TSTP Solution File: GEO201+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO201+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/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 : n026.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 10:38:37 EDT 2023

% Result   : Theorem 6.15s 2.60s
% Output   : CNFRefutation 6.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   58 (  21 unt;   8 typ;   0 def)
%            Number of atoms       :  117 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   98 (  31   ~;  59   |;   1   &)
%                                         (   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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   68 (;  68   !;   0   ?;   0   :)

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

%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_1',type,
    '#skF_1': $i ).

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

tff(f_136,negated_conjecture,
    ~ ! [X,Y] :
        ( convergent_lines(X,Y)
       => ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

tff(f_81,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( convergent_lines(X,Z)
        | convergent_lines(Y,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).

tff(f_63,axiom,
    ! [X] : ~ convergent_lines(X,X),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).

tff(f_128,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => distinct_lines(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).

tff(f_75,axiom,
    ! [X,Y,Z] :
      ( distinct_lines(X,Y)
     => ( distinct_lines(X,Z)
        | distinct_lines(Y,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart5) ).

tff(f_111,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/sandbox2/benchmark/Axioms/GEO008+0.ax',cu1) ).

tff(f_98,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( ( apart_point_and_line(Z,X)
          | apart_point_and_line(Z,Y) )
       => distinct_points(Z,intersection_point(X,Y)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con2) ).

tff(f_57,axiom,
    ! [X] : ~ distinct_points(X,X),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).

tff(c_32,plain,
    convergent_lines('#skF_1','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_44,plain,
    ! [Y_42,Z_43,X_44] :
      ( convergent_lines(Y_42,Z_43)
      | convergent_lines(X_44,Z_43)
      | ~ convergent_lines(X_44,Y_42) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_48,plain,
    ! [Z_45] :
      ( convergent_lines('#skF_2',Z_45)
      | convergent_lines('#skF_1',Z_45) ),
    inference(resolution,[status(thm)],[c_32,c_44]) ).

tff(c_12,plain,
    ! [Y_11,Z_12,X_10] :
      ( convergent_lines(Y_11,Z_12)
      | convergent_lines(X_10,Z_12)
      | ~ convergent_lines(X_10,Y_11) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_176,plain,
    ! [Z_66,Z_67] :
      ( convergent_lines(Z_66,Z_67)
      | convergent_lines('#skF_2',Z_67)
      | convergent_lines('#skF_1',Z_66) ),
    inference(resolution,[status(thm)],[c_48,c_12]) ).

tff(c_6,plain,
    ! [X_3] : ~ convergent_lines(X_3,X_3),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_207,plain,
    ! [Z_68] :
      ( convergent_lines(Z_68,'#skF_2')
      | convergent_lines('#skF_1',Z_68) ),
    inference(resolution,[status(thm)],[c_176,c_6]) ).

tff(c_341,plain,
    ! [Z_77,Z_78] :
      ( convergent_lines(Z_77,Z_78)
      | convergent_lines('#skF_1',Z_78)
      | convergent_lines(Z_77,'#skF_2') ),
    inference(resolution,[status(thm)],[c_207,c_12]) ).

tff(c_375,plain,
    ! [Z_79] :
      ( convergent_lines(Z_79,'#skF_1')
      | convergent_lines(Z_79,'#skF_2') ),
    inference(resolution,[status(thm)],[c_341,c_6]) ).

tff(c_386,plain,
    convergent_lines('#skF_2','#skF_1'),
    inference(resolution,[status(thm)],[c_375,c_6]) ).

tff(c_30,plain,
    distinct_points(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_2','#skF_1')),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_28,plain,
    ! [X_29,Y_30] :
      ( distinct_lines(X_29,Y_30)
      | ~ convergent_lines(X_29,Y_30) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_62,plain,
    ! [Y_49,Z_50,X_51] :
      ( distinct_lines(Y_49,Z_50)
      | distinct_lines(X_51,Z_50)
      | ~ distinct_lines(X_51,Y_49) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_66,plain,
    ! [Y_52,Z_53,X_54] :
      ( distinct_lines(Y_52,Z_53)
      | distinct_lines(X_54,Z_53)
      | ~ convergent_lines(X_54,Y_52) ),
    inference(resolution,[status(thm)],[c_28,c_62]) ).

