TSTP Solution File: SET162+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n024.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 04:15:38 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n024.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 03:04:33 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 [0.000047s][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
% 0.13/0.37 % SZS output start Proof for theBenchmark.p
% 0.13/0.37 [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(union(A33_33, empty_set), A33_33)))
% 0.13/0.37 -> [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(union(A33_33, empty_set), A33_33))
% 0.13/0.37
% 0.13/0.37 [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))))
% 0.13/0.37 -> [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)))
% 0.13/0.37
% 0.13/0.37 [2] DELTA_NOT_FORALL : ~! [A33_33] : (equal_set(union(A33_33, empty_set), A33_33))
% 0.13/0.37 -> [3] ~equal_set(union(skolem_A3333, empty_set), skolem_A3333)
% 0.13/0.37
% 0.13/0.37 [3] Rewrite : ~equal_set(union(skolem_A3333, empty_set), skolem_A3333)
% 0.13/0.37 -> [4] ~(subset(union(skolem_A3333, empty_set), skolem_A3333) & subset(skolem_A3333, union(skolem_A3333, empty_set)))
% 0.13/0.37
% 0.13/0.37 [4] BETA_NOT_AND : ~(subset(union(skolem_A3333, empty_set), skolem_A3333) & subset(skolem_A3333, union(skolem_A3333, empty_set)))
% 0.13/0.37 -> [5] ~subset(union(skolem_A3333, empty_set), skolem_A3333)
% 0.13/0.37 -> [6] ~subset(skolem_A3333, union(skolem_A3333, empty_set))
% 0.13/0.37
% 0.13/0.37 [6] Rewrite : ~subset(skolem_A3333, union(skolem_A3333, empty_set))
% 0.13/0.37 -> [7] ~(member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), skolem_A3333) => member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), union(skolem_A3333, empty_set)))
% 0.13/0.37
% 0.13/0.37 [7] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), skolem_A3333) => member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), union(skolem_A3333, empty_set)))
% 0.13/0.37 -> [9] member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), skolem_A3333), ~member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), union(skolem_A3333, empty_set))
% 0.13/0.37
% 0.13/0.37 [9] Rewrite : ~member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), union(skolem_A3333, empty_set))
% 0.13/0.37 -> [11] ~(member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), skolem_A3333) | member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), empty_set))
% 0.13/0.37
% 0.13/0.37 [11] ALPHA_NOT_OR : ~(member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), skolem_A3333) | member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), empty_set))
% 0.13/0.37 -> [13] ~member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), skolem_A3333), ~member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), empty_set)
% 0.13/0.37
% 0.13/0.37 [13] CLOSURE : ~member(skolem_X77(skolem_A3333, union(skolem_A3333, empty_set)), skolem_A3333)
% 0.13/0.37
% 0.13/0.37 [5] Rewrite : ~subset(union(skolem_A3333, empty_set), skolem_A3333)
% 0.13/0.37 -> [8] ~(member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), union(skolem_A3333, empty_set)) => member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), skolem_A3333))
% 0.13/0.37
% 0.13/0.37 [8] ALPHA_NOT_IMPLY : ~(member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), union(skolem_A3333, empty_set)) => member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), skolem_A3333))
% 0.13/0.37 -> [10] member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), union(skolem_A3333, empty_set)), ~member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), skolem_A3333)
% 0.13/0.37
% 0.13/0.37 [10] Rewrite : member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), union(skolem_A3333, empty_set))
% 0.13/0.37 -> [12] (member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), skolem_A3333) | member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), empty_set))
% 0.13/0.37
% 0.13/0.37 [12] BETA_OR : (member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), skolem_A3333) | member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), empty_set))
% 0.13/0.37 -> [14] member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), skolem_A3333)
% 0.13/0.37 -> [15] member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), empty_set)
% 0.13/0.37
% 0.13/0.37 [14] CLOSURE : member(skolem_X77(union(skolem_A3333, empty_set), skolem_A3333), skolem_A3333)
% 0.13/0.37
% 0.13/0.37 [15] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.13/0.37 -> [16] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.13/0.37
% 0.13/0.37 [16] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.13/0.37 -> [17] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 0.13/0.37 -> [18] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 0.13/0.37
% 0.13/0.37 [17] Rewrite : ~subset(X10_0_0, X10_0_0)
% 0.13/0.37 -> [19] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 0.13/0.37
% 0.13/0.37 [19] 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))
% 0.13/0.37 -> [20] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.13/0.37
% 0.13/0.37 [20] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.13/0.37
% 0.13/0.37 [18] Rewrite : subset(X10_0_0, X10_0_0)
% 0.13/0.37 -> [21] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 0.13/0.37
% 0.13/0.37 [21] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.13/0.37 -> [22] ~member(X18_0_1, empty_set)
% 0.13/0.37
% 0.13/0.37 [22] CLOSURE : ~member(X18_0_1, empty_set)
% 0.13/0.37
% 0.13/0.37 % SZS output end Proof for theBenchmark.p
% 0.13/0.37 [0.025797s][1][Res] 102 goroutines created
% 0.13/0.37 ==== Result ====
% 0.13/0.37 [0.025830s][1][Res] VALID
% 0.13/0.37 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------