TSTP Solution File: SET014+4 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET014+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 04:14:44 EDT 2022
% Result : Theorem 2.26s 0.73s
% Output : Proof 2.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET014+4 : TPTP v8.1.0. Released v2.2.0.
% 0.05/0.11 % Command : goeland -dmt -presko -proof %s
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Sep 3 01:06:55 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.15/0.31 [DMT] DMT loaded with preskolemization
% 0.15/0.31 [EQ] equality loaded.
% 0.15/0.31 [0.000069s][1][MAIN] Problem : theBenchmark.p
% 0.15/0.32 Conjecture not found
% 0.15/0.32 Start search
% 0.15/0.32 nb_step : 1 - limit : 15
% 0.15/0.32 Launch Gotab with destructive = true
% 2.26/0.72 % SZS output start Proof for theBenchmark.p
% 2.26/0.73 [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, X34_34, Y35_35] : (((subset(X34_34, A33_33) & subset(Y35_35, A33_33)) <=> subset(union(X34_34, Y35_35), A33_33))))
% 2.26/0.73 -> [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, X34_34, Y35_35] : (((subset(X34_34, A33_33) & subset(Y35_35, A33_33)) <=> subset(union(X34_34, Y35_35), A33_33)))
% 2.26/0.73
% 2.26/0.73 [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))))
% 2.26/0.73 -> [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)))
% 2.26/0.73
% 2.26/0.73 [2] DELTA_NOT_FORALL : ~! [A33_33, X34_34, Y35_35] : (((subset(X34_34, A33_33) & subset(Y35_35, A33_33)) <=> subset(union(X34_34, Y35_35), A33_33)))
% 2.26/0.73 -> [3] ~((subset(skolem_X3434, skolem_A3333) & subset(skolem_Y3535, skolem_A3333)) <=> subset(union(skolem_X3434, skolem_Y3535), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [3] BETA_NOT_EQUIV : ~((subset(skolem_X3434, skolem_A3333) & subset(skolem_Y3535, skolem_A3333)) <=> subset(union(skolem_X3434, skolem_Y3535), skolem_A3333))
% 2.26/0.73 -> [4] ~(subset(skolem_X3434, skolem_A3333) & subset(skolem_Y3535, skolem_A3333)), subset(union(skolem_X3434, skolem_Y3535), skolem_A3333)
% 2.26/0.73 -> [5] (subset(skolem_X3434, skolem_A3333) & subset(skolem_Y3535, skolem_A3333)), ~subset(union(skolem_X3434, skolem_Y3535), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [4] Rewrite : subset(union(skolem_X3434, skolem_Y3535), skolem_A3333)
% 2.26/0.73 -> [7] ! [X7_7] : ((member(X7_7, union(skolem_X3434, skolem_Y3535)) => member(X7_7, skolem_A3333)))
% 2.26/0.73
% 2.26/0.73 [7] BETA_NOT_AND : ~(subset(skolem_X3434, skolem_A3333) & subset(skolem_Y3535, skolem_A3333))
% 2.26/0.73 -> [9] ~subset(skolem_X3434, skolem_A3333)
% 2.26/0.73 -> [10] ~subset(skolem_Y3535, skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [10] Rewrite : ~subset(skolem_Y3535, skolem_A3333)
% 2.26/0.73 -> [13] ~(member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_Y3535) => member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [13] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_Y3535) => member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [15] member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_Y3535), ~member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [15] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 2.26/0.73 -> [22] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 2.26/0.73
% 2.26/0.73 [22] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 2.26/0.73 -> [25] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 2.26/0.73 -> [26] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 2.26/0.73
% 2.26/0.73 [25] Rewrite : ~subset(X10_1_0, X10_1_0)
% 2.26/0.73 -> [29] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 2.26/0.73
% 2.26/0.73 [29] 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))
% 2.26/0.73 -> [30] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 2.26/0.73
% 2.26/0.73 [30] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 2.26/0.73
% 2.26/0.73 [26] Rewrite : subset(X10_1_0, X10_1_0)
% 2.26/0.73 -> [31] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 2.26/0.73
% 2.26/0.73 [31] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 2.26/0.73 -> [33] ~member(X18_0_1, empty_set)