tff(c_72,plain,
    ! [Z_53] :
      ( distinct_lines('#skF_2',Z_53)
      | distinct_lines('#skF_1',Z_53) ),
    inference(resolution,[status(thm)],[c_32,c_66]) ).

tff(c_1096,plain,
    ! [Y_121,V_122,U_123,X_124] :
      ( apart_point_and_line(Y_121,V_122)
      | apart_point_and_line(Y_121,U_123)
      | apart_point_and_line(X_124,V_122)
      | apart_point_and_line(X_124,U_123)
      | ~ distinct_lines(U_123,V_122)
      | ~ distinct_points(X_124,Y_121) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_1251,plain,
    ! [Y_128,Z_129,X_130] :
      ( apart_point_and_line(Y_128,Z_129)
      | apart_point_and_line(Y_128,'#skF_2')
      | apart_point_and_line(X_130,Z_129)
      | apart_point_and_line(X_130,'#skF_2')
      | ~ distinct_points(X_130,Y_128)
      | distinct_lines('#skF_1',Z_129) ),
    inference(resolution,[status(thm)],[c_72,c_1096]) ).

tff(c_1278,plain,
    ! [Z_129] :
      ( apart_point_and_line(intersection_point('#skF_2','#skF_1'),Z_129)
      | apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_2')
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_129)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
      | distinct_lines('#skF_1',Z_129) ),
    inference(resolution,[status(thm)],[c_30,c_1251]) ).

tff(c_1781,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
    inference(splitLeft,[status(thm)],[c_1278]) ).

tff(c_283,plain,
    ! [Z_72,Y_73,X_74] :
      ( ~ apart_point_and_line(Z_72,Y_73)
      | distinct_points(Z_72,intersection_point(X_74,Y_73))
      | ~ convergent_lines(X_74,Y_73) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_2,plain,
    ! [X_1] : ~ distinct_points(X_1,X_1),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_291,plain,
    ! [X_74,Y_73] :
      ( ~ apart_point_and_line(intersection_point(X_74,Y_73),Y_73)
      | ~ convergent_lines(X_74,Y_73) ),
    inference(resolution,[status(thm)],[c_283,c_2]) ).

tff(c_1786,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_1781,c_291]) ).

tff(c_1795,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_1786]) ).

tff(c_1797,plain,
    ~ apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
    inference(splitRight,[status(thm)],[c_1278]) ).

tff(c_1796,plain,
    ! [Z_129] :
      ( apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_2')
      | apart_point_and_line(intersection_point('#skF_2','#skF_1'),Z_129)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_129)
      | distinct_lines('#skF_1',Z_129) ),
    inference(splitRight,[status(thm)],[c_1278]) ).

tff(c_2108,plain,
    apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_2'),
    inference(splitLeft,[status(thm)],[c_1796]) ).

tff(c_85,plain,
    ! [Z_56,X_57,Y_58] :
      ( ~ apart_point_and_line(Z_56,X_57)
      | distinct_points(Z_56,intersection_point(X_57,Y_58))
      | ~ convergent_lines(X_57,Y_58) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_93,plain,
    ! [X_57,Y_58] :
      ( ~ apart_point_and_line(intersection_point(X_57,Y_58),X_57)
      | ~ convergent_lines(X_57,Y_58) ),
    inference(resolution,[status(thm)],[c_85,c_2]) ).

tff(c_2115,plain,
    ~ convergent_lines('#skF_2','#skF_1'),
    inference(resolution,[status(thm)],[c_2108,c_93]) ).

tff(c_2125,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_2115]) ).

tff(c_2127,plain,
    ~ apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_2'),
    inference(splitRight,[status(thm)],[c_1796]) ).

