TSTP Solution File: SET697+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET697+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 6.15s 1.52s
% Output : Proof 6.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET697+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n028.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 07:32:38 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 [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 15
% 0.12/0.34 Launch Gotab with destructive = true
% 6.15/1.52 % SZS output start Proof for theBenchmark.p
% 6.15/1.52 [0] ALPHA_AND : ((! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))) & ~! [A33_33, B34_34, E35_35] : (((subset(A33_33, E35_35) & subset(B34_34, E35_35)) => (subset(A33_33, B34_34) <=> equal_set(intersection(A33_33, difference(E35_35, B34_34)), empty_set)))))
% 6.15/1.52 -> [1] (! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11))) & ! [X18_18] : (~member(X18_18, empty_set)) & ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))), ~! [A33_33, B34_34, E35_35] : (((subset(A33_33, E35_35) & subset(B34_34, E35_35)) => (subset(A33_33, B34_34) <=> equal_set(intersection(A33_33, difference(E35_35, B34_34)), empty_set))))
% 6.15/1.52
% 6.15/1.52 [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))))
% 6.15/1.52 -> [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)))
% 6.15/1.52
% 6.15/1.52 [2] DELTA_NOT_FORALL : ~! [A33_33, B34_34, E35_35] : (((subset(A33_33, E35_35) & subset(B34_34, E35_35)) => (subset(A33_33, B34_34) <=> equal_set(intersection(A33_33, difference(E35_35, B34_34)), empty_set))))
% 6.15/1.52 -> [3] ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)))
% 6.15/1.52
% 6.15/1.52 [3] ALPHA_NOT_IMPLY : ~((subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)) => (subset(skolem_A3333, skolem_B3434) <=> equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)))
% 6.15/1.52 -> [4] (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535)), ~(subset(skolem_A3333, skolem_B3434) <=> equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set))
% 6.15/1.52
% 6.15/1.52 [4] ALPHA_AND : (subset(skolem_A3333, skolem_E3535) & subset(skolem_B3434, skolem_E3535))
% 6.15/1.52 -> [5] subset(skolem_A3333, skolem_E3535), subset(skolem_B3434, skolem_E3535)
% 6.15/1.52
% 6.15/1.52 [5] Rewrite : subset(skolem_A3333, skolem_E3535)
% 6.15/1.52 -> [6] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 6.15/1.52
% 6.15/1.52 [6] Rewrite : subset(skolem_B3434, skolem_E3535)
% 6.15/1.52 -> [7] ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 6.15/1.52
% 6.15/1.52 [7] BETA_NOT_EQUIV : ~(subset(skolem_A3333, skolem_B3434) <=> equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set))
% 6.15/1.52 -> [8] ~subset(skolem_A3333, skolem_B3434), equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)
% 6.15/1.52 -> [9] subset(skolem_A3333, skolem_B3434), ~equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)
% 6.15/1.52
% 6.15/1.52 [9] Rewrite : subset(skolem_A3333, skolem_B3434)
% 6.15/1.52 -> [10] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 6.15/1.52
% 6.15/1.52 [10] Rewrite : ~equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)
% 6.15/1.52 -> [13] ~(subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set) & subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))))
% 6.15/1.52
% 6.15/1.52 [13] BETA_NOT_AND : ~(subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set) & subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))))
% 6.15/1.52 -> [15] ~subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)
% 6.15/1.52 -> [16] ~subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52
% 6.15/1.52 [16] Rewrite : ~subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [17] ~(member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), empty_set) => member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))))
% 6.15/1.52
% 6.15/1.52 [17] ALPHA_NOT_IMPLY : ~(member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), empty_set) => member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))))
% 6.15/1.52 -> [19] member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), empty_set), ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52
% 6.15/1.52 [19] Rewrite : ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [24] ~(member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_A3333) & member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52
% 6.15/1.52 [24] BETA_NOT_AND : ~(member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_A3333) & member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [25] ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_A3333)
% 6.15/1.52 -> [26] ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [25] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 6.15/1.52 -> [33] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 6.15/1.52
% 6.15/1.52 [33] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 6.15/1.52 -> [34] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 6.15/1.52 -> [35] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 6.15/1.52
% 6.15/1.52 [35] Rewrite : subset(X10_1_0, X10_1_0)
% 6.15/1.52 -> [51] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 6.15/1.52
