TSTP Solution File: SET692+4 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET692+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 1.12s 0.58s
% Output : Proof 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n020.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 07:24:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000047s][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
% 1.12/0.58 % SZS output start Proof for theBenchmark.p
% 1.12/0.58 [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] : ((equal_set(A33_33, intersection(A33_33, B34_34)) <=> subset(A33_33, B34_34))))
% 1.12/0.58 -> [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] : ((equal_set(A33_33, intersection(A33_33, B34_34)) <=> subset(A33_33, B34_34)))
% 1.12/0.58
% 1.12/0.58 [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))))
% 1.12/0.58 -> [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)))
% 1.12/0.58
% 1.12/0.58 [2] DELTA_NOT_FORALL : ~! [A33_33, B34_34] : ((equal_set(A33_33, intersection(A33_33, B34_34)) <=> subset(A33_33, B34_34)))
% 1.12/0.58 -> [3] ~(equal_set(skolem_A3333, intersection(skolem_A3333, skolem_B3434)) <=> subset(skolem_A3333, skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [3] BETA_NOT_EQUIV : ~(equal_set(skolem_A3333, intersection(skolem_A3333, skolem_B3434)) <=> subset(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [4] ~equal_set(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), subset(skolem_A3333, skolem_B3434)
% 1.12/0.58 -> [5] equal_set(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), ~subset(skolem_A3333, skolem_B3434)
% 1.12/0.58
% 1.12/0.58 [5] Rewrite : equal_set(skolem_A3333, intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [6] (subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434)) & subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333))
% 1.12/0.58
% 1.12/0.58 [6] Rewrite : ~subset(skolem_A3333, skolem_B3434)
% 1.12/0.58 -> [8] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [8] ALPHA_AND : (subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434)) & subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333))
% 1.12/0.58 -> [9] subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333)
% 1.12/0.58
% 1.12/0.58 [9] Rewrite : subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [13] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, intersection(skolem_A3333, skolem_B3434))))
% 1.12/0.58
% 1.12/0.58 [13] Rewrite : subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333)
% 1.12/0.58 -> [16] ! [X7_7] : ((member(X7_7, intersection(skolem_A3333, skolem_B3434)) => member(X7_7, skolem_A3333)))
% 1.12/0.58
% 1.12/0.58 [16] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.12/0.58 -> [19] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 1.12/0.58
% 1.12/0.58 [19] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 1.12/0.58 -> [21] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.12/0.58
% 1.12/0.58 [21] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.12/0.58 -> [23] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 1.12/0.58 -> [24] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 1.12/0.58
% 1.12/0.58 [23] Rewrite : ~subset(X10_0_0, X10_0_0)
% 1.12/0.58 -> [31] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 1.12/0.58
% 1.12/0.58 [31] 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))
% 1.12/0.58 -> [32] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.12/0.58
% 1.12/0.58 [32] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.12/0.58
% 1.12/0.58 [24] Rewrite : subset(X10_0_0, X10_0_0)
% 1.12/0.58 -> [33] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 1.12/0.58
% 1.12/0.58 [33] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 1.12/0.58 -> [34] ~member(X18_0_1, empty_set)
% 1.12/0.58
% 1.12/0.58 [34] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 1.12/0.58 -> [38] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.12/0.58
% 1.12/0.58 [38] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.12/0.58 -> [40] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 1.12/0.58 -> [41] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 1.12/0.58
% 1.12/0.58 [40] CLOSURE : ~=(A23_0_2, A23_0_2)
% 1.12/0.58
% 1.12/0.58 [41] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, intersection(skolem_A3333, skolem_B3434))))
% 1.12/0.58 -> [45] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, skolem_B3434)))
% 1.12/0.58
% 1.12/0.58 [45] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, skolem_B3434)))
% 1.12/0.58 -> [46] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 1.12/0.58 -> [47] member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [46] CLOSURE : =
% 1.12/0.58
% 1.12/0.58 [47] Rewrite : member(skolem_X77(skolem_A3333, skolem_B3434), intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [48] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) & member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [48] ALPHA_AND : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) & member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.12/0.58 -> [49] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333), member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 1.12/0.58
% 1.12/0.58 [49] CLOSURE : =
% 1.12/0.58
% 1.12/0.58 [4] Rewrite : ~equal_set(skolem_A3333, intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [7] ~(subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434)) & subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333))
