TSTP Solution File: SET698+4 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET698+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n011.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 04:17:11 EDT 2022
% Result : Theorem 13.44s 3.20s
% Output : Proof 13.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET698+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 07:21:13 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 [DMT] DMT loaded with preskolemization
% 0.11/0.33 [EQ] equality loaded.
% 0.11/0.33 [0.000035s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.33 Conjecture not found
% 0.11/0.33 Start search
% 0.11/0.33 nb_step : 1 - limit : 15
% 0.11/0.33 Launch Gotab with destructive = true
% 13.39/3.19 % SZS output start Proof for theBenchmark.p
% 13.44/3.20 [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, B34_34, E35_35] : (((subset(A33_33, E35_35) & subset(B34_34, E35_35)) => (subset(A33_33, B34_34) <=> equal_set(union(difference(E35_35, A33_33), B34_34), E35_35)))))
% 13.44/3.20 -> [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, B34_34, E35_35] : (((subset(A33_33, E35_35) & subset(B34_34, E35_35)) => (subset(A33_33, B34_34) <=> equal_set(union(difference(E35_35, A33_33), B34_34), E35_35))))
% 13.44/3.20
% 13.44/3.20 [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))))
% 13.44/3.20 -> [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)))
% 13.44/3.20
% 13.44/3.20 [2] DELTA_NOT_FORALL : ~! [A33_33, B34_34, E35_35] : (((subset(A33_33, E35_35) & subset(B34_34, E35_35)) => (subset(A33_33, B34_34) <=> equal_set(union(difference(E35_35, A33_33), B34_34), E35_35))))
% 13.44/3.20 -> [3] ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)))
% 13.44/3.20
% 13.44/3.20 [3] ALPHA_NOT_IMPLY : ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)))
% 13.44/3.20 -> [4] (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)), ~(subset(skolem_A3333, skolem_B3434) <=> equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [4] ALPHA_AND : (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535))
% 13.44/3.20 -> [5] subset(skolem_A3333, skolem_E3535), subset(skolem_B3434, skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [5] Rewrite : subset(skolem_A3333, skolem_E3535)
% 13.44/3.20 -> [6] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 13.44/3.20
% 13.44/3.20 [6] Rewrite : subset(skolem_B3434, skolem_E3535)
% 13.44/3.20 -> [7] ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 13.44/3.20
% 13.44/3.20 [7] BETA_NOT_EQUIV : ~(subset(skolem_A3333, skolem_B3434) <=> equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535))
% 13.44/3.20 -> [8] ~subset(skolem_A3333, skolem_B3434), equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [9] subset(skolem_A3333, skolem_B3434), ~equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [9] Rewrite : subset(skolem_A3333, skolem_B3434)
% 13.44/3.20 -> [11] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 13.44/3.20
% 13.44/3.20 [11] Rewrite : ~equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [14] ~(subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535) & subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20
% 13.44/3.20 [14] BETA_NOT_AND : ~(subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535) & subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20 -> [15] ~subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [16] ~subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [15] Rewrite : ~subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [19] ~(member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)) => member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [19] ALPHA_NOT_IMPLY : ~(member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)) => member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535))
% 13.44/3.20 -> [21] member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), ~member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [21] Rewrite : member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [23] (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [23] BETA_OR : (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_B3434))
% 13.44/3.20 -> [27] member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [28] member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [27] Rewrite : member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [33] (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535) & ~member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [33] ALPHA_AND : (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535) & ~member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_A3333))
% 13.44/3.20 -> [34] member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535), ~member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [34] CLOSURE : member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [28] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 13.44/3.20 -> [35] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 13.44/3.20
% 13.44/3.20 [35] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 13.44/3.20 -> [37] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 13.44/3.20 -> [38] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 13.44/3.20
% 13.44/3.20 [37] Rewrite : ~subset(X10_1_0, X10_1_0)
% 13.44/3.20 -> [44] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 13.44/3.20
% 13.44/3.20 [44] 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))
% 13.44/3.20 -> [47] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 13.44/3.20
% 13.44/3.20 [47] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 13.44/3.20
% 13.44/3.20 [38] Rewrite : subset(X10_1_0, X10_1_0)
% 13.44/3.20 -> [45] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 13.44/3.20
% 13.44/3.20 [45] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 13.44/3.20 -> [49] ~member(X18_1_1, empty_set)
