TSTP Solution File: SET690+4 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET690+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 3.74s 0.92s
% Output : Proof 3.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SET690+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 07:31:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 [DMT] DMT loaded with preskolemization
% 0.12/0.35 [EQ] equality loaded.
% 0.12/0.35 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 15
% 0.12/0.35 Launch Gotab with destructive = true
% 3.74/0.92 % SZS output start Proof for theBenchmark.p
% 3.74/0.92 [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] : ((equal_set(union(intersection(A34_34, B35_35), C36_36), intersection(A34_34, union(B35_35, C36_36))) <=> subset(C36_36, A34_34))))
% 3.74/0.92 -> [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] : ((equal_set(union(intersection(A34_34, B35_35), C36_36), intersection(A34_34, union(B35_35, C36_36))) <=> subset(C36_36, A34_34)))
% 3.74/0.92
% 3.74/0.92 [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))))
% 3.74/0.92 -> [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)))
% 3.74/0.92
% 3.74/0.92 [2] DELTA_NOT_FORALL : ~! [A34_34, B35_35, C36_36] : ((equal_set(union(intersection(A34_34, B35_35), C36_36), intersection(A34_34, union(B35_35, C36_36))) <=> subset(C36_36, A34_34)))
% 3.74/0.92 -> [3] ~(equal_set(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) <=> subset(skolem_C3636, skolem_A3434))
% 3.74/0.92
% 3.74/0.92 [3] BETA_NOT_EQUIV : ~(equal_set(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) <=> subset(skolem_C3636, skolem_A3434))
% 3.74/0.92 -> [4] ~equal_set(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), subset(skolem_C3636, skolem_A3434)
% 3.74/0.92 -> [5] equal_set(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), ~subset(skolem_C3636, skolem_A3434)
% 3.74/0.92
% 3.74/0.92 [5] Rewrite : equal_set(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [7] (subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) & subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [7] Rewrite : ~subset(skolem_C3636, skolem_A3434)
% 3.74/0.92 -> [11] ~(member(skolem_X88(skolem_C3636, skolem_A3434), skolem_C3636) => member(skolem_X88(skolem_C3636, skolem_A3434), skolem_A3434))
% 3.74/0.92
% 3.74/0.92 [11] ALPHA_AND : (subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) & subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)))
% 3.74/0.92 -> [12] subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [12] Rewrite : subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [17] ! [X8_8] : ((member(X8_8, union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)) => member(X8_8, intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))))
% 3.74/0.92
% 3.74/0.92 [17] Rewrite : subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92 -> [18] ! [X8_8] : ((member(X8_8, intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) => member(X8_8, union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))))
% 3.74/0.92
% 3.74/0.92 [18] ALPHA_NOT_IMPLY : ~(member(skolem_X88(skolem_C3636, skolem_A3434), skolem_C3636) => member(skolem_X88(skolem_C3636, skolem_A3434), skolem_A3434))
% 3.74/0.92 -> [20] member(skolem_X88(skolem_C3636, skolem_A3434), skolem_C3636), ~member(skolem_X88(skolem_C3636, skolem_A3434), skolem_A3434)
% 3.74/0.92
% 3.74/0.92 [20] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 3.74/0.92 -> [23] (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 3.74/0.92
% 3.74/0.92 [23] BETA_EQUIV : (member(X11_0_0, power_set(X11_0_0)) <=> subset(X11_0_0, X11_0_0))
% 3.74/0.92 -> [25] ~member(X11_0_0, power_set(X11_0_0)), ~subset(X11_0_0, X11_0_0)
% 3.74/0.92 -> [26] member(X11_0_0, power_set(X11_0_0)), subset(X11_0_0, X11_0_0)
% 3.74/0.92
% 3.74/0.92 [25] Rewrite : ~subset(X11_0_0, X11_0_0)
% 3.74/0.92 -> [30] ~(member(skolem_X88(X11_0_0, X11_0_0), X11_0_0) => member(skolem_X88(X11_0_0, X11_0_0), X11_0_0))
% 3.74/0.92
% 3.74/0.92 [30] 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))
% 3.74/0.92 -> [31] member(skolem_X88(X11_0_0, X11_0_0), X11_0_0), ~member(skolem_X88(X11_0_0, X11_0_0), X11_0_0)
% 3.74/0.92
% 3.74/0.92 [31] CLOSURE : ~member(skolem_X88(X11_0_0, X11_0_0), X11_0_0)
% 3.74/0.92
% 3.74/0.92 [26] Rewrite : subset(X11_0_0, X11_0_0)
% 3.74/0.92 -> [34] ! [X8_8] : ((member(X8_8, X11_0_0) => member(X8_8, X11_0_0)))
% 3.74/0.92
% 3.74/0.92 [34] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 3.74/0.92 -> [36] ~member(X19_0_1, empty_set)
