TSTP Solution File: SET695+4 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n020.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 04:17:10 EDT 2022
% Result : Theorem 3.35s 0.99s
% Output : Proof 3.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n020.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 07:24:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000038s][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
% 3.35/0.99 % SZS output start Proof for theBenchmark.p
% 3.35/0.99 [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(difference(E35_35, B34_34), difference(E35_35, A33_33))))))
% 3.35/0.99 -> [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(difference(E35_35, B34_34), difference(E35_35, A33_33)))))
% 3.35/0.99
% 3.35/0.99 [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))))
% 3.35/0.99 -> [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)))
% 3.35/0.99
% 3.35/0.99 [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(difference(E35_35, B34_34), difference(E35_35, A33_33)))))
% 3.35/0.99 -> [3] ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333))))
% 3.35/0.99
% 3.35/0.99 [3] ALPHA_NOT_IMPLY : ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333))))
% 3.35/0.99 -> [4] (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)), ~(subset(skolem_A3333, skolem_B3434) <=> subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99
% 3.35/0.99 [4] ALPHA_AND : (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535))
% 3.35/0.99 -> [5] subset(skolem_A3333, skolem_E3535), subset(skolem_B3434, skolem_E3535)
% 3.35/0.99
% 3.35/0.99 [5] Rewrite : subset(skolem_A3333, skolem_E3535)
% 3.35/0.99 -> [6] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 3.35/0.99
% 3.35/0.99 [6] Rewrite : subset(skolem_B3434, skolem_E3535)
% 3.35/0.99 -> [7] ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 3.35/0.99
% 3.35/0.99 [7] BETA_NOT_EQUIV : ~(subset(skolem_A3333, skolem_B3434) <=> subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99 -> [8] ~subset(skolem_A3333, skolem_B3434), subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99 -> [9] subset(skolem_A3333, skolem_B3434), ~subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99
% 3.35/0.99 [8] Rewrite : ~subset(skolem_A3333, skolem_B3434)
% 3.35/0.99 -> [11] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 3.35/0.99
% 3.35/0.99 [11] Rewrite : subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99 -> [13] ! [X7_7] : ((member(X7_7, difference(skolem_E3535, skolem_B3434)) => member(X7_7, difference(skolem_E3535, skolem_A3333))))
% 3.35/0.99
% 3.35/0.99 [13] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 3.35/0.99 -> [15] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [15] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 3.35/0.99 -> [17] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 3.35/0.99
% 3.35/0.99 [17] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 3.35/0.99 -> [18] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 3.35/0.99 -> [19] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 3.35/0.99
% 3.35/0.99 [18] Rewrite : ~subset(X10_0_0, X10_0_0)
% 3.35/0.99 -> [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))
% 3.35/0.99
% 3.35/0.99 [23] 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))
% 3.35/0.99 -> [25] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 3.35/0.99
% 3.35/0.99 [25] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 3.35/0.99
% 3.35/0.99 [19] Rewrite : subset(X10_0_0, X10_0_0)
% 3.35/0.99 -> [22] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 3.35/0.99
% 3.35/0.99 [22] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 3.35/0.99 -> [24] ~member(X18_0_1, empty_set)
% 3.35/0.99
% 3.35/0.99 [24] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 3.35/0.99 -> [26] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 3.35/0.99
% 3.35/0.99 [26] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 3.35/0.99 -> [29] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 3.35/0.99 -> [30] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 3.35/0.99
% 3.35/0.99 [29] CLOSURE : ~=(A23_0_2, A23_0_2)
% 3.35/0.99
% 3.35/0.99 [30] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 3.35/0.99 -> [42] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 3.35/0.99
% 3.35/0.99 [42] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 3.35/0.99 -> [43] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 3.35/0.99 -> [44] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 3.35/0.99
% 3.35/0.99 [43] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [44] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 3.35/0.99 -> [45] (member(X7_1_4, skolem_B3434) => member(X7_1_4, skolem_E3535))
% 3.35/0.99
% 3.35/0.99 [45] BETA_IMPLY : (member(X7_1_4, skolem_B3434) => member(X7_1_4, skolem_E3535))
% 3.35/0.99 -> [46] ~member(X7_1_4, skolem_B3434)
% 3.35/0.99 -> [47] member(X7_1_4, skolem_E3535)
% 3.35/0.99
% 3.35/0.99 [47] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, difference(skolem_E3535, skolem_B3434)) => member(X7_7, difference(skolem_E3535, skolem_A3333))))
% 3.35/0.99 -> [48] (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99
% 3.35/0.99 [48] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99 -> [49] ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 3.35/0.99 -> [50] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99
% 3.35/0.99 [50] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99 -> [57] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 3.35/0.99
% 3.35/0.99 [57] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 3.35/0.99 -> [58] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 3.35/0.99
% 3.35/0.99 [58] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [49] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 3.35/0.99 -> [72] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 3.35/0.99 -> [73] ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [73] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99 -> [74] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [74] CLOSURE : member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [72] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [46] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, difference(skolem_E3535, skolem_B3434)) => member(X7_7, difference(skolem_E3535, skolem_A3333))))
% 3.35/0.99 -> [51] (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99
