TSTP Solution File: SET146+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n009.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 04:15:35 EDT 2022
% Result : Theorem 3.43s 1.12s
% Output : Proof 3.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n009.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 02:51:35 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 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 12
% 0.12/0.34 Launch Gotab with destructive = true
% 3.43/1.12 % SZS output start Proof for theBenchmark.p
% 3.43/1.12 [0] ALPHA_AND : (! [B6_6] : (~member(B6_6, empty_set)) & ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> (subset(B7_7, C8_8) & subset(C8_8, B7_7)))) & ! [B9_9, C10_10] : (=(intersection(B9_9, C10_10), intersection(C10_10, B9_9))) & ! [B14_14] : (subset(B14_14, B14_14)) & ! [B17_17, C18_18] : ((=(B17_17, C18_18) <=> ! [D19_19] : ((member(D19_19, B17_17) <=> member(D19_19, C18_18))))) & ~! [B20_20] : (=(intersection(B20_20, empty_set), empty_set)))
% 3.43/1.12 -> [1] ! [B6_6] : (~member(B6_6, empty_set)), ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> (subset(B7_7, C8_8) & subset(C8_8, B7_7)))), ! [B9_9, C10_10] : (=(intersection(B9_9, C10_10), intersection(C10_10, B9_9))), ! [B14_14] : (subset(B14_14, B14_14)), ! [B17_17, C18_18] : ((=(B17_17, C18_18) <=> ! [D19_19] : ((member(D19_19, B17_17) <=> member(D19_19, C18_18))))), ~! [B20_20] : (=(intersection(B20_20, empty_set), empty_set))
% 3.43/1.12
% 3.43/1.12 [1] DELTA_NOT_FORALL : ~! [B20_20] : (=(intersection(B20_20, empty_set), empty_set))
% 3.43/1.12 -> [2] ~=(intersection(skolem_B2020, empty_set), empty_set)
% 3.43/1.12
% 3.43/1.12 [2] GAMMA_FORALL : ! [B6_6] : (~member(B6_6, empty_set))
% 3.43/1.12 -> [3] ~member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), empty_set)
% 3.43/1.12
% 3.43/1.12 [3] GAMMA_FORALL : ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> (subset(B7_7, C8_8) & subset(C8_8, B7_7))))
% 3.43/1.12 -> [4] (=(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) <=> (subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set))))
% 3.43/1.12
% 3.43/1.12 [4] BETA_EQUIV : (=(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) <=> (subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set))))
% 3.43/1.12 -> [5] ~=(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)), ~(subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)))
% 3.43/1.12 -> [6] =(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)), (subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)))
% 3.43/1.12
% 3.43/1.12 [5] CLOSURE : ~=(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12
% 3.43/1.12 [7] Rewrite : subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12 -> [8] ! [D13_13] : ((member(D13_13, intersection(skolem_B2020, empty_set)) => member(D13_13, intersection(skolem_B2020, empty_set))))
% 3.43/1.12
% 3.43/1.12 [8] GAMMA_FORALL : ! [B9_9, C10_10] : (=(intersection(B9_9, C10_10), intersection(C10_10, B9_9)))
% 3.43/1.12 -> [9] =(intersection(B9_0_2, C10_0_2), intersection(C10_0_2, B9_0_2))
% 3.43/1.12
% 3.43/1.12 [9] GAMMA_FORALL : ! [B14_14] : (subset(B14_14, B14_14))
% 3.43/1.12 -> [10] subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12
% 3.43/1.12 [10] Rewrite : subset(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12 -> [11] ! [D13_13] : ((member(D13_13, intersection(skolem_B2020, empty_set)) => member(D13_13, intersection(skolem_B2020, empty_set))))
% 3.43/1.12
% 3.43/1.12 [11] GAMMA_FORALL : ! [B17_17, C18_18] : ((=(B17_17, C18_18) <=> ! [D19_19] : ((member(D19_19, B17_17) <=> member(D19_19, C18_18)))))