% 3.74/0.92
% 3.74/0.92 [36] GAMMA_FORALL : ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 3.74/0.92 -> [42] (member(A24_0_2, singleton(A24_0_2)) <=> =(A24_0_2, A24_0_2))
% 3.74/0.92
% 3.74/0.92 [42] BETA_EQUIV : (member(A24_0_2, singleton(A24_0_2)) <=> =(A24_0_2, A24_0_2))
% 3.74/0.92 -> [45] ~member(A24_0_2, singleton(A24_0_2)), ~=(A24_0_2, A24_0_2)
% 3.74/0.92 -> [46] member(A24_0_2, singleton(A24_0_2)), =(A24_0_2, A24_0_2)
% 3.74/0.92
% 3.74/0.92 [45] CLOSURE : ~=(A24_0_2, A24_0_2)
% 3.74/0.92
% 3.74/0.92 [46] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)) => member(X8_8, intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))))
% 3.74/0.92 -> [64] (member(skolem_X88(skolem_C3636, skolem_A3434), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)) => member(skolem_X88(skolem_C3636, skolem_A3434), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))))
% 3.74/0.92
% 3.74/0.92 [64] BETA_IMPLY : (member(skolem_X88(skolem_C3636, skolem_A3434), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)) => member(skolem_X88(skolem_C3636, skolem_A3434), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))))
% 3.74/0.92 -> [65] ~member(skolem_X88(skolem_C3636, skolem_A3434), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92 -> [66] member(skolem_X88(skolem_C3636, skolem_A3434), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [66] Rewrite : member(skolem_X88(skolem_C3636, skolem_A3434), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [67] (member(skolem_X88(skolem_C3636, skolem_A3434), skolem_A3434) & member(skolem_X88(skolem_C3636, skolem_A3434), union(skolem_B3535, skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [67] ALPHA_AND : (member(skolem_X88(skolem_C3636, skolem_A3434), skolem_A3434) & member(skolem_X88(skolem_C3636, skolem_A3434), union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [68] member(skolem_X88(skolem_C3636, skolem_A3434), skolem_A3434), member(skolem_X88(skolem_C3636, skolem_A3434), union(skolem_B3535, skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [68] CLOSURE : =
% 3.74/0.92
% 3.74/0.92 [65] Rewrite : ~member(skolem_X88(skolem_C3636, skolem_A3434), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92 -> [69] ~(member(skolem_X88(skolem_C3636, skolem_A3434), intersection(skolem_A3434, skolem_B3535)) | member(skolem_X88(skolem_C3636, skolem_A3434), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [69] ALPHA_NOT_OR : ~(member(skolem_X88(skolem_C3636, skolem_A3434), intersection(skolem_A3434, skolem_B3535)) | member(skolem_X88(skolem_C3636, skolem_A3434), skolem_C3636))
% 3.74/0.92 -> [70] ~member(skolem_X88(skolem_C3636, skolem_A3434), intersection(skolem_A3434, skolem_B3535)), ~member(skolem_X88(skolem_C3636, skolem_A3434), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [70] CLOSURE : =
% 3.74/0.92
% 3.74/0.92 [4] Rewrite : ~equal_set(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [6] ~(subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) & subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [6] Rewrite : subset(skolem_C3636, skolem_A3434)
% 3.74/0.92 -> [8] ! [X8_8] : ((member(X8_8, skolem_C3636) => member(X8_8, skolem_A3434)))
% 3.74/0.92
% 3.74/0.92 [8] BETA_NOT_AND : ~(subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) & subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)))
% 3.74/0.92 -> [9] ~subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [10] ~subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [10] Rewrite : ~subset(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92 -> [14] ~(member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) => member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [14] ALPHA_NOT_IMPLY : ~(member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))) => member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)))
% 3.74/0.92 -> [16] member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [16] Rewrite : member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [19] (member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_A3434) & member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(skolem_B3535, skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [19] Rewrite : ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92 -> [22] ~(member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, skolem_B3535)) | member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [22] ALPHA_AND : (member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_A3434) & member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [27] member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_A3434), member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(skolem_B3535, skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [27] Rewrite : member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), union(skolem_B3535, skolem_C3636))
