TSTP Solution File: SET688+4 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET688+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n029.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 04:17:09 EDT 2022
% Result : Theorem 5.94s 1.32s
% Output : Proof 5.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET688+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n029.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 07:31:15 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.34 [DMT] DMT loaded with preskolemization
% 0.19/0.34 [EQ] equality loaded.
% 0.19/0.34 [0.000058s][1][MAIN] Problem : theBenchmark.p
% 0.19/0.34 Conjecture not found
% 0.19/0.34 Start search
% 0.19/0.34 nb_step : 1 - limit : 15
% 0.19/0.34 Launch Gotab with destructive = true
% 5.94/1.32 % SZS output start Proof for theBenchmark.p
% 5.94/1.32 [0] ALPHA_AND : ((! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))) & ! [X19_19] : (~member(X19_19, empty_set)) & ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))) & ~! [A34_34, B35_35, C36_36] : (((((subset(A34_34, B35_35) & ~equal_set(A34_34, B35_35)) & subset(B35_35, C36_36)) & ~equal_set(B35_35, C36_36)) => ~equal_set(A34_34, C36_36))))
% 5.94/1.32 -> [1] (! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))) & ! [X19_19] : (~member(X19_19, empty_set)) & ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))), ~! [A34_34, B35_35, C36_36] : (((((subset(A34_34, B35_35) & ~equal_set(A34_34, B35_35)) & subset(B35_35, C36_36)) & ~equal_set(B35_35, C36_36)) => ~equal_set(A34_34, C36_36)))
% 5.94/1.32
% 5.94/1.32 [1] ALPHA_AND : (! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))) & ! [X19_19] : (~member(X19_19, empty_set)) & ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24))))
% 5.94/1.32 -> [2] ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12))), ! [X19_19] : (~member(X19_19, empty_set)), ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 5.94/1.32
% 5.94/1.32 [2] DELTA_NOT_FORALL : ~! [A34_34, B35_35, C36_36] : (((((subset(A34_34, B35_35) & ~equal_set(A34_34, B35_35)) & subset(B35_35, C36_36)) & ~equal_set(B35_35, C36_36)) => ~equal_set(A34_34, C36_36)))
% 5.94/1.32 -> [3] ~((((subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535)) & subset(skolem_B3535, skolem_C3636)) & ~equal_set(skolem_B3535, skolem_C3636)) => ~equal_set(skolem_A3434, skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [3] ALPHA_NOT_IMPLY : ~((((subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535)) & subset(skolem_B3535, skolem_C3636)) & ~equal_set(skolem_B3535, skolem_C3636)) => ~equal_set(skolem_A3434, skolem_C3636))
% 5.94/1.32 -> [4] (((subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535)) & subset(skolem_B3535, skolem_C3636)) & ~equal_set(skolem_B3535, skolem_C3636)), ~~equal_set(skolem_A3434, skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [4] ALPHA_AND : (((subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535)) & subset(skolem_B3535, skolem_C3636)) & ~equal_set(skolem_B3535, skolem_C3636))
% 5.94/1.32 -> [5] ((subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535)) & subset(skolem_B3535, skolem_C3636)), ~equal_set(skolem_B3535, skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [5] Rewrite : ~equal_set(skolem_B3535, skolem_C3636)
% 5.94/1.32 -> [6] ~(subset(skolem_B3535, skolem_C3636) & subset(skolem_C3636, skolem_B3535))
% 5.94/1.32
% 5.94/1.32 [6] ALPHA_NOT_NOT : ~~equal_set(skolem_A3434, skolem_C3636)
% 5.94/1.32 -> [7] equal_set(skolem_A3434, skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [7] Rewrite : equal_set(skolem_A3434, skolem_C3636)
% 5.94/1.32 -> [8] (subset(skolem_A3434, skolem_C3636) & subset(skolem_C3636, skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [8] ALPHA_AND : ((subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535)) & subset(skolem_B3535, skolem_C3636))
