TSTP Solution File: SET867+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n027.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 04:17:43 EDT 2022
% Result : Theorem 35.18s 13.62s
% Output : Proof 35.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n027.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 08:40:35 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 [0.000038s][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
% 35.18/13.62 % SZS output start Proof for theBenchmark.p
% 35.18/13.62 [0] ALPHA_AND : (! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4))) & ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6)))) & ! [A8_8, B9_9] : ((=(B9_9, union(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, A8_8))))))) & empty(empty_set) & ? [A12_12] : (empty(A12_12)) & ? [A13_13] : (~empty(A13_13)) & ~=(union(empty_set), empty_set))
% 35.18/13.62 -> [1] ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4))), ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6)))), ! [A8_8, B9_9] : ((=(B9_9, union(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, A8_8))))))), empty(empty_set), ? [A12_12] : (empty(A12_12)), ? [A13_13] : (~empty(A13_13)), ~=(union(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [1] DELTA_EXISTS : ? [A12_12] : (empty(A12_12))
% 35.18/13.62 -> [2] empty(skolem_A1212)
% 35.18/13.62
% 35.18/13.62 [2] DELTA_EXISTS : ? [A13_13] : (~empty(A13_13))
% 35.18/13.62 -> [3] ~empty(skolem_A1313)
% 35.18/13.62
% 35.18/13.62 [3] GAMMA_FORALL : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62 -> [4] (in(skolem_A1313, skolem_B77(skolem_A1313)) => ~in(skolem_B77(skolem_A1313), skolem_A1313))
% 35.18/13.62
% 35.18/13.62 [4] BETA_IMPLY : (in(skolem_A1313, skolem_B77(skolem_A1313)) => ~in(skolem_B77(skolem_A1313), skolem_A1313))
% 35.18/13.62 -> [5] ~in(skolem_A1313, skolem_B77(skolem_A1313))
% 35.18/13.62 -> [6] ~in(skolem_B77(skolem_A1313), skolem_A1313)
% 35.18/13.62
% 35.18/13.62 [6] GAMMA_FORALL : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [10] (=(empty_set, empty_set) <=> ! [B7_7] : (~in(B7_7, empty_set)))
% 35.18/13.62
% 35.18/13.62 [10] BETA_EQUIV : (=(empty_set, empty_set) <=> ! [B7_7] : (~in(B7_7, empty_set)))
% 35.18/13.62 -> [11] ~=(empty_set, empty_set), ~! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [12] =(empty_set, empty_set), ! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62
% 35.18/13.62 [11] DELTA_NOT_FORALL : ~! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [15] ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [15] ALPHA_NOT_NOT : ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62 -> [16] in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [16] CLOSURE : in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [12] GAMMA_FORALL : ! [A8_8, B9_9] : ((=(B9_9, union(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, A8_8)))))))
% 35.18/13.62 -> [17] (=(union(empty_set), union(empty_set)) <=> ! [C10_10] : ((in(C10_10, union(empty_set)) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set))))))
% 35.18/13.62
% 35.18/13.62 [17] BETA_EQUIV : (=(union(empty_set), union(empty_set)) <=> ! [C10_10] : ((in(C10_10, union(empty_set)) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set))))))
% 35.18/13.62 -> [19] ~=(union(empty_set), union(empty_set)), ~! [C10_10] : ((in(C10_10, union(empty_set)) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set)))))
% 35.18/13.62 -> [20] =(union(empty_set), union(empty_set)), ! [C10_10] : ((in(C10_10, union(empty_set)) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set)))))
% 35.18/13.62
% 35.18/13.62 [19] DELTA_NOT_FORALL : ~! [C10_10] : ((in(C10_10, union(empty_set)) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set)))))
% 35.18/13.62 -> [23] ~(in(skolem_C1010(union(empty_set), empty_set), union(empty_set)) <=> ? [D11_11] : ((in(skolem_C1010(union(empty_set), empty_set), D11_11) & in(D11_11, empty_set))))
% 35.18/13.62
% 35.18/13.62 [23] CLOSURE : ~! [C10_10] : ((in(C10_10, union(empty_set)) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set)))))
% 35.18/13.62