% 3.43/1.12 -> [12] (=(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) <=> ! [D19_19] : ((member(D19_19, intersection(skolem_B2020, empty_set)) <=> member(D19_19, intersection(skolem_B2020, empty_set)))))
% 3.43/1.12
% 3.43/1.12 [12] BETA_EQUIV : (=(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)) <=> ! [D19_19] : ((member(D19_19, intersection(skolem_B2020, empty_set)) <=> member(D19_19, intersection(skolem_B2020, empty_set)))))
% 3.43/1.12 -> [13] ~=(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)), ~! [D19_19] : ((member(D19_19, intersection(skolem_B2020, empty_set)) <=> member(D19_19, intersection(skolem_B2020, empty_set))))
% 3.43/1.12 -> [14] =(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)), ! [D19_19] : ((member(D19_19, intersection(skolem_B2020, empty_set)) <=> member(D19_19, intersection(skolem_B2020, empty_set))))
% 3.43/1.12
% 3.43/1.12 [13] DELTA_NOT_FORALL : ~! [D19_19] : ((member(D19_19, intersection(skolem_B2020, empty_set)) <=> member(D19_19, intersection(skolem_B2020, empty_set))))
% 3.43/1.12 -> [15] ~(member(skolem_D1919(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)), intersection(skolem_B2020, empty_set)) <=> member(skolem_D1919(intersection(skolem_B2020, empty_set), intersection(skolem_B2020, empty_set)), intersection(skolem_B2020, empty_set)))
% 3.43/1.12
% 3.43/1.12 [15] CLOSURE : ~! [D19_19] : ((member(D19_19, intersection(skolem_B2020, empty_set)) <=> member(D19_19, intersection(skolem_B2020, empty_set))))
% 3.43/1.12
% 3.43/1.12 [14] GAMMA_FORALL : ! [D13_13] : ((member(D13_13, intersection(skolem_B2020, empty_set)) => member(D13_13, intersection(skolem_B2020, empty_set))))
% 3.43/1.12 -> [16] (member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)) => member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)))
% 3.43/1.12
% 3.43/1.12 [16] BETA_IMPLY : (member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)) => member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)))
% 3.43/1.12 -> [17] ~member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12 -> [18] member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12
% 3.43/1.12 [17] GAMMA_FORALL : ! [D13_13] : ((member(D13_13, empty_set) => member(D13_13, empty_set)))
% 3.43/1.12 -> [19] (member(D13_1_6, empty_set) => member(D13_1_6, empty_set))
% 3.43/1.12
% 3.43/1.12 [19] BETA_IMPLY : (member(D13_1_6, empty_set) => member(D13_1_6, empty_set))
% 3.43/1.12 -> [20] ~member(D13_1_6, empty_set)
% 3.43/1.12 -> [21] member(D13_1_6, empty_set)
% 3.43/1.12
% 3.43/1.12 [20] GAMMA_FORALL : ! [D19_19] : ((member(D19_19, intersection(skolem_B2020, empty_set)) <=> member(D19_19, intersection(skolem_B2020, empty_set))))
% 3.43/1.12 -> [22] (member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)) <=> member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)))
% 3.43/1.12
% 3.43/1.12 [22] BETA_EQUIV : (member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)) <=> member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)))
% 3.43/1.12 -> [23] ~member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12 -> [24] member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12
% 3.43/1.12 [23] : ! [B6_6] : (~member(B6_6, empty_set))
% 3.43/1.12 -> [25] ! [B6_6] : (~member(B6_6, empty_set))
% 3.43/1.12
% 3.43/1.12 [25] GAMMA_FORALL : ! [B6_6] : (~member(B6_6, empty_set))
% 3.43/1.12 -> [26] ~member(skolem_D1313(empty_set, intersection(skolem_B2020, empty_set)), empty_set)
% 3.43/1.12
% 3.43/1.12 [26] GAMMA_FORALL : ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> (subset(B7_7, C8_8) & subset(C8_8, B7_7))))
% 3.43/1.12 -> [27] ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> (subset(B7_7, C8_8) & subset(C8_8, B7_7))))
% 3.43/1.12