% 5.94/1.32 -> [9] (subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535)), subset(skolem_B3535, skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [9] Rewrite : subset(skolem_B3535, skolem_C3636)
% 5.94/1.32 -> [10] ! [X8_8] : ((member(X8_8, skolem_B3535) => member(X8_8, skolem_C3636)))
% 5.94/1.32
% 5.94/1.32 [10] ALPHA_AND : (subset(skolem_A3434, skolem_C3636) & subset(skolem_C3636, skolem_A3434))
% 5.94/1.32 -> [11] subset(skolem_A3434, skolem_C3636), subset(skolem_C3636, skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [11] Rewrite : subset(skolem_A3434, skolem_C3636)
% 5.94/1.32 -> [12] ! [X8_8] : ((member(X8_8, skolem_A3434) => member(X8_8, skolem_C3636)))
% 5.94/1.32
% 5.94/1.32 [12] Rewrite : subset(skolem_C3636, skolem_A3434)
% 5.94/1.32 -> [13] ! [X8_8] : ((member(X8_8, skolem_C3636) => member(X8_8, skolem_A3434)))
% 5.94/1.32
% 5.94/1.32 [13] ALPHA_AND : (subset(skolem_A3434, skolem_B3535) & ~equal_set(skolem_A3434, skolem_B3535))
% 5.94/1.32 -> [14] subset(skolem_A3434, skolem_B3535), ~equal_set(skolem_A3434, skolem_B3535)
% 5.94/1.32
% 5.94/1.32 [14] Rewrite : subset(skolem_A3434, skolem_B3535)
% 5.94/1.32 -> [15] ! [X8_8] : ((member(X8_8, skolem_A3434) => member(X8_8, skolem_B3535)))
% 5.94/1.32
% 5.94/1.32 [15] Rewrite : ~equal_set(skolem_A3434, skolem_B3535)
% 5.94/1.32 -> [16] ~(subset(skolem_A3434, skolem_B3535) & subset(skolem_B3535, skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [16] BETA_NOT_AND : ~(subset(skolem_B3535, skolem_C3636) & subset(skolem_C3636, skolem_B3535))
% 5.94/1.32 -> [17] ~subset(skolem_B3535, skolem_C3636)
% 5.94/1.32 -> [18] ~subset(skolem_C3636, skolem_B3535)
% 5.94/1.32
% 5.94/1.32 [17] Rewrite : ~subset(skolem_B3535, skolem_C3636)
% 5.94/1.32 -> [20] ~(member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [20] ALPHA_NOT_IMPLY : ~(member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636))
% 5.94/1.32 -> [22] member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535), ~member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [22] BETA_NOT_AND : ~(subset(skolem_A3434, skolem_B3535) & subset(skolem_B3535, skolem_A3434))
% 5.94/1.32 -> [25] ~subset(skolem_A3434, skolem_B3535)
% 5.94/1.32 -> [26] ~subset(skolem_B3535, skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [25] Rewrite : ~subset(skolem_A3434, skolem_B3535)
% 5.94/1.32 -> [28] ~(member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32
% 5.94/1.32 [28] ALPHA_NOT_IMPLY : ~(member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32 -> [32] member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434), ~member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535)
% 5.94/1.32
% 5.94/1.32 [32] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 5.94/1.32 -> [35] (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 5.94/1.32
% 5.94/1.32 [35] BETA_EQUIV : (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 5.94/1.32 -> [36] ~member(X11_0_0, power_set(X11_0_0)), ~subset(X11_0_0, X11_0_0)
% 5.94/1.32 -> [37] member(X11_0_0, power_set(X11_0_0)), subset(X11_0_0, X11_0_0)
% 5.94/1.32
% 5.94/1.32 [36] Rewrite : ~subset(X11_0_0, X11_0_0)
% 5.94/1.32 -> [47] ~(member(skolem_X88(X11_0_0, X11_0_0), X11_0_0) => member(skolem_X88(X11_0_0, X11_0_0), X11_0_0))
% 5.94/1.32
% 5.94/1.32 [47] ALPHA_NOT_IMPLY : ~(member(skolem_X88(X11_0_0, X11_0_0), X11_0_0) => member(skolem_X88(X11_0_0, X11_0_0), X11_0_0))
% 5.94/1.32 -> [49] member(skolem_X88(X11_0_0, X11_0_0), X11_0_0), ~member(skolem_X88(X11_0_0, X11_0_0), X11_0_0)
% 5.94/1.32
% 5.94/1.32 [49] CLOSURE : ~member(skolem_X88(X11_0_0, X11_0_0), X11_0_0)
% 5.94/1.32
% 5.94/1.32 [37] Rewrite : subset(X11_0_0, X11_0_0)
