TSTP Solution File: SEU143+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU143+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n007.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 05:55:31 EDT 2022
% Result : Theorem 115.92s 30.66s
% Output : Proof 115.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU143+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 09:24:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 8
% 0.12/0.34 Launch Gotab with destructive = true
% 115.92/30.66 % SZS output start Proof for theBenchmark.p
% 115.92/30.66 [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))))) & ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8)))) & $true & $true & empty(empty_set) & ? [A11_11] : (empty(A11_11)) & ? [A12_12] : (~empty(A12_12)) & ~! [A10_10] : (~=(singleton(A10_10), empty_set)))
% 115.92/30.66 -> [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))))), ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8)))), $true, empty(empty_set), ? [A11_11] : (empty(A11_11)), ? [A12_12] : (~empty(A12_12)), ~! [A10_10] : (~=(singleton(A10_10), empty_set))
% 115.92/30.66
% 115.92/30.66 [1] DELTA_EXISTS : ? [A11_11] : (empty(A11_11))
% 115.92/30.66 -> [2] empty(skolem_A1111)
% 115.92/30.66
% 115.92/30.66 [2] DELTA_EXISTS : ? [A12_12] : (~empty(A12_12))
% 115.92/30.66 -> [3] ~empty(skolem_A1212)
% 115.92/30.66
% 115.92/30.66 [3] DELTA_NOT_FORALL : ~! [A10_10] : (~=(singleton(A10_10), empty_set))
% 115.92/30.66 -> [4] ~~=(singleton(skolem_A1010), empty_set)
% 115.92/30.66
% 115.92/30.66 [4] ALPHA_NOT_NOT : ~~=(singleton(skolem_A1010), empty_set)
% 115.92/30.66 -> [5] =(singleton(skolem_A1010), empty_set)
% 115.92/30.66
% 115.92/30.66 [5] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 115.92/30.66 -> [6] (in(skolem_A1212, skolem_B99(skolem_A1212)) => ~in(skolem_B99(skolem_A1212), skolem_A1212))
% 115.92/30.66
% 115.92/30.66 [6] BETA_IMPLY : (in(skolem_A1212, skolem_B99(skolem_A1212)) => ~in(skolem_B99(skolem_A1212), skolem_A1212))
% 115.92/30.66 -> [7] ~in(skolem_A1212, skolem_B99(skolem_A1212))
% 115.92/30.66 -> [8] ~in(skolem_B99(skolem_A1212), skolem_A1212)
% 115.92/30.66
% 115.92/30.66 [8] GAMMA_FORALL : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 115.92/30.66 -> [9] (=(singleton(A5_0_1), singleton(A5_0_1)) <=> ! [C7_7] : ((in(C7_7, singleton(A5_0_1)) <=> =(C7_7, A5_0_1))))
% 115.92/30.66
% 115.92/30.66 [9] BETA_EQUIV : (=(singleton(A5_0_1), singleton(A5_0_1)) <=> ! [C7_7] : ((in(C7_7, singleton(A5_0_1)) <=> =(C7_7, A5_0_1))))
% 115.92/30.66 -> [10] ~=(singleton(A5_0_1), singleton(A5_0_1)), ~! [C7_7] : ((in(C7_7, singleton(A5_0_1)) <=> =(C7_7, A5_0_1)))
% 115.92/30.66 -> [11] =(singleton(A5_0_1), singleton(A5_0_1)), ! [C7_7] : ((in(C7_7, singleton(A5_0_1)) <=> =(C7_7, A5_0_1)))
% 115.92/30.66
% 115.92/30.66 [10] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(A5_0_1)) <=> =(C7_7, A5_0_1)))
% 115.92/30.66 -> [15] ~(in(skolem_C77(singleton(A5_0_1), A5_0_1), singleton(A5_0_1)) <=> =(skolem_C77(singleton(A5_0_1), A5_0_1), A5_0_1))
% 115.92/30.66
% 115.92/30.66 [15] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(A5_0_1)) <=> =(C7_7, A5_0_1)))
% 115.92/30.66
% 115.92/30.66 [11] GAMMA_FORALL : ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8))))
% 115.92/30.66 -> [17] (=(skolem_A1212, empty_set) <=> ! [B9_9] : (~in(B9_9, skolem_A1212)))
% 115.92/30.66
% 115.92/30.66 [17] BETA_EQUIV : (=(skolem_A1212, empty_set) <=> ! [B9_9] : (~in(B9_9, skolem_A1212)))
% 115.92/30.66 -> [18] ~=(skolem_A1212, empty_set), ~! [B9_9] : (~in(B9_9, skolem_A1212))
% 115.92/30.66 -> [19] =(skolem_A1212, empty_set), ! [B9_9] : (~in(B9_9, skolem_A1212))
% 115.92/30.66
% 115.92/30.66 [19] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [24] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [12] BETA_EQUIV : (=(skolem_A1212, singleton(skolem_A1010)) <=> ! [C7_7] : ((in(C7_7, skolem_A1212) <=> =(C7_7, skolem_A1010))))
% 115.92/30.66 -> [27] ~=(skolem_A1212, singleton(skolem_A1010)), ~! [C7_7] : ((in(C7_7, skolem_A1212) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66 -> [28] =(skolem_A1212, singleton(skolem_A1010)), ! [C7_7] : ((in(C7_7, skolem_A1212) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66
% 115.92/30.66 [28] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [29] BETA_NOT_EQUIV : ~(in(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1212) <=> =(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1010))
