TSTP Solution File: SET602+4 by Goeland---1.0.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Goeland---1.0.0
% Problem  : SET602+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : goeland -dmt -presko -proof %s

% Computer : n012.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 04:16:48 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET602+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12  % Command    : goeland -dmt -presko -proof %s
% 0.12/0.33  % Computer : n012.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 06:51:34 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  [DMT] DMT loaded with preskolemization
% 0.12/0.33  [EQ] equality loaded.
% 0.12/0.33  [0.000041s][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
% 0.12/0.36  % SZS output start Proof for theBenchmark.p
% 0.12/0.36  [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)))) & ~! [E33_33] :  (equal_set(difference(E33_33, E33_33), empty_set)))
% 0.12/0.36  	-> [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)))), ~! [E33_33] :  (equal_set(difference(E33_33, E33_33), empty_set))
% 0.12/0.36  
% 0.12/0.36  [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))))
% 0.12/0.36  	-> [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)))
% 0.12/0.36  
% 0.12/0.36  [2] DELTA_NOT_FORALL : ~! [E33_33] :  (equal_set(difference(E33_33, E33_33), empty_set))
% 0.12/0.36  	-> [3] ~equal_set(difference(skolem_E3333, skolem_E3333), empty_set)
% 0.12/0.36  
% 0.12/0.36  [3] Rewrite : ~equal_set(difference(skolem_E3333, skolem_E3333), empty_set)
% 0.12/0.36  	-> [4] ~(subset(difference(skolem_E3333, skolem_E3333), empty_set) & subset(empty_set, difference(skolem_E3333, skolem_E3333)))
% 0.12/0.36  
% 0.12/0.36  [4] BETA_NOT_AND : ~(subset(difference(skolem_E3333, skolem_E3333), empty_set) & subset(empty_set, difference(skolem_E3333, skolem_E3333)))
% 0.12/0.36  	-> [5] ~subset(difference(skolem_E3333, skolem_E3333), empty_set)
% 0.12/0.36  	-> [6] ~subset(empty_set, difference(skolem_E3333, skolem_E3333))
% 0.12/0.36  
% 0.12/0.36  [5] Rewrite : ~subset(difference(skolem_E3333, skolem_E3333), empty_set)
% 0.12/0.36  	-> [8] ~(member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), difference(skolem_E3333, skolem_E3333)) => member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), empty_set))
% 0.12/0.36  
% 0.12/0.36  [8] ALPHA_NOT_IMPLY : ~(member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), difference(skolem_E3333, skolem_E3333)) => member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), empty_set))
% 0.12/0.36  	-> [10] member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), difference(skolem_E3333, skolem_E3333)), ~member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), empty_set)
% 0.12/0.36  
% 0.12/0.36  [10] Rewrite : member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), difference(skolem_E3333, skolem_E3333))
% 0.12/0.36  	-> [11] (member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), skolem_E3333) & ~member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), skolem_E3333))
% 0.12/0.36  
% 0.12/0.36  [11] ALPHA_AND : (member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), skolem_E3333) & ~member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), skolem_E3333))
% 0.12/0.36  	-> [15] member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), skolem_E3333), ~member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), skolem_E3333)
% 0.12/0.36  
% 0.12/0.36  [15] CLOSURE : member(skolem_X77(difference(skolem_E3333, skolem_E3333), empty_set), skolem_E3333)
% 0.12/0.36  
% 0.12/0.36  [6] Rewrite : ~subset(empty_set, difference(skolem_E3333, skolem_E3333))
% 0.12/0.36  	-> [7] ~(member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), empty_set) => member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), difference(skolem_E3333, skolem_E3333)))
% 0.12/0.36  