% 3.35/0.99 [51] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)) => member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99 -> [52] ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 3.35/0.99 -> [53] member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99
% 3.35/0.99 [53] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99 -> [67] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 3.35/0.99
% 3.35/0.99 [67] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333))
% 3.35/0.99 -> [68] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 3.35/0.99
% 3.35/0.99 [68] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [52] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 3.35/0.99 -> [75] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 3.35/0.99 -> [76] ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [76] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99 -> [77] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [77] CLOSURE : member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [75] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [9] Rewrite : subset(skolem_A3333, skolem_B3434)
% 3.35/0.99 -> [10] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 3.35/0.99
% 3.35/0.99 [10] Rewrite : ~subset(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99 -> [12] ~(member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434)) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99
% 3.35/0.99 [12] ALPHA_NOT_IMPLY : ~(member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434)) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333)))
% 3.35/0.99 -> [14] member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434)), ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99
% 3.35/0.99 [14] Rewrite : member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_B3434))
% 3.35/0.99 -> [16] (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 3.35/0.99
% 3.35/0.99 [16] Rewrite : ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), difference(skolem_E3535, skolem_A3333))
% 3.35/0.99 -> [20] ~(member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333))
% 3.35/0.99
% 3.35/0.99 [20] ALPHA_AND : (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 3.35/0.99 -> [21] member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535), ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [21] BETA_NOT_AND : ~(member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535) & ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333))
% 3.35/0.99 -> [27] ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535)
% 3.35/0.99 -> [28] ~~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 3.35/0.99
% 3.35/0.99 [27] CLOSURE : ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535)
% 3.35/0.99
% 3.35/0.99 [28] ALPHA_NOT_NOT : ~~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 3.35/0.99 -> [31] member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 3.35/0.99
% 3.35/0.99 [31] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 3.35/0.99 -> [32] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 3.35/0.99
% 3.35/0.99 [32] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 3.35/0.99 -> [33] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 3.35/0.99 -> [34] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 3.35/0.99
% 3.35/0.99 [33] Rewrite : ~subset(X10_1_0, X10_1_0)
% 3.35/0.99 -> [36] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 3.35/0.99
% 3.35/0.99 [36] 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))
% 3.35/0.99 -> [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)
% 3.35/0.99
% 3.35/0.99 [38] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 3.35/0.99
% 3.35/0.99 [34] Rewrite : subset(X10_1_0, X10_1_0)
% 3.35/0.99 -> [35] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 3.35/0.99
% 3.35/0.99 [35] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 3.35/0.99 -> [37] ~member(X18_1_1, empty_set)
% 3.35/0.99
% 3.35/0.99 [37] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 3.35/0.99 -> [39] (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 3.35/0.99
% 3.35/0.99 [39] BETA_EQUIV : (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 3.35/0.99 -> [40] ~member(A23_1_2, singleton(A23_1_2)), ~=(A23_1_2, A23_1_2)
% 3.35/0.99 -> [41] member(A23_1_2, singleton(A23_1_2)), =(A23_1_2, A23_1_2)
% 3.35/0.99
% 3.35/0.99 [40] CLOSURE : ~=(A23_1_2, A23_1_2)
% 3.35/0.99
% 3.35/0.99 [41] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 3.35/0.99 -> [54] (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535))
% 3.35/0.99
% 3.35/0.99 [54] BETA_IMPLY : (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535))
% 3.35/0.99 -> [55] ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 3.35/0.99 -> [56] member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_E3535)
% 3.35/0.99
% 3.35/0.99 [55] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [56] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 3.35/0.99 -> [69] (member(X7_5_4, skolem_B3434) => member(X7_5_4, skolem_E3535))
% 3.35/0.99
% 3.35/0.99 [69] BETA_IMPLY : (member(X7_5_4, skolem_B3434) => member(X7_5_4, skolem_E3535))
% 3.35/0.99 -> [70] ~member(X7_5_4, skolem_B3434)
% 3.35/0.99 -> [71] member(X7_5_4, skolem_E3535)
% 3.35/0.99
% 3.35/0.99 [71] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 3.35/0.99 -> [78] (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 3.35/0.99
% 3.35/0.99 [78] BETA_IMPLY : (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 3.35/0.99 -> [79] ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 3.35/0.99 -> [80] member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [80] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [79] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [70] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 3.35/0.99 -> [81] (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 3.35/0.99
% 3.35/0.99 [81] BETA_IMPLY : (member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333) => member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434))
% 3.35/0.99 -> [82] ~member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_A3333)
% 3.35/0.99 -> [83] member(skolem_X77(difference(skolem_E3535, skolem_B3434), difference(skolem_E3535, skolem_A3333)), skolem_B3434)
% 3.35/0.99
% 3.35/0.99 [83] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 [82] CLOSURE : =
% 3.35/0.99
% 3.35/0.99 % SZS output end Proof for theBenchmark.p
% 3.35/0.99 [0.647578s][1][Res] 1529 goroutines created
% 3.35/0.99 ==== Result ====
% 3.35/0.99 [0.647613s][1][Res] VALID
% 3.35/0.99 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------