TSTP Solution File: GEO177+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO177+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n002.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 10:38:27 EDT 2023

% Result   : Theorem 12.73s 4.27s
% Output   : CNFRefutation 12.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   69 (  25 unt;  10 typ;   0 def)
%            Number of atoms       :  142 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  107 (  24   ~;  73   |;   3   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   62 (;  62   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ distinct_points > distinct_lines > convergent_lines > apart_point_and_line > line_connecting > intersection_point > #nlpp > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(line_connecting,type,
    line_connecting: ( $i * $i ) > $i ).

tff(distinct_points,type,
    distinct_points: ( $i * $i ) > $o ).

tff(intersection_point,type,
    intersection_point: ( $i * $i ) > $i ).

tff(apart_point_and_line,type,
    apart_point_and_line: ( $i * $i ) > $o ).

tff(convergent_lines,type,
    convergent_lines: ( $i * $i ) > $o ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_3',type,
    '#skF_3': $i ).

tff('#skF_1',type,
    '#skF_1': $i ).

tff(distinct_lines,type,
    distinct_lines: ( $i * $i ) > $o ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff(f_58,axiom,
    ! [X] : ~ distinct_points(X,X),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).

tff(f_144,negated_conjecture,
    ~ ! [X,Y,U,V] :
        ( ( distinct_points(X,Y)
          & distinct_points(U,V) )
       => ( ( apart_point_and_line(X,line_connecting(U,V))
            | apart_point_and_line(Y,line_connecting(U,V)) )
         => ( apart_point_and_line(U,line_connecting(X,Y))
            | apart_point_and_line(V,line_connecting(X,Y)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

tff(f_125,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_lines(Y,Z)
        | apart_point_and_line(X,Z) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq2) ).

tff(f_112,axiom,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & distinct_lines(U,V) )
     => ( apart_point_and_line(X,U)
        | apart_point_and_line(X,V)
        | apart_point_and_line(Y,U)
        | apart_point_and_line(Y,V) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',cu1) ).

tff(f_91,axiom,
    ! [X,Y,Z] :
      ( distinct_points(X,Y)
     => ( apart_point_and_line(Z,line_connecting(X,Y))
       => ( distinct_points(Z,X)
          & distinct_points(Z,Y) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con1) ).

tff(f_119,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_points(X,Z)
        | apart_point_and_line(Z,Y) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq1) ).

tff(c_2,plain,
    ! [X_1] : ~ distinct_points(X_1,X_1),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_38,plain,
    distinct_points('#skF_1','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_30,plain,
    ~ apart_point_and_line('#skF_4',line_connecting('#skF_1','#skF_2')),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_36,plain,
    distinct_points('#skF_3','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_34,plain,
    ( apart_point_and_line('#skF_2',line_connecting('#skF_3','#skF_4'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_3','#skF_4')) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_52,plain,
    apart_point_and_line('#skF_1',line_connecting('#skF_3','#skF_4')),
    inference(splitLeft,[status(thm)],[c_34]) ).

tff(c_61,plain,
    ! [X_43,Z_44,Y_45] :
      ( apart_point_and_line(X_43,Z_44)
      | distinct_lines(Y_45,Z_44)
      | ~ apart_point_and_line(X_43,Y_45) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_67,plain,
    ! [Z_44] :
      ( apart_point_and_line('#skF_1',Z_44)
      | distinct_lines(line_connecting('#skF_3','#skF_4'),Z_44) ),
    inference(resolution,[status(thm)],[c_52,c_61]) ).