% 5.94/1.32 -> [51] ! [X8_8] : ((member(X8_8, X11_0_0) => member(X8_8, X11_0_0)))
% 5.94/1.32
% 5.94/1.32 [51] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 5.94/1.32 -> [54] ~member(X19_0_1, empty_set)
% 5.94/1.32
% 5.94/1.32 [54] GAMMA_FORALL : ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 5.94/1.32 -> [66] (member(A24_1_2, singleton(A24_1_2)) <=> =(A24_1_2, A24_1_2))
% 5.94/1.32
% 5.94/1.32 [66] BETA_EQUIV : (member(A24_1_2, singleton(A24_1_2)) <=> =(A24_1_2, A24_1_2))
% 5.94/1.32 -> [67] ~member(A24_1_2, singleton(A24_1_2)), ~=(A24_1_2, A24_1_2)
% 5.94/1.32 -> [68] member(A24_1_2, singleton(A24_1_2)), =(A24_1_2, A24_1_2)
% 5.94/1.32
% 5.94/1.32 [67] CLOSURE : ~=(A24_1_2, A24_1_2)
% 5.94/1.32
% 5.94/1.32 [68] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_B3535) => member(X8_8, skolem_C3636)))
% 5.94/1.32 -> [81] (member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [81] BETA_IMPLY : (member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636))
% 5.94/1.32 -> [82] ~member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535)
% 5.94/1.32 -> [83] member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [83] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [82] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [26] Rewrite : ~subset(skolem_B3535, skolem_A3434)
% 5.94/1.32 -> [29] ~(member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [29] ALPHA_NOT_IMPLY : ~(member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32 -> [33] member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535), ~member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [33] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 5.94/1.32 -> [39] (member(X11_2_0, power_set(X11_2_0)) <=> subset(X11_2_0, X11_2_0))
% 5.94/1.32
% 5.94/1.32 [39] BETA_EQUIV : (member(X11_2_0, power_set(X11_2_0)) <=> subset(X11_2_0, X11_2_0))
% 5.94/1.32 -> [43] ~member(X11_2_0, power_set(X11_2_0)), ~subset(X11_2_0, X11_2_0)
% 5.94/1.32 -> [44] member(X11_2_0, power_set(X11_2_0)), subset(X11_2_0, X11_2_0)
% 5.94/1.32
% 5.94/1.32 [43] Rewrite : ~subset(X11_2_0, X11_2_0)
% 5.94/1.32 -> [48] ~(member(skolem_X88(X11_2_0, X11_2_0), X11_2_0) => member(skolem_X88(X11_2_0, X11_2_0), X11_2_0))
% 5.94/1.32
% 5.94/1.32 [48] ALPHA_NOT_IMPLY : ~(member(skolem_X88(X11_2_0, X11_2_0), X11_2_0) => member(skolem_X88(X11_2_0, X11_2_0), X11_2_0))
% 5.94/1.32 -> [50] member(skolem_X88(X11_2_0, X11_2_0), X11_2_0), ~member(skolem_X88(X11_2_0, X11_2_0), X11_2_0)
% 5.94/1.32
% 5.94/1.32 [50] CLOSURE : ~member(skolem_X88(X11_2_0, X11_2_0), X11_2_0)
% 5.94/1.32
% 5.94/1.32 [44] Rewrite : subset(X11_2_0, X11_2_0)
% 5.94/1.32 -> [60] ! [X8_8] : ((member(X8_8, X11_2_0) => member(X8_8, X11_2_0)))
% 5.94/1.32
% 5.94/1.32 [60] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 5.94/1.32 -> [65] ~member(X19_3_1, empty_set)
% 5.94/1.32
% 5.94/1.32 [65] GAMMA_FORALL : ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 5.94/1.32 -> [72] (member(A24_3_2, singleton(A24_3_2)) <=> =(A24_3_2, A24_3_2))
% 5.94/1.32
% 5.94/1.32 [72] BETA_EQUIV : (member(A24_3_2, singleton(A24_3_2)) <=> =(A24_3_2, A24_3_2))
% 5.94/1.32 -> [73] ~member(A24_3_2, singleton(A24_3_2)), ~=(A24_3_2, A24_3_2)
% 5.94/1.32 -> [74] member(A24_3_2, singleton(A24_3_2)), =(A24_3_2, A24_3_2)
% 5.94/1.32
% 5.94/1.32 [73] CLOSURE : ~=(A24_3_2, A24_3_2)
% 5.94/1.32
% 5.94/1.32 [74] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_B3535) => member(X8_8, skolem_C3636)))
% 5.94/1.32 -> [84] (member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [84] BETA_IMPLY : (member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636))
% 5.94/1.32 -> [85] ~member(skolem_X88(skolem_B3535, skolem_C3636), skolem_B3535)