% 0.12/0.36  [7] ALPHA_NOT_IMPLY : ~(member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), empty_set) => member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), difference(skolem_E3333, skolem_E3333)))
% 0.12/0.36  	-> [9] member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), empty_set), ~member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), difference(skolem_E3333, skolem_E3333))
% 0.12/0.36  
% 0.12/0.36  [9] Rewrite : ~member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), difference(skolem_E3333, skolem_E3333))
% 0.12/0.36  	-> [12] ~(member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333) & ~member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333))
% 0.12/0.36  
% 0.12/0.36  [12] BETA_NOT_AND : ~(member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333) & ~member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333))
% 0.12/0.36  	-> [13] ~member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333)
% 0.12/0.36  	-> [14] ~~member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333)
% 0.12/0.36  
% 0.12/0.36  [13] GAMMA_FORALL : ! [X10_10, A11_11] :  ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.12/0.36  	-> [17] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.12/0.36  
% 0.12/0.36  [17] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 0.12/0.36  	-> [18] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 0.12/0.36  	-> [19] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 0.12/0.36  
% 0.12/0.36  [19] Rewrite : subset(X10_0_0, X10_0_0)
% 0.12/0.36  	-> [24] ! [X7_7] :  ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 0.12/0.36  
% 0.12/0.36  [24] GAMMA_FORALL : ! [X18_18] :  (~member(X18_18, empty_set))
% 0.12/0.36  	-> [26] ~member(X18_0_1, empty_set)
% 0.12/0.36  
% 0.12/0.36  [26] CLOSURE : ~member(X18_0_1, empty_set)
% 0.12/0.36  
% 0.12/0.36  [18] Rewrite : ~subset(X10_0_0, X10_0_0)
% 0.12/0.36  	-> [23] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 0.12/0.36  
% 0.12/0.36  [23] 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))
% 0.12/0.36  	-> [25] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.12/0.36  
% 0.12/0.36  [25] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 0.12/0.36  
% 0.12/0.36  [14] ALPHA_NOT_NOT : ~~member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333)
% 0.12/0.36  	-> [16] member(skolem_X77(empty_set, difference(skolem_E3333, skolem_E3333)), skolem_E3333)
% 0.12/0.36  
% 0.12/0.36  [16] GAMMA_FORALL : ! [X10_10, A11_11] :  ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 0.12/0.36  	-> [20] (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 0.12/0.36  
% 0.12/0.36  [20] BETA_EQUIV : (member(X10_1_0, power_set(X10_1_0)) <=> subset(X10_1_0, X10_1_0))
% 0.12/0.36  	-> [21] ~member(X10_1_0, power_set(X10_1_0)), ~subset(X10_1_0, X10_1_0)
% 0.12/0.36  	-> [22] member(X10_1_0, power_set(X10_1_0)), subset(X10_1_0, X10_1_0)
% 0.12/0.36  
% 0.12/0.36  [22] Rewrite : subset(X10_1_0, X10_1_0)
% 0.12/0.36  	-> [28] ! [X7_7] :  ((member(X7_7, X10_1_0) => member(X7_7, X10_1_0)))
% 0.12/0.36  
% 0.12/0.36  [28] GAMMA_FORALL : ! [X18_18] :  (~member(X18_18, empty_set))
% 0.12/0.36  	-> [30] ~member(X18_1_1, empty_set)
% 0.12/0.36  
% 0.12/0.36  [30] CLOSURE : ~member(X18_1_1, empty_set)
% 0.12/0.36  
% 0.12/0.36  [21] Rewrite : ~subset(X10_1_0, X10_1_0)
% 0.12/0.36  	-> [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))
% 0.12/0.36  
% 0.12/0.36  [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))
% 0.12/0.36  	-> [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)
% 0.12/0.36  
% 0.12/0.36  [29] CLOSURE : ~member(skolem_X77(X10_1_0, X10_1_0), X10_1_0)
% 0.12/0.36  
% 0.12/0.36  % SZS output end Proof for theBenchmark.p
% 0.12/0.36  [0.029655s][1][Res] 155 goroutines created
% 0.12/0.36  ==== Result ====
% 0.12/0.36  [0.029678s][1][Res] VALID
% 0.12/0.36  % SZS status Theorem for theBenchmark.p
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