% 2.26/0.73
% 2.26/0.73 [33] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 2.26/0.73 -> [41] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 2.26/0.73
% 2.26/0.73 [41] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 2.26/0.73 -> [42] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 2.26/0.73 -> [43] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 2.26/0.73
% 2.26/0.73 [42] CLOSURE : ~=(A23_0_2, A23_0_2)
% 2.26/0.73
% 2.26/0.73 [43] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, union(skolem_X3434, skolem_Y3535)) => member(X7_7, skolem_A3333)))
% 2.26/0.73 -> [61] (member(skolem_X77(skolem_Y3535, skolem_A3333), union(skolem_X3434, skolem_Y3535)) => member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [61] BETA_IMPLY : (member(skolem_X77(skolem_Y3535, skolem_A3333), union(skolem_X3434, skolem_Y3535)) => member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [62] ~member(skolem_X77(skolem_Y3535, skolem_A3333), union(skolem_X3434, skolem_Y3535))
% 2.26/0.73 -> [63] member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [63] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [62] Rewrite : ~member(skolem_X77(skolem_Y3535, skolem_A3333), union(skolem_X3434, skolem_Y3535))
% 2.26/0.73 -> [67] ~(member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_X3434) | member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_Y3535))
% 2.26/0.73
% 2.26/0.73 [67] ALPHA_NOT_OR : ~(member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_X3434) | member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_Y3535))
% 2.26/0.73 -> [68] ~member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_X3434), ~member(skolem_X77(skolem_Y3535, skolem_A3333), skolem_Y3535)
% 2.26/0.73
% 2.26/0.73 [68] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [9] Rewrite : ~subset(skolem_X3434, skolem_A3333)
% 2.26/0.73 -> [12] ~(member(skolem_X77(skolem_X3434, skolem_A3333), skolem_X3434) => member(skolem_X77(skolem_X3434, skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [12] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_X3434, skolem_A3333), skolem_X3434) => member(skolem_X77(skolem_X3434, skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [14] member(skolem_X77(skolem_X3434, skolem_A3333), skolem_X3434), ~member(skolem_X77(skolem_X3434, skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [14] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 2.26/0.73 -> [18] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 2.26/0.73
% 2.26/0.73 [18] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 2.26/0.73 -> [20] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 2.26/0.73 -> [21] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 2.26/0.73
% 2.26/0.73 [20] Rewrite : ~subset(X10_0_0, X10_0_0)
% 2.26/0.73 -> [27] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 2.26/0.73
% 2.26/0.73 [27] 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))
% 2.26/0.73 -> [28] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 2.26/0.73
% 2.26/0.73 [28] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 2.26/0.73
% 2.26/0.73 [21] Rewrite : subset(X10_0_0, X10_0_0)
% 2.26/0.73 -> [32] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 2.26/0.73
% 2.26/0.73 [32] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 2.26/0.73 -> [34] ~member(X18_1_1, empty_set)
% 2.26/0.73
% 2.26/0.73 [34] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 2.26/0.73 -> [44] (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 2.26/0.73
% 2.26/0.73 [44] BETA_EQUIV : (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 2.26/0.73 -> [46] ~member(A23_1_2, singleton(A23_1_2)), ~=(A23_1_2, A23_1_2)
% 2.26/0.73 -> [47] member(A23_1_2, singleton(A23_1_2)), =(A23_1_2, A23_1_2)
% 2.26/0.73
% 2.26/0.73 [46] CLOSURE : ~=(A23_1_2, A23_1_2)
% 2.26/0.73
% 2.26/0.73 [47] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, union(skolem_X3434, skolem_Y3535)) => member(X7_7, skolem_A3333)))
