TSTP Solution File: SET696+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET696+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n003.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 04:17:10 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET696+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n003.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 07:23:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000073s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 15
% 0.12/0.34 Launch Gotab with destructive = true
% 0.19/0.38 % SZS output start Proof for theBenchmark.p
% 0.19/0.39 [0] ALPHA_AND : ((! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))) & ~! [A33_33, E34_34] : ((subset(A33_33, E34_34) => equal_set(intersection(difference(E34_34, A33_33), A33_33), empty_set))))
% 0.19/0.39 -> [1] (! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))), ~! [A33_33, E34_34] : ((subset(A33_33, E34_34) => equal_set(intersection(difference(E34_34, A33_33), A33_33), empty_set)))
% 0.19/0.39
% 0.19/0.39 [1] ALPHA_AND : (! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23))))
% 0.19/0.39 -> [2] ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))), ! [X18_18] : (~member(X18_18, empty_set)), ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 0.19/0.39
% 0.19/0.39 [2] DELTA_NOT_FORALL : ~! [A33_33, E34_34] : ((subset(A33_33, E34_34) => equal_set(intersection(difference(E34_34, A33_33), A33_33), empty_set)))
% 0.19/0.39 -> [3] ~(subset(skolem_A3333, skolem_E3434) => equal_set(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set))
% 0.19/0.39
% 0.19/0.39 [3] ALPHA_NOT_IMPLY : ~(subset(skolem_A3333, skolem_E3434) => equal_set(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set))
% 0.19/0.39 -> [4] subset(skolem_A3333, skolem_E3434), ~equal_set(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set)
% 0.19/0.39
% 0.19/0.39 [4] Rewrite : subset(skolem_A3333, skolem_E3434)
% 0.19/0.39 -> [5] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3434)))
% 0.19/0.39
% 0.19/0.39 [5] Rewrite : ~equal_set(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set)
% 0.19/0.39 -> [6] ~(subset(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set) & subset(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 0.19/0.39
% 0.19/0.39 [6] BETA_NOT_AND : ~(subset(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set) & subset(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 0.19/0.39 -> [7] ~subset(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set)
% 0.19/0.39 -> [8] ~subset(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 0.19/0.39
% 0.19/0.39 [7] Rewrite : ~subset(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set)
% 0.19/0.39 -> [11] ~(member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)) => member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), empty_set))
% 0.19/0.39
% 0.19/0.39 [11] ALPHA_NOT_IMPLY : ~(member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)) => member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), empty_set))
% 0.19/0.39 -> [12] member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), ~member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), empty_set)
% 0.19/0.39
% 0.19/0.39 [12] Rewrite : member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 0.19/0.39 -> [13] (member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), difference(skolem_E3434, skolem_A3333)) & member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_A3333))
% 0.19/0.39
% 0.19/0.39 [13] ALPHA_AND : (member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), difference(skolem_E3434, skolem_A3333)) & member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_A3333))
% 0.19/0.39 -> [17] member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), difference(skolem_E3434, skolem_A3333)), member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_A3333)
% 0.19/0.39
% 0.19/0.39 [17] Rewrite : member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), difference(skolem_E3434, skolem_A3333))
% 0.19/0.39 -> [24] (member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_E3434) & ~member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_A3333))
% 0.19/0.39
% 0.19/0.39 [24] ALPHA_AND : (member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_E3434) & ~member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_A3333))
% 0.19/0.39 -> [33] member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_E3434), ~member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_A3333)
% 0.19/0.39
% 0.19/0.39 [33] CLOSURE : ~member(skolem_X77(intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333), empty_set), skolem_A3333)
% 0.19/0.39
% 0.19/0.39 [8] Rewrite : ~subset(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 0.19/0.39 -> [9] ~(member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), empty_set) => member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 0.19/0.39
% 0.19/0.39 [9] ALPHA_NOT_IMPLY : ~(member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), empty_set) => member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 0.19/0.39 -> [10] member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), empty_set), ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 0.19/0.39