% 3.43/1.12 [27] GAMMA_FORALL : ! [B7_7, C8_8] : ((=(B7_7, C8_8) <=> (subset(B7_7, C8_8) & subset(C8_8, B7_7))))
% 3.43/1.12 -> [28] (=(empty_set, intersection(skolem_B2020, empty_set)) <=> (subset(empty_set, intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), empty_set)))
% 3.43/1.12
% 3.43/1.12 [28] BETA_EQUIV : (=(empty_set, intersection(skolem_B2020, empty_set)) <=> (subset(empty_set, intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), empty_set)))
% 3.43/1.12 -> [29] ~=(empty_set, intersection(skolem_B2020, empty_set)), ~(subset(empty_set, intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), empty_set))
% 3.43/1.12 -> [30] =(empty_set, intersection(skolem_B2020, empty_set)), (subset(empty_set, intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), empty_set))
% 3.43/1.12
% 3.43/1.12 [30] ALPHA_AND : (subset(empty_set, intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), empty_set))
% 3.43/1.12 -> [31] subset(empty_set, intersection(skolem_B2020, empty_set)), subset(intersection(skolem_B2020, empty_set), empty_set)
% 3.43/1.12
% 3.43/1.12 [31] CLOSURE : =
% 3.43/1.12
% 3.43/1.12 [29] BETA_NOT_AND : ~(subset(empty_set, intersection(skolem_B2020, empty_set)) & subset(intersection(skolem_B2020, empty_set), empty_set))
% 3.43/1.12 -> [38] ~subset(empty_set, intersection(skolem_B2020, empty_set))
% 3.43/1.12 -> [39] ~subset(intersection(skolem_B2020, empty_set), empty_set)
% 3.43/1.12
% 3.43/1.12 [38] Rewrite : ~subset(empty_set, intersection(skolem_B2020, empty_set))
% 3.43/1.12 -> [40] ~(member(skolem_D1313(empty_set, intersection(skolem_B2020, empty_set)), empty_set) => member(skolem_D1313(empty_set, intersection(skolem_B2020, empty_set)), intersection(skolem_B2020, empty_set)))
% 3.43/1.12
% 3.43/1.12 [40] ALPHA_NOT_IMPLY : ~(member(skolem_D1313(empty_set, intersection(skolem_B2020, empty_set)), empty_set) => member(skolem_D1313(empty_set, intersection(skolem_B2020, empty_set)), intersection(skolem_B2020, empty_set)))
% 3.43/1.12 -> [41] member(skolem_D1313(empty_set, intersection(skolem_B2020, empty_set)), empty_set), ~member(skolem_D1313(empty_set, intersection(skolem_B2020, empty_set)), intersection(skolem_B2020, empty_set))
% 3.43/1.12
% 3.43/1.12 [41] CLOSURE : =
% 3.43/1.12
% 3.43/1.12 [39] ALPHA_NOT_IMPLY : ~(member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)) => member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), empty_set))
% 3.43/1.12 -> [44] member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set)), ~member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), empty_set)
% 3.43/1.12
% 3.43/1.12 [44] CLOSURE : =
% 3.43/1.12
% 3.43/1.12 [24] CLOSURE : =
% 3.43/1.12
% 3.43/1.12 [21] CLOSURE : =
% 3.43/1.12
% 3.43/1.12 [18] Rewrite : member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), intersection(skolem_B2020, empty_set))
% 3.43/1.12 -> [45] (member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), skolem_B2020) & member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), empty_set))
% 3.43/1.12
% 3.43/1.12 [45] ALPHA_AND : (member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), skolem_B2020) & member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), empty_set))
% 3.43/1.12 -> [46] member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), skolem_B2020), member(skolem_D1313(intersection(skolem_B2020, empty_set), empty_set), empty_set)
% 3.43/1.12
% 3.43/1.12 [46] CLOSURE : =
% 3.43/1.12
% 3.43/1.12 % SZS output end Proof for theBenchmark.p
% 3.43/1.12 [0.784154s][1][Res] 3632 goroutines created
% 3.43/1.12 ==== Result ====
% 3.43/1.12 [0.784189s][1][Res] VALID
% 3.43/1.12 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------