% 1.12/0.58
% 1.12/0.58 [7] Rewrite : subset(skolem_A3333, skolem_B3434)
% 1.12/0.58 -> [10] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 1.12/0.58
% 1.12/0.58 [10] BETA_NOT_AND : ~(subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434)) & subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333))
% 1.12/0.58 -> [11] ~subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [12] ~subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333)
% 1.12/0.58
% 1.12/0.58 [12] Rewrite : ~subset(intersection(skolem_A3333, skolem_B3434), skolem_A3333)
% 1.12/0.58 -> [14] ~(member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), intersection(skolem_A3333, skolem_B3434)) => member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_A3333))
% 1.12/0.58
% 1.12/0.58 [14] ALPHA_NOT_IMPLY : ~(member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), intersection(skolem_A3333, skolem_B3434)) => member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_A3333))
% 1.12/0.58 -> [17] member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), intersection(skolem_A3333, skolem_B3434)), ~member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_A3333)
% 1.12/0.58
% 1.12/0.58 [17] Rewrite : member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [20] (member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_A3333) & member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [20] ALPHA_AND : (member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_A3333) & member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_B3434))
% 1.12/0.58 -> [27] member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_A3333), member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_B3434)
% 1.12/0.58
% 1.12/0.58 [27] CLOSURE : member(skolem_X77(intersection(skolem_A3333, skolem_B3434), skolem_A3333), skolem_A3333)
% 1.12/0.58
% 1.12/0.58 [11] Rewrite : ~subset(skolem_A3333, intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [15] ~(member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), intersection(skolem_A3333, skolem_B3434)))
% 1.12/0.58
% 1.12/0.58 [15] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), intersection(skolem_A3333, skolem_B3434)))
% 1.12/0.58 -> [18] member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333), ~member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [18] Rewrite : ~member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), intersection(skolem_A3333, skolem_B3434))
% 1.12/0.58 -> [22] ~(member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333) & member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [22] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333) & member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_B3434))
% 1.12/0.58 -> [25] ~member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333)
% 1.12/0.58 -> [26] ~member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_B3434)
% 1.12/0.58
% 1.12/0.58 [25] CLOSURE : ~member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333)
% 1.12/0.58
% 1.12/0.58 [26] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 1.12/0.58 -> [28] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 1.12/0.58
% 1.12/0.58 [28] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 1.12/0.58 -> [29] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 1.12/0.58 -> [30] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 1.12/0.58
% 1.12/0.58 [29] Rewrite : ~subset(X10_1_0, X10_1_0)
% 1.12/0.58 -> [35] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 1.12/0.58
% 1.12/0.58 [35] 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))
% 1.12/0.58 -> [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)
% 1.12/0.58
% 1.12/0.58 [36] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 1.12/0.58
% 1.12/0.58 [30] Rewrite : subset(X10_1_0, X10_1_0)
% 1.12/0.58 -> [37] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 1.12/0.58
% 1.12/0.58 [37] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 1.12/0.58 -> [39] ~member(X18_1_1, empty_set)
% 1.12/0.58
% 1.12/0.58 [39] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 1.12/0.58 -> [42] (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 1.12/0.58
% 1.12/0.58 [42] BETA_EQUIV : (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 1.12/0.58 -> [43] ~member(A23_1_2, singleton(A23_1_2)), ~=(A23_1_2, A23_1_2)
% 1.12/0.58 -> [44] member(A23_1_2, singleton(A23_1_2)), =(A23_1_2, A23_1_2)
% 1.12/0.58
% 1.12/0.58 [43] CLOSURE : ~=(A23_1_2, A23_1_2)
% 1.12/0.58
% 1.12/0.58 [44] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 1.12/0.58 -> [50] (member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_B3434))
% 1.12/0.58
% 1.12/0.58 [50] BETA_IMPLY : (member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333) => member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_B3434))
% 1.12/0.58 -> [51] ~member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_A3333)
% 1.12/0.58 -> [52] member(skolem_X77(skolem_A3333, intersection(skolem_A3333, skolem_B3434)), skolem_B3434)
% 1.12/0.58
% 1.12/0.58 [52] CLOSURE : =
% 1.12/0.58
% 1.12/0.58 [51] CLOSURE : =
% 1.12/0.58
% 1.12/0.58 % SZS output end Proof for theBenchmark.p
% 1.12/0.58 [0.244203s][1][Res] 530 goroutines created
% 1.12/0.58 ==== Result ====
% 1.12/0.58 [0.244226s][1][Res] VALID
% 1.12/0.58 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------