TSTP Solution File: SET019+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET019+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n017.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 04:14:49 EDT 2022
% Result : Theorem 1.13s 0.59s
% Output : Proof 1.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET019+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 00:39:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Conjecture not found
% 0.13/0.34 Start search
% 0.13/0.34 nb_step : 1 - limit : 15
% 0.13/0.34 Launch Gotab with destructive = true
% 1.13/0.59 % SZS output start Proof for theBenchmark.p
% 1.13/0.59 [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] : (((subset(A33_33, B34_34) & subset(B34_34, A33_33)) => equal_set(A33_33, B34_34))))
% 1.13/0.59 -> [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] : (((subset(A33_33, B34_34) & subset(B34_34, A33_33)) => equal_set(A33_33, B34_34)))
% 1.13/0.59
% 1.13/0.59 [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))))
% 1.13/0.59 -> [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)))
% 1.13/0.59
% 1.13/0.59 [2] DELTA_NOT_FORALL : ~! [A33_33, B34_34] : (((subset(A33_33, B34_34) & subset(B34_34, A33_33)) => equal_set(A33_33, B34_34)))
% 1.13/0.59 -> [3] ~((subset(skolem_A3333, skolem_B3434) & subset(skolem_B3434, skolem_A3333)) => equal_set(skolem_A3333, skolem_B3434))
% 1.13/0.59
% 1.13/0.59 [3] ALPHA_NOT_IMPLY : ~((subset(skolem_A3333, skolem_B3434) & subset(skolem_B3434, skolem_A3333)) => equal_set(skolem_A3333, skolem_B3434))
% 1.13/0.59 -> [4] (subset(skolem_A3333, skolem_B3434) & subset(skolem_B3434, skolem_A3333)), ~equal_set(skolem_A3333, skolem_B3434)
% 1.13/0.59
% 1.13/0.59 [4] Rewrite : ~equal_set(skolem_A3333, skolem_B3434)
% 1.13/0.59 -> [5] ~(subset(skolem_A3333, skolem_B3434) & subset(skolem_B3434, skolem_A3333))
% 1.13/0.59
% 1.13/0.59 [5] ALPHA_AND : (subset(skolem_A3333, skolem_B3434) & subset(skolem_B3434, skolem_A3333))
% 1.13/0.59 -> [6] subset(skolem_A3333, skolem_B3434), subset(skolem_B3434, skolem_A3333)
% 1.13/0.59
% 1.13/0.59 [6] Rewrite : subset(skolem_A3333, skolem_B3434)
% 1.13/0.59 -> [7] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 1.13/0.59
% 1.13/0.59 [7] Rewrite : subset(skolem_B3434, skolem_A3333)
% 1.13/0.59 -> [8] ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_A3333)))
% 1.13/0.59
% 1.13/0.59 [8] BETA_NOT_AND : ~(subset(skolem_A3333, skolem_B3434) & subset(skolem_B3434, skolem_A3333))
% 1.13/0.59 -> [9] ~subset(skolem_A3333, skolem_B3434)
% 1.13/0.59 -> [10] ~subset(skolem_B3434, skolem_A3333)
% 1.13/0.59
% 1.13/0.59 [9] Rewrite : ~subset(skolem_A3333, skolem_B3434)
% 1.13/0.59 -> [13] ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.13/0.59
% 1.13/0.59 [13] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.13/0.59 -> [14] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333), ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 1.13/0.59
% 1.13/0.59 [14] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 1.13/0.59 -> [16] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 1.13/0.59
% 1.13/0.59 [16] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 1.13/0.59 -> [19] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 1.13/0.59 -> [20] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 1.13/0.59
% 1.13/0.59 [19] Rewrite : ~subset(X10_1_0, X10_1_0)
% 1.13/0.59 -> [24] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 1.13/0.59
% 1.13/0.59 [24] 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))
% 1.13/0.59 -> [26] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 1.13/0.59
% 1.13/0.59 [26] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 1.13/0.59
% 1.13/0.59 [20] Rewrite : subset(X10_1_0, X10_1_0)
% 1.13/0.59 -> [25] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 1.13/0.59
% 1.13/0.59 [25] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 1.13/0.59 -> [28] ~member(X18_1_1, empty_set)
% 1.13/0.59
% 1.13/0.59 [28] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 1.13/0.59 -> [30] (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 1.13/0.59
% 1.13/0.59 [30] BETA_EQUIV : (member(A23_1_2, singleton(A23_1_2)) <=> =(A23_1_2, A23_1_2))
% 1.13/0.59 -> [33] ~member(A23_1_2, singleton(A23_1_2)), ~=(A23_1_2, A23_1_2)
% 1.13/0.59 -> [34] member(A23_1_2, singleton(A23_1_2)), =(A23_1_2, A23_1_2)
% 1.13/0.59
% 1.13/0.59 [33] CLOSURE : ~=(A23_1_2, A23_1_2)
% 1.13/0.59
