TSTP Solution File: GEO202+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO202+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 : n006.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 10:38:38 EDT 2023

% Result   : Theorem 11.33s 3.87s
% Output   : CNFRefutation 11.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   58 (  21 unt;   9 typ;   0 def)
%            Number of atoms       :  123 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  105 (  31   ~;  62   |;   4   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   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   :   57 (;  57   !;   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_141,negated_conjecture,
    ~ ! [X,Y,Z] :
        ( ( distinct_points(X,Y)
          & distinct_points(X,Z)
          & convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )
       => ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

tff(f_70,axiom,
    ! [X,Y,Z] :
      ( distinct_points(X,Y)
     => ( distinct_points(X,Z)
        | distinct_points(Y,Z) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).

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

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_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/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).

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

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(c_32,plain,
    convergent_lines(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_30,plain,
    distinct_points(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),'#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_56,plain,
    ! [Y_48,Z_49,X_50] :
      ( distinct_points(Y_48,Z_49)
      | distinct_points(X_50,Z_49)
      | ~ distinct_points(X_50,Y_48) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_63,plain,
    ! [Z_49] :
      ( distinct_points('#skF_1',Z_49)
      | distinct_points(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),Z_49) ),
    inference(resolution,[status(thm)],[c_30,c_56]) ).

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_1313,plain,
    ! [Y_120,V_121,U_122,X_123] :
      ( apart_point_and_line(Y_120,V_121)
      | apart_point_and_line(Y_120,U_122)
      | apart_point_and_line(X_123,V_121)
      | apart_point_and_line(X_123,U_122)
      | ~ distinct_lines(U_122,V_121)
      | ~ distinct_points(X_123,Y_120) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_2960,plain,
    ! [Y_185,Y_186,X_187,X_188] :
      ( apart_point_and_line(Y_185,Y_186)
      | apart_point_and_line(Y_185,X_187)
      | apart_point_and_line(X_188,Y_186)
      | apart_point_and_line(X_188,X_187)
      | ~ distinct_points(X_188,Y_185)
      | ~ convergent_lines(X_187,Y_186) ),
    inference(resolution,[status(thm)],[c_28,c_1313]) ).

tff(c_5852,plain,
    ! [Z_279,Y_280,X_281] :
      ( apart_point_and_line(Z_279,Y_280)
      | apart_point_and_line(Z_279,X_281)
      | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),Y_280)
      | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),X_281)
      | ~ convergent_lines(X_281,Y_280)
      | distinct_points('#skF_1',Z_279) ),
    inference(resolution,[status(thm)],[c_63,c_2960]) ).

tff(c_5879,plain,
    ! [Z_279] :
      ( apart_point_and_line(Z_279,line_connecting('#skF_1','#skF_3'))
      | apart_point_and_line(Z_279,line_connecting('#skF_1','#skF_2'))
      | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_3'))
      | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_2'))
      | distinct_points('#skF_1',Z_279) ),
    inference(resolution,[status(thm)],[c_32,c_5852]) ).

tff(c_6852,plain,
    apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_2')),
    inference(splitLeft,[status(thm)],[c_5879]) ).

tff(c_786,plain,
    ! [Z_96,X_97,Y_98] :
      ( ~ apart_point_and_line(Z_96,X_97)
      | distinct_points(Z_96,intersection_point(X_97,Y_98))
      | ~ convergent_lines(X_97,Y_98) ),
    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_794,plain,
    ! [X_97,Y_98] :
      ( ~ apart_point_and_line(intersection_point(X_97,Y_98),X_97)
      | ~ convergent_lines(X_97,Y_98) ),
    inference(resolution,[status(thm)],[c_786,c_2]) ).

tff(c_6997,plain,
    ~ convergent_lines(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),
    inference(resolution,[status(thm)],[c_6852,c_794]) ).

tff(c_7017,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_6997]) ).

tff(c_7019,plain,
    ~ apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_5879]) ).

tff(c_36,plain,
    distinct_points('#skF_1','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_3476,plain,
    ! [Y_194,X_195] :
      ( apart_point_and_line('#skF_2',Y_194)
      | apart_point_and_line('#skF_2',X_195)
      | apart_point_and_line('#skF_1',Y_194)
      | apart_point_and_line('#skF_1',X_195)
      | ~ convergent_lines(X_195,Y_194) ),
    inference(resolution,[status(thm)],[c_36,c_2960]) ).

tff(c_3512,plain,
    ( apart_point_and_line('#skF_2',line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line('#skF_2',line_connecting('#skF_1','#skF_2'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_32,c_3476]) ).

tff(c_4171,plain,
    apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')),
    inference(splitLeft,[status(thm)],[c_3512]) ).

