_A1111)
% 23.36/5.39
% 23.36/5.39 [2] DELTA_EXISTS : ? [A12_12] : (~empty(A12_12))
% 23.36/5.39 -> [3] ~empty(skolem_A1212)
% 23.36/5.39
% 23.36/5.39 [3] DELTA_NOT_FORALL : ~! [A15_15, B16_16] : ((subset(singleton(A15_15), singleton(B16_16)) => =(A15_15, B16_16)))
% 23.36/5.39 -> [4] ~(subset(singleton(skolem_A1515), singleton(skolem_B1616)) => =(skolem_A1515, skolem_B1616))
% 23.36/5.39
% 23.36/5.39 [4] ALPHA_NOT_IMPLY : ~(subset(singleton(skolem_A1515), singleton(skolem_B1616)) => =(skolem_A1515, skolem_B1616))
% 23.36/5.39 -> [5] subset(singleton(skolem_A1515), singleton(skolem_B1616)), ~=(skolem_A1515, skolem_B1616)
% 23.36/5.39
% 23.36/5.39 [5] Rewrite : subset(singleton(skolem_A1515), singleton(skolem_B1616))
% 23.36/5.39 -> [6] (=(singleton(skolem_A1515), empty_set) | =(singleton(skolem_A1515), singleton(skolem_B1616)))
% 23.36/5.39
% 23.36/5.39 [6] BETA_OR : (=(singleton(skolem_A1515), empty_set) | =(singleton(skolem_A1515), singleton(skolem_B1616)))
% 23.36/5.39 -> [7] =(singleton(skolem_A1515), empty_set)
% 23.36/5.39 -> [8] =(singleton(skolem_A1515), singleton(skolem_B1616))
% 23.36/5.39
% 23.36/5.39 [7] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 23.36/5.39 -> [12] (in(A3_1_0, B4_1_0) => ~in(B4_1_0, A3_1_0))
% 23.36/5.39
% 23.36/5.39 [12] BETA_IMPLY : (in(A3_1_0, B4_1_0) => ~in(B4_1_0, A3_1_0))
% 23.36/5.39 -> [13] ~in(A3_1_0, B4_1_0)
% 23.36/5.39 -> [14] ~in(B4_1_0, A3_1_0)
% 23.36/5.39
% 23.36/5.39 [14] GAMMA_FORALL : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 23.36/5.39 -> [24] (=(singleton(A5_3_1), singleton(A5_3_1)) <=> ! [C7_7] : ((in(C7_7, singleton(A5_3_1)) <=> =(C7_7, A5_3_1))))
% 23.36/5.39
% 23.36/5.39 [24] BETA_EQUIV : (=(singleton(A5_3_1), singleton(A5_3_1)) <=> ! [C7_7] : ((in(C7_7, singleton(A5_3_1)) <=> =(C7_7, A5_3_1))))
% 23.36/5.39 -> [25] ~=(singleton(A5_3_1), singleton(A5_3_1)), ~! [C7_7] : ((in(C7_7, singleton(A5_3_1)) <=> =(C7_7, A5_3_1)))
% 23.36/5.39 -> [26] =(singleton(A5_3_1), singleton(A5_3_1)), ! [C7_7] : ((in(C7_7, singleton(A5_3_1)) <=> =(C7_7, A5_3_1)))
% 23.36/5.39
% 23.36/5.39 [25] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(A5_3_1)) <=> =(C7_7, A5_3_1)))
% 23.36/5.39 -> [30] ~(in(skolem_C77(singleton(A5_3_1), A5_3_1), singleton(A5_3_1)) <=> =(skolem_C77(singleton(A5_3_1), A5_3_1), A5_3_1))
% 23.36/5.39
% 23.36/5.39 [30] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(A5_3_1)) <=> =(C7_7, A5_3_1)))
% 23.36/5.39
% 23.36/5.39 [26] GAMMA_FORALL : ! [A8_8] : (~=(singleton(A8_8), empty_set))
% 23.36/5.39 -> [31] ~=(singleton(A8_0_2), empty_set)
% 23.36/5.39
% 23.36/5.39 [31] CLOSURE : ~=(singleton(A8_0_2), empty_set)
% 23.36/5.39
% 23.36/5.39 [13] GAMMA_FORALL : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 23.36/5.39 -> [21] (=(singleton(A5_2_1), singleton(A5_2_1)) <=> ! [C7_7] : ((in(C7_7, singleton(A5_2_1)) <=> =(C7_7, A5_2_1))))