tff(c_1337,plain,
    ! [Y_126,V_127,U_128,X_129] :
      ( apart_point_and_line(Y_126,V_127)
      | apart_point_and_line(Y_126,U_128)
      | apart_point_and_line(X_129,V_127)
      | apart_point_and_line(X_129,U_128)
      | ~ distinct_lines(U_128,V_127)
      | ~ distinct_points(X_129,Y_126) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_7179,plain,
    ! [Y_318,Z_319,X_320] :
      ( apart_point_and_line(Y_318,Z_319)
      | apart_point_and_line(Y_318,line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line(X_320,Z_319)
      | apart_point_and_line(X_320,line_connecting('#skF_3','#skF_4'))
      | ~ distinct_points(X_320,Y_318)
      | apart_point_and_line('#skF_1',Z_319) ),
    inference(resolution,[status(thm)],[c_67,c_1337]) ).

tff(c_7970,plain,
    ! [Z_319] :
      ( apart_point_and_line('#skF_4',Z_319)
      | apart_point_and_line('#skF_4',line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line('#skF_3',Z_319)
      | apart_point_and_line('#skF_3',line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line('#skF_1',Z_319) ),
    inference(resolution,[status(thm)],[c_36,c_7179]) ).

tff(c_8198,plain,
    apart_point_and_line('#skF_3',line_connecting('#skF_3','#skF_4')),
    inference(splitLeft,[status(thm)],[c_7970]) ).

tff(c_16,plain,
    ! [Z_15,X_13,Y_14] :
      ( distinct_points(Z_15,X_13)
      | ~ apart_point_and_line(Z_15,line_connecting(X_13,Y_14))
      | ~ distinct_points(X_13,Y_14) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_8208,plain,
    ( distinct_points('#skF_3','#skF_3')
    | ~ distinct_points('#skF_3','#skF_4') ),
    inference(resolution,[status(thm)],[c_8198,c_16]) ).

tff(c_8220,plain,
    distinct_points('#skF_3','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_8208]) ).

tff(c_8222,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_8220]) ).

tff(c_8223,plain,
    ! [Z_319] :
      ( apart_point_and_line('#skF_4',line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line('#skF_4',Z_319)
      | apart_point_and_line('#skF_3',Z_319)
      | apart_point_and_line('#skF_1',Z_319) ),
    inference(splitRight,[status(thm)],[c_7970]) ).

tff(c_8590,plain,
    apart_point_and_line('#skF_4',line_connecting('#skF_3','#skF_4')),
    inference(splitLeft,[status(thm)],[c_8223]) ).

tff(c_14,plain,
    ! [Z_15,Y_14,X_13] :
      ( distinct_points(Z_15,Y_14)
      | ~ apart_point_and_line(Z_15,line_connecting(X_13,Y_14))
      | ~ distinct_points(X_13,Y_14) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_8597,plain,
    ( distinct_points('#skF_4','#skF_4')
    | ~ distinct_points('#skF_3','#skF_4') ),
    inference(resolution,[status(thm)],[c_8590,c_14]) ).

tff(c_8609,plain,
    distinct_points('#skF_4','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_8597]) ).

tff(c_8611,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_8609]) ).

tff(c_8624,plain,
    ! [Z_340] :
      ( apart_point_and_line('#skF_4',Z_340)
      | apart_point_and_line('#skF_3',Z_340)
      | apart_point_and_line('#skF_1',Z_340) ),
    inference(splitRight,[status(thm)],[c_8223]) ).

tff(c_32,plain,
    ~ apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_2')),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_8646,plain,
    ( apart_point_and_line('#skF_4',line_connecting('#skF_1','#skF_2'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_8624,c_32]) ).

tff(c_8658,plain,
    apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')),
    inference(negUnitSimplification,[status(thm)],[c_30,c_8646]) ).

tff(c_8668,plain,
    ( distinct_points('#skF_1','#skF_1')
    | ~ distinct_points('#skF_1','#skF_2') ),
    inference(resolution,[status(thm)],[c_8658,c_16]) ).

tff(c_8680,plain,
    distinct_points('#skF_1','#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_8668]) ).

tff(c_8682,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_8680]) ).