% 5.94/1.32 -> [86] member(skolem_X88(skolem_B3535, skolem_C3636), skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [86] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [85] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [18] Rewrite : ~subset(skolem_C3636, skolem_B3535)
% 5.94/1.32 -> [19] ~(member(skolem_X88(skolem_C3636, skolem_B3535), skolem_C3636) => member(skolem_X88(skolem_C3636, skolem_B3535), skolem_B3535))
% 5.94/1.32
% 5.94/1.32 [19] ALPHA_NOT_IMPLY : ~(member(skolem_X88(skolem_C3636, skolem_B3535), skolem_C3636) => member(skolem_X88(skolem_C3636, skolem_B3535), skolem_B3535))
% 5.94/1.32 -> [21] member(skolem_X88(skolem_C3636, skolem_B3535), skolem_C3636), ~member(skolem_X88(skolem_C3636, skolem_B3535), skolem_B3535)
% 5.94/1.32
% 5.94/1.32 [21] BETA_NOT_AND : ~(subset(skolem_A3434, skolem_B3535) & subset(skolem_B3535, skolem_A3434))
% 5.94/1.32 -> [23] ~subset(skolem_A3434, skolem_B3535)
% 5.94/1.32 -> [24] ~subset(skolem_B3535, skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [24] Rewrite : ~subset(skolem_B3535, skolem_A3434)
% 5.94/1.32 -> [27] ~(member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [27] ALPHA_NOT_IMPLY : ~(member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32 -> [30] member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535), ~member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [30] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 5.94/1.32 -> [38] (member(X11_1_0, power_set(X11_1_0)) <=> subset(X11_1_0, X11_1_0))
% 5.94/1.32
% 5.94/1.32 [38] BETA_EQUIV : (member(X11_1_0, power_set(X11_1_0)) <=> subset(X11_1_0, X11_1_0))
% 5.94/1.32 -> [41] ~member(X11_1_0, power_set(X11_1_0)), ~subset(X11_1_0, X11_1_0)
% 5.94/1.32 -> [42] member(X11_1_0, power_set(X11_1_0)), subset(X11_1_0, X11_1_0)
% 5.94/1.32
% 5.94/1.32 [41] Rewrite : ~subset(X11_1_0, X11_1_0)
% 5.94/1.32 -> [57] ~(member(skolem_X88(X11_1_0, X11_1_0), X11_1_0) => member(skolem_X88(X11_1_0, X11_1_0), X11_1_0))
% 5.94/1.32
% 5.94/1.32 [57] ALPHA_NOT_IMPLY : ~(member(skolem_X88(X11_1_0, X11_1_0), X11_1_0) => member(skolem_X88(X11_1_0, X11_1_0), X11_1_0))
% 5.94/1.32 -> [58] member(skolem_X88(X11_1_0, X11_1_0), X11_1_0), ~member(skolem_X88(X11_1_0, X11_1_0), X11_1_0)
% 5.94/1.32
% 5.94/1.32 [58] CLOSURE : ~member(skolem_X88(X11_1_0, X11_1_0), X11_1_0)
% 5.94/1.32
% 5.94/1.32 [42] Rewrite : subset(X11_1_0, X11_1_0)
% 5.94/1.32 -> [52] ! [X8_8] : ((member(X8_8, X11_1_0) => member(X8_8, X11_1_0)))
% 5.94/1.32
% 5.94/1.32 [52] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 5.94/1.32 -> [55] ~member(X19_1_1, empty_set)
% 5.94/1.32
% 5.94/1.32 [55] GAMMA_FORALL : ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 5.94/1.32 -> [62] (member(A24_0_2, singleton(A24_0_2)) <=> =(A24_0_2, A24_0_2))
% 5.94/1.32
% 5.94/1.32 [62] BETA_EQUIV : (member(A24_0_2, singleton(A24_0_2)) <=> =(A24_0_2, A24_0_2))
% 5.94/1.32 -> [63] ~member(A24_0_2, singleton(A24_0_2)), ~=(A24_0_2, A24_0_2)
% 5.94/1.32 -> [64] member(A24_0_2, singleton(A24_0_2)), =(A24_0_2, A24_0_2)
% 5.94/1.32
% 5.94/1.32 [63] CLOSURE : ~=(A24_0_2, A24_0_2)
% 5.94/1.32
% 5.94/1.32 [64] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_B3535) => member(X8_8, skolem_C3636)))
% 5.94/1.32 -> [78] (member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [78] BETA_IMPLY : (member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636))
% 5.94/1.32 -> [79] ~member(skolem_X88(skolem_B3535, skolem_A3434), skolem_B3535)
% 5.94/1.32 -> [80] member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [79] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [80] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_A3434) => member(X8_8, skolem_C3636)))
% 5.94/1.32 -> [90] (member(X8_5_4, skolem_A3434) => member(X8_5_4, skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [90] BETA_IMPLY : (member(X8_5_4, skolem_A3434) => member(X8_5_4, skolem_C3636))
