TSTP Solution File: SET347+4 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n020.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 04:16:07 EDT 2022
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.11/0.33 % Computer : n020.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 04:38:59 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 [DMT] DMT loaded with preskolemization
% 0.11/0.34 [EQ] equality loaded.
% 0.11/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.34 Conjecture not found
% 0.11/0.34 Start search
% 0.11/0.34 nb_step : 1 - limit : 14
% 0.11/0.34 Launch Gotab with destructive = true
% 0.11/0.36 % SZS output start Proof for theBenchmark.p
% 0.11/0.36 [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)))) & ~equal_set(sum(empty_set), empty_set))
% 0.11/0.36 -> [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)))), ~equal_set(sum(empty_set), empty_set)
% 0.11/0.36
% 0.11/0.36 [1] Rewrite : ~equal_set(sum(empty_set), empty_set)
% 0.11/0.36 -> [2] ~(subset(sum(empty_set), empty_set) & subset(empty_set, sum(empty_set)))
% 0.11/0.36
% 0.11/0.36 [2] 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))))
% 0.11/0.36 -> [3] ! [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)))
% 0.11/0.36
% 0.11/0.36 [3] BETA_NOT_AND : ~(subset(sum(empty_set), empty_set) & subset(empty_set, sum(empty_set)))
% 0.11/0.36 -> [4] ~subset(sum(empty_set), empty_set)
% 0.11/0.36 -> [5] ~subset(empty_set, sum(empty_set))
% 0.11/0.36
% 0.11/0.36 [5] Rewrite : ~subset(empty_set, sum(empty_set))
% 0.11/0.36 -> [6] ~(member(skolem_X77(empty_set, sum(empty_set)), empty_set) => member(skolem_X77(empty_set, sum(empty_set)), sum(empty_set)))
% 0.11/0.36
% 0.11/0.36 [6] ALPHA_NOT_IMPLY : ~(member(skolem_X77(empty_set, sum(empty_set)), empty_set) => member(skolem_X77(empty_set, sum(empty_set)), sum(empty_set)))
% 0.11/0.36 -> [8] member(skolem_X77(empty_set, sum(empty_set)), empty_set), ~member(skolem_X77(empty_set, sum(empty_set)), sum(empty_set))
% 0.11/0.36
% 0.11/0.36 [8] Rewrite : ~member(skolem_X77(empty_set, sum(empty_set)), sum(empty_set))
% 0.11/0.36 -> [11] ~? [Y29_29] : ((member(Y29_29, empty_set) & member(skolem_X77(empty_set, sum(empty_set)), Y29_29)))
% 0.11/0.36
% 0.11/0.36 [11] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.11/0.36 -> [12] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.11/0.36
% 0.11/0.36 [12] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.11/0.36 -> [13] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 0.11/0.36 -> [14] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 0.11/0.36
% 0.11/0.36 [14] Rewrite : subset(X10_0_0, X10_0_0)
% 0.11/0.36 -> [17] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 0.11/0.36
% 0.11/0.36 [17] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.11/0.36 -> [19] ~member(X18_0_1, empty_set)
% 0.11/0.36
% 0.11/0.36 [19] CLOSURE : ~member(X18_0_1, empty_set)
% 0.11/0.36
% 0.11/0.36 [13] Rewrite : ~subset(X10_0_0, X10_0_0)
% 0.11/0.36 -> [16] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 0.11/0.36
% 0.11/0.36 [16] 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))
% 0.11/0.36 -> [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)
% 0.11/0.36
% 0.11/0.36 [18] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.11/0.36
% 0.11/0.36 [4] Rewrite : ~subset(sum(empty_set), empty_set)
% 0.11/0.36 -> [7] ~(member(skolem_X77(sum(empty_set), empty_set), sum(empty_set)) => member(skolem_X77(sum(empty_set), empty_set), empty_set))
% 0.11/0.36
% 0.11/0.36 [7] ALPHA_NOT_IMPLY : ~(member(skolem_X77(sum(empty_set), empty_set), sum(empty_set)) => member(skolem_X77(sum(empty_set), empty_set), empty_set))
% 0.11/0.36 -> [9] member(skolem_X77(sum(empty_set), empty_set), sum(empty_set)), ~member(skolem_X77(sum(empty_set), empty_set), empty_set)
% 0.11/0.36
% 0.11/0.36 [9] Rewrite : member(skolem_X77(sum(empty_set), empty_set), sum(empty_set))
% 0.11/0.36 -> [10] (member(skolem_Y2929(empty_set, skolem_X77(sum(empty_set), empty_set)), empty_set) & member(skolem_X77(sum(empty_set), empty_set), skolem_Y2929(empty_set, skolem_X77(sum(empty_set), empty_set))))
% 0.11/0.36
% 0.11/0.36 [10] ALPHA_AND : (member(skolem_Y2929(empty_set, skolem_X77(sum(empty_set), empty_set)), empty_set) & member(skolem_X77(sum(empty_set), empty_set), skolem_Y2929(empty_set, skolem_X77(sum(empty_set), empty_set))))
% 0.11/0.36 -> [15] member(skolem_Y2929(empty_set, skolem_X77(sum(empty_set), empty_set)), empty_set), member(skolem_X77(sum(empty_set), empty_set), skolem_Y2929(empty_set, skolem_X77(sum(empty_set), empty_set)))
% 0.11/0.36
% 0.11/0.36 [15] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.11/0.36 -> [20] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 0.11/0.36
% 0.11/0.36 [20] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 0.11/0.36 -> [21] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 0.11/0.36 -> [22] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 0.11/0.36
% 0.11/0.36 [22] Rewrite : subset(X10_1_0, X10_1_0)
% 0.11/0.36 -> [24] ! [X7_7] : ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 0.11/0.36
% 0.11/0.36 [24] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.11/0.36 -> [26] ~member(X18_1_1, empty_set)
% 0.11/0.36
% 0.11/0.36 [26] CLOSURE : ~member(X18_1_1, empty_set)
% 0.11/0.36
% 0.11/0.36 [21] Rewrite : ~subset(X10_1_0, X10_1_0)
% 0.11/0.36 -> [23] ~(member(skolem_X77(X10_1_0, X10_1_0), X10_1_0) => member(skolem_X77(X10_1_0, X10_1_0), X10_1_0))
% 0.11/0.36
% 0.11/0.36 [23] 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))
% 0.11/0.36 -> [25] member(skolem_X77(X10_1_0, X10_1_0), X10_1_0), ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 0.11/0.36
% 0.11/0.36 [25] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 0.11/0.36
% 0.11/0.36 % SZS output end Proof for theBenchmark.p
% 0.11/0.36 [0.024750s][1][Res] 151 goroutines created
% 0.11/0.36 ==== Result ====
% 0.11/0.36 [0.024782s][1][Res] VALID
% 0.11/0.36 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------