TSTP Solution File: SET699+4 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET699+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n028.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 6.35s 1.56s
% Output : Proof 6.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SET699+4 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.10 % Command : goeland -dmt -presko -proof %s
% 0.10/0.30 % Computer : n028.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 07:33:38 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 [DMT] DMT loaded with preskolemization
% 0.10/0.30 [EQ] equality loaded.
% 0.10/0.30 [0.000033s][1][MAIN] Problem : theBenchmark.p
% 0.10/0.31 Conjecture not found
% 0.10/0.31 Start search
% 0.10/0.31 nb_step : 1 - limit : 15
% 0.10/0.31 Launch Gotab with destructive = true
% 6.35/1.56 % SZS output start Proof for theBenchmark.p
% 6.35/1.56 [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) <=> subset(intersection(A33_33, difference(E35_35, B34_34)), difference(E35_35, A33_33))))))
% 6.35/1.56 -> [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) <=> subset(intersection(A33_33, difference(E35_35, B34_34)), difference(E35_35, A33_33)))))
% 6.35/1.56
% 6.35/1.56 [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))))
% 6.35/1.56 -> [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)))
% 6.35/1.56
% 6.35/1.56 [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) <=> subset(intersection(A33_33, difference(E35_35, B34_34)), difference(E35_35, A33_33)))))
% 6.35/1.56 -> [3] ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333))))
% 6.35/1.56
% 6.35/1.56 [3] ALPHA_NOT_IMPLY : ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333))))
% 6.35/1.56 -> [4] (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)), ~(subset(skolem_A3333, skolem_B3434) <=> subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56
% 6.35/1.56 [4] ALPHA_AND : (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535))
% 6.35/1.56 -> [5] subset(skolem_A3333, skolem_E3535), subset(skolem_B3434, skolem_E3535)
% 6.35/1.56
% 6.35/1.56 [5] Rewrite : subset(skolem_A3333, skolem_E3535)
% 6.35/1.56 -> [6] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 6.35/1.56
% 6.35/1.56 [6] Rewrite : subset(skolem_B3434, skolem_E3535)
% 6.35/1.56 -> [7] ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 6.35/1.56
% 6.35/1.56 [7] BETA_NOT_EQUIV : ~(subset(skolem_A3333, skolem_B3434) <=> subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56 -> [8] ~subset(skolem_A3333, skolem_B3434), subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56 -> [9] subset(skolem_A3333, skolem_B3434), ~subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56
% 6.35/1.56 [8] Rewrite : ~subset(skolem_A3333, skolem_B3434)
% 6.35/1.56 -> [10] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [10] Rewrite : subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56 -> [12] ! [X7_7] : ((member(X7_7, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(X7_7, difference(skolem_E3535, skolem_A3333))))
% 6.35/1.56
% 6.35/1.56 [12] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.35/1.56 -> [14] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [14] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 6.35/1.56 -> [16] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 6.35/1.56
% 6.35/1.56 [16] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 6.35/1.56 -> [17] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 6.35/1.56 -> [18] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 6.35/1.56
% 6.35/1.56 [17] Rewrite : ~subset(X10_0_0, X10_0_0)
% 6.35/1.56 -> [21] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 6.35/1.56
% 6.35/1.56 [21] 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))
% 6.35/1.56 -> [23] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 6.35/1.56
% 6.35/1.56 [23] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 6.35/1.56
% 6.35/1.56 [18] Rewrite : subset(X10_0_0, X10_0_0)
% 6.35/1.56 -> [20] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 6.35/1.56
% 6.35/1.56 [20] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 6.35/1.56 -> [22] ~member(X18_0_1, empty_set)
% 6.35/1.56
% 6.35/1.56 [22] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 6.35/1.56 -> [24] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 6.35/1.56
% 6.35/1.56 [24] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 6.35/1.56 -> [25] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 6.35/1.56 -> [26] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 6.35/1.56
% 6.35/1.56 [25] CLOSURE : ~=(A23_0_2, A23_0_2)
% 6.35/1.56
% 6.35/1.56 [26] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 6.35/1.56 -> [44] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 6.35/1.56
% 6.35/1.56 [44] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 6.35/1.56 -> [45] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.35/1.56 -> [46] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 6.35/1.56
% 6.35/1.56 [45] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [46] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 6.35/1.56 -> [47] (member(X7_1_4, skolem_B3434) => member(X7_1_4, skolem_E3535))
% 6.35/1.56
% 6.35/1.56 [47] BETA_IMPLY : (member(X7_1_4, skolem_B3434) => member(X7_1_4, skolem_E3535))
% 6.35/1.56 -> [48] ~member(X7_1_4, skolem_B3434)
% 6.35/1.56 -> [49] member(X7_1_4, skolem_E3535)
% 6.35/1.56
% 6.35/1.56 [49] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(X7_7, difference(skolem_E3535, skolem_A3333))))
% 6.35/1.56 -> [50] (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56
% 6.35/1.56 [50] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56 -> [51] ~member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.35/1.56 -> [52] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56
% 6.35/1.56 [52] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56 -> [56] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 6.35/1.56
% 6.35/1.56 [56] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 6.35/1.56 -> [57] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.35/1.56
% 6.35/1.56 [57] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [51] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) & member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)))
% 6.35/1.56 -> [80] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.35/1.56 -> [81] ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [80] CLOSURE : ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.35/1.56
% 6.35/1.56 [81] Rewrite : ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.35/1.56 -> [82] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [82] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.35/1.56 -> [83] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 6.35/1.56 -> [84] ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [84] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56 -> [85] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [85] CLOSURE : member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [83] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [48] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(X7_7, difference(skolem_E3535, skolem_A3333))))