% 5.94/1.32 -> [91] ~member(X8_5_4, skolem_A3434)
% 5.94/1.32 -> [92] member(X8_5_4, skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [92] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_C3636) => member(X8_8, skolem_A3434)))
% 5.94/1.32 -> [99] (member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [99] BETA_IMPLY : (member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32 -> [100] ~member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636)
% 5.94/1.32 -> [101] member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [101] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [100] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [91] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_C3636) => member(X8_8, skolem_A3434)))
% 5.94/1.32 -> [102] (member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [102] BETA_IMPLY : (member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636) => member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434))
% 5.94/1.32 -> [103] ~member(skolem_X88(skolem_B3535, skolem_A3434), skolem_C3636)
% 5.94/1.32 -> [104] member(skolem_X88(skolem_B3535, skolem_A3434), skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [104] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [103] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [23] Rewrite : ~subset(skolem_A3434, skolem_B3535)
% 5.94/1.32 -> [31] ~(member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32
% 5.94/1.32 [31] ALPHA_NOT_IMPLY : ~(member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32 -> [34] member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434), ~member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535)
% 5.94/1.32
% 5.94/1.32 [34] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 5.94/1.32 -> [40] (member(X11_3_0, power_set(X11_3_0)) <=> subset(X11_3_0, X11_3_0))
% 5.94/1.32
% 5.94/1.32 [40] BETA_EQUIV : (member(X11_3_0, power_set(X11_3_0)) <=> subset(X11_3_0, X11_3_0))
% 5.94/1.32 -> [45] ~member(X11_3_0, power_set(X11_3_0)), ~subset(X11_3_0, X11_3_0)
% 5.94/1.32 -> [46] member(X11_3_0, power_set(X11_3_0)), subset(X11_3_0, X11_3_0)
% 5.94/1.32
% 5.94/1.32 [45] Rewrite : ~subset(X11_3_0, X11_3_0)
% 5.94/1.32 -> [53] ~(member(skolem_X88(X11_3_0, X11_3_0), X11_3_0) => member(skolem_X88(X11_3_0, X11_3_0), X11_3_0))
% 5.94/1.32
% 5.94/1.32 [53] ALPHA_NOT_IMPLY : ~(member(skolem_X88(X11_3_0, X11_3_0), X11_3_0) => member(skolem_X88(X11_3_0, X11_3_0), X11_3_0))
% 5.94/1.32 -> [56] member(skolem_X88(X11_3_0, X11_3_0), X11_3_0), ~member(skolem_X88(X11_3_0, X11_3_0), X11_3_0)
% 5.94/1.32
% 5.94/1.32 [56] CLOSURE : ~member(skolem_X88(X11_3_0, X11_3_0), X11_3_0)
% 5.94/1.32
% 5.94/1.32 [46] Rewrite : subset(X11_3_0, X11_3_0)
% 5.94/1.32 -> [59] ! [X8_8] : ((member(X8_8, X11_3_0) => member(X8_8, X11_3_0)))
% 5.94/1.32
% 5.94/1.32 [59] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 5.94/1.32 -> [61] ~member(X19_2_1, empty_set)
% 5.94/1.32
% 5.94/1.32 [61] GAMMA_FORALL : ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 5.94/1.32 -> [69] (member(A24_2_2, singleton(A24_2_2)) <=> =(A24_2_2, A24_2_2))
% 5.94/1.32
% 5.94/1.32 [69] BETA_EQUIV : (member(A24_2_2, singleton(A24_2_2)) <=> =(A24_2_2, A24_2_2))
% 5.94/1.32 -> [70] ~member(A24_2_2, singleton(A24_2_2)), ~=(A24_2_2, A24_2_2)
% 5.94/1.32 -> [71] member(A24_2_2, singleton(A24_2_2)), =(A24_2_2, A24_2_2)
% 5.94/1.32
% 5.94/1.32 [70] CLOSURE : ~=(A24_2_2, A24_2_2)
% 5.94/1.32
% 5.94/1.32 [71] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_B3535) => member(X8_8, skolem_C3636)))
% 5.94/1.32 -> [75] (member(X8_0_3, skolem_B3535) => member(X8_0_3, skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [75] BETA_IMPLY : (member(X8_0_3, skolem_B3535) => member(X8_0_3, skolem_C3636))