% 23.36/5.39
% 23.36/5.39 [21] BETA_EQUIV : (=(singleton(A5_2_1), singleton(A5_2_1)) <=> ! [C7_7] : ((in(C7_7, singleton(A5_2_1)) <=> =(C7_7, A5_2_1))))
% 23.36/5.39 -> [22] ~=(singleton(A5_2_1), singleton(A5_2_1)), ~! [C7_7] : ((in(C7_7, singleton(A5_2_1)) <=> =(C7_7, A5_2_1)))
% 23.36/5.39 -> [23] =(singleton(A5_2_1), singleton(A5_2_1)), ! [C7_7] : ((in(C7_7, singleton(A5_2_1)) <=> =(C7_7, A5_2_1)))
% 23.36/5.39
% 23.36/5.39 [22] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(A5_2_1)) <=> =(C7_7, A5_2_1)))
% 23.36/5.39 -> [29] ~(in(skolem_C77(singleton(A5_2_1), A5_2_1), singleton(A5_2_1)) <=> =(skolem_C77(singleton(A5_2_1), A5_2_1), A5_2_1))
% 23.36/5.39
% 23.36/5.39 [29] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(A5_2_1)) <=> =(C7_7, A5_2_1)))
% 23.36/5.39
% 23.36/5.39 [23] GAMMA_FORALL : ! [A8_8] : (~=(singleton(A8_8), empty_set))
% 23.36/5.39 -> [32] ~=(singleton(A8_1_2), empty_set)
% 23.36/5.39
% 23.36/5.39 [32] CLOSURE : ~=(singleton(A8_1_2), empty_set)
% 23.36/5.39
% 23.36/5.39 [8] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 23.36/5.39 -> [9] (in(singleton(skolem_A1515), singleton(singleton(skolem_B1616))) => ~in(singleton(singleton(skolem_B1616)), singleton(skolem_A1515)))
% 23.36/5.39
% 23.36/5.39 [9] BETA_IMPLY : (in(singleton(skolem_A1515), singleton(singleton(skolem_B1616))) => ~in(singleton(singleton(skolem_B1616)), singleton(skolem_A1515)))
% 23.36/5.39 -> [10] ~in(singleton(skolem_A1515), singleton(singleton(skolem_B1616)))
% 23.36/5.39 -> [11] ~in(singleton(singleton(skolem_B1616)), singleton(skolem_A1515))
% 23.36/5.39
% 23.36/5.39 [10] GAMMA_FORALL : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 23.36/5.39 -> [16] (=(singleton(singleton(skolem_B1616)), singleton(singleton(skolem_B1616))) <=> ! [C7_7] : ((in(C7_7, singleton(singleton(skolem_B1616))) <=> =(C7_7, singleton(skolem_B1616)))))
% 23.36/5.39
% 23.36/5.39 [16] BETA_EQUIV : (=(singleton(singleton(skolem_B1616)), singleton(singleton(skolem_B1616))) <=> ! [C7_7] : ((in(C7_7, singleton(singleton(skolem_B1616))) <=> =(C7_7, singleton(skolem_B1616)))))
% 23.36/5.39 -> [19] ~=(singleton(singleton(skolem_B1616)), singleton(singleton(skolem_B1616))), ~! [C7_7] : ((in(C7_7, singleton(singleton(skolem_B1616))) <=> =(C7_7, singleton(skolem_B1616))))
% 23.36/5.39 -> [20] =(singleton(singleton(skolem_B1616)), singleton(singleton(skolem_B1616))), ! [C7_7] : ((in(C7_7, singleton(singleton(skolem_B1616))) <=> =(C7_7, singleton(skolem_B1616))))
% 23.36/5.39
% 23.36/5.39 [19] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(singleton(skolem_B1616))) <=> =(C7_7, singleton(skolem_B1616))))
