TSTP Solution File: SET591+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n006.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 04:16:44 EDT 2022
% Result : Theorem 1.06s 0.77s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 06:48:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000048s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Start search
% 0.13/0.34 nb_step : 1 - limit : 9
% 0.13/0.34 Launch Gotab with destructive = true
% 1.06/0.77 % SZS output start Proof for theBenchmark.p
% 1.06/0.77 [0] ALPHA_AND : (! [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] : (subset(B12_12, B12_12)) & ~! [B15_15, C16_16] : ((subset(B15_15, difference(C16_16, B15_15)) => =(B15_15, empty_set))))
% 1.06/0.77 -> [1] ! [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] : (subset(B12_12, B12_12)), ~! [B15_15, C16_16] : ((subset(B15_15, difference(C16_16, B15_15)) => =(B15_15, empty_set)))
% 1.06/0.77
% 1.06/0.77 [1] DELTA_NOT_FORALL : ~! [B15_15, C16_16] : ((subset(B15_15, difference(C16_16, B15_15)) => =(B15_15, empty_set)))
% 1.06/0.77 -> [2] ~(subset(skolem_B1515, difference(skolem_C1616, skolem_B1515)) => =(skolem_B1515, empty_set))
% 1.06/0.77
% 1.06/0.77 [2] ALPHA_NOT_IMPLY : ~(subset(skolem_B1515, difference(skolem_C1616, skolem_B1515)) => =(skolem_B1515, empty_set))
% 1.06/0.77 -> [3] subset(skolem_B1515, difference(skolem_C1616, skolem_B1515)), ~=(skolem_B1515, empty_set)
% 1.06/0.77
% 1.06/0.77 [3] Rewrite : subset(skolem_B1515, difference(skolem_C1616, skolem_B1515))
% 1.06/0.77 -> [4] ! [D5_5] : ((member(D5_5, skolem_B1515) => member(D5_5, difference(skolem_C1616, skolem_B1515))))
% 1.06/0.77
% 1.06/0.77 [4] GAMMA_FORALL : ! [B9_9] : (~member(B9_9, empty_set))
% 1.06/0.77 -> [5] ~member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 [5] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 1.06/0.77 -> [6] (=(empty_set, empty_set) <=> (subset(empty_set, empty_set) & subset(empty_set, empty_set)))
% 1.06/0.77
% 1.06/0.77 [6] BETA_EQUIV : (=(empty_set, empty_set) <=> (subset(empty_set, empty_set) & subset(empty_set, empty_set)))
% 1.06/0.77 -> [7] ~=(empty_set, empty_set), ~(subset(empty_set, empty_set) & subset(empty_set, empty_set))
% 1.06/0.77 -> [8] =(empty_set, empty_set), (subset(empty_set, empty_set) & subset(empty_set, empty_set))
% 1.06/0.77
% 1.06/0.77 [7] CLOSURE : ~=(empty_set, empty_set)
% 1.06/0.77
% 1.06/0.77 [9] Rewrite : subset(empty_set, empty_set)
% 1.06/0.77 -> [10] ! [D5_5] : ((member(D5_5, empty_set) => member(D5_5, empty_set)))
% 1.06/0.77
% 1.06/0.77 [10] GAMMA_FORALL : ! [B12_12] : (subset(B12_12, B12_12))
% 1.06/0.77 -> [11] subset(empty_set, empty_set)
% 1.06/0.77
% 1.06/0.77 [11] Rewrite : subset(empty_set, empty_set)
% 1.06/0.77 -> [12] ! [D5_5] : ((member(D5_5, empty_set) => member(D5_5, empty_set)))
% 1.06/0.77
% 1.06/0.77 [12] GAMMA_FORALL : ! [D5_5] : ((member(D5_5, skolem_B1515) => member(D5_5, difference(skolem_C1616, skolem_B1515))))
% 1.06/0.77 -> [13] (member(skolem_D55(skolem_B1515, empty_set), skolem_B1515) => member(skolem_D55(skolem_B1515, empty_set), difference(skolem_C1616, skolem_B1515)))
% 1.06/0.77
% 1.06/0.77 [13] BETA_IMPLY : (member(skolem_D55(skolem_B1515, empty_set), skolem_B1515) => member(skolem_D55(skolem_B1515, empty_set), difference(skolem_C1616, skolem_B1515)))
% 1.06/0.77 -> [14] ~member(skolem_D55(skolem_B1515, empty_set), skolem_B1515)
% 1.06/0.77 -> [15] member(skolem_D55(skolem_B1515, empty_set), difference(skolem_C1616, skolem_B1515))