% 2.26/0.73 -> [64] (member(skolem_X77(skolem_X3434, skolem_A3333), union(skolem_X3434, skolem_Y3535)) => member(skolem_X77(skolem_X3434, skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [64] BETA_IMPLY : (member(skolem_X77(skolem_X3434, skolem_A3333), union(skolem_X3434, skolem_Y3535)) => member(skolem_X77(skolem_X3434, skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [65] ~member(skolem_X77(skolem_X3434, skolem_A3333), union(skolem_X3434, skolem_Y3535))
% 2.26/0.73 -> [66] member(skolem_X77(skolem_X3434, skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [66] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [65] Rewrite : ~member(skolem_X77(skolem_X3434, skolem_A3333), union(skolem_X3434, skolem_Y3535))
% 2.26/0.73 -> [70] ~(member(skolem_X77(skolem_X3434, skolem_A3333), skolem_X3434) | member(skolem_X77(skolem_X3434, skolem_A3333), skolem_Y3535))
% 2.26/0.73
% 2.26/0.73 [70] ALPHA_NOT_OR : ~(member(skolem_X77(skolem_X3434, skolem_A3333), skolem_X3434) | member(skolem_X77(skolem_X3434, skolem_A3333), skolem_Y3535))
% 2.26/0.73 -> [73] ~member(skolem_X77(skolem_X3434, skolem_A3333), skolem_X3434), ~member(skolem_X77(skolem_X3434, skolem_A3333), skolem_Y3535)
% 2.26/0.73
% 2.26/0.73 [73] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [5] Rewrite : ~subset(union(skolem_X3434, skolem_Y3535), skolem_A3333)
% 2.26/0.73 -> [6] ~(member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), union(skolem_X3434, skolem_Y3535)) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [6] ALPHA_AND : (subset(skolem_X3434, skolem_A3333) & subset(skolem_Y3535, skolem_A3333))
% 2.26/0.73 -> [8] subset(skolem_X3434, skolem_A3333), subset(skolem_Y3535, skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [8] Rewrite : subset(skolem_X3434, skolem_A3333)
% 2.26/0.73 -> [11] ! [X7_7] : ((member(X7_7, skolem_X3434) => member(X7_7, skolem_A3333)))
% 2.26/0.73
% 2.26/0.73 [11] Rewrite : subset(skolem_Y3535, skolem_A3333)
% 2.26/0.73 -> [16] ! [X7_7] : ((member(X7_7, skolem_Y3535) => member(X7_7, skolem_A3333)))
% 2.26/0.73
% 2.26/0.73 [16] ALPHA_NOT_IMPLY : ~(member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), union(skolem_X3434, skolem_Y3535)) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [17] member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), union(skolem_X3434, skolem_Y3535)), ~member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [17] Rewrite : member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), union(skolem_X3434, skolem_Y3535))
% 2.26/0.73 -> [19] (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434) | member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_Y3535))
% 2.26/0.73
% 2.26/0.73 [19] BETA_OR : (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434) | member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_Y3535))
% 2.26/0.73 -> [23] member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434)
% 2.26/0.73 -> [24] member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_Y3535)
% 2.26/0.73
% 2.26/0.73 [23] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 2.26/0.73 -> [36] (member(X10_3_0, power_set(X10_3_0)) <=> subset(X10_3_0, X10_3_0))
% 2.26/0.73
% 2.26/0.73 [36] BETA_EQUIV : (member(X10_3_0, power_set(X10_3_0)) <=> subset(X10_3_0, X10_3_0))
% 2.26/0.73 -> [39] ~member(X10_3_0, power_set(X10_3_0)), ~subset(X10_3_0, X10_3_0)
% 2.26/0.73 -> [40] member(X10_3_0, power_set(X10_3_0)), subset(X10_3_0, X10_3_0)
% 2.26/0.73
% 2.26/0.73 [39] Rewrite : ~subset(X10_3_0, X10_3_0)
% 2.26/0.73 -> [48] ~(member(skolem_X77(X10_3_0, X10_3_0), X10_3_0) => member(skolem_X77(X10_3_0, X10_3_0), X10_3_0))
% 2.26/0.73
% 2.26/0.73 [48] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_3_0, X10_3_0), X10_3_0) => member(skolem_X77(X10_3_0, X10_3_0), X10_3_0))
% 2.26/0.73 -> [50] member(skolem_X77(X10_3_0, X10_3_0), X10_3_0), ~member(skolem_X77(X10_3_0, X10_3_0), X10_3_0)
% 2.26/0.73
% 2.26/0.73 [50] CLOSURE : ~member(skolem_X77(X10_3_0, X10_3_0), X10_3_0)
% 2.26/0.73
% 2.26/0.73 [40] Rewrite : subset(X10_3_0, X10_3_0)
% 2.26/0.73 -> [53] ! [X7_7] : ((member(X7_7, X10_3_0) => member(X7_7, X10_3_0)))
% 2.26/0.73
% 2.26/0.73 [53] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 2.26/0.73 -> [54] ~member(X18_3_1, empty_set)