% 6.35/1.56 -> [53] (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56
% 6.35/1.56 [53] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56 -> [54] ~member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.35/1.56 -> [55] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56
% 6.35/1.56 [55] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56 -> [61] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 6.35/1.56
% 6.35/1.56 [61] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 6.35/1.56 -> [62] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.35/1.56
% 6.35/1.56 [62] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [54] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) & member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)))
% 6.35/1.56 -> [86] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.35/1.56 -> [87] ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [86] CLOSURE : ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.35/1.56
% 6.35/1.56 [87] Rewrite : ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.35/1.56 -> [88] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [88] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.35/1.56 -> [89] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 6.35/1.56 -> [90] ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [90] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56 -> [91] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [91] CLOSURE : member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [89] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [9] Rewrite : subset(skolem_A3333, skolem_B3434)
% 6.35/1.56 -> [11] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 6.35/1.56
% 6.35/1.56 [11] Rewrite : ~subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56 -> [13] ~(member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56
% 6.35/1.56 [13] ALPHA_NOT_IMPLY : ~(member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333)))
% 6.35/1.56 -> [15] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56
% 6.35/1.56 [15] Rewrite : member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.35/1.56 -> [19] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) & member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434)))
% 6.35/1.56
% 6.35/1.56 [19] Rewrite : ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333))
% 6.35/1.56 -> [27] ~(member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333))
% 6.35/1.56
% 6.35/1.56 [27] ALPHA_AND : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) & member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434)))
% 6.35/1.56 -> [28] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333), member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [28] Rewrite : member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434))
% 6.35/1.56 -> [29] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [29] ALPHA_AND : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 6.35/1.56 -> [30] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535), ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [30] BETA_NOT_AND : ~(member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333))
% 6.35/1.56 -> [31] ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535)
% 6.35/1.56 -> [32] ~~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 6.35/1.56
% 6.35/1.56 [31] CLOSURE : ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535)
% 6.35/1.56
% 6.35/1.56 [32] ALPHA_NOT_NOT : ~~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 6.35/1.56 -> [33] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 6.35/1.56
% 6.35/1.56 [33] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 6.35/1.56 -> [34] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 6.35/1.56
% 6.35/1.56 [34] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 6.35/1.56 -> [35] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 6.35/1.56 -> [36] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 6.35/1.56
% 6.35/1.56 [35] Rewrite : ~subset(X10_1_0, X10_1_0)
% 6.35/1.56 -> [38] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 6.35/1.56
% 6.35/1.56 [38] 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))
% 6.35/1.56 -> [40] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 6.35/1.56
% 6.35/1.56 [40] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 6.35/1.56
% 6.35/1.56 [36] Rewrite : subset(X10_1_0, X10_1_0)
% 6.35/1.56 -> [37] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 6.35/1.56
% 6.35/1.56 [37] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 6.35/1.56 -> [39] ~member(X18_1_1, empty_set)
% 6.35/1.56
% 6.35/1.56 [39] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 6.35/1.56 -> [41] (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 6.35/1.56
% 6.35/1.56 [41] BETA_EQUIV : (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 6.35/1.56 -> [42] ~member(A23_1_2, singleton(A23_1_2)), ~=(A23_1_2, A23_1_2)
% 6.35/1.56 -> [43] member(A23_1_2, singleton(A23_1_2)), =(A23_1_2, A23_1_2)
% 6.35/1.56
% 6.35/1.56 [42] CLOSURE : ~=(A23_1_2, A23_1_2)
% 6.35/1.56
% 6.35/1.56 [43] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 6.35/1.56 -> [70] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535))
% 6.35/1.56
% 6.35/1.56 [70] BETA_IMPLY : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535))
% 6.35/1.56 -> [71] ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 6.35/1.56 -> [72] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_E3535)
% 6.35/1.56
% 6.35/1.56 [71] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [72] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 6.35/1.56 -> [77] (member(X7_5_4, skolem_B3434) => member(X7_5_4, skolem_E3535))
% 6.35/1.56
% 6.35/1.56 [77] BETA_IMPLY : (member(X7_5_4, skolem_B3434) => member(X7_5_4, skolem_E3535))
% 6.35/1.56 -> [78] ~member(X7_5_4, skolem_B3434)
% 6.35/1.56 -> [79] member(X7_5_4, skolem_E3535)
% 6.35/1.56
% 6.35/1.56 [78] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 6.35/1.56 -> [92] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [92] BETA_IMPLY : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 6.35/1.56 -> [93] ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 6.35/1.56 -> [94] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [94] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [93] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [79] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 6.35/1.56 -> [95] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 6.35/1.56
% 6.35/1.56 [95] BETA_IMPLY : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 6.35/1.56 -> [96] ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 6.35/1.56 -> [97] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), difference(skolem_E3535, skolem_A3333)), skolem_B3434)
% 6.35/1.56
% 6.35/1.56 [97] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 [96] CLOSURE : =
% 6.35/1.56
% 6.35/1.56 % SZS output end Proof for theBenchmark.p
% 6.35/1.56 [1.259262s][1][Res] 1921 goroutines created
% 6.35/1.56 ==== Result ====
% 6.35/1.56 [1.259308s][1][Res] VALID
% 6.35/1.56 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------