TSTP Solution File: SET351+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n015.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 04:16:08 EDT 2022
% Result : Theorem 2.75s 0.83s
% Output : Proof 2.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n015.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 04:51:25 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 [0.000059s][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
% 2.75/0.83 % SZS output start Proof for theBenchmark.p
% 2.75/0.83 [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] : (equal_set(sum(singleton(A33_33)), A33_33)))
% 2.75/0.83 -> [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] : (equal_set(sum(singleton(A33_33)), A33_33))
% 2.75/0.83
% 2.75/0.83 [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))))
% 2.75/0.83 -> [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)))
% 2.75/0.83
% 2.75/0.83 [2] DELTA_NOT_FORALL : ~! [A33_33] : (equal_set(sum(singleton(A33_33)), A33_33))
% 2.75/0.83 -> [3] ~equal_set(sum(singleton(skolem_A3333)), skolem_A3333)
% 2.75/0.83
% 2.75/0.83 [3] Rewrite : ~equal_set(sum(singleton(skolem_A3333)), skolem_A3333)
% 2.75/0.83 -> [4] ~(subset(sum(singleton(skolem_A3333)), skolem_A3333) & subset(skolem_A3333, sum(singleton(skolem_A3333))))
% 2.75/0.83
% 2.75/0.83 [4] BETA_NOT_AND : ~(subset(sum(singleton(skolem_A3333)), skolem_A3333) & subset(skolem_A3333, sum(singleton(skolem_A3333))))
% 2.75/0.83 -> [5] ~subset(sum(singleton(skolem_A3333)), skolem_A3333)
% 2.75/0.83 -> [6] ~subset(skolem_A3333, sum(singleton(skolem_A3333)))
% 2.75/0.83
% 2.75/0.83 [6] Rewrite : ~subset(skolem_A3333, sum(singleton(skolem_A3333)))
% 2.75/0.83 -> [7] ~(member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), sum(singleton(skolem_A3333))))
% 2.75/0.83
% 2.75/0.83 [7] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), sum(singleton(skolem_A3333))))
% 2.75/0.83 -> [10] member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), skolem_A3333), ~member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), sum(singleton(skolem_A3333)))
% 2.75/0.83
% 2.75/0.83 [10] Rewrite : ~member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), sum(singleton(skolem_A3333)))
% 2.75/0.83 -> [12] ~? [Y29_29] : ((member(Y29_29, singleton(skolem_A3333)) & member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), Y29_29)))
% 2.75/0.83
% 2.75/0.83 [12] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 2.75/0.83 -> [13] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 2.75/0.83
% 2.75/0.83 [13] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 2.75/0.83 -> [14] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 2.75/0.83 -> [15] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 2.75/0.83
% 2.75/0.83 [14] Rewrite : ~subset(X10_0_0, X10_0_0)
% 2.75/0.83 -> [17] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 2.75/0.83
% 2.75/0.83 [17] 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))
% 2.75/0.83 -> [18] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 2.75/0.83
% 2.75/0.83 [18] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 2.75/0.83
% 2.75/0.83 [15] Rewrite : subset(X10_0_0, X10_0_0)
% 2.75/0.83 -> [19] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 2.75/0.83
% 2.75/0.83 [19] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 2.75/0.83 -> [20] ~member(X18_0_1, empty_set)
% 2.75/0.83
% 2.75/0.83 [20] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 2.75/0.83 -> [24] (member(skolem_A3333, singleton(skolem_A3333)) <=> =(skolem_A3333, skolem_A3333))
% 2.75/0.83
% 2.75/0.83 [24] BETA_EQUIV : (member(skolem_A3333, singleton(skolem_A3333)) <=> =(skolem_A3333, skolem_A3333))
% 2.75/0.83 -> [25] ~member(skolem_A3333, singleton(skolem_A3333)), ~=(skolem_A3333, skolem_A3333)
% 2.75/0.83 -> [26] member(skolem_A3333, singleton(skolem_A3333)), =(skolem_A3333, skolem_A3333)
% 2.75/0.83
% 2.75/0.83 [25] CLOSURE : ~=(skolem_A3333, skolem_A3333)
% 2.75/0.83
% 2.75/0.83 [26] GAMMA_NOT_EXISTS : ~? [Y29_29] : ((member(Y29_29, singleton(skolem_A3333)) & member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), Y29_29)))
% 2.75/0.83 -> [34] ~(member(skolem_A3333, singleton(skolem_A3333)) & member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), skolem_A3333))
