TSTP Solution File: SET012+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n011.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 04:14:42 EDT 2022
% Result : Theorem 1.51s 0.62s
% Output : Proof 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n011.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 01:00:28 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 [0.000040s][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
% 1.51/0.62 % SZS output start Proof for theBenchmark.p
% 1.51/0.62 [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(difference(E34_34, difference(E34_34, A33_33)), A33_33))))
% 1.51/0.62 -> [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(difference(E34_34, difference(E34_34, A33_33)), A33_33)))
% 1.51/0.62
% 1.51/0.62 [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))))
% 1.51/0.62 -> [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)))
% 1.51/0.62
% 1.51/0.62 [2] DELTA_NOT_FORALL : ~! [A33_33, E34_34] : ((subset(A33_33, E34_34) => equal_set(difference(E34_34, difference(E34_34, A33_33)), A33_33)))
% 1.51/0.62 -> [3] ~(subset(skolem_A3333, skolem_E3434) => equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333))
% 1.51/0.62
% 1.51/0.62 [3] ALPHA_NOT_IMPLY : ~(subset(skolem_A3333, skolem_E3434) => equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333))
% 1.51/0.62 -> [4] subset(skolem_A3333, skolem_E3434), ~equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62
% 1.51/0.62 [4] Rewrite : subset(skolem_A3333, skolem_E3434)
% 1.51/0.62 -> [5] ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3434)))
% 1.51/0.62
% 1.51/0.62 [5] Rewrite : ~equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62 -> [6] ~(subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333) & subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62
% 1.51/0.62 [6] BETA_NOT_AND : ~(subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333) & subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62 -> [7] ~subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62 -> [8] ~subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62
% 1.51/0.62 [7] Rewrite : ~subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62 -> [10] ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))) => member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62
% 1.51/0.62 [10] ALPHA_NOT_IMPLY : ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))) => member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62 -> [12] member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62
% 1.51/0.62 [12] Rewrite : member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62 -> [14] (member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62
% 1.51/0.62 [14] ALPHA_AND : (member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62 -> [18] member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434), ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62
% 1.51/0.62 [18] Rewrite : ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62 -> [27] ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62
% 1.51/0.62 [27] BETA_NOT_AND : ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62 -> [29] ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434)
% 1.51/0.62 -> [30] ~~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62
% 1.51/0.62 [29] CLOSURE : ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434)
% 1.51/0.62
% 1.51/0.62 [30] ALPHA_NOT_NOT : ~~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62 -> [31] member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62
% 1.51/0.62 [31] CLOSURE : member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62
% 1.51/0.62 [8] Rewrite : ~subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62 -> [9] ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62
% 1.51/0.62 [9] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62 -> [11] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333), ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62
% 1.51/0.62 [11] Rewrite : ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62 -> [13] ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62
% 1.51/0.62 [13] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62 -> [15] ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434)
% 1.51/0.62 -> [16] ~~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62
% 1.51/0.62 [16] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62 -> [17] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62
% 1.51/0.62 [17] Rewrite : member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62 -> [20] (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333))
% 1.51/0.62
% 1.51/0.62 [20] ALPHA_AND : (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333))
% 1.51/0.62 -> [23] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434), ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333)
% 1.51/0.62
% 1.51/0.62 [23] CLOSURE : ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333)
% 1.51/0.62
% 1.51/0.62 [15] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 1.51/0.62 -> [19] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.51/0.62
% 1.51/0.62 [19] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.51/0.62 -> [21] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 1.51/0.62 -> [22] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 1.51/0.62
% 1.51/0.62 [21] Rewrite : ~subset(X10_0_0, X10_0_0)
% 1.51/0.62 -> [24] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 1.51/0.62
% 1.51/0.62 [24] 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))
% 1.51/0.62 -> [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)
% 1.51/0.62
% 1.51/0.62 [26] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.51/0.62
% 1.51/0.62 [22] Rewrite : subset(X10_0_0, X10_0_0)
% 1.51/0.62 -> [25] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 1.51/0.62
% 1.51/0.62 [25] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 1.51/0.62 -> [28] ~member(X18_0_1, empty_set)
% 1.51/0.62
% 1.51/0.62 [28] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 1.51/0.62 -> [32] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.51/0.62
% 1.51/0.62 [32] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.51/0.62 -> [33] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 1.51/0.62 -> [34] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 1.51/0.62
% 1.51/0.62 [33] CLOSURE : ~=(A23_0_2, A23_0_2)
% 1.51/0.62
% 1.51/0.62 [34] GAMMA_FORALL : ! [X7_7] : ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3434)))
% 1.51/0.62 -> [35] (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434))
% 1.51/0.62
% 1.51/0.62 [35] BETA_IMPLY : (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434))
% 1.51/0.62 -> [36] ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333)
% 1.51/0.62 -> [37] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434)
% 1.51/0.62
% 1.51/0.62 [36] CLOSURE : =
% 1.51/0.62
% 1.51/0.62 [37] CLOSURE : =
% 1.51/0.62
% 1.51/0.62 % SZS output end Proof for theBenchmark.p
% 1.51/0.62 [0.279616s][1][Res] 351 goroutines created
% 1.51/0.62 ==== Result ====
% 1.51/0.62 [0.279640s][1][Res] VALID
% 1.51/0.62 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------