% 0.19/0.39 [10] Rewrite : ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 0.19/0.39 -> [14] ~(member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333)) & member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 0.19/0.39
% 0.19/0.39 [14] BETA_NOT_AND : ~(member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333)) & member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 0.19/0.39 -> [15] ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333))
% 0.19/0.39 -> [16] ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 0.19/0.39
% 0.19/0.39 [16] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.19/0.39 -> [19] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.19/0.39
% 0.19/0.39 [19] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.19/0.39 -> [20] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 0.19/0.39 -> [21] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 0.19/0.39
% 0.19/0.39 [20] Rewrite : ~subset(X10_0_0, X10_0_0)
% 0.19/0.39 -> [30] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 0.19/0.39
% 0.19/0.39 [30] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 0.19/0.39 -> [34] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.19/0.39
% 0.19/0.39 [34] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.19/0.39
% 0.19/0.39 [21] Rewrite : subset(X10_0_0, X10_0_0)
% 0.19/0.39 -> [35] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 0.19/0.39
% 0.19/0.39 [35] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.19/0.39 -> [36] ~member(X18_0_1, empty_set)
% 0.19/0.39
% 0.19/0.39 [36] CLOSURE : ~member(X18_0_1, empty_set)
% 0.19/0.39
% 0.19/0.39 [15] Rewrite : ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333))
% 0.19/0.39 -> [18] ~(member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434) & ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 0.19/0.39
% 0.19/0.39 [18] BETA_NOT_AND : ~(member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434) & ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 0.19/0.39 -> [22] ~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434)
% 0.19/0.39 -> [23] ~~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 0.19/0.39
% 0.19/0.39 [22] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.19/0.39 -> [26] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 0.19/0.39
% 0.19/0.39 [26] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 0.19/0.39 -> [27] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 0.19/0.39 -> [28] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 0.19/0.39
% 0.19/0.39 [28] Rewrite : subset(X10_1_0, X10_1_0)
% 0.19/0.39 -> [39] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 0.19/0.39
% 0.19/0.39 [39] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.19/0.39 -> [41] ~member(X18_1_1, empty_set)
% 0.19/0.39
% 0.19/0.39 [41] CLOSURE : ~member(X18_1_1, empty_set)
% 0.19/0.39
% 0.19/0.39 [27] Rewrite : ~subset(X10_1_0, X10_1_0)
% 0.19/0.39 -> [37] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 0.19/0.39
% 0.19/0.39 [37] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 0.19/0.39 -> [38] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 0.19/0.39
% 0.19/0.39 [38] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 0.19/0.39
% 0.19/0.39 [23] ALPHA_NOT_NOT : ~~member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 0.19/0.39 -> [25] member(skolem_X77(empty_set, intersection(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 0.19/0.39
% 0.19/0.39 [25] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.19/0.39 -> [29] (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 0.19/0.39
% 0.19/0.39 [29] BETA_EQUIV : (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 0.19/0.39 -> [31] ~member(X10_2_0, power_set(X10_2_0)), ~subset(X10_2_0, X10_2_0)
% 0.19/0.39 -> [32] member(X10_2_0, power_set(X10_2_0)), subset(X10_2_0, X10_2_0)
% 0.19/0.39
% 0.19/0.39 [31] Rewrite : ~subset(X10_2_0, X10_2_0)
% 0.19/0.39 -> [40] ~(member(skolem_X77(X10_2_0, X10_2_0), X10_2_0) => member(skolem_X77(X10_2_0, X10_2_0), X10_2_0))
% 0.19/0.39
% 0.19/0.39 [40] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_2_0, X10_2_0), X10_2_0) => member(skolem_X77(X10_2_0, X10_2_0), X10_2_0))
% 0.19/0.39 -> [42] member(skolem_X77(X10_2_0, X10_2_0), X10_2_0), ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 0.19/0.39
% 0.19/0.39 [42] CLOSURE : ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 0.19/0.39
% 0.19/0.39 [32] Rewrite : subset(X10_2_0, X10_2_0)
% 0.19/0.39 -> [43] ! [X7_7] : ((member(X7_7, X10_2_0) => member(X7_7, X10_2_0)))
% 0.19/0.39
% 0.19/0.39 [43] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.19/0.39 -> [44] ~member(X18_2_1, empty_set)
% 0.19/0.39
% 0.19/0.39 [44] CLOSURE : ~member(X18_2_1, empty_set)
% 0.19/0.39
% 0.19/0.39 % SZS output end Proof for theBenchmark.p
% 0.19/0.39 [0.044388s][1][Res] 239 goroutines created
% 0.19/0.39 ==== Result ====
% 0.19/0.39 [0.044423s][1][Res] VALID
% 0.19/0.39 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------