% 6.15/1.52 [51] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 6.15/1.52 -> [54] ~member(X18_1_1, empty_set)
% 6.15/1.52
% 6.15/1.52 [54] CLOSURE : ~member(X18_1_1, empty_set)
% 6.15/1.52
% 6.15/1.52 [34] Rewrite : ~subset(X10_1_0, X10_1_0)
% 6.15/1.52 -> [47] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 6.15/1.52
% 6.15/1.52 [47] 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))
% 6.15/1.52 -> [49] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 6.15/1.52
% 6.15/1.52 [49] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 6.15/1.52
% 6.15/1.52 [26] Rewrite : ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52 -> [32] ~(member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_E3535) & ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [32] BETA_NOT_AND : ~(member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_E3535) & ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_B3434))
% 6.15/1.52 -> [36] ~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_E3535)
% 6.15/1.52 -> [37] ~~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [36] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 6.15/1.52 -> [43] (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 6.15/1.52
% 6.15/1.52 [43] BETA_EQUIV : (member(X10_2_0, power_set(X10_2_0)) <=> subset(X10_2_0, X10_2_0))
% 6.15/1.52 -> [44] ~member(X10_2_0, power_set(X10_2_0)), ~subset(X10_2_0, X10_2_0)
% 6.15/1.52 -> [45] member(X10_2_0, power_set(X10_2_0)), subset(X10_2_0, X10_2_0)
% 6.15/1.52
% 6.15/1.52 [45] Rewrite : subset(X10_2_0, X10_2_0)
% 6.15/1.52 -> [58] ! [X7_7] : ((member(X7_7, X10_2_0) => member(X7_7, X10_2_0)))
% 6.15/1.52
% 6.15/1.52 [58] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 6.15/1.52 -> [60] ~member(X18_2_1, empty_set)
% 6.15/1.52
% 6.15/1.52 [60] CLOSURE : ~member(X18_2_1, empty_set)
% 6.15/1.52
% 6.15/1.52 [44] Rewrite : ~subset(X10_2_0, X10_2_0)
% 6.15/1.52 -> [59] ~(member(skolem_X77(X10_2_0, X10_2_0), X10_2_0) => member(skolem_X77(X10_2_0, X10_2_0), X10_2_0))
% 6.15/1.52
% 6.15/1.52 [59] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_2_0, X10_2_0), X10_2_0) => member(skolem_X77(X10_2_0, X10_2_0), X10_2_0))
% 6.15/1.52 -> [61] member(skolem_X77(X10_2_0, X10_2_0), X10_2_0), ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 6.15/1.52
% 6.15/1.52 [61] CLOSURE : ~member(skolem_X77(X10_2_0, X10_2_0), X10_2_0)
% 6.15/1.52
% 6.15/1.52 [37] ALPHA_NOT_NOT : ~~member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_B3434)
% 6.15/1.52 -> [38] member(skolem_X77(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [38] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 6.15/1.52 -> [50] (member(X10_3_0, power_set(X10_3_0)) <=> subset(X10_3_0, X10_3_0))
% 6.15/1.52
% 6.15/1.52 [50] BETA_EQUIV : (member(X10_3_0, power_set(X10_3_0)) <=> subset(X10_3_0, X10_3_0))
% 6.15/1.52 -> [52] ~member(X10_3_0, power_set(X10_3_0)), ~subset(X10_3_0, X10_3_0)
% 6.15/1.52 -> [53] member(X10_3_0, power_set(X10_3_0)), subset(X10_3_0, X10_3_0)
% 6.15/1.52
% 6.15/1.52 [53] Rewrite : subset(X10_3_0, X10_3_0)
% 6.15/1.52 -> [65] ! [X7_7] : ((member(X7_7, X10_3_0) => member(X7_7, X10_3_0)))
% 6.15/1.52
% 6.15/1.52 [65] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 6.15/1.52 -> [67] ~member(X18_3_1, empty_set)
% 6.15/1.52
% 6.15/1.52 [67] CLOSURE : ~member(X18_3_1, empty_set)
% 6.15/1.52
% 6.15/1.52 [52] Rewrite : ~subset(X10_3_0, X10_3_0)
% 6.15/1.52 -> [66] ~(member(skolem_X77(X10_3_0, X10_3_0), X10_3_0) => member(skolem_X77(X10_3_0, X10_3_0), X10_3_0))
% 6.15/1.52
% 6.15/1.52 [66] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_3_0, X10_3_0), X10_3_0) => member(skolem_X77(X10_3_0, X10_3_0), X10_3_0))
% 6.15/1.52 -> [68] member(skolem_X77(X10_3_0, X10_3_0), X10_3_0), ~member(skolem_X77(X10_3_0, X10_3_0), X10_3_0)
% 6.15/1.52
% 6.15/1.52 [68] CLOSURE : ~member(skolem_X77(X10_3_0, X10_3_0), X10_3_0)
% 6.15/1.52
% 6.15/1.52 [15] Rewrite : ~subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)
% 6.15/1.52 -> [18] ~(member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), empty_set))
% 6.15/1.52
% 6.15/1.52 [18] ALPHA_NOT_IMPLY : ~(member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), empty_set))
% 6.15/1.52 -> [20] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))), ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), empty_set)
% 6.15/1.52
% 6.15/1.52 [20] Rewrite : member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [22] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) & member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52
% 6.15/1.52 [22] ALPHA_AND : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) & member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [27] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333), member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [27] Rewrite : member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52 -> [39] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_E3535) & ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [39] ALPHA_AND : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_E3535) & ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434))