% 1.13/0.59 [34] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 1.13/0.59 -> [38] (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.13/0.59
% 1.13/0.59 [38] BETA_IMPLY : (member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333) => member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434))
% 1.13/0.59 -> [39] ~member(skolem_X77(skolem_A3333, skolem_B3434), skolem_A3333)
% 1.13/0.59 -> [40] member(skolem_X77(skolem_A3333, skolem_B3434), skolem_B3434)
% 1.13/0.59
% 1.13/0.59 [40] CLOSURE : =
% 1.13/0.59
% 1.13/0.59 [39] CLOSURE : =
% 1.13/0.59
% 1.13/0.59 [10] Rewrite : ~subset(skolem_B3434, skolem_A3333)
% 1.13/0.59 -> [11] ~(member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434) => member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333))
% 1.13/0.59
% 1.13/0.59 [11] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434) => member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333))
% 1.13/0.59 -> [12] member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434), ~member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333)
% 1.13/0.59
% 1.13/0.59 [12] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 1.13/0.59 -> [15] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.13/0.59
% 1.13/0.59 [15] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.13/0.59 -> [17] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 1.13/0.59 -> [18] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 1.13/0.59
% 1.13/0.59 [17] Rewrite : ~subset(X10_0_0, X10_0_0)
% 1.13/0.59 -> [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))
% 1.13/0.59
% 1.13/0.59 [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))
% 1.13/0.59 -> [22] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.13/0.59
% 1.13/0.59 [22] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.13/0.59
% 1.13/0.59 [18] Rewrite : subset(X10_0_0, X10_0_0)
% 1.13/0.59 -> [23] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 1.13/0.59
% 1.13/0.59 [23] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 1.13/0.59 -> [27] ~member(X18_0_1, empty_set)
% 1.13/0.59
% 1.13/0.59 [27] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 1.13/0.59 -> [29] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.13/0.59
% 1.13/0.59 [29] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.13/0.59 -> [31] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 1.13/0.59 -> [32] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 1.13/0.59
% 1.13/0.59 [31] CLOSURE : ~=(A23_0_2, A23_0_2)
% 1.13/0.59
% 1.13/0.59 [32] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_B3434)))
% 1.13/0.59 -> [35] (member(X7_0_3, skolem_A3333) => member(X7_0_3, skolem_B3434))
% 1.13/0.59
% 1.13/0.59 [35] BETA_IMPLY : (member(X7_0_3, skolem_A3333) => member(X7_0_3, skolem_B3434))
% 1.13/0.59 -> [36] ~member(X7_0_3, skolem_A3333)
% 1.13/0.59 -> [37] member(X7_0_3, skolem_B3434)
% 1.13/0.59
% 1.13/0.59 [37] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_A3333)))
% 1.13/0.59 -> [41] (member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434) => member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333))
% 1.13/0.59
% 1.13/0.59 [41] BETA_IMPLY : (member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434) => member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333))
% 1.13/0.59 -> [42] ~member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434)
% 1.13/0.59 -> [43] member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333)
% 1.13/0.59
% 1.13/0.59 [43] CLOSURE : =
% 1.13/0.59
% 1.13/0.59 [42] CLOSURE : =
% 1.13/0.59
% 1.13/0.59 [36] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_B3434) => member(X7_7, skolem_A3333)))
% 1.13/0.59 -> [44] (member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434) => member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333))
% 1.13/0.59
% 1.13/0.59 [44] BETA_IMPLY : (member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434) => member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333))
% 1.13/0.59 -> [45] ~member(skolem_X77(skolem_B3434, skolem_A3333), skolem_B3434)
% 1.13/0.59 -> [46] member(skolem_X77(skolem_B3434, skolem_A3333), skolem_A3333)
% 1.13/0.59
% 1.13/0.59 [46] CLOSURE : =
% 1.13/0.59
% 1.13/0.59 [45] CLOSURE : =
% 1.13/0.59
% 1.13/0.59 % SZS output end Proof for theBenchmark.p
% 1.13/0.59 [0.249149s][1][Res] 573 goroutines created
% 1.13/0.59 ==== Result ====
% 1.13/0.59 [0.249183s][1][Res] VALID
% 1.13/0.59 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------