TSTP Solution File: GEO191+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO191+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 : n008.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 10:38:33 EDT 2023

% Result   : Theorem 12.59s 4.31s
% Output   : CNFRefutation 12.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   69 (  26 unt;  10 typ;   0 def)
%            Number of atoms       :  145 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  126 (  40   ~;  77   |;   3   &)
%                                         (   0 <=>;   6  =>;   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   :   76 (;  76   !;   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_144,negated_conjecture,
    ~ ! [X,Y,U,V] :
        ( ( convergent_lines(X,Y)
          & convergent_lines(U,V)
          & ( apart_point_and_line(intersection_point(X,Y),U)
            | apart_point_and_line(intersection_point(X,Y),V) ) )
       => ( apart_point_and_line(intersection_point(U,V),X)
          | apart_point_and_line(intersection_point(U,V),Y) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

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

tff(c_32,plain,
    ~ apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

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

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

tff(c_52,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_3'),
    inference(splitLeft,[status(thm)],[c_34]) ).

tff(c_53,plain,
    ! [Z_39,Y_40,X_41] :
      ( apart_point_and_line(Z_39,Y_40)
      | distinct_points(X_41,Z_39)
      | ~ apart_point_and_line(X_41,Y_40) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_56,plain,
    ! [Z_39] :
      ( apart_point_and_line(Z_39,'#skF_3')
      | distinct_points(intersection_point('#skF_1','#skF_2'),Z_39) ),
    inference(resolution,[status(thm)],[c_52,c_53]) ).

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_965,plain,
    ! [Y_118,V_119,U_120,X_121] :
      ( apart_point_and_line(Y_118,V_119)
      | apart_point_and_line(Y_118,U_120)
      | apart_point_and_line(X_121,V_119)
      | apart_point_and_line(X_121,U_120)
      | ~ distinct_lines(U_120,V_119)
      | ~ distinct_points(X_121,Y_118) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_1992,plain,
    ! [Y_167,Y_168,X_169,X_170] :
      ( apart_point_and_line(Y_167,Y_168)
      | apart_point_and_line(Y_167,X_169)
      | apart_point_and_line(X_170,Y_168)
      | apart_point_and_line(X_170,X_169)
      | ~ distinct_points(X_170,Y_167)
      | ~ convergent_lines(X_169,Y_168) ),
    inference(resolution,[status(thm)],[c_28,c_965]) ).

tff(c_4540,plain,
    ! [Z_277,Y_278,X_279] :
      ( apart_point_and_line(Z_277,Y_278)
      | apart_point_and_line(Z_277,X_279)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Y_278)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),X_279)
      | ~ convergent_lines(X_279,Y_278)
      | apart_point_and_line(Z_277,'#skF_3') ),
    inference(resolution,[status(thm)],[c_56,c_1992]) ).

tff(c_4725,plain,
    ! [Z_277] :
      ( apart_point_and_line(Z_277,'#skF_2')
      | apart_point_and_line(Z_277,'#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')
      | apart_point_and_line(Z_277,'#skF_3') ),
    inference(resolution,[status(thm)],[c_38,c_4540]) ).

tff(c_4979,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1'),
    inference(splitLeft,[status(thm)],[c_4725]) ).

tff(c_380,plain,
    ! [Z_75,X_76,Y_77] :
      ( ~ apart_point_and_line(Z_75,X_76)
      | distinct_points(Z_75,intersection_point(X_76,Y_77))
      | ~ convergent_lines(X_76,Y_77) ),
    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_388,plain,
    ! [X_76,Y_77] :
      ( ~ apart_point_and_line(intersection_point(X_76,Y_77),X_76)
      | ~ convergent_lines(X_76,Y_77) ),
    inference(resolution,[status(thm)],[c_380,c_2]) ).

tff(c_4986,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_4979,c_388]) ).

tff(c_4996,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_4986]) ).

tff(c_4997,plain,
    ! [Z_277] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
      | apart_point_and_line(Z_277,'#skF_2')
      | apart_point_and_line(Z_277,'#skF_1')
      | apart_point_and_line(Z_277,'#skF_3') ),
    inference(splitRight,[status(thm)],[c_4725]) ).

tff(c_8217,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
    inference(splitLeft,[status(thm)],[c_4997]) ).

