TSTP Solution File: SET012+4 by Goeland---1.0.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Goeland---1.0.0
% Problem  : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : goeland -dmt -presko -proof %s

% Computer : n011.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 04:14:42 EDT 2022

% Result   : Theorem 1.51s 0.62s
% Output   : Proof 1.51s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET012+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12  % Command    : goeland -dmt -presko -proof %s
% 0.12/0.33  % Computer : n011.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 01:00:28 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  [DMT] DMT loaded with preskolemization
% 0.12/0.34  [EQ] equality loaded.
% 0.12/0.34  [0.000040s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35  Conjecture not found
% 0.12/0.35  Start search
% 0.12/0.35  nb_step : 1 - limit : 15
% 0.12/0.35  Launch Gotab with destructive = true
% 1.51/0.62  % SZS output start Proof for theBenchmark.p
% 1.51/0.62  [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, E34_34] :  ((subset(A33_33, E34_34) => equal_set(difference(E34_34, difference(E34_34, A33_33)), A33_33))))
% 1.51/0.62  	-> [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, E34_34] :  ((subset(A33_33, E34_34) => equal_set(difference(E34_34, difference(E34_34, A33_33)), A33_33)))
% 1.51/0.62  
% 1.51/0.62  [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))))
% 1.51/0.62  	-> [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)))
% 1.51/0.62  
% 1.51/0.62  [2] DELTA_NOT_FORALL : ~! [A33_33, E34_34] :  ((subset(A33_33, E34_34) => equal_set(difference(E34_34, difference(E34_34, A33_33)), A33_33)))
% 1.51/0.62  	-> [3] ~(subset(skolem_A3333, skolem_E3434) => equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333))
% 1.51/0.62  
% 1.51/0.62  [3] ALPHA_NOT_IMPLY : ~(subset(skolem_A3333, skolem_E3434) => equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333))
% 1.51/0.62  	-> [4] subset(skolem_A3333, skolem_E3434), ~equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62  
% 1.51/0.62  [4] Rewrite : subset(skolem_A3333, skolem_E3434)
% 1.51/0.62  	-> [5] ! [X7_7] :  ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3434)))
% 1.51/0.62  
% 1.51/0.62  [5] Rewrite : ~equal_set(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62  	-> [6] ~(subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333) & subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62  
% 1.51/0.62  [6] BETA_NOT_AND : ~(subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333) & subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62  	-> [7] ~subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62  	-> [8] ~subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  
% 1.51/0.62  [7] Rewrite : ~subset(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333)
% 1.51/0.62  	-> [10] ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))) => member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62  
% 1.51/0.62  [10] ALPHA_NOT_IMPLY : ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))) => member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62  	-> [12] member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62  
% 1.51/0.62  [12] Rewrite : member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  	-> [14] (member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  
% 1.51/0.62  [14] ALPHA_AND : (member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  	-> [18] member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434), ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62  
% 1.51/0.62  [18] Rewrite : ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62  	-> [27] ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62  
% 1.51/0.62  [27] BETA_NOT_AND : ~(member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434) & ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333))
% 1.51/0.62  	-> [29] ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434)
% 1.51/0.62  	-> [30] ~~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62  
% 1.51/0.62  [29] CLOSURE : ~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_E3434)
% 1.51/0.62  
% 1.51/0.62  [30] ALPHA_NOT_NOT : ~~member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62  	-> [31] member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62  