% 23.36/5.39 -> [28] ~(in(skolem_C77(singleton(singleton(skolem_B1616)), singleton(skolem_B1616)), singleton(singleton(skolem_B1616))) <=> =(skolem_C77(singleton(singleton(skolem_B1616)), singleton(skolem_B1616)), singleton(skolem_B1616)))
% 23.36/5.39
% 23.36/5.39 [28] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(singleton(skolem_B1616))) <=> =(C7_7, singleton(skolem_B1616))))
% 23.36/5.39
% 23.36/5.39 [33] GAMMA_FORALL : ! [A13_13, B14_14] : (subset(A13_13, A13_13))
% 23.36/5.39 -> [35] subset(A13_0_3, A13_0_3)
% 23.36/5.39
% 23.36/5.39 [35] GAMMA_FORALL : ! [C7_7] : ((in(C7_7, singleton(singleton(skolem_B1616))) <=> =(C7_7, singleton(skolem_B1616))))
% 23.36/5.39 -> [37] (in(singleton(skolem_A1515), singleton(singleton(skolem_B1616))) <=> =(singleton(skolem_A1515), singleton(skolem_B1616)))
% 23.36/5.39
% 23.36/5.39 [37] BETA_EQUIV : (in(singleton(skolem_A1515), singleton(singleton(skolem_B1616))) <=> =(singleton(skolem_A1515), singleton(skolem_B1616)))
% 23.36/5.39 -> [38] ~in(singleton(skolem_A1515), singleton(singleton(skolem_B1616))), ~=(singleton(skolem_A1515), singleton(skolem_B1616))
% 23.36/5.39 -> [39] in(singleton(skolem_A1515), singleton(singleton(skolem_B1616))), =(singleton(skolem_A1515), singleton(skolem_B1616))
% 23.36/5.39
% 23.36/5.39 [38] CLOSURE : =
% 23.36/5.39
% 23.36/5.39 [39] CLOSURE : =
% 23.36/5.39
% 23.36/5.39 [15] BETA_EQUIV : (=(singleton(skolem_A1515), singleton(skolem_B1616)) <=> ! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_B1616))))
% 23.36/5.39 -> [67] ~=(singleton(skolem_A1515), singleton(skolem_B1616)), ~! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_B1616)))
% 23.36/5.39 -> [68] =(singleton(skolem_A1515), singleton(skolem_B1616)), ! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_B1616)))
% 23.36/5.39
% 23.36/5.39 [67] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_B1616)))
% 23.36/5.39 -> [69] ~(in(skolem_C77(singleton(skolem_A1515), skolem_B1616), singleton(skolem_A1515)) <=> =(skolem_C77(singleton(skolem_A1515), skolem_B1616), skolem_B1616))
% 23.36/5.39
% 23.36/5.39 [69] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_B1616)))
% 23.36/5.39
% 23.36/5.39 [70] GAMMA_FORALL : ! [A13_13, B14_14] : (subset(A13_13, A13_13))
% 23.36/5.39 -> [71] subset(A13_2_3, A13_2_3)
% 23.36/5.39
% 23.36/5.39 [71] GAMMA_FORALL : ! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_B1616)))
% 23.36/5.39 -> [72] (in(skolem_B1616, singleton(skolem_A1515)) <=> =(skolem_B1616, skolem_B1616))
% 23.36/5.39
% 23.36/5.39 [72] BETA_EQUIV : (in(skolem_B1616, singleton(skolem_A1515)) <=> =(skolem_B1616, skolem_B1616))
% 23.36/5.39 -> [73] ~in(skolem_B1616, singleton(skolem_A1515)), ~=(skolem_B1616, skolem_B1616)
% 23.36/5.39 -> [74] in(skolem_B1616, singleton(skolem_A1515)), =(skolem_B1616, skolem_B1616)
% 23.36/5.39