tff(c_787,plain,
    ! [Z_104,Y_105,X_106] :
      ( ~ apart_point_and_line(Z_104,Y_105)
      | distinct_points(Z_104,intersection_point(X_106,Y_105))
      | ~ convergent_lines(X_106,Y_105) ),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_795,plain,
    ! [X_106,Y_105] :
      ( ~ apart_point_and_line(intersection_point(X_106,Y_105),Y_105)
      | ~ convergent_lines(X_106,Y_105) ),
    inference(resolution,[status(thm)],[c_787,c_2]) ).

tff(c_8232,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_8217,c_795]) ).

tff(c_8252,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_8232]) ).

tff(c_8265,plain,
    ! [Z_406] :
      ( apart_point_and_line(Z_406,'#skF_2')
      | apart_point_and_line(Z_406,'#skF_1')
      | apart_point_and_line(Z_406,'#skF_3') ),
    inference(splitRight,[status(thm)],[c_4997]) ).

tff(c_30,plain,
    ~ apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_8295,plain,
    ( apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_1')
    | apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_3') ),
    inference(resolution,[status(thm)],[c_8265,c_30]) ).

tff(c_8311,plain,
    apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_3'),
    inference(negUnitSimplification,[status(thm)],[c_32,c_8295]) ).

tff(c_8326,plain,
    ~ convergent_lines('#skF_3','#skF_4'),
    inference(resolution,[status(thm)],[c_8311,c_388]) ).

tff(c_8346,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_8326]) ).

tff(c_8347,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_4'),
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_8404,plain,
    ! [Z_420,Y_421,X_422] :
      ( apart_point_and_line(Z_420,Y_421)
      | distinct_points(X_422,Z_420)
      | ~ apart_point_and_line(X_422,Y_421) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_8410,plain,
    ! [Z_420] :
      ( apart_point_and_line(Z_420,'#skF_4')
      | distinct_points(intersection_point('#skF_1','#skF_2'),Z_420) ),
    inference(resolution,[status(thm)],[c_8347,c_8404]) ).

tff(c_9553,plain,
    ! [Y_494,V_495,U_496,X_497] :
      ( apart_point_and_line(Y_494,V_495)
      | apart_point_and_line(Y_494,U_496)
      | apart_point_and_line(X_497,V_495)
      | apart_point_and_line(X_497,U_496)
      | ~ distinct_lines(U_496,V_495)
      | ~ distinct_points(X_497,Y_494) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_10473,plain,
    ! [Y_542,Y_543,X_544,X_545] :
      ( apart_point_and_line(Y_542,Y_543)
      | apart_point_and_line(Y_542,X_544)
      | apart_point_and_line(X_545,Y_543)
      | apart_point_and_line(X_545,X_544)
      | ~ distinct_points(X_545,Y_542)
      | ~ convergent_lines(X_544,Y_543) ),
    inference(resolution,[status(thm)],[c_28,c_9553]) ).

tff(c_13597,plain,
    ! [Z_680,Y_681,X_682] :
      ( apart_point_and_line(Z_680,Y_681)
      | apart_point_and_line(Z_680,X_682)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Y_681)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),X_682)
      | ~ convergent_lines(X_682,Y_681)
      | apart_point_and_line(Z_680,'#skF_4') ),
    inference(resolution,[status(thm)],[c_8410,c_10473]) ).

tff(c_13908,plain,
    ! [Z_680] :
      ( apart_point_and_line(Z_680,'#skF_2')
      | apart_point_and_line(Z_680,'#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')
      | apart_point_and_line(Z_680,'#skF_4') ),
    inference(resolution,[status(thm)],[c_38,c_13597]) ).

tff(c_14096,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1'),
    inference(splitLeft,[status(thm)],[c_13908]) ).

tff(c_8799,plain,
    ! [Z_451,X_452,Y_453] :
      ( ~ apart_point_and_line(Z_451,X_452)
      | distinct_points(Z_451,intersection_point(X_452,Y_453))
      | ~ convergent_lines(X_452,Y_453) ),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_8807,plain,
    ! [X_452,Y_453] :
      ( ~ apart_point_and_line(intersection_point(X_452,Y_453),X_452)
      | ~ convergent_lines(X_452,Y_453) ),
    inference(resolution,[status(thm)],[c_8799,c_2]) ).

