TSTP Solution File: SET603+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SET603+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n014.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 04:16:49 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET603+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n014.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 06:53:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000036s][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
% 0.13/0.38 % SZS output start Proof for theBenchmark.p
% 0.13/0.38 [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)))) & ~! [E33_33] : (equal_set(difference(E33_33, empty_set), E33_33)))
% 0.13/0.38 -> [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)))), ~! [E33_33] : (equal_set(difference(E33_33, empty_set), E33_33))
% 0.13/0.38
% 0.13/0.38 [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))))
% 0.13/0.38 -> [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)))
% 0.13/0.38
% 0.13/0.38 [2] DELTA_NOT_FORALL : ~! [E33_33] : (equal_set(difference(E33_33, empty_set), E33_33))
% 0.13/0.38 -> [3] ~equal_set(difference(skolem_E3333, empty_set), skolem_E3333)
% 0.13/0.38
% 0.13/0.38 [3] Rewrite : ~equal_set(difference(skolem_E3333, empty_set), skolem_E3333)
% 0.13/0.38 -> [4] ~(subset(difference(skolem_E3333, empty_set), skolem_E3333) & subset(skolem_E3333, difference(skolem_E3333, empty_set)))
% 0.13/0.38
% 0.13/0.38 [4] BETA_NOT_AND : ~(subset(difference(skolem_E3333, empty_set), skolem_E3333) & subset(skolem_E3333, difference(skolem_E3333, empty_set)))
% 0.13/0.38 -> [5] ~subset(difference(skolem_E3333, empty_set), skolem_E3333)
% 0.13/0.38 -> [6] ~subset(skolem_E3333, difference(skolem_E3333, empty_set))
% 0.13/0.38
% 0.13/0.38 [5] Rewrite : ~subset(difference(skolem_E3333, empty_set), skolem_E3333)
% 0.13/0.38 -> [8] ~(member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), difference(skolem_E3333, empty_set)) => member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), skolem_E3333))
% 0.13/0.38
% 0.13/0.38 [8] ALPHA_NOT_IMPLY : ~(member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), difference(skolem_E3333, empty_set)) => member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), skolem_E3333))
% 0.13/0.38 -> [10] member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), difference(skolem_E3333, empty_set)), ~member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), skolem_E3333)
% 0.13/0.38
% 0.13/0.38 [10] Rewrite : member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), difference(skolem_E3333, empty_set))
% 0.13/0.38 -> [12] (member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), skolem_E3333) & ~member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), empty_set))
% 0.13/0.38
% 0.13/0.38 [12] ALPHA_AND : (member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), skolem_E3333) & ~member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), empty_set))
% 0.13/0.38 -> [16] member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), skolem_E3333), ~member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), empty_set)
% 0.13/0.38
% 0.13/0.38 [16] CLOSURE : member(skolem_X77(difference(skolem_E3333, empty_set), skolem_E3333), skolem_E3333)
% 0.13/0.38
% 0.13/0.38 [6] Rewrite : ~subset(skolem_E3333, difference(skolem_E3333, empty_set))
% 0.13/0.38 -> [7] ~(member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), skolem_E3333) => member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), difference(skolem_E3333, empty_set)))
% 0.13/0.38
% 0.13/0.38 [7] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), skolem_E3333) => member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), difference(skolem_E3333, empty_set)))
% 0.13/0.38 -> [9] member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), skolem_E3333), ~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), difference(skolem_E3333, empty_set))
% 0.13/0.38
% 0.13/0.38 [9] Rewrite : ~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), difference(skolem_E3333, empty_set))
% 0.13/0.38 -> [11] ~(member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), skolem_E3333) & ~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), empty_set))
% 0.13/0.38
% 0.13/0.38 [11] BETA_NOT_AND : ~(member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), skolem_E3333) & ~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), empty_set))
% 0.13/0.38 -> [13] ~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), skolem_E3333)
% 0.13/0.38 -> [14] ~~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), empty_set)
% 0.13/0.38
% 0.13/0.38 [13] CLOSURE : ~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), skolem_E3333)
% 0.13/0.38
% 0.13/0.38 [14] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), empty_set)
% 0.13/0.38 -> [15] member(skolem_X77(skolem_E3333, difference(skolem_E3333, empty_set)), empty_set)
% 0.13/0.38
% 0.13/0.38 [15] GAMMA_FORALL : ! [X10_10, A11_11] : ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.13/0.38 -> [17] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.13/0.38
% 0.13/0.38 [17] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.13/0.38 -> [18] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 0.13/0.38 -> [19] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 0.13/0.38
% 0.13/0.38 [19] Rewrite : subset(X10_0_0, X10_0_0)
% 0.13/0.38 -> [21] ! [X7_7] : ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 0.13/0.38
% 0.13/0.38 [21] GAMMA_FORALL : ! [X18_18] : (~member(X18_18, empty_set))
% 0.13/0.38 -> [23] ~member(X18_0_1, empty_set)
% 0.13/0.38
% 0.13/0.38 [23] CLOSURE : ~member(X18_0_1, empty_set)
% 0.13/0.38
% 0.13/0.38 [18] Rewrite : ~subset(X10_0_0, X10_0_0)
% 0.13/0.38 -> [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))
% 0.13/0.38
% 0.13/0.38 [20] 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))
% 0.13/0.38 -> [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)
% 0.13/0.38
% 0.13/0.38 [22] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.13/0.38
% 0.13/0.38 % SZS output end Proof for theBenchmark.p
% 0.13/0.38 [0.025310s][1][Res] 108 goroutines created
% 0.13/0.38 ==== Result ====
% 0.13/0.38 [0.025344s][1][Res] VALID
% 0.13/0.38 % SZS status Theorem for theBenchmark.p
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