TSTP Solution File: SET595+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET595+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n001.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 04:16:46 EDT 2022
% Result : Theorem 1.51s 0.64s
% Output : Proof 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET595+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 07:11:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 15
% 0.13/0.35 Launch Gotab with destructive = true
% 1.51/0.64 % SZS output start Proof for theBenchmark.p
% 1.51/0.64 [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, E34_34] : ((subset(A33_33, E34_34) => equal_set(union(difference(E34_34, A33_33), A33_33), E34_34))))
% 1.51/0.64 -> [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, E34_34] : ((subset(A33_33, E34_34) => equal_set(union(difference(E34_34, A33_33), A33_33), E34_34)))
% 1.51/0.64
% 1.51/0.64 [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))))
% 1.51/0.64 -> [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)))
% 1.51/0.64
% 1.51/0.64 [2] DELTA_NOT_FORALL : ~! [A33_33, E34_34] : ((subset(A33_33, E34_34) => equal_set(union(difference(E34_34, A33_33), A33_33), E34_34)))
% 1.51/0.64 -> [3] ~(subset(skolem_A3333, skolem_E3434) => equal_set(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434))
% 1.51/0.64
% 1.51/0.64 [3] ALPHA_NOT_IMPLY : ~(subset(skolem_A3333, skolem_E3434) => equal_set(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434))
% 1.51/0.64 -> [4] subset(skolem_A3333, skolem_E3434), ~equal_set(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434)
% 1.51/0.64
% 1.51/0.64 [4] Rewrite : subset(skolem_A3333, skolem_E3434)
% 1.51/0.64 -> [5] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3434)))
% 1.51/0.64
% 1.51/0.64 [5] Rewrite : ~equal_set(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434)
% 1.51/0.64 -> [6] ~(subset(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434) & subset(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 1.51/0.64
% 1.51/0.64 [6] BETA_NOT_AND : ~(subset(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434) & subset(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 1.51/0.64 -> [7] ~subset(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434)
% 1.51/0.64 -> [8] ~subset(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 1.51/0.64
% 1.51/0.64 [8] Rewrite : ~subset(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 1.51/0.64 -> [9] ~(member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434) => member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), union(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 1.51/0.64
% 1.51/0.64 [9] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434) => member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), union(difference(skolem_E3434, skolem_A3333), skolem_A3333)))
% 1.51/0.64 -> [10] member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434), ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), union(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 1.51/0.64
% 1.51/0.64 [10] Rewrite : ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), union(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 1.51/0.64 -> [13] ~(member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333)) | member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 1.51/0.64
% 1.51/0.64 [13] ALPHA_NOT_OR : ~(member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333)) | member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 1.51/0.64 -> [15] ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333)), ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 1.51/0.64
% 1.51/0.64 [15] Rewrite : ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), difference(skolem_E3434, skolem_A3333))
% 1.51/0.64 -> [20] ~(member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434) & ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 1.51/0.64
% 1.51/0.64 [20] BETA_NOT_AND : ~(member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434) & ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333))
% 1.51/0.64 -> [24] ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434)
% 1.51/0.64 -> [25] ~~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 1.51/0.64
% 1.51/0.64 [24] CLOSURE : ~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_E3434)
% 1.51/0.64
% 1.51/0.64 [25] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 1.51/0.64 -> [28] member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 1.51/0.64
% 1.51/0.64 [28] CLOSURE : member(skolem_X77(skolem_E3434, union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), skolem_A3333)
% 1.51/0.64
% 1.51/0.64 [7] Rewrite : ~subset(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434)
% 1.51/0.64 -> [11] ~(member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), union(difference(skolem_E3434, skolem_A3333), skolem_A3333)) => member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434))
% 1.51/0.64
% 1.51/0.64 [11] ALPHA_NOT_IMPLY : ~(member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), union(difference(skolem_E3434, skolem_A3333), skolem_A3333)) => member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434))
% 1.51/0.64 -> [12] member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), union(difference(skolem_E3434, skolem_A3333), skolem_A3333)), ~member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434)
% 1.51/0.64
% 1.51/0.64 [12] Rewrite : member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), union(difference(skolem_E3434, skolem_A3333), skolem_A3333))
% 1.51/0.64 -> [14] (member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), difference(skolem_E3434, skolem_A3333)) | member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333))
% 1.51/0.64
% 1.51/0.64 [14] BETA_OR : (member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), difference(skolem_E3434, skolem_A3333)) | member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333))
% 1.51/0.64 -> [16] member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), difference(skolem_E3434, skolem_A3333))
% 1.51/0.64 -> [17] member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333)
% 1.51/0.64
% 1.51/0.64 [16] Rewrite : member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), difference(skolem_E3434, skolem_A3333))
% 1.51/0.64 -> [18] (member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434) & ~member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333))
% 1.51/0.64
% 1.51/0.64 [18] ALPHA_AND : (member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434) & ~member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333))
% 1.51/0.64 -> [21] member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434), ~member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333)
% 1.51/0.64
% 1.51/0.64 [21] CLOSURE : member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434)
% 1.51/0.64
% 1.51/0.64 [17] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 1.51/0.64 -> [19] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.51/0.64
% 1.51/0.64 [19] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.51/0.64 -> [22] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 1.51/0.64 -> [23] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 1.51/0.64
% 1.51/0.64 [22] Rewrite : ~subset(X10_0_0, X10_0_0)
% 1.51/0.64 -> [26] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 1.51/0.64
% 1.51/0.64 [26] 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))
% 1.51/0.64 -> [29] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.51/0.64
% 1.51/0.64 [29] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.51/0.64
% 1.51/0.64 [23] Rewrite : subset(X10_0_0, X10_0_0)
% 1.51/0.64 -> [27] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 1.51/0.64
% 1.51/0.64 [27] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 1.51/0.64 -> [30] ~member(X18_0_1, empty_set)
% 1.51/0.64
% 1.51/0.64 [30] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 1.51/0.64 -> [31] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.51/0.64
% 1.51/0.64 [31] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.51/0.64 -> [32] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 1.51/0.64 -> [33] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 1.51/0.64
% 1.51/0.64 [32] CLOSURE : ~=(A23_0_2, A23_0_2)
% 1.51/0.64
% 1.51/0.64 [33] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3434)))
% 1.51/0.64 -> [34] (member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333) => member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434))
% 1.51/0.64
% 1.51/0.64 [34] BETA_IMPLY : (member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333) => member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434))
% 1.51/0.64 -> [35] ~member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_A3333)
% 1.51/0.64 -> [36] member(skolem_X77(union(difference(skolem_E3434, skolem_A3333), skolem_A3333), skolem_E3434), skolem_E3434)
% 1.51/0.64
% 1.51/0.64 [36] CLOSURE : =
% 1.51/0.64
% 1.51/0.64 [35] CLOSURE : =
% 1.51/0.64
% 1.51/0.64 % SZS output end Proof for theBenchmark.p
% 1.51/0.64 [0.294234s][1][Res] 349 goroutines created
% 1.51/0.64 ==== Result ====
% 1.51/0.64 [0.294257s][1][Res] VALID
% 1.51/0.64 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------