TSTP Solution File: SET603+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n029.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 04:16:48 EDT 2022
% Result : Theorem 23.83s 5.48s
% Output : Proof 23.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n029.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 07:02:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000039s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 13
% 0.13/0.35 Launch Gotab with destructive = true
% 23.83/5.47 % SZS output start Proof for theBenchmark.p
% 23.83/5.48 [0] ALPHA_AND : (! [B3_3, C4_4] : ((! [D5_5] : ((member(D5_5, B3_3) <=> member(D5_5, C4_4))) => =(B3_3, C4_4))) & ! [B9_9] : (~member(B9_9, empty_set)) & ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10)))) & ! [B12_12, C13_13] : ((=(B12_12, C13_13) <=> ! [D14_14] : ((member(D14_14, B12_12) <=> member(D14_14, C13_13))))) & ! [B18_18] : (subset(B18_18, B18_18)) & ~! [B21_21] : (=(difference(B21_21, empty_set), B21_21)))
% 23.83/5.48 -> [1] ! [B3_3, C4_4] : ((! [D5_5] : ((member(D5_5, B3_3) <=> member(D5_5, C4_4))) => =(B3_3, C4_4))), ! [B9_9] : (~member(B9_9, empty_set)), ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10)))), ! [B12_12, C13_13] : ((=(B12_12, C13_13) <=> ! [D14_14] : ((member(D14_14, B12_12) <=> member(D14_14, C13_13))))), ! [B18_18] : (subset(B18_18, B18_18)), ~! [B21_21] : (=(difference(B21_21, empty_set), B21_21))
% 23.83/5.48
% 23.83/5.48 [1] DELTA_NOT_FORALL : ~! [B21_21] : (=(difference(B21_21, empty_set), B21_21))
% 23.83/5.48 -> [2] ~=(difference(skolem_B2121, empty_set), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [2] GAMMA_FORALL : ! [B3_3, C4_4] : ((! [D5_5] : ((member(D5_5, B3_3) <=> member(D5_5, C4_4))) => =(B3_3, C4_4)))
% 23.83/5.48 -> [3] (! [D5_5] : ((member(D5_5, B3_0_0) <=> member(D5_5, B3_0_0))) => =(B3_0_0, B3_0_0))
% 23.83/5.48
% 23.83/5.48 [3] BETA_IMPLY : (! [D5_5] : ((member(D5_5, B3_0_0) <=> member(D5_5, B3_0_0))) => =(B3_0_0, B3_0_0))
% 23.83/5.48 -> [4] ~! [D5_5] : ((member(D5_5, B3_0_0) <=> member(D5_5, B3_0_0)))
% 23.83/5.48 -> [5] =(B3_0_0, B3_0_0)
% 23.83/5.48
% 23.83/5.48 [4] DELTA_NOT_FORALL : ~! [D5_5] : ((member(D5_5, B3_0_0) <=> member(D5_5, B3_0_0)))
% 23.83/5.48 -> [6] ~(member(skolem_D55(B3_0_0, B3_0_0), B3_0_0) <=> member(skolem_D55(B3_0_0, B3_0_0), B3_0_0))
% 23.83/5.48
% 23.83/5.48 [6] BETA_NOT_EQUIV : ~(member(skolem_D55(B3_0_0, B3_0_0), B3_0_0) <=> member(skolem_D55(B3_0_0, B3_0_0), B3_0_0))
% 23.83/5.48 -> [7] ~member(skolem_D55(B3_0_0, B3_0_0), B3_0_0), member(skolem_D55(B3_0_0, B3_0_0), B3_0_0)
% 23.83/5.48 -> [8] member(skolem_D55(B3_0_0, B3_0_0), B3_0_0), ~member(skolem_D55(B3_0_0, B3_0_0), B3_0_0)
% 23.83/5.48
% 23.83/5.48 [7] CLOSURE : member(skolem_D55(B3_0_0, B3_0_0), B3_0_0)
% 23.83/5.48
% 23.83/5.48 [8] CLOSURE : ~member(skolem_D55(B3_0_0, B3_0_0), B3_0_0)
% 23.83/5.48
% 23.83/5.48 [5] GAMMA_FORALL : ! [B9_9] : (~member(B9_9, empty_set))
% 23.83/5.48 -> [9] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48
% 23.83/5.48 [9] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 23.83/5.48 -> [10] (=(skolem_B2121, skolem_B2121) <=> (subset(skolem_B2121, skolem_B2121) & subset(skolem_B2121, skolem_B2121)))
% 23.83/5.48
% 23.83/5.48 [10] BETA_EQUIV : (=(skolem_B2121, skolem_B2121) <=> (subset(skolem_B2121, skolem_B2121) & subset(skolem_B2121, skolem_B2121)))
% 23.83/5.48 -> [11] ~=(skolem_B2121, skolem_B2121), ~(subset(skolem_B2121, skolem_B2121) & subset(skolem_B2121, skolem_B2121))
% 23.83/5.48 -> [12] =(skolem_B2121, skolem_B2121), (subset(skolem_B2121, skolem_B2121) & subset(skolem_B2121, skolem_B2121))
% 23.83/5.48