tff(c_8683,plain,
    apart_point_and_line('#skF_2',line_connecting('#skF_3','#skF_4')),
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_8715,plain,
    ! [X_349,Z_350,Y_351] :
      ( apart_point_and_line(X_349,Z_350)
      | distinct_lines(Y_351,Z_350)
      | ~ apart_point_and_line(X_349,Y_351) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_8718,plain,
    ! [Z_350] :
      ( apart_point_and_line('#skF_2',Z_350)
      | distinct_lines(line_connecting('#skF_3','#skF_4'),Z_350) ),
    inference(resolution,[status(thm)],[c_8683,c_8715]) ).

tff(c_9758,plain,
    ! [Y_419,V_420,U_421,X_422] :
      ( apart_point_and_line(Y_419,V_420)
      | apart_point_and_line(Y_419,U_421)
      | apart_point_and_line(X_422,V_420)
      | apart_point_and_line(X_422,U_421)
      | ~ distinct_lines(U_421,V_420)
      | ~ distinct_points(X_422,Y_419) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_15779,plain,
    ! [Y_619,Z_620,X_621] :
      ( apart_point_and_line(Y_619,Z_620)
      | apart_point_and_line(Y_619,line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line(X_621,Z_620)
      | apart_point_and_line(X_621,line_connecting('#skF_3','#skF_4'))
      | ~ distinct_points(X_621,Y_619)
      | apart_point_and_line('#skF_2',Z_620) ),
    inference(resolution,[status(thm)],[c_8718,c_9758]) ).

tff(c_16623,plain,
    ! [Z_620] :
      ( apart_point_and_line('#skF_4',Z_620)
      | apart_point_and_line('#skF_4',line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line('#skF_3',Z_620)
      | apart_point_and_line('#skF_3',line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line('#skF_2',Z_620) ),
    inference(resolution,[status(thm)],[c_36,c_15779]) ).

tff(c_16900,plain,
    apart_point_and_line('#skF_3',line_connecting('#skF_3','#skF_4')),
    inference(splitLeft,[status(thm)],[c_16623]) ).

tff(c_16907,plain,
    ( distinct_points('#skF_3','#skF_3')
    | ~ distinct_points('#skF_3','#skF_4') ),
    inference(resolution,[status(thm)],[c_16900,c_16]) ).

tff(c_16919,plain,
    distinct_points('#skF_3','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_16907]) ).

tff(c_16921,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_16919]) ).

tff(c_16922,plain,
    ! [Z_620] :
      ( apart_point_and_line('#skF_4',line_connecting('#skF_3','#skF_4'))
      | apart_point_and_line('#skF_4',Z_620)
      | apart_point_and_line('#skF_3',Z_620)
      | apart_point_and_line('#skF_2',Z_620) ),
    inference(splitRight,[status(thm)],[c_16623]) ).

tff(c_17485,plain,
    apart_point_and_line('#skF_4',line_connecting('#skF_3','#skF_4')),
    inference(splitLeft,[status(thm)],[c_16922]) ).

tff(c_17495,plain,
    ( distinct_points('#skF_4','#skF_4')
    | ~ distinct_points('#skF_3','#skF_4') ),
    inference(resolution,[status(thm)],[c_17485,c_14]) ).

tff(c_17507,plain,
    distinct_points('#skF_4','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_17495]) ).

tff(c_17509,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_17507]) ).

tff(c_17522,plain,
    ! [Z_646] :
      ( apart_point_and_line('#skF_4',Z_646)
      | apart_point_and_line('#skF_3',Z_646)
      | apart_point_and_line('#skF_2',Z_646) ),
    inference(splitRight,[status(thm)],[c_16922]) ).