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_4178,plain,
    ( distinct_points('#skF_1','#skF_1')
    | ~ distinct_points('#skF_1','#skF_2') ),
    inference(resolution,[status(thm)],[c_4171,c_16]) ).

tff(c_4190,plain,
    distinct_points('#skF_1','#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_4178]) ).

tff(c_4192,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_4190]) ).

tff(c_4194,plain,
    ~ apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')),
    inference(splitRight,[status(thm)],[c_3512]) ).

tff(c_34,plain,
    distinct_points('#skF_1','#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_3862,plain,
    ! [Y_205,X_206] :
      ( apart_point_and_line('#skF_3',Y_205)
      | apart_point_and_line('#skF_3',X_206)
      | apart_point_and_line('#skF_1',Y_205)
      | apart_point_and_line('#skF_1',X_206)
      | ~ convergent_lines(X_206,Y_205) ),
    inference(resolution,[status(thm)],[c_34,c_2960]) ).

tff(c_3898,plain,
    ( apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_2'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_32,c_3862]) ).

tff(c_4859,plain,
    ( apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line('#skF_3',line_connecting('#skF_1','#skF_2'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3')) ),
    inference(negUnitSimplification,[status(thm)],[c_4194,c_3898]) ).

tff(c_4860,plain,
    apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3')),
    inference(splitLeft,[status(thm)],[c_4859]) ).

tff(c_4867,plain,
    ( distinct_points('#skF_1','#skF_1')
    | ~ distinct_points('#skF_1','#skF_3') ),
    inference(resolution,[status(thm)],[c_4860,c_16]) ).

tff(c_4879,plain,
    distinct_points('#skF_1','#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_4867]) ).

tff(c_4881,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2,c_4879]) ).

tff(c_4883,plain,
    ~ apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3')),
    inference(splitRight,[status(thm)],[c_4859]) ).

tff(c_5264,plain,
    ! [Y_249,X_250] :
      ( apart_point_and_line('#skF_1',Y_249)
      | apart_point_and_line('#skF_1',X_250)
      | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),Y_249)
      | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),X_250)
      | ~ convergent_lines(X_250,Y_249) ),
    inference(resolution,[status(thm)],[c_30,c_2960]) ).

tff(c_5282,plain,
    ( apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line('#skF_1',line_connecting('#skF_1','#skF_2'))
    | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_2')) ),
    inference(resolution,[status(thm)],[c_32,c_5264]) ).

tff(c_5307,plain,
    ( apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_3'))
    | apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_4194,c_4883,c_5282]) ).

tff(c_13362,plain,
    apart_point_and_line(intersection_point(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),line_connecting('#skF_1','#skF_3')),
    inference(negUnitSimplification,[status(thm)],[c_7019,c_5307]) ).

tff(c_86,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_94,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_86,c_2]) ).

tff(c_13379,plain,
    ~ convergent_lines(line_connecting('#skF_1','#skF_2'),line_connecting('#skF_1','#skF_3')),
    inference(resolution,[status(thm)],[c_13362,c_94]) ).

tff(c_13401,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_13379]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GEO202+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
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri Aug  4 00:18:58 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 11.33/3.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.33/3.88  
% 11.33/3.88  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.43/3.91  
% 11.43/3.91  Inference rules
% 11.43/3.91  ----------------------
% 11.43/3.91  #Ref     : 0
% 11.43/3.91  #Sup     : 1780
% 11.43/3.91  #Fact    : 802
% 11.43/3.91  #Define  : 0
% 11.43/3.91  #Split   : 5
% 11.43/3.91  #Chain   : 0
% 11.43/3.91  #Close   : 0
% 11.43/3.91  
% 11.43/3.91  Ordering : KBO
% 11.43/3.91  
% 11.43/3.91  Simplification rules
% 11.43/3.91  ----------------------
% 11.43/3.91  #Subsume      : 927
% 11.43/3.91  #Demod        : 489
% 11.43/3.91  #Tautology    : 399
% 11.43/3.91  #SimpNegUnit  : 422
% 11.43/3.91  #BackRed      : 0
% 11.43/3.91  
% 11.43/3.91  #Partial instantiations: 0
% 11.43/3.91  #Strategies tried      : 1
% 11.43/3.91  
% 11.43/3.91  Timing (in seconds)
% 11.43/3.91  ----------------------
% 11.43/3.92  Preprocessing        : 0.47
% 11.43/3.92  Parsing              : 0.26
% 11.43/3.92  CNF conversion       : 0.03
% 11.43/3.92  Main loop            : 2.35
% 11.43/3.92  Inferencing          : 0.85
% 11.43/3.92  Reduction            : 0.47
% 11.43/3.92  Demodulation         : 0.28
% 11.43/3.92  BG Simplification    : 0.04
% 11.43/3.92  Subsumption          : 0.84
% 11.43/3.92  Abstraction          : 0.05
% 11.43/3.92  MUC search           : 0.00
% 11.43/3.92  Cooper               : 0.00
% 11.43/3.92  Total                : 2.87
% 11.43/3.92  Index Insertion      : 0.00
% 11.43/3.92  Index Deletion       : 0.00
% 11.43/3.92  Index Matching       : 0.00
% 11.43/3.92  BG Taut test         : 0.00
%------------------------------------------------------------------------------