TSTP Solution File: GEG025_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEG025_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n010.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 Aug 22 10:37:49 EDT 2023

% Result   : Theorem 18.27s 6.03s
% Output   : CNFRefutation 18.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   47 (  22 unt;  19 typ;   0 def)
%            Number of atoms       :   56 (  30 equ)
%            Maximal formula atoms :   24 (   2 avg)
%            Number of connectives :   41 (  13   ~;   5   |;  22   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   84 (  25 atm;  10 fun;  49 num;   0 var)
%            Number of types       :    2 (   1 usr;   1 ari)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   42 (  18 usr;  39 con; 0-2 aty)
%            Number of variables   :   24 (;  23   !;   1   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
%$ d > #nlpp > inh > saarbruecken > munich > kiel > hamburg > frankfurt > cologne > berlin

%Foreground sorts:
tff(city,type,
    city: $tType ).

%Background operators:
tff('#skE_7',type,
    '#skE_7': $int ).

tff('#skE_2',type,
    '#skE_2': $int ).

tff('#skE_1',type,
    '#skE_1': $int ).

tff('#skE_6',type,
    '#skE_6': $int ).

tff('#skE_5',type,
    '#skE_5': $int ).

tff('#skE_8',type,
    '#skE_8': $int ).

tff('#skE_4',type,
    '#skE_4': $int ).

tff('#skE_3',type,
    '#skE_3': $int ).

tff('#skE_9',type,
    '#skE_9': $int ).

%Foreground operators:
tff(munich,type,
    munich: city ).

tff(kiel,type,
    kiel: city ).

tff(d,type,
    d: ( city * city ) > $int ).

tff(frankfurt,type,
    frankfurt: city ).

tff(berlin,type,
    berlin: city ).

tff(cologne,type,
    cologne: city ).

tff(saarbruecken,type,
    saarbruecken: city ).

tff(hamburg,type,
    hamburg: city ).

tff(inh,type,
    inh: city > $int ).

tff(f_80,negated_conjecture,
    ~ ( ( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
        & ! [X: city,Y: city,Z: city] : $lesseq(d(X,Z),$sum(d(X,Y),d(Y,Z)))
        & ! [X: city] : ( d(X,X) = 0 )
        & ( d(berlin,munich) = 510 )
        & ( d(berlin,cologne) = 480 )
        & ( d(berlin,frankfurt) = 420 )
        & ( d(saarbruecken,frankfurt) = 160 )
        & ( d(saarbruecken,cologne) = 190 )
        & ( d(hamburg,cologne) = 360 )
        & ( d(hamburg,frankfurt) = 390 )
        & ( d(cologne,frankfurt) = 150 )
        & ( d(hamburg,kiel) = 90 )
        & ( d(hamburg,berlin) = 250 )
        & ( d(munich,frankfurt) = 300 )
        & ( d(munich,saarbruecken) = 360 )
        & ( inh(berlin) = 3442675 )
        & ( inh(hamburg) = 1774224 )
        & ( inh(munich) = 1330440 )
        & ( inh(cologne) = 998105 )
        & ( inh(frankfurt) = 671927 )
        & ( inh(saarbruecken) = 175810 )
        & ( inh(kiel) = 238281 ) )
     => ? [X: city] :
          ( $lesseq(d(saarbruecken,X),600)
          & $lesseq(3000000,inh(X)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_big_city_distance_2) ).

tff(c_64,plain,
    inh(berlin) = 3442675,
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_56,plain,
    d(saarbruecken,cologne) = 190,
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_49,plain,
    ! [Y_2: city,X_1: city] : ( d(Y_2,X_1) = d(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_150,plain,
    d(cologne,saarbruecken) = 190,
    inference(superposition,[status(thm),theory(equality)],[c_56,c_49]) ).

tff(c_53,plain,
    d(berlin,cologne) = 480,
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_45,plain,
    ! [X_3: city,Z_5: city,Y_4: city] : $lesseq(d(X_3,Z_5),$sum(d(X_3,Y_4),d(Y_4,Z_5))),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_296,plain,
    ! [X_11: city,Y_12: city,Z_13: city] : ~ $less($sum(d(X_11,Y_12),d(Y_12,Z_13)),d(X_11,Z_13)),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_45]) ).

tff(c_4740,plain,
    ! [Z_322: city] : ~ $less($sum(480,d(cologne,Z_322)),d(berlin,Z_322)),
    inference(superposition,[status(thm),theory(equality)],[c_53,c_296]) ).

tff(c_4809,plain,
    ~ $less($sum(480,190),d(berlin,saarbruecken)),
    inference(superposition,[status(thm),theory(equality)],[c_150,c_4740]) ).

tff(c_4811,plain,
    ~ $less(670,d(berlin,saarbruecken)),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4809]) ).