% 23.83/5.48 [11] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [13] Rewrite : subset(skolem_B2121, skolem_B2121)
% 23.83/5.48 -> [14] ! [D17_17] : ((member(D17_17, skolem_B2121) => member(D17_17, skolem_B2121)))
% 23.83/5.48
% 23.83/5.48 [14] GAMMA_FORALL : ! [B12_12, C13_13] : ((=(B12_12, C13_13) <=> ! [D14_14] : ((member(D14_14, B12_12) <=> member(D14_14, C13_13)))))
% 23.83/5.48 -> [15] (=(skolem_B2121, skolem_B2121) <=> ! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121))))
% 23.83/5.48
% 23.83/5.48 [15] BETA_EQUIV : (=(skolem_B2121, skolem_B2121) <=> ! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121))))
% 23.83/5.48 -> [16] ~=(skolem_B2121, skolem_B2121), ~! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48 -> [17] =(skolem_B2121, skolem_B2121), ! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48
% 23.83/5.48 [16] DELTA_NOT_FORALL : ~! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48 -> [18] ~(member(skolem_D1414(skolem_B2121, skolem_B2121), skolem_B2121) <=> member(skolem_D1414(skolem_B2121, skolem_B2121), skolem_B2121))
% 23.83/5.48
% 23.83/5.48 [18] CLOSURE : ~! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48
% 23.83/5.48 [17] GAMMA_FORALL : ! [B18_18] : (subset(B18_18, B18_18))
% 23.83/5.48 -> [19] subset(empty_set, empty_set)
% 23.83/5.48
% 23.83/5.48 [19] Rewrite : subset(empty_set, empty_set)
% 23.83/5.48 -> [20] ! [D17_17] : ((member(D17_17, empty_set) => member(D17_17, empty_set)))
% 23.83/5.48
% 23.83/5.48 [20] GAMMA_FORALL : ! [D17_17] : ((member(D17_17, skolem_B2121) => member(D17_17, skolem_B2121)))
% 23.83/5.48 -> [21] (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) => member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48
% 23.83/5.48 [21] BETA_IMPLY : (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) => member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48 -> [22] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48 -> [23] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [22] GAMMA_FORALL : ! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48 -> [24] (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) <=> member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48
% 23.83/5.48 [24] BETA_EQUIV : (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) <=> member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48 -> [25] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48 -> [26] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [26] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [27] BETA_IMPLY : (member(D17_1_7, empty_set) => member(D17_1_7, empty_set))
% 23.83/5.48 -> [39] ~member(D17_1_7, empty_set)
% 23.83/5.48 -> [40] member(D17_1_7, empty_set)
% 23.83/5.48
% 23.83/5.48 [40] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [42] BETA_IMPLY : (! [D5_5] : ((member(D5_5, B3_2_0) <=> member(D5_5, B3_2_0))) => =(B3_2_0, B3_2_0))
% 23.83/5.48 -> [50] ~! [D5_5] : ((member(D5_5, B3_2_0) <=> member(D5_5, B3_2_0)))
% 23.83/5.48 -> [51] =(B3_2_0, B3_2_0)
% 23.83/5.48
% 23.83/5.48 [50] DELTA_NOT_FORALL : ~! [D5_5] : ((member(D5_5, B3_2_0) <=> member(D5_5, B3_2_0)))
% 23.83/5.48 -> [52] ~(member(skolem_D55(B3_2_0, B3_2_0), B3_2_0) <=> member(skolem_D55(B3_2_0, B3_2_0), B3_2_0))
% 23.83/5.48
% 23.83/5.48 [52] BETA_NOT_EQUIV : ~(member(skolem_D55(B3_2_0, B3_2_0), B3_2_0) <=> member(skolem_D55(B3_2_0, B3_2_0), B3_2_0))
% 23.83/5.48 -> [53] ~member(skolem_D55(B3_2_0, B3_2_0), B3_2_0), member(skolem_D55(B3_2_0, B3_2_0), B3_2_0)
% 23.83/5.48 -> [54] member(skolem_D55(B3_2_0, B3_2_0), B3_2_0), ~member(skolem_D55(B3_2_0, B3_2_0), B3_2_0)
% 23.83/5.48