% 6.15/1.52 -> [42] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_E3535), ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [42] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 6.15/1.52 -> [62] (member(X10_4_0, power_set(X10_4_0)) <=> subset(X10_4_0, X10_4_0))
% 6.15/1.52
% 6.15/1.52 [62] BETA_EQUIV : (member(X10_4_0, power_set(X10_4_0)) <=> subset(X10_4_0, X10_4_0))
% 6.15/1.52 -> [63] ~member(X10_4_0, power_set(X10_4_0)), ~subset(X10_4_0, X10_4_0)
% 6.15/1.52 -> [64] member(X10_4_0, power_set(X10_4_0)), subset(X10_4_0, X10_4_0)
% 6.15/1.52
% 6.15/1.52 [63] Rewrite : ~subset(X10_4_0, X10_4_0)
% 6.15/1.52 -> [69] ~(member(skolem_X77(X10_4_0, X10_4_0), X10_4_0) => member(skolem_X77(X10_4_0, X10_4_0), X10_4_0))
% 6.15/1.52
% 6.15/1.52 [69] ALPHA_NOT_IMPLY : ~(member(skolem_X77(X10_4_0, X10_4_0), X10_4_0) => member(skolem_X77(X10_4_0, X10_4_0), X10_4_0))
% 6.15/1.52 -> [71] member(skolem_X77(X10_4_0, X10_4_0), X10_4_0), ~member(skolem_X77(X10_4_0, X10_4_0), X10_4_0)
% 6.15/1.52
% 6.15/1.52 [71] CLOSURE : ~member(skolem_X77(X10_4_0, X10_4_0), X10_4_0)
% 6.15/1.52
% 6.15/1.52 [64] Rewrite : subset(X10_4_0, X10_4_0)
% 6.15/1.52 -> [70] ! [X7_7] : ((member(X7_7, X10_4_0) => member(X7_7, X10_4_0)))
% 6.15/1.52
% 6.15/1.52 [70] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 6.15/1.52 -> [72] ~member(X18_4_1, empty_set)
% 6.15/1.52
% 6.15/1.52 [72] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 6.15/1.52 -> [73] (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 6.15/1.52
% 6.15/1.52 [73] BETA_EQUIV : (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 6.15/1.52 -> [74] ~member(A23_1_2, singleton(A23_1_2)), ~=(A23_1_2, A23_1_2)
% 6.15/1.52 -> [75] member(A23_1_2, singleton(A23_1_2)), =(A23_1_2, A23_1_2)
% 6.15/1.52
% 6.15/1.52 [74] CLOSURE : ~=(A23_1_2, A23_1_2)
% 6.15/1.52
% 6.15/1.52 [75] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 6.15/1.52 -> [98] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_E3535))
% 6.15/1.52
% 6.15/1.52 [98] BETA_IMPLY : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_E3535))
% 6.15/1.52 -> [99] ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333)
% 6.15/1.52 -> [100] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_E3535)
% 6.15/1.52
% 6.15/1.52 [99] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [100] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_E3535)))
% 6.15/1.52 -> [105] (member(X7_5_4, skolem_B3434) => member(X7_5_4, skolem_E3535))
% 6.15/1.52
% 6.15/1.52 [105] BETA_IMPLY : (member(X7_5_4, skolem_B3434) => member(X7_5_4, skolem_E3535))
% 6.15/1.52 -> [106] ~member(X7_5_4, skolem_B3434)
% 6.15/1.52 -> [107] member(X7_5_4, skolem_E3535)
% 6.15/1.52
% 6.15/1.52 [107] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 6.15/1.52 -> [114] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [114] BETA_IMPLY : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434))
% 6.15/1.52 -> [115] ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333)
% 6.15/1.52 -> [116] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [116] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [115] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [106] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 6.15/1.52 -> [119] (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [119] BETA_IMPLY : (member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333) => member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434))
% 6.15/1.52 -> [120] ~member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_A3333)
% 6.15/1.52 -> [121] member(skolem_X77(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [121] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [120] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [8] Rewrite : ~subset(skolem_A3333, skolem_B3434)
% 6.15/1.52 -> [11] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [11] Rewrite : equal_set(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)
% 6.15/1.52 -> [12] (subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set) & subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))))
% 6.15/1.52
% 6.15/1.52 [12] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.15/1.52 -> [14] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [14] ALPHA_AND : (subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set) & subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))))
% 6.15/1.52 -> [21] subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set), subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52
% 6.15/1.52 [21] Rewrite : subset(intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)), empty_set)
% 6.15/1.52 -> [23] ! [X7_7] : ((member(X7_7, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(X7_7, empty_set)))
% 6.15/1.52
% 6.15/1.52 [23] Rewrite : subset(empty_set, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [28] ! [X7_7] : ((member(X7_7, empty_set) => member(X7_7, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))))
% 6.15/1.52
% 6.15/1.52 [28] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 6.15/1.52 -> [29] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 6.15/1.52
% 6.15/1.52 [29] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 6.15/1.52 -> [30] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 6.15/1.52 -> [31] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 6.15/1.52