tff(c_6485,plain,
    d(berlin,saarbruecken) = '#skE_7',
    inference(define,[status(thm),theory(equality)],[c_4811]) ).

tff(c_2,plain,
    ! [X_7: city] :
      ( ~ $lesseq(3000000,inh(X_7))
      | ~ $lesseq(d(saarbruecken,X_7),600) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_1263,plain,
    ! [X_27: city] :
      ( $less(inh(X_27),3000000)
      | $less(600,d(saarbruecken,X_27)) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).

tff(c_13735,plain,
    ! [X_1260: city] :
      ( $less(inh(X_1260),3000000)
      | $less(600,d(X_1260,saarbruecken)) ),
    inference(superposition,[status(thm),theory(equality)],[c_49,c_1263]) ).

tff(c_13744,plain,
    ( $less(inh(berlin),3000000)
    | $less(600,'#skE_7') ),
    inference(superposition,[status(thm),theory(equality)],[c_6485,c_13735]) ).

tff(c_13772,plain,
    ( $less(3442675,3000000)
    | $less(600,'#skE_7') ),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_13744]) ).

tff(c_13774,plain,
    $less(600,'#skE_7'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_13772]) ).

tff(c_54,plain,
    d(berlin,frankfurt) = 420,
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_55,plain,
    d(saarbruecken,frankfurt) = 160,
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_198,plain,
    d(frankfurt,saarbruecken) = 160,
    inference(superposition,[status(thm),theory(equality)],[c_49,c_55]) ).

tff(c_50,plain,
    ! [X_3: city,Y_4: city,Z_5: city] : ~ $less($sum(d(X_3,Y_4),d(Y_4,Z_5)),d(X_3,Z_5)),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_45]) ).

tff(c_6758,plain,
    ! [Y_4: city] : ~ $less($sum(d(berlin,Y_4),d(Y_4,saarbruecken)),'#skE_7'),
    inference(superposition,[status(thm),theory(equality)],[c_6485,c_50]) ).

tff(c_7725,plain,
    ! [Y_724: city] : ~ $less($sum(d(Y_724,saarbruecken),d(berlin,Y_724)),'#skE_7'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6758]) ).

tff(c_7743,plain,
    ~ $less($sum(160,d(berlin,frankfurt)),'#skE_7'),
    inference(superposition,[status(thm),theory(equality)],[c_198,c_7725]) ).

tff(c_7800,plain,
    ~ $less($sum(160,420),'#skE_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_7743]) ).

tff(c_7802,plain,
    ~ $less(580,'#skE_7'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7800]) ).

tff(c_13787,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_13774,c_7802]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GEG025_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 19:51:58 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 18.27/6.03  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.27/6.03  
% 18.27/6.03  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.27/6.06  
% 18.27/6.06  Inference rules
% 18.27/6.06  ----------------------
% 18.27/6.06  #Ref     : 0
% 18.27/6.06  #Sup     : 2059
% 18.27/6.06  #Fact    : 0
% 18.27/6.06  #Define  : 9
% 18.27/6.06  #Split   : 0
% 18.27/6.06  #Chain   : 0
% 18.27/6.06  #Close   : 1
% 18.27/6.06  
% 18.27/6.06  Ordering : LPO
% 18.27/6.06  
% 18.27/6.06  Simplification rules
% 18.27/6.06  ----------------------
% 18.27/6.06  #Subsume      : 300
% 18.27/6.06  #Demod        : 1620
% 18.27/6.06  #Tautology    : 598
% 18.27/6.06  #SimpNegUnit  : 0
% 18.27/6.06  #BackRed      : 0
% 18.27/6.06  
% 18.27/6.06  #Partial instantiations: 0
% 18.27/6.06  #Strategies tried      : 1
% 18.27/6.06  
% 18.27/6.06  Timing (in seconds)
% 18.27/6.06  ----------------------
% 18.27/6.10  Preprocessing        : 0.51
% 18.27/6.10  Parsing              : 0.29
% 18.27/6.10  CNF conversion       : 0.03
% 18.27/6.10  Main loop            : 4.54
% 18.27/6.10  Inferencing          : 0.41
% 18.27/6.10  Reduction            : 0.65
% 18.27/6.10  Demodulation         : 0.52
% 18.27/6.10  BG Simplification    : 0.12
% 18.27/6.10  Subsumption          : 0.50
% 18.27/6.10  Abstraction          : 0.07
% 18.27/6.10  MUC search           : 0.03
% 18.27/6.10  Cooper               : 2.67
% 18.27/6.10  Total                : 5.09
% 18.27/6.10  Index Insertion      : 0.00
% 18.27/6.10  Index Deletion       : 0.00
% 18.27/6.10  Index Matching       : 0.00
% 18.27/6.10  BG Taut test         : 0.00
%------------------------------------------------------------------------------