% 115.92/30.66 -> [30] ~in(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1212), =(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1010)
% 115.92/30.66 -> [31] in(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1212), ~=(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1010)
% 115.92/30.66
% 115.92/30.66 [31] GAMMA_FORALL : ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8))))
% 115.92/30.66 -> [32] (=(empty_set, empty_set) <=> ! [B9_9] : (~in(B9_9, empty_set)))
% 115.92/30.66
% 115.92/30.66 [32] BETA_EQUIV : (=(empty_set, empty_set) <=> ! [B9_9] : (~in(B9_9, empty_set)))
% 115.92/30.66 -> [33] ~=(empty_set, empty_set), ~! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66 -> [34] =(empty_set, empty_set), ! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66
% 115.92/30.66 [33] DELTA_NOT_FORALL : ~! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66 -> [38] ~~in(skolem_B99(empty_set), empty_set)
% 115.92/30.66
% 115.92/30.66 [38] ALPHA_NOT_NOT : ~~in(skolem_B99(empty_set), empty_set)
% 115.92/30.66 -> [39] in(skolem_B99(empty_set), empty_set)
% 115.92/30.66
% 115.92/30.66 [39] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [34] GAMMA_FORALL : ! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66 -> [42] ~in(skolem_A1010, empty_set)
% 115.92/30.66
% 115.92/30.66 [42] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 115.92/30.66 -> [47] ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 115.92/30.66
% 115.92/30.66 [47] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 115.92/30.66 -> [48] (in(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1212) => ~in(skolem_A1212, skolem_C77(skolem_A1212, skolem_A1010)))
% 115.92/30.66
% 115.92/30.66 [48] BETA_IMPLY : (in(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1212) => ~in(skolem_A1212, skolem_C77(skolem_A1212, skolem_A1010)))
% 115.92/30.66 -> [49] ~in(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1212)
% 115.92/30.66 -> [50] ~in(skolem_A1212, skolem_C77(skolem_A1212, skolem_A1010))
% 115.92/30.66
% 115.92/30.66 [49] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [50] : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 115.92/30.66 -> [55] ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 115.92/30.66
% 115.92/30.66 [55] GAMMA_FORALL : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 115.92/30.66 -> [56] (=(singleton(skolem_A1010), singleton(skolem_A1010)) <=> ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010))))
% 115.92/30.66
% 115.92/30.66 [56] BETA_EQUIV : (=(singleton(skolem_A1010), singleton(skolem_A1010)) <=> ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010))))
% 115.92/30.66 -> [57] ~=(singleton(skolem_A1010), singleton(skolem_A1010)), ~! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66 -> [58] =(singleton(skolem_A1010), singleton(skolem_A1010)), ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66
% 115.92/30.66 [57] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66 -> [60] ~(in(skolem_C77(singleton(skolem_A1010), skolem_A1010), singleton(skolem_A1010)) <=> =(skolem_C77(singleton(skolem_A1010), skolem_A1010), skolem_A1010))
% 115.92/30.66
% 115.92/30.66 [60] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66
% 115.92/30.66 [58] GAMMA_FORALL : ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66 -> [61] (in(skolem_A1010, singleton(skolem_A1010)) <=> =(skolem_A1010, skolem_A1010))
% 115.92/30.66
% 115.92/30.66 [61] BETA_EQUIV : (in(skolem_A1010, singleton(skolem_A1010)) <=> =(skolem_A1010, skolem_A1010))
% 115.92/30.66 -> [62] ~in(skolem_A1010, singleton(skolem_A1010)), ~=(skolem_A1010, skolem_A1010)
% 115.92/30.66 -> [63] in(skolem_A1010, singleton(skolem_A1010)), =(skolem_A1010, skolem_A1010)
% 115.92/30.66
% 115.92/30.66 [62] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [63] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [30] GAMMA_FORALL : ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8))))
% 115.92/30.66 -> [35] (=(skolem_A1212, empty_set) <=> ! [B9_9] : (~in(B9_9, skolem_A1212)))
% 115.92/30.66
% 115.92/30.66 [35] BETA_EQUIV : (=(skolem_A1212, empty_set) <=> ! [B9_9] : (~in(B9_9, skolem_A1212)))
% 115.92/30.66 -> [36] ~=(skolem_A1212, empty_set), ~! [B9_9] : (~in(B9_9, skolem_A1212))