tff(c_2292,plain,
    ! [Y_179,Y_180,X_181,X_182] :
      ( apart_point_and_line(Y_179,Y_180)
      | apart_point_and_line(Y_179,X_181)
      | apart_point_and_line(X_182,Y_180)
      | apart_point_and_line(X_182,X_181)
      | ~ distinct_points(X_182,Y_179)
      | ~ convergent_lines(X_181,Y_180) ),
    inference(resolution,[status(thm)],[c_28,c_1096]) ).

tff(c_2570,plain,
    ! [Y_191,X_192] :
      ( apart_point_and_line(intersection_point('#skF_2','#skF_1'),Y_191)
      | apart_point_and_line(intersection_point('#skF_2','#skF_1'),X_192)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Y_191)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),X_192)
      | ~ convergent_lines(X_192,Y_191) ),
    inference(resolution,[status(thm)],[c_30,c_2292]) ).

tff(c_2664,plain,
    ( apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_2')
    | apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_1')
    | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
    | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1') ),
    inference(resolution,[status(thm)],[c_32,c_2570]) ).

tff(c_2745,plain,
    ( apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_1')
    | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1') ),
    inference(negUnitSimplification,[status(thm)],[c_1797,c_2127,c_2664]) ).

tff(c_2746,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1'),
    inference(splitLeft,[status(thm)],[c_2745]) ).

tff(c_2753,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_2746,c_93]) ).

tff(c_2763,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_2753]) ).

tff(c_2764,plain,
    apart_point_and_line(intersection_point('#skF_2','#skF_1'),'#skF_1'),
    inference(splitRight,[status(thm)],[c_2745]) ).

tff(c_2772,plain,
    ~ convergent_lines('#skF_2','#skF_1'),
    inference(resolution,[status(thm)],[c_2764,c_291]) ).

tff(c_2782,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_2772]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO201+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % 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
% 0.13/0.34  % Computer : n026.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
% 0.13/0.35  % DateTime : Fri Aug  4 00:30:17 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 6.15/2.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.15/2.61  
% 6.15/2.61  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.38/2.64  
% 6.38/2.64  Inference rules
% 6.38/2.64  ----------------------
% 6.38/2.64  #Ref     : 0
% 6.38/2.64  #Sup     : 447
% 6.38/2.64  #Fact    : 122
% 6.38/2.64  #Define  : 0
% 6.38/2.64  #Split   : 3
% 6.38/2.64  #Chain   : 0
% 6.38/2.64  #Close   : 0
% 6.38/2.64  
% 6.38/2.64  Ordering : KBO
% 6.38/2.64  
% 6.38/2.64  Simplification rules
% 6.38/2.64  ----------------------
% 6.38/2.64  #Subsume      : 127
% 6.38/2.64  #Demod        : 97
% 6.38/2.64  #Tautology    : 93
% 6.38/2.64  #SimpNegUnit  : 51
% 6.38/2.64  #BackRed      : 0
% 6.38/2.64  
% 6.38/2.64  #Partial instantiations: 0
% 6.38/2.64  #Strategies tried      : 1
% 6.38/2.64  
% 6.38/2.64  Timing (in seconds)
% 6.38/2.64  ----------------------
% 6.38/2.65  Preprocessing        : 0.50
% 6.38/2.65  Parsing              : 0.28
% 6.38/2.65  CNF conversion       : 0.03
% 6.38/2.65  Main loop            : 0.96
% 6.38/2.65  Inferencing          : 0.34
% 6.38/2.65  Reduction            : 0.19
% 6.38/2.65  Demodulation         : 0.11
% 6.38/2.65  BG Simplification    : 0.03
% 6.38/2.65  Subsumption          : 0.34
% 6.38/2.65  Abstraction          : 0.03
% 6.38/2.65  MUC search           : 0.00
% 6.38/2.65  Cooper               : 0.00
% 6.38/2.65  Total                : 1.53
% 6.38/2.65  Index Insertion      : 0.00
% 6.38/2.65  Index Deletion       : 0.00
% 6.38/2.65  Index Matching       : 0.00
% 6.38/2.65  BG Taut test         : 0.00
%------------------------------------------------------------------------------