% 3.74/0.92 -> [38] (member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_B3535) | member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [38] ALPHA_NOT_OR : ~(member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, skolem_B3535)) | member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_C3636))
% 3.74/0.92 -> [41] ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, skolem_B3535)), ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [41] Rewrite : ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), intersection(skolem_A3434, skolem_B3535))
% 3.74/0.92 -> [50] ~(member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_A3434) & member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_B3535))
% 3.74/0.92
% 3.74/0.92 [50] BETA_OR : (member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_B3535) | member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_C3636))
% 3.74/0.92 -> [56] member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_B3535)
% 3.74/0.92 -> [57] member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [57] CLOSURE : member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [56] BETA_NOT_AND : ~(member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_A3434) & member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_B3535))
% 3.74/0.92 -> [62] ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_A3434)
% 3.74/0.92 -> [63] ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_B3535)
% 3.74/0.92
% 3.74/0.92 [62] CLOSURE : ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_A3434)
% 3.74/0.92
% 3.74/0.92 [63] CLOSURE : ~member(skolem_X88(intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), skolem_B3535)
% 3.74/0.92
% 3.74/0.92 [9] Rewrite : ~subset(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [13] ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)) => member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))))
% 3.74/0.92
% 3.74/0.92 [13] ALPHA_NOT_IMPLY : ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)) => member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))))
% 3.74/0.92 -> [15] member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636)), ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [15] Rewrite : member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(intersection(skolem_A3434, skolem_B3535), skolem_C3636))
% 3.74/0.92 -> [21] (member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, skolem_B3535)) | member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [21] Rewrite : ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [24] ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434) & member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(skolem_B3535, skolem_C3636)))
% 3.74/0.92
% 3.74/0.92 [24] BETA_OR : (member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, skolem_B3535)) | member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636))
% 3.74/0.92 -> [28] member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, skolem_B3535))
% 3.74/0.92 -> [29] member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [28] Rewrite : member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), intersection(skolem_A3434, skolem_B3535))
% 3.74/0.92 -> [35] (member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434) & member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535))
% 3.74/0.92
% 3.74/0.92 [35] ALPHA_AND : (member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434) & member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535))
% 3.74/0.92 -> [37] member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434), member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535)
% 3.74/0.92
% 3.74/0.92 [37] BETA_NOT_AND : ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434) & member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [48] ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434)
% 3.74/0.92 -> [49] ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(skolem_B3535, skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [48] CLOSURE : ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434)