% 1.06/0.77
% 1.06/0.77 [14] GAMMA_FORALL : ! [D5_5] : ((member(D5_5, empty_set) => member(D5_5, empty_set)))
% 1.06/0.77 -> [17] (member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), empty_set))
% 1.06/0.77
% 1.06/0.77 [17] BETA_IMPLY : (member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), empty_set))
% 1.06/0.77 -> [19] ~member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77 -> [20] member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 [20] CLOSURE : member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 [21] BETA_IMPLY : (member(D5_2_5, empty_set) => member(D5_2_5, empty_set))
% 1.06/0.77 -> [65] ~member(D5_2_5, empty_set)
% 1.06/0.77 -> [66] member(D5_2_5, empty_set)
% 1.06/0.77
% 1.06/0.77 [65] : ! [B9_9] : (~member(B9_9, empty_set))
% 1.06/0.77 -> [67] ! [B9_9] : (~member(B9_9, empty_set))
% 1.06/0.77
% 1.06/0.77 [67] GAMMA_FORALL : ! [B9_9] : (~member(B9_9, empty_set))
% 1.06/0.77 -> [68] ~member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 [68] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 1.06/0.77 -> [69] ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 1.06/0.77
% 1.06/0.77 [69] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 1.06/0.77 -> [70] (=(empty_set, skolem_B1515) <=> (subset(empty_set, skolem_B1515) & subset(skolem_B1515, empty_set)))
% 1.06/0.77
% 1.06/0.77 [70] BETA_EQUIV : (=(empty_set, skolem_B1515) <=> (subset(empty_set, skolem_B1515) & subset(skolem_B1515, empty_set)))
% 1.06/0.77 -> [71] ~=(empty_set, skolem_B1515), ~(subset(empty_set, skolem_B1515) & subset(skolem_B1515, empty_set))
% 1.06/0.77 -> [72] =(empty_set, skolem_B1515), (subset(empty_set, skolem_B1515) & subset(skolem_B1515, empty_set))
% 1.06/0.77
% 1.06/0.77 [72] ALPHA_AND : (subset(empty_set, skolem_B1515) & subset(skolem_B1515, empty_set))
% 1.06/0.77 -> [74] subset(empty_set, skolem_B1515), subset(skolem_B1515, empty_set)
% 1.06/0.77
% 1.06/0.77 [74] CLOSURE : =
% 1.06/0.77
% 1.06/0.77 [71] BETA_NOT_AND : ~(subset(empty_set, skolem_B1515) & subset(skolem_B1515, empty_set))
% 1.06/0.77 -> [79] ~subset(empty_set, skolem_B1515)
% 1.06/0.77 -> [80] ~subset(skolem_B1515, empty_set)
% 1.06/0.77
% 1.06/0.77 [79] Rewrite : ~subset(empty_set, skolem_B1515)
% 1.06/0.77 -> [81] ~(member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), skolem_B1515))
% 1.06/0.77
% 1.06/0.77 [81] ALPHA_NOT_IMPLY : ~(member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), skolem_B1515))
% 1.06/0.77 -> [83] member(skolem_D55(empty_set, skolem_B1515), empty_set), ~member(skolem_D55(empty_set, skolem_B1515), skolem_B1515)
% 1.06/0.77
% 1.06/0.77 [83] CLOSURE : member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 [80] ALPHA_NOT_IMPLY : ~(member(skolem_D55(skolem_B1515, empty_set), skolem_B1515) => member(skolem_D55(skolem_B1515, empty_set), empty_set))
% 1.06/0.77 -> [85] member(skolem_D55(skolem_B1515, empty_set), skolem_B1515), ~member(skolem_D55(skolem_B1515, empty_set), empty_set)
% 1.06/0.77
% 1.06/0.77 [85] CLOSURE : member(skolem_D55(skolem_B1515, empty_set), skolem_B1515)
% 1.06/0.77
% 1.06/0.77 [66] CLOSURE : member(D5_2_5, empty_set)
% 1.06/0.77
% 1.06/0.77 [15] ALPHA_AND : (member(skolem_D55(skolem_B1515, empty_set), skolem_C1616) & ~member(skolem_D55(skolem_B1515, empty_set), skolem_B1515))
% 1.06/0.77 -> [86] member(skolem_D55(skolem_B1515, empty_set), skolem_C1616), ~member(skolem_D55(skolem_B1515, empty_set), skolem_B1515)