% 23.36/5.39 [73] CLOSURE : =
% 23.36/5.39
% 23.36/5.39 [74] : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 23.36/5.39 -> [75] ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 23.36/5.39
% 23.36/5.39 [75] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 23.36/5.39 -> [76] (in(skolem_B1616, singleton(skolem_A1515)) => ~in(singleton(skolem_A1515), skolem_B1616))
% 23.36/5.39
% 23.36/5.39 [76] BETA_IMPLY : (in(skolem_B1616, singleton(skolem_A1515)) => ~in(singleton(skolem_A1515), skolem_B1616))
% 23.36/5.39 -> [77] ~in(skolem_B1616, singleton(skolem_A1515))
% 23.36/5.39 -> [78] ~in(singleton(skolem_A1515), skolem_B1616)
% 23.36/5.39
% 23.36/5.39 [77] CLOSURE : =
% 23.36/5.39
% 23.36/5.39 [78] : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 23.36/5.39 -> [79] ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 23.36/5.39
% 23.36/5.39 [79] GAMMA_FORALL : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 23.36/5.39 -> [80] (=(singleton(skolem_A1515), singleton(skolem_A1515)) <=> ! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_A1515))))
% 23.36/5.39
% 23.36/5.39 [80] BETA_EQUIV : (=(singleton(skolem_A1515), singleton(skolem_A1515)) <=> ! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_A1515))))
% 23.36/5.39 -> [81] ~=(singleton(skolem_A1515), singleton(skolem_A1515)), ~! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_A1515)))
% 23.36/5.39 -> [82] =(singleton(skolem_A1515), singleton(skolem_A1515)), ! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_A1515)))
% 23.36/5.39
% 23.36/5.39 [81] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_A1515)))
% 23.36/5.39 -> [83] ~(in(skolem_C77(singleton(skolem_A1515), skolem_A1515), singleton(skolem_A1515)) <=> =(skolem_C77(singleton(skolem_A1515), skolem_A1515), skolem_A1515))
% 23.36/5.39
% 23.36/5.39 [83] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_A1515)))
% 23.36/5.39
% 23.36/5.39 [82] GAMMA_FORALL : ! [C7_7] : ((in(C7_7, singleton(skolem_A1515)) <=> =(C7_7, skolem_A1515)))
% 23.36/5.39 -> [84] (in(skolem_B1616, singleton(skolem_A1515)) <=> =(skolem_B1616, skolem_A1515))
% 23.36/5.39
% 23.36/5.39 [84] BETA_EQUIV : (in(skolem_B1616, singleton(skolem_A1515)) <=> =(skolem_B1616, skolem_A1515))
% 23.36/5.39 -> [85] ~in(skolem_B1616, singleton(skolem_A1515)), ~=(skolem_B1616, skolem_A1515)
% 23.36/5.39 -> [86] in(skolem_B1616, singleton(skolem_A1515)), =(skolem_B1616, skolem_A1515)
% 23.36/5.39
% 23.36/5.39 [85] CLOSURE : =
% 23.36/5.39
% 23.36/5.39 [86] CLOSURE : =
% 23.36/5.39
% 23.36/5.39 % SZS output end Proof for theBenchmark.p
% 23.36/5.39 [5.044550s][1][Res] 40891 goroutines created
% 23.36/5.39 ==== Result ====
% 23.36/5.39 [5.044601s][1][Res] VALID
% 23.36/5.39 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------