% 3.74/0.92
% 3.74/0.92 [49] Rewrite : ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(skolem_B3535, skolem_C3636))
% 3.74/0.92 -> [55] ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535) | member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [55] ALPHA_NOT_OR : ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535) | member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636))
% 3.74/0.92 -> [59] ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535), ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [59] CLOSURE : ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535)
% 3.74/0.92
% 3.74/0.92 [29] BETA_NOT_AND : ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434) & member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(skolem_B3535, skolem_C3636)))
% 3.74/0.92 -> [32] ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434)
% 3.74/0.92 -> [33] ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(skolem_B3535, skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [33] Rewrite : ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), union(skolem_B3535, skolem_C3636))
% 3.74/0.92 -> [39] ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535) | member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636))
% 3.74/0.92
% 3.74/0.92 [39] ALPHA_NOT_OR : ~(member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535) | member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636))
% 3.74/0.92 -> [47] ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_B3535), ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [47] CLOSURE : ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636)
% 3.74/0.92
% 3.74/0.92 [32] GAMMA_FORALL : ! [X11_11, A12_12] : ((member(X11_11, power_set(A12_12)) <=> subset(X11_11, A12_12)))
% 3.74/0.92 -> [40] (member(X11_1_0, power_set(X11_1_0)) <=> subset(X11_1_0, X11_1_0))
% 3.74/0.92
% 3.74/0.92 [40] BETA_EQUIV : (member(X11_1_0, power_set(X11_1_0)) <=> subset(X11_1_0, X11_1_0))
% 3.74/0.92 -> [43] ~member(X11_1_0, power_set(X11_1_0)), ~subset(X11_1_0, X11_1_0)
% 3.74/0.92 -> [44] member(X11_1_0, power_set(X11_1_0)), subset(X11_1_0, X11_1_0)
% 3.74/0.92
% 3.74/0.92 [43] Rewrite : ~subset(X11_1_0, X11_1_0)
% 3.74/0.92 -> [51] ~(member(skolem_X88(X11_1_0, X11_1_0), X11_1_0) => member(skolem_X88(X11_1_0, X11_1_0), X11_1_0))
% 3.74/0.92
% 3.74/0.92 [51] 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))
% 3.74/0.92 -> [52] member(skolem_X88(X11_1_0, X11_1_0), X11_1_0), ~member(skolem_X88(X11_1_0, X11_1_0), X11_1_0)
% 3.74/0.92
% 3.74/0.92 [52] CLOSURE : ~member(skolem_X88(X11_1_0, X11_1_0), X11_1_0)
% 3.74/0.92
% 3.74/0.92 [44] Rewrite : subset(X11_1_0, X11_1_0)
% 3.74/0.92 -> [53] ! [X8_8] : ((member(X8_8, X11_1_0) => member(X8_8, X11_1_0)))
% 3.74/0.92
% 3.74/0.92 [53] GAMMA_FORALL : ! [X19_19] : (~member(X19_19, empty_set))
% 3.74/0.92 -> [54] ~member(X19_1_1, empty_set)
% 3.74/0.92
% 3.74/0.92 [54] GAMMA_FORALL : ! [X23_23, A24_24] : ((member(X23_23, singleton(A24_24)) <=> =(X23_23, A24_24)))
% 3.74/0.92 -> [58] (member(A24_1_2, singleton(A24_1_2)) <=> =(A24_1_2, A24_1_2))
% 3.74/0.92
% 3.74/0.92 [58] BETA_EQUIV : (member(A24_1_2, singleton(A24_1_2)) <=> =(A24_1_2, A24_1_2))
% 3.74/0.92 -> [60] ~member(A24_1_2, singleton(A24_1_2)), ~=(A24_1_2, A24_1_2)
% 3.74/0.92 -> [61] member(A24_1_2, singleton(A24_1_2)), =(A24_1_2, A24_1_2)
% 3.74/0.92
% 3.74/0.92 [60] CLOSURE : ~=(A24_1_2, A24_1_2)
% 3.74/0.92
% 3.74/0.92 [61] GAMMA_FORALL : ! [X8_8] : ((member(X8_8, skolem_C3636) => member(X8_8, skolem_A3434)))
% 3.74/0.92 -> [71] (member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636) => member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434))
% 3.74/0.92
% 3.74/0.92 [71] BETA_IMPLY : (member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636) => member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434))
% 3.74/0.92 -> [72] ~member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_C3636)
% 3.74/0.92 -> [73] member(skolem_X88(union(intersection(skolem_A3434, skolem_B3535), skolem_C3636), intersection(skolem_A3434, union(skolem_B3535, skolem_C3636))), skolem_A3434)
% 3.74/0.92
% 3.74/0.92 [73] CLOSURE : =
% 3.74/0.92
% 3.74/0.92 [72] CLOSURE : =
% 3.74/0.92
% 3.74/0.92 % SZS output end Proof for theBenchmark.p
% 3.74/0.92 [0.569095s][1][Res] 789 goroutines created
% 3.74/0.92 ==== Result ====
% 3.74/0.92 [0.569116s][1][Res] VALID
% 3.74/0.92 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------