% 5.94/1.32 -> [76] ~member(X8_0_3, skolem_B3535)
% 5.94/1.32 -> [77] member(X8_0_3, skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [77] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_A3434) => member(X8_8, skolem_C3636)))
% 5.94/1.32 -> [87] (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [87] BETA_IMPLY : (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_C3636))
% 5.94/1.32 -> [88] ~member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434)
% 5.94/1.32 -> [89] member(skolem_X88(skolem_A3434, skolem_B3535), skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [88] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [89] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_C3636) => member(X8_8, skolem_A3434)))
% 5.94/1.32 -> [96] (member(skolem_X88(skolem_C3636, skolem_B3535), skolem_C3636) => member(skolem_X88(skolem_C3636, skolem_B3535), skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [96] BETA_IMPLY : (member(skolem_X88(skolem_C3636, skolem_B3535), skolem_C3636) => member(skolem_X88(skolem_C3636, skolem_B3535), skolem_A3434))
% 5.94/1.32 -> [97] ~member(skolem_X88(skolem_C3636, skolem_B3535), skolem_C3636)
% 5.94/1.32 -> [98] member(skolem_X88(skolem_C3636, skolem_B3535), skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [97] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [98] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_A3434) => member(X8_8, skolem_B3535)))
% 5.94/1.32 -> [108] (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32
% 5.94/1.32 [108] BETA_IMPLY : (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32 -> [109] ~member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434)
% 5.94/1.32 -> [110] member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535)
% 5.94/1.32
% 5.94/1.32 [110] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [109] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [76] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_A3434) => member(X8_8, skolem_C3636)))
% 5.94/1.32 -> [93] (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_C3636))
% 5.94/1.32
% 5.94/1.32 [93] BETA_IMPLY : (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_C3636))
% 5.94/1.32 -> [94] ~member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434)
% 5.94/1.32 -> [95] member(skolem_X88(skolem_A3434, skolem_B3535), skolem_C3636)
% 5.94/1.32
% 5.94/1.32 [94] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [95] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_C3636) => member(X8_8, skolem_A3434)))
% 5.94/1.32 -> [105] (member(X8_10_5, skolem_C3636) => member(X8_10_5, skolem_A3434))
% 5.94/1.32
% 5.94/1.32 [105] BETA_IMPLY : (member(X8_10_5, skolem_C3636) => member(X8_10_5, skolem_A3434))
% 5.94/1.32 -> [106] ~member(X8_10_5, skolem_C3636)
% 5.94/1.32 -> [107] member(X8_10_5, skolem_A3434)
% 5.94/1.32
% 5.94/1.32 [106] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [107] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_A3434) => member(X8_8, skolem_B3535)))
% 5.94/1.32 -> [111] (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32
% 5.94/1.32 [111] BETA_IMPLY : (member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434) => member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535))
% 5.94/1.32 -> [112] ~member(skolem_X88(skolem_A3434, skolem_B3535), skolem_A3434)
% 5.94/1.32 -> [113] member(skolem_X88(skolem_A3434, skolem_B3535), skolem_B3535)
% 5.94/1.32
% 5.94/1.32 [113] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 [112] CLOSURE : =
% 5.94/1.32
% 5.94/1.32 % SZS output end Proof for theBenchmark.p
% 5.94/1.32 [0.980554s][1][Res] 2857 goroutines created
% 5.94/1.32 ==== Result ====
% 5.94/1.32 [0.980587s][1][Res] VALID
% 5.94/1.32 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------