tff(c_14103,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_14096,c_8807]) ).

tff(c_14113,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_14103]) ).

tff(c_14114,plain,
    ! [Z_680] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
      | apart_point_and_line(Z_680,'#skF_2')
      | apart_point_and_line(Z_680,'#skF_1')
      | apart_point_and_line(Z_680,'#skF_4') ),
    inference(splitRight,[status(thm)],[c_13908]) ).

tff(c_17529,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
    inference(splitLeft,[status(thm)],[c_14114]) ).

tff(c_9001,plain,
    ! [Z_465,Y_466,X_467] :
      ( ~ apart_point_and_line(Z_465,Y_466)
      | distinct_points(Z_465,intersection_point(X_467,Y_466))
      | ~ convergent_lines(X_467,Y_466) ),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_9009,plain,
    ! [X_467,Y_466] :
      ( ~ apart_point_and_line(intersection_point(X_467,Y_466),Y_466)
      | ~ convergent_lines(X_467,Y_466) ),
    inference(resolution,[status(thm)],[c_9001,c_2]) ).

tff(c_17544,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_17529,c_9009]) ).

tff(c_17566,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_17544]) ).

tff(c_17579,plain,
    ! [Z_807] :
      ( apart_point_and_line(Z_807,'#skF_2')
      | apart_point_and_line(Z_807,'#skF_1')
      | apart_point_and_line(Z_807,'#skF_4') ),
    inference(splitRight,[status(thm)],[c_14114]) ).

tff(c_17609,plain,
    ( apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_1')
    | apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_4') ),
    inference(resolution,[status(thm)],[c_17579,c_30]) ).

tff(c_17625,plain,
    apart_point_and_line(intersection_point('#skF_3','#skF_4'),'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_32,c_17609]) ).

tff(c_17640,plain,
    ~ convergent_lines('#skF_3','#skF_4'),
    inference(resolution,[status(thm)],[c_17625,c_9009]) ).

tff(c_17660,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_17640]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GEO191+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
% 0.16/0.35  % Computer : n008.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Fri Aug  4 00:29:18 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 12.59/4.31  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.59/4.32  
% 12.59/4.32  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.59/4.36  
% 12.59/4.36  Inference rules
% 12.59/4.36  ----------------------
% 12.59/4.36  #Ref     : 0
% 12.59/4.36  #Sup     : 3059
% 12.59/4.36  #Fact    : 760
% 12.59/4.36  #Define  : 0
% 12.59/4.36  #Split   : 5
% 12.59/4.36  #Chain   : 0
% 12.59/4.36  #Close   : 0
% 12.59/4.36  
% 12.59/4.36  Ordering : KBO
% 12.59/4.36  
% 12.59/4.36  Simplification rules
% 12.59/4.36  ----------------------
% 12.59/4.36  #Subsume      : 810
% 12.59/4.36  #Demod        : 664
% 12.59/4.36  #Tautology    : 628
% 12.59/4.36  #SimpNegUnit  : 266
% 12.59/4.36  #BackRed      : 0
% 12.59/4.36  
% 12.59/4.36  #Partial instantiations: 0
% 12.59/4.36  #Strategies tried      : 1
% 12.59/4.36  
% 12.59/4.36  Timing (in seconds)
% 12.59/4.36  ----------------------
% 12.59/4.36  Preprocessing        : 0.51
% 12.59/4.36  Parsing              : 0.28
% 12.59/4.36  CNF conversion       : 0.03
% 12.59/4.36  Main loop            : 2.77
% 12.59/4.36  Inferencing          : 1.01
% 12.59/4.36  Reduction            : 0.58
% 12.59/4.36  Demodulation         : 0.34
% 12.59/4.36  BG Simplification    : 0.06
% 12.59/4.36  Subsumption          : 0.95
% 12.59/4.36  Abstraction          : 0.06
% 12.59/4.36  MUC search           : 0.00
% 12.59/4.36  Cooper               : 0.00
% 12.59/4.36  Total                : 3.34
% 12.59/4.36  Index Insertion      : 0.00
% 12.59/4.36  Index Deletion       : 0.00
% 12.59/4.36  Index Matching       : 0.00
% 12.59/4.36  BG Taut test         : 0.00
%------------------------------------------------------------------------------