% 115.92/30.66 -> [37] =(skolem_A1212, empty_set), ! [B9_9] : (~in(B9_9, skolem_A1212))
% 115.92/30.66
% 115.92/30.66 [37] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [41] : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 115.92/30.66 -> [43] ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 115.92/30.66
% 115.92/30.66 [43] GAMMA_FORALL : ! [A3_3, B4_4] : ((in(A3_3, B4_4) => ~in(B4_4, A3_3)))
% 115.92/30.66 -> [44] (in(skolem_B99(skolem_A1212), skolem_A1212) => ~in(skolem_A1212, skolem_B99(skolem_A1212)))
% 115.92/30.66
% 115.92/30.66 [44] BETA_IMPLY : (in(skolem_B99(skolem_A1212), skolem_A1212) => ~in(skolem_A1212, skolem_B99(skolem_A1212)))
% 115.92/30.66 -> [45] ~in(skolem_B99(skolem_A1212), skolem_A1212)
% 115.92/30.66 -> [46] ~in(skolem_A1212, skolem_B99(skolem_A1212))
% 115.92/30.66
% 115.92/30.66 [45] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [46] : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 115.92/30.66 -> [51] ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 115.92/30.66
% 115.92/30.66 [51] GAMMA_FORALL : ! [A5_5, B6_6] : ((=(B6_6, singleton(A5_5)) <=> ! [C7_7] : ((in(C7_7, B6_6) <=> =(C7_7, A5_5)))))
% 115.92/30.66 -> [52] (=(singleton(skolem_A1010), singleton(skolem_A1010)) <=> ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010))))
% 115.92/30.66
% 115.92/30.66 [52] BETA_EQUIV : (=(singleton(skolem_A1010), singleton(skolem_A1010)) <=> ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010))))
% 115.92/30.66 -> [53] ~=(singleton(skolem_A1010), singleton(skolem_A1010)), ~! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66 -> [54] =(singleton(skolem_A1010), singleton(skolem_A1010)), ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66
% 115.92/30.66 [53] DELTA_NOT_FORALL : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66 -> [59] ~(in(skolem_C77(singleton(skolem_A1010), skolem_A1010), singleton(skolem_A1010)) <=> =(skolem_C77(singleton(skolem_A1010), skolem_A1010), skolem_A1010))
% 115.92/30.66
% 115.92/30.66 [59] CLOSURE : ~! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66
% 115.92/30.66 [54] GAMMA_FORALL : ! [C7_7] : ((in(C7_7, singleton(skolem_A1010)) <=> =(C7_7, skolem_A1010)))
% 115.92/30.66 -> [64] (in(skolem_C77(skolem_A1212, skolem_A1010), singleton(skolem_A1010)) <=> =(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1010))
% 115.92/30.66
% 115.92/30.66 [64] BETA_EQUIV : (in(skolem_C77(skolem_A1212, skolem_A1010), singleton(skolem_A1010)) <=> =(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1010))
% 115.92/30.66 -> [65] ~in(skolem_C77(skolem_A1212, skolem_A1010), singleton(skolem_A1010)), ~=(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1010)
% 115.92/30.66 -> [66] in(skolem_C77(skolem_A1212, skolem_A1010), singleton(skolem_A1010)), =(skolem_C77(skolem_A1212, skolem_A1010), skolem_A1010)
% 115.92/30.66
% 115.92/30.66 [65] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [66] : ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8))))
% 115.92/30.66 -> [163] ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8))))
% 115.92/30.66
% 115.92/30.66 [163] GAMMA_FORALL : ! [A8_8] : ((=(A8_8, empty_set) <=> ! [B9_9] : (~in(B9_9, A8_8))))
% 115.92/30.66 -> [164] (=(empty_set, empty_set) <=> ! [B9_9] : (~in(B9_9, empty_set)))
% 115.92/30.66
% 115.92/30.66 [164] BETA_EQUIV : (=(empty_set, empty_set) <=> ! [B9_9] : (~in(B9_9, empty_set)))
% 115.92/30.66 -> [165] ~=(empty_set, empty_set), ~! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66 -> [166] =(empty_set, empty_set), ! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66
% 115.92/30.66 [165] DELTA_NOT_FORALL : ~! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66 -> [167] ~~in(skolem_B99(empty_set), empty_set)
% 115.92/30.66
% 115.92/30.66 [167] ALPHA_NOT_NOT : ~~in(skolem_B99(empty_set), empty_set)
% 115.92/30.66 -> [168] in(skolem_B99(empty_set), empty_set)
% 115.92/30.66
% 115.92/30.66 [168] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 [166] GAMMA_FORALL : ! [B9_9] : (~in(B9_9, empty_set))
% 115.92/30.66 -> [169] ~in(B9_11_4, empty_set)
% 115.92/30.66
% 115.92/30.66 [169] CLOSURE : =
% 115.92/30.66
% 115.92/30.66 % SZS output end Proof for theBenchmark.p
% 115.92/30.66 [30.322787s][1][Res] 308935 goroutines created
% 115.92/30.66 ==== Result ====
% 115.92/30.66 [30.322828s][1][Res] VALID
% 115.92/30.66 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------