% 2.26/0.73
% 2.26/0.73 [54] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 2.26/0.73 -> [58] (member(A23_3_2, singleton(A23_3_2)) <=> =(A23_3_2, A23_3_2))
% 2.26/0.73
% 2.26/0.73 [58] BETA_EQUIV : (member(A23_3_2, singleton(A23_3_2)) <=> =(A23_3_2, A23_3_2))
% 2.26/0.73 -> [59] ~member(A23_3_2, singleton(A23_3_2)), ~=(A23_3_2, A23_3_2)
% 2.26/0.73 -> [60] member(A23_3_2, singleton(A23_3_2)), =(A23_3_2, A23_3_2)
% 2.26/0.73
% 2.26/0.73 [59] CLOSURE : ~=(A23_3_2, A23_3_2)
% 2.26/0.73
% 2.26/0.73 [60] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_X3434) => member(X7_7, skolem_A3333)))
% 2.26/0.73 -> [74] (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [74] BETA_IMPLY : (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [75] ~member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434)
% 2.26/0.73 -> [76] member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [76] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [75] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [24] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 2.26/0.73 -> [35] (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 2.26/0.73
% 2.26/0.73 [35] BETA_EQUIV : (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 2.26/0.73 -> [37] ~member(X10_2_0, power_set(X10_2_0)), ~subset(X10_2_0, X10_2_0)
% 2.26/0.73 -> [38] member(X10_2_0, power_set(X10_2_0)), subset(X10_2_0, X10_2_0)
% 2.26/0.73
% 2.26/0.73 [37] Rewrite : ~subset(X10_2_0, X10_2_0)
% 2.26/0.73 -> [45] ~(member(skolem_X77(X10_2_0, X10_2_0), X10_2_0) => member(skolem_X77(X10_2_0, X10_2_0), X10_2_0))
% 2.26/0.73
% 2.26/0.73 [45] 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))
% 2.26/0.73 -> [49] member(skolem_X77(X10_2_0, X10_2_0), X10_2_0), ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 2.26/0.73
% 2.26/0.73 [49] CLOSURE : ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 2.26/0.73
% 2.26/0.73 [38] Rewrite : subset(X10_2_0, X10_2_0)
% 2.26/0.73 -> [51] ! [X7_7] : ((member(X7_7, X10_2_0) => member(X7_7, X10_2_0)))
% 2.26/0.73
% 2.26/0.73 [51] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 2.26/0.73 -> [52] ~member(X18_2_1, empty_set)
% 2.26/0.73
% 2.26/0.73 [52] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 2.26/0.73 -> [55] (member(A23_2_2, singleton(A23_2_2)) <=> =(A23_2_2, A23_2_2))
% 2.26/0.73
% 2.26/0.73 [55] BETA_EQUIV : (member(A23_2_2, singleton(A23_2_2)) <=> =(A23_2_2, A23_2_2))
% 2.26/0.73 -> [56] ~member(A23_2_2, singleton(A23_2_2)), ~=(A23_2_2, A23_2_2)
% 2.26/0.73 -> [57] member(A23_2_2, singleton(A23_2_2)), =(A23_2_2, A23_2_2)
% 2.26/0.73
% 2.26/0.73 [56] CLOSURE : ~=(A23_2_2, A23_2_2)
% 2.26/0.73
% 2.26/0.73 [57] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_X3434) => member(X7_7, skolem_A3333)))
% 2.26/0.73 -> [69] (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [69] BETA_IMPLY : (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [71] ~member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_X3434)
% 2.26/0.73 -> [72] member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [72] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [71] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_Y3535) => member(X7_7, skolem_A3333)))
% 2.26/0.73 -> [77] (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_Y3535) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73
% 2.26/0.73 [77] BETA_IMPLY : (member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_Y3535) => member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333))
% 2.26/0.73 -> [78] ~member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_Y3535)
% 2.26/0.73 -> [79] member(skolem_X77(union(skolem_X3434, skolem_Y3535), skolem_A3333), skolem_A3333)
% 2.26/0.73
% 2.26/0.73 [78] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 [79] CLOSURE : =
% 2.26/0.73
% 2.26/0.73 % SZS output end Proof for theBenchmark.p
% 2.26/0.73 [0.413333s][1][Res] 1076 goroutines created
% 2.26/0.73 ==== Result ====
% 2.26/0.73 [0.413368s][1][Res] VALID
% 2.26/0.73 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------