% 13.44/3.20
% 13.44/3.20 [49] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 13.44/3.20 -> [55] (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 13.44/3.20
% 13.44/3.20 [55] BETA_EQUIV : (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 13.44/3.20 -> [56] ~member(A23_1_2, singleton(A23_1_2)), ~=(A23_1_2, A23_1_2)
% 13.44/3.20 -> [57] member(A23_1_2, singleton(A23_1_2)), =(A23_1_2, A23_1_2)
% 13.44/3.20
% 13.44/3.20 [56] CLOSURE : ~=(A23_1_2, A23_1_2)
% 13.44/3.20
% 13.44/3.20 [57] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 13.44/3.20 -> [71] (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_A3333) => member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [71] BETA_IMPLY : (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_A3333) => member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535))
% 13.44/3.20 -> [72] ~member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_A3333)
% 13.44/3.20 -> [73] member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [73] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [72] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 13.44/3.20 -> [80] (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_B3434) => member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [80] BETA_IMPLY : (member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_B3434) => member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535))
% 13.44/3.20 -> [81] ~member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_B3434)
% 13.44/3.20 -> [82] member(skolem_X77(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [81] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [82] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [16] Rewrite : ~subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [17] ~(member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20
% 13.44/3.20 [17] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20 -> [20] member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535), ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [20] Rewrite : ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [24] ~(member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [24] ALPHA_NOT_OR : ~(member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434))
% 13.44/3.20 -> [25] ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), difference(skolem_E3535, skolem_A3333)), ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [25] Rewrite : ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [29] ~(member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535) & ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [29] BETA_NOT_AND : ~(member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535) & ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333))
% 13.44/3.20 -> [40] ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535)
% 13.44/3.20 -> [41] ~~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [40] CLOSURE : ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [41] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333)
% 13.44/3.20 -> [42] member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [42] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 13.44/3.20 -> [48] (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 13.44/3.20
% 13.44/3.20 [48] BETA_EQUIV : (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 13.44/3.20 -> [50] ~member(X10_2_0, power_set(X10_2_0)), ~subset(X10_2_0, X10_2_0)
% 13.44/3.20 -> [51] member(X10_2_0, power_set(X10_2_0)), subset(X10_2_0, X10_2_0)
% 13.44/3.20
% 13.44/3.20 [50] Rewrite : ~subset(X10_2_0, X10_2_0)
% 13.44/3.20 -> [58] ~(member(skolem_X77(X10_2_0, X10_2_0), X10_2_0) => member(skolem_X77(X10_2_0, X10_2_0), X10_2_0))
% 13.44/3.20
% 13.44/3.20 [58] 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))
% 13.44/3.20 -> [60] member(skolem_X77(X10_2_0, X10_2_0), X10_2_0), ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 13.44/3.20
% 13.44/3.20 [60] CLOSURE : ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 13.44/3.20
% 13.44/3.20 [51] Rewrite : subset(X10_2_0, X10_2_0)
% 13.44/3.20 -> [59] ! [X7_7] : ((member(X7_7, X10_2_0) => member(X7_7, X10_2_0)))
% 13.44/3.20
% 13.44/3.20 [59] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 13.44/3.20 -> [61] ~member(X18_2_1, empty_set)
% 13.44/3.20
% 13.44/3.20 [61] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 13.44/3.20 -> [62] (member(A23_2_2, singleton(A23_2_2)) <=> =(A23_2_2, A23_2_2))
% 13.44/3.20
% 13.44/3.20 [62] BETA_EQUIV : (member(A23_2_2, singleton(A23_2_2)) <=> =(A23_2_2, A23_2_2))
% 13.44/3.20 -> [63] ~member(A23_2_2, singleton(A23_2_2)), ~=(A23_2_2, A23_2_2)
% 13.44/3.20 -> [64] member(A23_2_2, singleton(A23_2_2)), =(A23_2_2, A23_2_2)
% 13.44/3.20
% 13.44/3.20 [63] CLOSURE : ~=(A23_2_2, A23_2_2)
% 13.44/3.20
% 13.44/3.20 [64] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 13.44/3.20 -> [83] (member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [83] BETA_IMPLY : (member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535))
% 13.44/3.20 -> [84] ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333)
% 13.44/3.20 -> [85] member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [84] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [85] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 13.44/3.20 -> [100] (member(X7_9_4, skolem_B3434) => member(X7_9_4, skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [100] BETA_IMPLY : (member(X7_9_4, skolem_B3434) => member(X7_9_4, skolem_E3535))
% 13.44/3.20 -> [101] ~member(X7_9_4, skolem_B3434)
% 13.44/3.20 -> [102] member(X7_9_4, skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [102] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 13.44/3.20 -> [119] (member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [119] BETA_IMPLY : (member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434))
