TSTP Solution File: GEO172+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO172+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 : n018.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 10:38:24 EDT 2023

% Result   : Theorem 4.30s 2.23s
% Output   : CNFRefutation 4.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   41 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :   80 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   74 (  26   ~;  39   |;   3   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   48 (;  48   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ distinct_points > distinct_lines > convergent_lines > apart_point_and_line > line_connecting > intersection_point > #nlpp > #skF_2 > #skF_3 > #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_3',type,
    '#skF_3': $i ).

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

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

tff(f_61,axiom,
    ! [X] : ~ distinct_lines(X,X),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).

tff(f_143,negated_conjecture,
    ~ ! [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/theBenchmark.p',con) ).

tff(f_129,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => distinct_lines(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).

tff(f_76,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_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/sandbox2/benchmark/Axioms/GEO008+0.ax',cu1) ).

tff(f_99,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_58,axiom,
    ! [X] : ~ distinct_points(X,X),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).

tff(c_4,plain,
    ! [X_2] : ~ distinct_lines(X_2,X_2),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_34,plain,
    ~ apart_point_and_line('#skF_3','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_143]) ).

tff(c_36,plain,
    convergent_lines('#skF_1','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_143]) ).

tff(c_32,plain,
    ~ apart_point_and_line('#skF_3','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_143]) ).

tff(c_30,plain,
    distinct_points('#skF_3',intersection_point('#skF_1','#skF_2')),
    inference(cnfTransformation,[status(thm)],[f_143]) ).

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_129]) ).

tff(c_46,plain,
    ! [Y_36,Z_37,X_38] :
      ( distinct_lines(Y_36,Z_37)
      | distinct_lines(X_38,Z_37)
      | ~ distinct_lines(X_38,Y_36) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_90,plain,
    ! [Y_58,Z_59,X_60] :
      ( distinct_lines(Y_58,Z_59)
      | distinct_lines(X_60,Z_59)
      | ~ convergent_lines(X_60,Y_58) ),
    inference(resolution,[status(thm)],[c_28,c_46]) ).

tff(c_96,plain,
    ! [Z_59] :
      ( distinct_lines('#skF_2',Z_59)
      | distinct_lines('#skF_1',Z_59) ),
    inference(resolution,[status(thm)],[c_36,c_90]) ).

tff(c_944,plain,
    ! [Y_117,V_118,U_119,X_120] :
      ( apart_point_and_line(Y_117,V_118)
      | apart_point_and_line(Y_117,U_119)
      | apart_point_and_line(X_120,V_118)
      | apart_point_and_line(X_120,U_119)
      | ~ distinct_lines(U_119,V_118)
      | ~ distinct_points(X_120,Y_117) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_1127,plain,
    ! [Y_124,Z_125,X_126] :
      ( apart_point_and_line(Y_124,Z_125)
      | apart_point_and_line(Y_124,'#skF_2')
      | apart_point_and_line(X_126,Z_125)
      | apart_point_and_line(X_126,'#skF_2')
      | ~ distinct_points(X_126,Y_124)
      | distinct_lines('#skF_1',Z_125) ),
    inference(resolution,[status(thm)],[c_96,c_944]) ).

tff(c_1143,plain,
    ! [Z_125] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_125)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
      | apart_point_and_line('#skF_3',Z_125)
      | apart_point_and_line('#skF_3','#skF_2')
      | distinct_lines('#skF_1',Z_125) ),
    inference(resolution,[status(thm)],[c_30,c_1127]) ).

tff(c_1155,plain,
    ! [Z_125] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_125)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
      | apart_point_and_line('#skF_3',Z_125)
      | distinct_lines('#skF_1',Z_125) ),
    inference(negUnitSimplification,[status(thm)],[c_32,c_1143]) ).

tff(c_1479,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
    inference(splitLeft,[status(thm)],[c_1155]) ).

tff(c_80,plain,
    ! [Z_53,Y_54,X_55] :
      ( ~ apart_point_and_line(Z_53,Y_54)
      | distinct_points(Z_53,intersection_point(X_55,Y_54))
      | ~ convergent_lines(X_55,Y_54) ),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