% 23.83/5.48 [53] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [54] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [51] : ! [B9_9] : (~member(B9_9, empty_set))
% 23.83/5.48 -> [55] ! [B9_9] : (~member(B9_9, empty_set))
% 23.83/5.48
% 23.83/5.48 [55] GAMMA_FORALL : ! [B9_9] : (~member(B9_9, empty_set))
% 23.83/5.48 -> [56] ~member(B9_1_1, empty_set)
% 23.83/5.48
% 23.83/5.48 [56] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 23.83/5.48 -> [57] ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 23.83/5.48
% 23.83/5.48 [57] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 23.83/5.48 -> [58] (=(empty_set, empty_set) <=> (subset(empty_set, empty_set) & subset(empty_set, empty_set)))
% 23.83/5.48
% 23.83/5.48 [58] BETA_EQUIV : (=(empty_set, empty_set) <=> (subset(empty_set, empty_set) & subset(empty_set, empty_set)))
% 23.83/5.48 -> [59] ~=(empty_set, empty_set), ~(subset(empty_set, empty_set) & subset(empty_set, empty_set))
% 23.83/5.48 -> [60] =(empty_set, empty_set), (subset(empty_set, empty_set) & subset(empty_set, empty_set))
% 23.83/5.48
% 23.83/5.48 [59] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [61] Rewrite : subset(empty_set, empty_set)
% 23.83/5.48 -> [62] ! [D17_17] : ((member(D17_17, empty_set) => member(D17_17, empty_set)))
% 23.83/5.48
% 23.83/5.48 [62] GAMMA_FORALL : ! [D17_17] : ((member(D17_17, empty_set) => member(D17_17, empty_set)))
% 23.83/5.48 -> [63] (member(B9_1_1, empty_set) => member(B9_1_1, empty_set))
% 23.83/5.48
% 23.83/5.48 [63] BETA_IMPLY : (member(B9_1_1, empty_set) => member(B9_1_1, empty_set))
% 23.83/5.48 -> [64] ~member(B9_1_1, empty_set)
% 23.83/5.48 -> [65] member(B9_1_1, empty_set)
% 23.83/5.48
% 23.83/5.48 [65] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [67] BETA_EQUIV : (=(difference(skolem_B2121, empty_set), skolem_B2121) <=> ! [D14_14] : ((member(D14_14, difference(skolem_B2121, empty_set)) <=> member(D14_14, skolem_B2121))))
% 23.83/5.48 -> [73] ~=(difference(skolem_B2121, empty_set), skolem_B2121), ~! [D14_14] : ((member(D14_14, difference(skolem_B2121, empty_set)) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48 -> [74] =(difference(skolem_B2121, empty_set), skolem_B2121), ! [D14_14] : ((member(D14_14, difference(skolem_B2121, empty_set)) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48
% 23.83/5.48 [74] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [75] BETA_NOT_EQUIV : ~(member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set)) <=> member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48 -> [76] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set)), member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48 -> [77] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set)), ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [76] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [77] Rewrite : member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set))
% 23.83/5.48 -> [78] (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) & ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48
% 23.83/5.48 [78] ALPHA_AND : (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) & ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48 -> [79] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121), ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48
% 23.83/5.48 [79] CLOSURE : member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [23] GAMMA_FORALL : ! [D14_14] : ((member(D14_14, skolem_B2121) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48 -> [80] (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) <=> member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48