% 13.44/3.20 -> [120] ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333)
% 13.44/3.20 -> [121] member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [121] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [120] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [101] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 13.44/3.20 -> [122] (member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [122] BETA_IMPLY : (member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434))
% 13.44/3.20 -> [123] ~member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_A3333)
% 13.44/3.20 -> [124] member(skolem_X77(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [124] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [123] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [8] Rewrite : ~subset(skolem_A3333, skolem_B3434)
% 13.44/3.20 -> [10] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [10] Rewrite : equal_set(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [12] (subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535) & subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20
% 13.44/3.20 [12] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20 -> [13] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [13] ALPHA_AND : (subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535) & subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20 -> [18] subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535), subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [18] Rewrite : subset(union(difference(skolem_E3535, skolem_A3333), skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [22] ! [X7_7] : ((member(X7_7, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)) => member(X7_7, skolem_E3535)))
% 13.44/3.20
% 13.44/3.20 [22] Rewrite : subset(skolem_E3535, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [26] ! [X7_7] : ((member(X7_7, skolem_E3535) => member(X7_7, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))))
% 13.44/3.20
% 13.44/3.20 [26] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 13.44/3.20 -> [30] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 13.44/3.20
% 13.44/3.20 [30] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 13.44/3.20 -> [31] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 13.44/3.20 -> [32] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 13.44/3.20
% 13.44/3.20 [31] Rewrite : ~subset(X10_0_0, X10_0_0)
% 13.44/3.20 -> [36] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 13.44/3.20
% 13.44/3.20 [36] 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))
% 13.44/3.20 -> [39] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 13.44/3.20
% 13.44/3.20 [39] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 13.44/3.20
% 13.44/3.20 [32] Rewrite : subset(X10_0_0, X10_0_0)
% 13.44/3.20 -> [43] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 13.44/3.20
% 13.44/3.20 [43] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 13.44/3.20 -> [46] ~member(X18_0_1, empty_set)
% 13.44/3.20
% 13.44/3.20 [46] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 13.44/3.20 -> [52] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 13.44/3.20
% 13.44/3.20 [52] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 13.44/3.20 -> [53] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 13.44/3.20 -> [54] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 13.44/3.20
% 13.44/3.20 [53] CLOSURE : ~=(A23_0_2, A23_0_2)
% 13.44/3.20
% 13.44/3.20 [54] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 13.44/3.20 -> [65] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [65] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 13.44/3.20 -> [66] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20 -> [67] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [66] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [67] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 13.44/3.20 -> [68] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [68] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 13.44/3.20 -> [69] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 13.44/3.20 -> [70] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [70] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)) => member(X7_7, skolem_E3535)))
% 13.44/3.20 -> [74] (member(X7_3_5, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)) => member(X7_3_5, skolem_E3535))
% 13.44/3.20
% 13.44/3.20 [74] BETA_IMPLY : (member(X7_3_5, union(difference(skolem_E3535, skolem_A3333), skolem_B3434)) => member(X7_3_5, skolem_E3535))
% 13.44/3.20 -> [75] ~member(X7_3_5, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [76] member(X7_3_5, skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [75] Rewrite : ~member(X7_3_5, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [86] ~(member(X7_3_5, difference(skolem_E3535, skolem_A3333)) | member(X7_3_5, skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [86] ALPHA_NOT_OR : ~(member(X7_3_5, difference(skolem_E3535, skolem_A3333)) | member(X7_3_5, skolem_B3434))
% 13.44/3.20 -> [87] ~member(X7_3_5, difference(skolem_E3535, skolem_A3333)), ~member(X7_3_5, skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [87] Rewrite : ~member(X7_3_5, difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [99] ~(member(X7_3_5, skolem_E3535) & ~member(X7_3_5, skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [99] BETA_NOT_AND : ~(member(X7_3_5, skolem_E3535) & ~member(X7_3_5, skolem_A3333))
% 13.44/3.20 -> [111] ~member(X7_3_5, skolem_E3535)
% 13.44/3.20 -> [112] ~~member(X7_3_5, skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [112] ALPHA_NOT_NOT : ~~member(X7_3_5, skolem_A3333)
% 13.44/3.20 -> [113] member(X7_3_5, skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [113] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_E3535) => member(X7_7, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))))