tff(c_24,plain,
    ! [Z_25,Y_24,X_23] :
      ( apart_point_and_line(Z_25,Y_24)
      | distinct_points(X_23,Z_25)
      | ~ apart_point_and_line(X_23,Y_24) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_17562,plain,
    ! [Z_647,Z_648] :
      ( apart_point_and_line(Z_647,Z_648)
      | distinct_points('#skF_2',Z_647)
      | apart_point_and_line('#skF_4',Z_648)
      | apart_point_and_line('#skF_3',Z_648) ),
    inference(resolution,[status(thm)],[c_17522,c_24]) ).

tff(c_17623,plain,
    ! [Z_647] :
      ( apart_point_and_line(Z_647,line_connecting('#skF_1','#skF_2'))
      | distinct_points('#skF_2',Z_647)
      | apart_point_and_line('#skF_4',line_connecting('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_17562,c_32]) ).

tff(c_17648,plain,
    ! [Z_649] :
      ( apart_point_and_line(Z_649,line_connecting('#skF_1','#skF_2'))
      | distinct_points('#skF_2',Z_649) ),
    inference(negUnitSimplification,[status(thm)],[c_30,c_17623]) ).

tff(c_17666,plain,
    ! [Z_649] :
      ( distinct_points(Z_649,'#skF_2')
      | ~ distinct_points('#skF_1','#skF_2')
      | distinct_points('#skF_2',Z_649) ),
    inference(resolution,[status(thm)],[c_17648,c_14]) ).

tff(c_17686,plain,
    ! [Z_649] :
      ( distinct_points(Z_649,'#skF_2')
      | distinct_points('#skF_2',Z_649) ),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_17666]) ).

tff(c_17705,plain,
    distinct_points('#skF_2','#skF_2'),
    inference(factorization,[status(thm),theory(equality)],[c_17686]) ).

tff(c_17709,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_17705]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GEO177+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.34  % Computer : n002.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Fri Aug  4 01:02:31 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 12.73/4.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.82/4.28  
% 12.82/4.28  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.82/4.31  
% 12.82/4.31  Inference rules
% 12.82/4.31  ----------------------
% 12.82/4.31  #Ref     : 0
% 12.82/4.31  #Sup     : 2464
% 12.82/4.31  #Fact    : 1034
% 12.82/4.31  #Define  : 0
% 12.82/4.31  #Split   : 5
% 12.82/4.31  #Chain   : 0
% 12.82/4.31  #Close   : 0
% 12.82/4.31  
% 12.82/4.31  Ordering : KBO
% 12.82/4.31  
% 12.82/4.31  Simplification rules
% 12.82/4.31  ----------------------
% 12.82/4.31  #Subsume      : 1187
% 12.82/4.31  #Demod        : 733
% 12.82/4.31  #Tautology    : 659
% 12.82/4.31  #SimpNegUnit  : 379
% 12.82/4.31  #BackRed      : 0
% 12.82/4.31  
% 12.82/4.31  #Partial instantiations: 0
% 12.82/4.31  #Strategies tried      : 1
% 12.82/4.31  
% 12.82/4.31  Timing (in seconds)
% 12.82/4.31  ----------------------
% 12.82/4.31  Preprocessing        : 0.49
% 12.82/4.31  Parsing              : 0.27
% 12.82/4.31  CNF conversion       : 0.03
% 12.82/4.31  Main loop            : 2.74
% 12.82/4.31  Inferencing          : 0.92
% 12.82/4.31  Reduction            : 0.57
% 12.82/4.31  Demodulation         : 0.34
% 12.82/4.31  BG Simplification    : 0.06
% 12.82/4.31  Subsumption          : 1.04
% 12.82/4.31  Abstraction          : 0.07
% 12.82/4.31  MUC search           : 0.00
% 12.82/4.31  Cooper               : 0.00
% 12.82/4.31  Total                : 3.29
% 12.82/4.31  Index Insertion      : 0.00
% 12.82/4.32  Index Deletion       : 0.00
% 12.82/4.32  Index Matching       : 0.00
% 12.82/4.32  BG Taut test         : 0.00
%------------------------------------------------------------------------------