% 23.83/5.48 [80] BETA_EQUIV : (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) <=> member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48 -> [81] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48 -> [82] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [81] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [83] BETA_IMPLY : (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set) => member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48 -> [115] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48 -> [116] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48
% 23.83/5.48 [115] : ! [B3_3, C4_4] : ((! [D5_5] : ((member(D5_5, B3_3) <=> member(D5_5, C4_4))) => =(B3_3, C4_4)))
% 23.83/5.48 -> [117] ! [B3_3, C4_4] : ((! [D5_5] : ((member(D5_5, B3_3) <=> member(D5_5, C4_4))) => =(B3_3, C4_4)))
% 23.83/5.48
% 23.83/5.48 [117] GAMMA_FORALL : ! [B3_3, C4_4] : ((! [D5_5] : ((member(D5_5, B3_3) <=> member(D5_5, C4_4))) => =(B3_3, C4_4)))
% 23.83/5.48 -> [118] (! [D5_5] : ((member(D5_5, B3_4_0) <=> member(D5_5, B3_4_0))) => =(B3_4_0, B3_4_0))
% 23.83/5.48
% 23.83/5.48 [118] BETA_IMPLY : (! [D5_5] : ((member(D5_5, B3_4_0) <=> member(D5_5, B3_4_0))) => =(B3_4_0, B3_4_0))
% 23.83/5.48 -> [119] ~! [D5_5] : ((member(D5_5, B3_4_0) <=> member(D5_5, B3_4_0)))
% 23.83/5.48 -> [120] =(B3_4_0, B3_4_0)
% 23.83/5.48
% 23.83/5.48 [119] DELTA_NOT_FORALL : ~! [D5_5] : ((member(D5_5, B3_4_0) <=> member(D5_5, B3_4_0)))
% 23.83/5.48 -> [121] ~(member(skolem_D55(B3_4_0, B3_4_0), B3_4_0) <=> member(skolem_D55(B3_4_0, B3_4_0), B3_4_0))
% 23.83/5.48
% 23.83/5.48 [121] BETA_NOT_EQUIV : ~(member(skolem_D55(B3_4_0, B3_4_0), B3_4_0) <=> member(skolem_D55(B3_4_0, B3_4_0), B3_4_0))
% 23.83/5.48 -> [122] ~member(skolem_D55(B3_4_0, B3_4_0), B3_4_0), member(skolem_D55(B3_4_0, B3_4_0), B3_4_0)
% 23.83/5.48 -> [123] member(skolem_D55(B3_4_0, B3_4_0), B3_4_0), ~member(skolem_D55(B3_4_0, B3_4_0), B3_4_0)
% 23.83/5.48
% 23.83/5.48 [122] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [123] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [120] : ! [B9_9] : (~member(B9_9, empty_set))
% 23.83/5.48 -> [124] ! [B9_9] : (~member(B9_9, empty_set))
% 23.83/5.48
% 23.83/5.48 [124] GAMMA_FORALL : ! [B9_9] : (~member(B9_9, empty_set))
% 23.83/5.48 -> [125] ~member(B9_3_1, empty_set)
% 23.83/5.48
% 23.83/5.48 [125] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 23.83/5.48 -> [126] ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 23.83/5.48
% 23.83/5.48 [126] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 23.83/5.48 -> [127] (=(empty_set, empty_set) <=> (subset(empty_set, empty_set) & subset(empty_set, empty_set)))
% 23.83/5.48
% 23.83/5.48 [127] BETA_EQUIV : (=(empty_set, empty_set) <=> (subset(empty_set, empty_set) & subset(empty_set, empty_set)))
% 23.83/5.48 -> [128] ~=(empty_set, empty_set), ~(subset(empty_set, empty_set) & subset(empty_set, empty_set))
% 23.83/5.48 -> [129] =(empty_set, empty_set), (subset(empty_set, empty_set) & subset(empty_set, empty_set))
% 23.83/5.48
% 23.83/5.48 [128] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [130] Rewrite : subset(empty_set, empty_set)
% 23.83/5.48 -> [131] ! [D17_17] : ((member(D17_17, empty_set) => member(D17_17, empty_set)))
% 23.83/5.48
% 23.83/5.48 [131] GAMMA_FORALL : ! [D17_17] : ((member(D17_17, empty_set) => member(D17_17, empty_set)))
% 23.83/5.48 -> [132] (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set) => member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48
% 23.83/5.48 [132] BETA_IMPLY : (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set) => member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48 -> [133] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48 -> [134] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48