% 6.15/1.52 [30] Rewrite : ~subset(X10_0_0, X10_0_0)
% 6.15/1.52 -> [46] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 6.15/1.52
% 6.15/1.52 [46] 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))
% 6.15/1.52 -> [48] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 6.15/1.52
% 6.15/1.52 [48] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 6.15/1.52
% 6.15/1.52 [31] Rewrite : subset(X10_0_0, X10_0_0)
% 6.15/1.52 -> [40] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 6.15/1.52
% 6.15/1.52 [40] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 6.15/1.52 -> [41] ~member(skolem_X77(skolem_A3333, skolem_B3434), empty_set)
% 6.15/1.52
% 6.15/1.52 [41] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 6.15/1.52 -> [55] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 6.15/1.52
% 6.15/1.52 [55] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 6.15/1.52 -> [56] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 6.15/1.52 -> [57] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 6.15/1.52
% 6.15/1.52 [56] CLOSURE : ~=(A23_0_2, A23_0_2)
% 6.15/1.52
% 6.15/1.52 [57] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3535)))
% 6.15/1.52 -> [76] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 6.15/1.52
% 6.15/1.52 [76] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535))
% 6.15/1.52 -> [77] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.15/1.52 -> [78] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 6.15/1.52
% 6.15/1.52 [77] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [79] BETA_IMPLY : (member(X7_1_4, skolem_B3434) => member(X7_1_4, skolem_E3535))
% 6.15/1.52 -> [135] ~member(X7_1_4, skolem_B3434)
% 6.15/1.52 -> [136] member(X7_1_4, skolem_E3535)
% 6.15/1.52
% 6.15/1.52 [136] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(X7_7, empty_set)))
% 6.15/1.52 -> [137] (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), empty_set))
% 6.15/1.52
% 6.15/1.52 [137] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), empty_set))
% 6.15/1.52 -> [138] ~member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [139] member(skolem_X77(skolem_A3333, skolem_B3434), empty_set)
% 6.15/1.52
% 6.15/1.52 [138] Rewrite : ~member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [144] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) & member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52
% 6.15/1.52 [144] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) & member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [147] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.15/1.52 -> [148] ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [147] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [148] Rewrite : ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52 -> [153] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [153] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.15/1.52 -> [154] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 6.15/1.52 -> [155] ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [155] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.15/1.52 -> [156] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [156] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [154] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [139] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [135] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(X7_7, empty_set)))
% 6.15/1.52 -> [140] (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), empty_set))
% 6.15/1.52
% 6.15/1.52 [140] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434))) => member(skolem_X77(skolem_A3333, skolem_B3434), empty_set))
% 6.15/1.52 -> [141] ~member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [142] member(skolem_X77(skolem_A3333, skolem_B3434), empty_set)
% 6.15/1.52
% 6.15/1.52 [142] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [141] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) & member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434)))
% 6.15/1.52 -> [157] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 6.15/1.52 -> [158] ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [157] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [158] Rewrite : ~member(skolem_X77(skolem_A3333, skolem_B3434), difference(skolem_E3535, skolem_B3434))
% 6.15/1.52 -> [159] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.15/1.52
% 6.15/1.52 [159] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535) & ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 6.15/1.52 -> [160] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_E3535)
% 6.15/1.52 -> [161] ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [160] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 [161] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.15/1.52 -> [162] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 6.15/1.52
% 6.15/1.52 [162] CLOSURE : =
% 6.15/1.52
% 6.15/1.52 % SZS output end Proof for theBenchmark.p
% 6.15/1.52 [1.177651s][1][Res] 3269 goroutines created
% 6.15/1.52 ==== Result ====
% 6.15/1.52 [1.177687s][1][Res] VALID
% 6.15/1.52 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------