% 35.18/13.62 [20] GAMMA_FORALL : ! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [26] ~in(skolem_D1111(skolem_B77(union(empty_set)), empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [26] GAMMA_FORALL : ! [C10_10] : ((in(C10_10, union(empty_set)) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set)))))
% 35.18/13.62 -> [30] (in(skolem_B77(union(empty_set)), union(empty_set)) <=> ? [D11_11] : ((in(skolem_B77(union(empty_set)), D11_11) & in(D11_11, empty_set))))
% 35.18/13.62
% 35.18/13.62 [30] BETA_EQUIV : (in(skolem_B77(union(empty_set)), union(empty_set)) <=> ? [D11_11] : ((in(skolem_B77(union(empty_set)), D11_11) & in(D11_11, empty_set))))
% 35.18/13.62 -> [31] ~in(skolem_B77(union(empty_set)), union(empty_set)), ~? [D11_11] : ((in(skolem_B77(union(empty_set)), D11_11) & in(D11_11, empty_set)))
% 35.18/13.62 -> [32] in(skolem_B77(union(empty_set)), union(empty_set)), ? [D11_11] : ((in(skolem_B77(union(empty_set)), D11_11) & in(D11_11, empty_set)))
% 35.18/13.62
% 35.18/13.62 [31] GAMMA_NOT_EXISTS : ~? [D11_11] : ((in(skolem_B77(union(empty_set)), D11_11) & in(D11_11, empty_set)))
% 35.18/13.62 -> [39] ~(in(skolem_B77(union(empty_set)), D11_1_5) & in(D11_1_5, empty_set))
% 35.18/13.62
% 35.18/13.62 [39] BETA_NOT_AND : ~(in(skolem_B77(union(empty_set)), D11_1_5) & in(D11_1_5, empty_set))
% 35.18/13.62 -> [41] ~in(skolem_B77(union(empty_set)), D11_1_5)
% 35.18/13.62 -> [42] ~in(D11_1_5, empty_set)
% 35.18/13.62
% 35.18/13.62 [41] : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62 -> [55] ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62
% 35.18/13.62 [55] GAMMA_FORALL : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62 -> [56] (in(union(empty_set), skolem_B77(union(empty_set))) => ~in(skolem_B77(union(empty_set)), union(empty_set)))
% 35.18/13.62
% 35.18/13.62 [56] BETA_IMPLY : (in(union(empty_set), skolem_B77(union(empty_set))) => ~in(skolem_B77(union(empty_set)), union(empty_set)))
% 35.18/13.62 -> [57] ~in(union(empty_set), skolem_B77(union(empty_set)))
% 35.18/13.62 -> [58] ~in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62
% 35.18/13.62 [58] : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [83] ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62
% 35.18/13.62 [83] GAMMA_FORALL : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [84] (=(union(empty_set), empty_set) <=> ! [B7_7] : (~in(B7_7, union(empty_set))))
% 35.18/13.62
% 35.18/13.62 [84] BETA_EQUIV : (=(union(empty_set), empty_set) <=> ! [B7_7] : (~in(B7_7, union(empty_set))))
% 35.18/13.62 -> [85] ~=(union(empty_set), empty_set), ~! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62 -> [86] =(union(empty_set), empty_set), ! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62
% 35.18/13.62 [86] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [102] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [90] BETA_EQUIV : (=(union(empty_set), empty_set) <=> ! [B7_7] : (~in(B7_7, union(empty_set))))
% 35.18/13.62 -> [113] ~=(union(empty_set), empty_set), ~! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62 -> [114] =(union(empty_set), empty_set), ! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62
% 35.18/13.62 [113] DELTA_NOT_FORALL : ~! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62 -> [119] ~~in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62
% 35.18/13.62 [119] ALPHA_NOT_NOT : ~~in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62 -> [120] in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62
% 35.18/13.62 [120] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [114] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [52] BETA_IMPLY : (in(union(empty_set), skolem_B77(union(empty_set))) => ~in(skolem_B77(union(empty_set)), union(empty_set)))
% 35.18/13.62 -> [125] ~in(union(empty_set), skolem_B77(union(empty_set)))
% 35.18/13.62 -> [126] ~in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62
% 35.18/13.62 [126] : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [143] ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62