% 2.75/0.83
% 2.75/0.83 [34] BETA_NOT_AND : ~(member(skolem_A3333, singleton(skolem_A3333)) & member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), skolem_A3333))
% 2.75/0.83 -> [35] ~member(skolem_A3333, singleton(skolem_A3333))
% 2.75/0.83 -> [36] ~member(skolem_X77(skolem_A3333, sum(singleton(skolem_A3333))), skolem_A3333)
% 2.75/0.83
% 2.75/0.83 [36] CLOSURE : =
% 2.75/0.83
% 2.75/0.83 [35] CLOSURE : =
% 2.75/0.83
% 2.75/0.83 [5] Rewrite : ~subset(sum(singleton(skolem_A3333)), skolem_A3333)
% 2.75/0.83 -> [8] ~(member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), sum(singleton(skolem_A3333))) => member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), skolem_A3333))
% 2.75/0.83
% 2.75/0.83 [8] ALPHA_NOT_IMPLY : ~(member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), sum(singleton(skolem_A3333))) => member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), skolem_A3333))
% 2.75/0.83 -> [9] member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), sum(singleton(skolem_A3333))), ~member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), skolem_A3333)
% 2.75/0.83
% 2.75/0.83 [9] Rewrite : member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), sum(singleton(skolem_A3333)))
% 2.75/0.83 -> [11] (member(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), singleton(skolem_A3333)) & member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333))))
% 2.75/0.83
% 2.75/0.83 [11] ALPHA_AND : (member(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), singleton(skolem_A3333)) & member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333))))
% 2.75/0.83 -> [16] member(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), singleton(skolem_A3333)), member(skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333), skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)))
% 2.75/0.83
% 2.75/0.83 [16] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 2.75/0.83 -> [21] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 2.75/0.83
% 2.75/0.83 [21] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 2.75/0.83 -> [22] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 2.75/0.83 -> [23] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 2.75/0.83
% 2.75/0.83 [22] Rewrite : ~subset(X10_1_0, X10_1_0)
% 2.75/0.83 -> [27] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 2.75/0.83
% 2.75/0.83 [27] 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))
% 2.75/0.83 -> [29] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 2.75/0.83
% 2.75/0.83 [29] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 2.75/0.83
% 2.75/0.83 [23] Rewrite : subset(X10_1_0, X10_1_0)
% 2.75/0.83 -> [28] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 2.75/0.83
% 2.75/0.83 [28] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 2.75/0.83 -> [30] ~member(X18_1_1, empty_set)
% 2.75/0.83
% 2.75/0.83 [30] GAMMA_FORALL : ! [X22_22, A23_23] : ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 2.75/0.83 -> [31] (member(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), singleton(skolem_A3333)) <=> =(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), skolem_A3333))
% 2.75/0.83
% 2.75/0.83 [31] BETA_EQUIV : (member(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), singleton(skolem_A3333)) <=> =(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), skolem_A3333))
% 2.75/0.83 -> [32] ~member(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), singleton(skolem_A3333)), ~=(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), skolem_A3333)
% 2.75/0.83 -> [33] member(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), singleton(skolem_A3333)), =(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), skolem_A3333)
% 2.75/0.83
% 2.75/0.83 [32] CLOSURE : ~=(skolem_Y2929(singleton(skolem_A3333), skolem_X77(sum(singleton(skolem_A3333)), skolem_A3333)), skolem_A3333)
% 2.75/0.83
% 2.75/0.83 [33] CLOSURE : =
% 2.75/0.83
% 2.75/0.83 % SZS output end Proof for theBenchmark.p
% 2.75/0.83 [0.489050s][1][Res] 1000 goroutines created
% 2.75/0.83 ==== Result ====
% 2.75/0.83 [0.489074s][1][Res] VALID
% 2.75/0.83 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------