% 23.83/5.48 [134] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [133] : ! [B12_12, C13_13] : ((=(B12_12, C13_13) <=> ! [D14_14] : ((member(D14_14, B12_12) <=> member(D14_14, C13_13)))))
% 23.83/5.48 -> [135] ! [B12_12, C13_13] : ((=(B12_12, C13_13) <=> ! [D14_14] : ((member(D14_14, B12_12) <=> member(D14_14, C13_13)))))
% 23.83/5.48
% 23.83/5.48 [135] GAMMA_FORALL : ! [B12_12, C13_13] : ((=(B12_12, C13_13) <=> ! [D14_14] : ((member(D14_14, B12_12) <=> member(D14_14, C13_13)))))
% 23.83/5.48 -> [136] (=(difference(skolem_B2121, empty_set), skolem_B2121) <=> ! [D14_14] : ((member(D14_14, difference(skolem_B2121, empty_set)) <=> member(D14_14, skolem_B2121))))
% 23.83/5.48
% 23.83/5.48 [136] BETA_EQUIV : (=(difference(skolem_B2121, empty_set), skolem_B2121) <=> ! [D14_14] : ((member(D14_14, difference(skolem_B2121, empty_set)) <=> member(D14_14, skolem_B2121))))
% 23.83/5.48 -> [137] ~=(difference(skolem_B2121, empty_set), skolem_B2121), ~! [D14_14] : ((member(D14_14, difference(skolem_B2121, empty_set)) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48 -> [138] =(difference(skolem_B2121, empty_set), skolem_B2121), ! [D14_14] : ((member(D14_14, difference(skolem_B2121, empty_set)) <=> member(D14_14, skolem_B2121)))
% 23.83/5.48
% 23.83/5.48 [138] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [139] BETA_NOT_EQUIV : ~(member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set)) <=> member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121))
% 23.83/5.48 -> [140] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set)), member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48 -> [141] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set)), ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [141] Rewrite : member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set))
% 23.83/5.48 -> [143] (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) & ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48
% 23.83/5.48 [143] ALPHA_AND : (member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) & ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48 -> [144] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121), ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48
% 23.83/5.48 [144] CLOSURE : member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [140] Rewrite : ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), difference(skolem_B2121, empty_set))
% 23.83/5.48 -> [142] ~(member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) & ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48
% 23.83/5.48 [142] BETA_NOT_AND : ~(member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121) & ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set))
% 23.83/5.48 -> [145] ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48 -> [146] ~~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48
% 23.83/5.48 [145] CLOSURE : ~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), skolem_B2121)
% 23.83/5.48
% 23.83/5.48 [146] ALPHA_NOT_NOT : ~~member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48 -> [147] member(skolem_D1414(difference(skolem_B2121, empty_set), skolem_B2121), empty_set)
% 23.83/5.48
% 23.83/5.48 [147] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 [116] CLOSURE : =
% 23.83/5.48
% 23.83/5.48 % SZS output end Proof for theBenchmark.p
% 23.83/5.48 [5.123322s][1][Res] 13913 goroutines created
% 23.83/5.48 ==== Result ====
% 23.83/5.48 [5.123357s][1][Res] VALID
% 23.83/5.48 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------