% 35.18/13.62 [143] GAMMA_FORALL : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [144] (=(union(empty_set), empty_set) <=> ! [B7_7] : (~in(B7_7, union(empty_set))))
% 35.18/13.62
% 35.18/13.62 [144] BETA_EQUIV : (=(union(empty_set), empty_set) <=> ! [B7_7] : (~in(B7_7, union(empty_set))))
% 35.18/13.62 -> [145] ~=(union(empty_set), empty_set), ~! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62 -> [146] =(union(empty_set), empty_set), ! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62
% 35.18/13.62 [146] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [150] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [140] BETA_EQUIV : (=(union(empty_set), empty_set) <=> ! [B7_7] : (~in(B7_7, union(empty_set))))
% 35.18/13.62 -> [155] ~=(union(empty_set), empty_set), ~! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62 -> [156] =(union(empty_set), empty_set), ! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62
% 35.18/13.62 [155] DELTA_NOT_FORALL : ~! [B7_7] : (~in(B7_7, union(empty_set)))
% 35.18/13.62 -> [157] ~~in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62
% 35.18/13.62 [157] ALPHA_NOT_NOT : ~~in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62 -> [158] in(skolem_B77(union(empty_set)), union(empty_set))
% 35.18/13.62
% 35.18/13.62 [158] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [156] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [40] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [7] BETA_EQUIV : (=(skolem_A1313, empty_set) <=> ! [B7_7] : (~in(B7_7, skolem_A1313)))
% 35.18/13.62 -> [289] ~=(skolem_A1313, empty_set), ~! [B7_7] : (~in(B7_7, skolem_A1313))
% 35.18/13.62 -> [290] =(skolem_A1313, empty_set), ! [B7_7] : (~in(B7_7, skolem_A1313))
% 35.18/13.62
% 35.18/13.62 [290] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [292] GAMMA_FORALL : ! [A8_8, B9_9] : ((=(B9_9, union(A8_8)) <=> ! [C10_10] : ((in(C10_10, B9_9) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, A8_8)))))))
% 35.18/13.62 -> [293] (=(empty_set, union(empty_set)) <=> ! [C10_10] : ((in(C10_10, empty_set) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set))))))
% 35.18/13.62
% 35.18/13.62 [293] BETA_EQUIV : (=(empty_set, union(empty_set)) <=> ! [C10_10] : ((in(C10_10, empty_set) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set))))))
% 35.18/13.62 -> [294] ~=(empty_set, union(empty_set)), ~! [C10_10] : ((in(C10_10, empty_set) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set)))))
% 35.18/13.62 -> [295] =(empty_set, union(empty_set)), ! [C10_10] : ((in(C10_10, empty_set) <=> ? [D11_11] : ((in(C10_10, D11_11) & in(D11_11, empty_set)))))
% 35.18/13.62
% 35.18/13.62 [295] CLOSURE : =
% 35.18/13.62
% 35.18/13.62 [296] BETA_NOT_EQUIV : ~(in(skolem_C1010(empty_set, empty_set), empty_set) <=> ? [D11_11] : ((in(skolem_C1010(empty_set, empty_set), D11_11) & in(D11_11, empty_set))))
% 35.18/13.62 -> [500] ~in(skolem_C1010(empty_set, empty_set), empty_set), ? [D11_11] : ((in(skolem_C1010(empty_set, empty_set), D11_11) & in(D11_11, empty_set)))
% 35.18/13.62 -> [501] in(skolem_C1010(empty_set, empty_set), empty_set), ~? [D11_11] : ((in(skolem_C1010(empty_set, empty_set), D11_11) & in(D11_11, empty_set)))
% 35.18/13.62
% 35.18/13.62 [501] GAMMA_NOT_EXISTS : ~? [D11_11] : ((in(skolem_C1010(empty_set, empty_set), D11_11) & in(D11_11, empty_set)))
% 35.18/13.62 -> [503] ~(in(skolem_C1010(empty_set, empty_set), empty_set) & in(empty_set, empty_set))
% 35.18/13.62
% 35.18/13.62 [503] BETA_NOT_AND : ~(in(skolem_C1010(empty_set, empty_set), empty_set) & in(empty_set, empty_set))
% 35.18/13.62 -> [504] ~in(skolem_C1010(empty_set, empty_set), empty_set)
% 35.18/13.62 -> [505] ~in(empty_set, empty_set)
% 35.18/13.62
% 35.18/13.62 [504] CLOSURE : ~in(skolem_C1010(empty_set, empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [505] : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62 -> [511] ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62
% 35.18/13.62 [511] GAMMA_FORALL : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62 -> [512] (in(skolem_B77(skolem_A1313), skolem_A1313) => ~in(skolem_A1313, skolem_B77(skolem_A1313)))