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

tff(c_88,plain,
    ! [X_55,Y_54] :
      ( ~ apart_point_and_line(intersection_point(X_55,Y_54),Y_54)
      | ~ convergent_lines(X_55,Y_54) ),
    inference(resolution,[status(thm)],[c_80,c_2]) ).

tff(c_1484,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_1479,c_88]) ).

tff(c_1493,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_1484]) ).

tff(c_1789,plain,
    ! [Z_158] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_158)
      | apart_point_and_line('#skF_3',Z_158)
      | distinct_lines('#skF_1',Z_158) ),
    inference(splitRight,[status(thm)],[c_1155]) ).

tff(c_735,plain,
    ! [Z_101,X_102,Y_103] :
      ( ~ apart_point_and_line(Z_101,X_102)
      | distinct_points(Z_101,intersection_point(X_102,Y_103))
      | ~ convergent_lines(X_102,Y_103) ),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_743,plain,
    ! [X_102,Y_103] :
      ( ~ apart_point_and_line(intersection_point(X_102,Y_103),X_102)
      | ~ convergent_lines(X_102,Y_103) ),
    inference(resolution,[status(thm)],[c_735,c_2]) ).

tff(c_1800,plain,
    ( ~ convergent_lines('#skF_1','#skF_2')
    | apart_point_and_line('#skF_3','#skF_1')
    | distinct_lines('#skF_1','#skF_1') ),
    inference(resolution,[status(thm)],[c_1789,c_743]) ).

tff(c_1824,plain,
    ( apart_point_and_line('#skF_3','#skF_1')
    | distinct_lines('#skF_1','#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_1800]) ).

tff(c_1826,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4,c_34,c_1824]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : GEO172+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/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
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Aug  4 00:38:36 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 4.30/2.23  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.30/2.23  
% 4.30/2.23  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.30/2.27  
% 4.30/2.27  Inference rules
% 4.30/2.27  ----------------------
% 4.30/2.27  #Ref     : 0
% 4.30/2.27  #Sup     : 299
% 4.30/2.27  #Fact    : 70
% 4.30/2.27  #Define  : 0
% 4.30/2.27  #Split   : 2
% 4.30/2.27  #Chain   : 0
% 4.30/2.27  #Close   : 0
% 4.30/2.27  
% 4.30/2.27  Ordering : KBO
% 4.30/2.27  
% 4.30/2.27  Simplification rules
% 4.30/2.27  ----------------------
% 4.30/2.27  #Subsume      : 63
% 4.30/2.27  #Demod        : 80
% 4.30/2.27  #Tautology    : 78
% 4.30/2.27  #SimpNegUnit  : 13
% 4.30/2.27  #BackRed      : 0
% 4.30/2.27  
% 4.30/2.27  #Partial instantiations: 0
% 4.30/2.27  #Strategies tried      : 1
% 4.30/2.27  
% 4.30/2.27  Timing (in seconds)
% 4.30/2.27  ----------------------
% 4.30/2.27  Preprocessing        : 0.46
% 4.30/2.27  Parsing              : 0.26
% 4.30/2.27  CNF conversion       : 0.03
% 4.30/2.27  Main loop            : 0.74
% 4.30/2.27  Inferencing          : 0.28
% 4.30/2.27  Reduction            : 0.16
% 4.30/2.27  Demodulation         : 0.09
% 4.30/2.27  BG Simplification    : 0.03
% 4.30/2.27  Subsumption          : 0.23
% 4.30/2.27  Abstraction          : 0.03
% 4.30/2.27  MUC search           : 0.00
% 4.30/2.27  Cooper               : 0.00
% 4.30/2.27  Total                : 1.26
% 4.30/2.27  Index Insertion      : 0.00
% 4.30/2.27  Index Deletion       : 0.00
% 4.30/2.27  Index Matching       : 0.00
% 4.30/2.27  BG Taut test         : 0.00
%------------------------------------------------------------------------------