% 13.44/3.20 -> [129] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) => member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20
% 13.44/3.20 [129] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) => member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20 -> [130] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [131] member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [131] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [137] (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [137] BETA_OR : (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20 -> [138] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [139] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [139] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [138] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [143] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [143] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20 -> [144] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [144] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [130] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [111] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [88] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) => member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20 -> [147] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [148] member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [147] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [148] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [150] (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [150] BETA_OR : (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20 -> [151] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [152] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [152] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [151] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [153] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [153] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20 -> [154] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [154] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [77] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 13.44/3.20 -> [167] ~member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20 -> [168] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20
% 13.44/3.20 [168] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_E3535) => member(X7_7, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))))
% 13.44/3.20 -> [171] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) => member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20
% 13.44/3.20 [171] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) => member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20 -> [172] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [173] member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [172] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [173] BETA_OR : (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20 -> [183] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [184] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [184] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [183] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [185] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [185] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20 -> [186] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [186] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [167] ALPHA_NOT_OR : ~(member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20 -> [202] ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [202] Rewrite : ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [203] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [203] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20 -> [204] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [205] ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [204] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [205] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20 -> [206] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [206] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_E3535) => member(X7_7, union(difference(skolem_E3535, skolem_A3333), skolem_B3434))))
% 13.44/3.20 -> [207] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) => member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20
% 13.44/3.20 [207] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) => member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434)))
% 13.44/3.20 -> [208] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 13.44/3.20 -> [209] member(skolem_X77(skolem_A3333, skolem_B3434), union(difference(skolem_E3535, skolem_A3333), skolem_B3434))
% 13.44/3.20
% 13.44/3.20 [208] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [209] BETA_OR : (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)) | member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 13.44/3.20 -> [215] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [216] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 13.44/3.20
% 13.44/3.20 [216] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 [215] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 13.44/3.20 -> [217] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20
% 13.44/3.20 [217] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 13.44/3.20 -> [218] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 13.44/3.20
% 13.44/3.20 [218] CLOSURE : =
% 13.44/3.20
% 13.44/3.20 % SZS output end Proof for theBenchmark.p
% 13.44/3.20 [2.864614s][1][Res] 5283 goroutines created
% 13.44/3.20 ==== Result ====
% 13.44/3.20 [2.864660s][1][Res] VALID
% 13.44/3.20 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------