% 1.06/0.77
% 1.06/0.77 [86] GAMMA_FORALL : ! [D5_5] : ((member(D5_5, empty_set) => member(D5_5, empty_set)))
% 1.06/0.77 -> [87] (member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), empty_set))
% 1.06/0.77
% 1.06/0.77 [87] BETA_IMPLY : (member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), empty_set))
% 1.06/0.77 -> [88] ~member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77 -> [89] member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 [88] : ! [B9_9] : (~member(B9_9, empty_set))
% 1.06/0.77 -> [90] ! [B9_9] : (~member(B9_9, empty_set))
% 1.06/0.77
% 1.06/0.77 [90] GAMMA_FORALL : ! [B9_9] : (~member(B9_9, empty_set))
% 1.06/0.77 -> [91] ~member(B9_4_0, empty_set)
% 1.06/0.77
% 1.06/0.77 [91] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 1.06/0.77 -> [92] ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 1.06/0.77
% 1.06/0.77 [92] GAMMA_FORALL : ! [B10_10, C11_11] : ((=(B10_10, C11_11) <=> (subset(B10_10, C11_11) & subset(C11_11, B10_10))))
% 1.06/0.77 -> [93] (=(skolem_B1515, empty_set) <=> (subset(skolem_B1515, empty_set) & subset(empty_set, skolem_B1515)))
% 1.06/0.77
% 1.06/0.77 [93] BETA_EQUIV : (=(skolem_B1515, empty_set) <=> (subset(skolem_B1515, empty_set) & subset(empty_set, skolem_B1515)))
% 1.06/0.77 -> [94] ~=(skolem_B1515, empty_set), ~(subset(skolem_B1515, empty_set) & subset(empty_set, skolem_B1515))
% 1.06/0.77 -> [95] =(skolem_B1515, empty_set), (subset(skolem_B1515, empty_set) & subset(empty_set, skolem_B1515))
% 1.06/0.77
% 1.06/0.77 [95] ALPHA_AND : (subset(skolem_B1515, empty_set) & subset(empty_set, skolem_B1515))
% 1.06/0.77 -> [96] subset(skolem_B1515, empty_set), subset(empty_set, skolem_B1515)
% 1.06/0.77
% 1.06/0.77 [96] CLOSURE : =
% 1.06/0.77
% 1.06/0.77 [94] BETA_NOT_AND : ~(subset(skolem_B1515, empty_set) & subset(empty_set, skolem_B1515))
% 1.06/0.77 -> [116] ~subset(skolem_B1515, empty_set)
% 1.06/0.77 -> [117] ~subset(empty_set, skolem_B1515)
% 1.06/0.77
% 1.06/0.77 [116] Rewrite : ~subset(skolem_B1515, empty_set)
% 1.06/0.77 -> [118] ~(member(skolem_D55(skolem_B1515, empty_set), skolem_B1515) => member(skolem_D55(skolem_B1515, empty_set), empty_set))
% 1.06/0.77
% 1.06/0.77 [118] ALPHA_NOT_IMPLY : ~(member(skolem_D55(skolem_B1515, empty_set), skolem_B1515) => member(skolem_D55(skolem_B1515, empty_set), empty_set))
% 1.06/0.77 -> [120] member(skolem_D55(skolem_B1515, empty_set), skolem_B1515), ~member(skolem_D55(skolem_B1515, empty_set), empty_set)
% 1.06/0.77
% 1.06/0.77 [120] CLOSURE : member(skolem_D55(skolem_B1515, empty_set), skolem_B1515)
% 1.06/0.77
% 1.06/0.77 [117] Rewrite : ~subset(empty_set, skolem_B1515)
% 1.06/0.77 -> [119] ~(member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), skolem_B1515))
% 1.06/0.77
% 1.06/0.77 [119] ALPHA_NOT_IMPLY : ~(member(skolem_D55(empty_set, skolem_B1515), empty_set) => member(skolem_D55(empty_set, skolem_B1515), skolem_B1515))
% 1.06/0.77 -> [121] member(skolem_D55(empty_set, skolem_B1515), empty_set), ~member(skolem_D55(empty_set, skolem_B1515), skolem_B1515)
% 1.06/0.77
% 1.06/0.77 [121] CLOSURE : member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 [89] CLOSURE : member(skolem_D55(empty_set, skolem_B1515), empty_set)
% 1.06/0.77
% 1.06/0.77 % SZS output end Proof for theBenchmark.p
% 1.06/0.77 [0.427329s][1][Res] 648 goroutines created
% 1.06/0.77 ==== Result ====
% 1.06/0.77 [0.427364s][1][Res] VALID
% 1.06/0.77 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------