% 1.51/0.62  [31] CLOSURE : member(skolem_X77(difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)), skolem_A3333), skolem_A3333)
% 1.51/0.62  
% 1.51/0.62  [8] Rewrite : ~subset(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  	-> [9] ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62  
% 1.51/0.62  [9] ALPHA_NOT_IMPLY : ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))))
% 1.51/0.62  	-> [11] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333), ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  
% 1.51/0.62  [11] Rewrite : ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  	-> [13] ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  
% 1.51/0.62  [13] BETA_NOT_AND : ~(member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333)))
% 1.51/0.62  	-> [15] ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434)
% 1.51/0.62  	-> [16] ~~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62  
% 1.51/0.62  [16] ALPHA_NOT_NOT : ~~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62  	-> [17] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62  
% 1.51/0.62  [17] Rewrite : member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), difference(skolem_E3434, skolem_A3333))
% 1.51/0.62  	-> [20] (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333))
% 1.51/0.62  
% 1.51/0.62  [20] ALPHA_AND : (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434) & ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333))
% 1.51/0.62  	-> [23] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434), ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333)
% 1.51/0.62  
% 1.51/0.62  [23] CLOSURE : ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333)
% 1.51/0.62  
% 1.51/0.62  [15] GAMMA_FORALL : ! [X10_10, A11_11] :  ((member(X10_10, power_set(A11_11)) <=> subset(X10_10, A11_11)))
% 1.51/0.62  	-> [19] (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.51/0.62  
% 1.51/0.62  [19] BETA_EQUIV : (member(X10_0_0, power_set(X10_0_0)) <=> subset(X10_0_0, X10_0_0))
% 1.51/0.62  	-> [21] ~member(X10_0_0, power_set(X10_0_0)), ~subset(X10_0_0, X10_0_0)
% 1.51/0.62  	-> [22] member(X10_0_0, power_set(X10_0_0)), subset(X10_0_0, X10_0_0)
% 1.51/0.62  
% 1.51/0.62  [21] Rewrite : ~subset(X10_0_0, X10_0_0)
% 1.51/0.62  	-> [24] ~(member(skolem_X77(X10_0_0, X10_0_0), X10_0_0) => member(skolem_X77(X10_0_0, X10_0_0), X10_0_0))
% 1.51/0.62  
% 1.51/0.62  [24] 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))
% 1.51/0.62  	-> [26] member(skolem_X77(X10_0_0, X10_0_0), X10_0_0), ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.51/0.62  
% 1.51/0.62  [26] CLOSURE : ~member(skolem_X77(X10_0_0, X10_0_0), X10_0_0)
% 1.51/0.62  
% 1.51/0.62  [22] Rewrite : subset(X10_0_0, X10_0_0)
% 1.51/0.62  	-> [25] ! [X7_7] :  ((member(X7_7, X10_0_0) => member(X7_7, X10_0_0)))
% 1.51/0.62  
% 1.51/0.62  [25] GAMMA_FORALL : ! [X18_18] :  (~member(X18_18, empty_set))
% 1.51/0.62  	-> [28] ~member(X18_0_1, empty_set)
% 1.51/0.62  
% 1.51/0.62  [28] GAMMA_FORALL : ! [X22_22, A23_23] :  ((member(X22_22, singleton(A23_23)) <=> =(X22_22, A23_23)))
% 1.51/0.62  	-> [32] (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.51/0.62  
% 1.51/0.62  [32] BETA_EQUIV : (member(A23_0_2, singleton(A23_0_2)) <=> =(A23_0_2, A23_0_2))
% 1.51/0.62  	-> [33] ~member(A23_0_2, singleton(A23_0_2)), ~=(A23_0_2, A23_0_2)
% 1.51/0.62  	-> [34] member(A23_0_2, singleton(A23_0_2)), =(A23_0_2, A23_0_2)
% 1.51/0.62  
% 1.51/0.62  [33] CLOSURE : ~=(A23_0_2, A23_0_2)
% 1.51/0.62  
% 1.51/0.62  [34] GAMMA_FORALL : ! [X7_7] :  ((member(X7_7, skolem_A3333) => member(X7_7, skolem_E3434)))
% 1.51/0.62  	-> [35] (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434))
% 1.51/0.62  
% 1.51/0.62  [35] BETA_IMPLY : (member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333) => member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434))
% 1.51/0.62  	-> [36] ~member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_A3333)
% 1.51/0.62  	-> [37] member(skolem_X77(skolem_A3333, difference(skolem_E3434, difference(skolem_E3434, skolem_A3333))), skolem_E3434)
% 1.51/0.62  
% 1.51/0.62  [36] CLOSURE : =
% 1.51/0.62  
% 1.51/0.62  [37] CLOSURE : =
% 1.51/0.62  
% 1.51/0.62  % SZS output end Proof for theBenchmark.p
% 1.51/0.62  [0.279616s][1][Res] 351 goroutines created
% 1.51/0.62  ==== Result ====
% 1.51/0.62  [0.279640s][1][Res] VALID
% 1.51/0.62  % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------