% 35.18/13.62
% 35.18/13.62 [512] BETA_IMPLY : (in(skolem_B77(skolem_A1313), skolem_A1313) => ~in(skolem_A1313, skolem_B77(skolem_A1313)))
% 35.18/13.62 -> [513] ~in(skolem_B77(skolem_A1313), skolem_A1313)
% 35.18/13.62 -> [514] ~in(skolem_A1313, skolem_B77(skolem_A1313))
% 35.18/13.62
% 35.18/13.62 [513] CLOSURE : ~in(skolem_B77(skolem_A1313), skolem_A1313)
% 35.18/13.62
% 35.18/13.62 [514] : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [519] ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62
% 35.18/13.62 [519] GAMMA_FORALL : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [520] (=(empty_set, empty_set) <=> ! [B7_7] : (~in(B7_7, empty_set)))
% 35.18/13.62
% 35.18/13.62 [520] BETA_EQUIV : (=(empty_set, empty_set) <=> ! [B7_7] : (~in(B7_7, empty_set)))
% 35.18/13.62 -> [521] ~=(empty_set, empty_set), ~! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [522] =(empty_set, empty_set), ! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62
% 35.18/13.62 [521] DELTA_NOT_FORALL : ~! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [525] ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [525] ALPHA_NOT_NOT : ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62 -> [526] in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [526] CLOSURE : ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [522] GAMMA_FORALL : ! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [527] ~in(B7_11_4, empty_set)
% 35.18/13.62
% 35.18/13.62 [527] CLOSURE : ~in(B7_11_4, empty_set)
% 35.18/13.62
% 35.18/13.62 [500] DELTA_EXISTS : ? [D11_11] : ((in(skolem_C1010(empty_set, empty_set), D11_11) & in(D11_11, empty_set)))
% 35.18/13.62 -> [502] (in(skolem_C1010(empty_set, empty_set), skolem_D1111) & in(skolem_D1111, empty_set))
% 35.18/13.62
% 35.18/13.62 [502] ALPHA_AND : (in(skolem_C1010(empty_set, empty_set), skolem_D1111) & in(skolem_D1111, empty_set))
% 35.18/13.62 -> [506] in(skolem_C1010(empty_set, empty_set), skolem_D1111), in(skolem_D1111, empty_set)
% 35.18/13.62
% 35.18/13.62 [506] ALPHA_AND : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62 -> [507] ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62
% 35.18/13.62 [507] GAMMA_FORALL : ! [A4_4, B5_5] : ((in(A4_4, B5_5) => ~in(B5_5, A4_4)))
% 35.18/13.62 -> [508] (in(skolem_D1111, empty_set) => ~in(empty_set, skolem_D1111))
% 35.18/13.62
% 35.18/13.62 [508] BETA_IMPLY : (in(skolem_D1111, empty_set) => ~in(empty_set, skolem_D1111))
% 35.18/13.62 -> [509] ~in(skolem_D1111, empty_set)
% 35.18/13.62 -> [510] ~in(empty_set, skolem_D1111)
% 35.18/13.62
% 35.18/13.62 [509] CLOSURE : ~in(skolem_D1111, empty_set)
% 35.18/13.62
% 35.18/13.62 [510] : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [515] ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62
% 35.18/13.62 [515] GAMMA_FORALL : ! [A6_6] : ((=(A6_6, empty_set) <=> ! [B7_7] : (~in(B7_7, A6_6))))
% 35.18/13.62 -> [516] (=(empty_set, empty_set) <=> ! [B7_7] : (~in(B7_7, empty_set)))
% 35.18/13.62
% 35.18/13.62 [516] BETA_EQUIV : (=(empty_set, empty_set) <=> ! [B7_7] : (~in(B7_7, empty_set)))
% 35.18/13.62 -> [517] ~=(empty_set, empty_set), ~! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [518] =(empty_set, empty_set), ! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62
% 35.18/13.62 [517] DELTA_NOT_FORALL : ~! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [523] ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [523] ALPHA_NOT_NOT : ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62 -> [524] in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [524] CLOSURE : ~~in(skolem_B77(empty_set), empty_set)
% 35.18/13.62
% 35.18/13.62 [518] GAMMA_FORALL : ! [B7_7] : (~in(B7_7, empty_set))
% 35.18/13.62 -> [528] ~in(B7_12_3, empty_set)
% 35.18/13.62
% 35.18/13.62 [528] CLOSURE : ~in(B7_12_3, empty_set)
% 35.18/13.62
% 35.18/13.62 % SZS output end Proof for theBenchmark.p
% 35.18/13.62 [13.281256s][1][Res] 71910 goroutines created
% 35.18/13.62 ==== Result ====
% 35.18/13.62 [13.281297s][1][Res] VALID
% 35.18/13.62 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------