TSTP Solution File: GEO203+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO203+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : n032.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 47.08s 35.29s
% Output   : CNFRefutation 47.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  108 (  37 unt;  19 typ;   0 def)
%            Number of atoms       :  198 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  170 (  61   ~;  86   |;   9   &)
%                                         (   2 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  16   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  137 (; 137   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ unorthogonal_lines > parallel_lines > orthogonal_lines > incident_point_and_line > equal_points > equal_lines > distinct_points > distinct_lines > convergent_lines > apart_point_and_line > point > line > parallel_through_point > orthogonal_through_point > 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(equal_lines,type,
    equal_lines: ( $i * $i ) > $o ).

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

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

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

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

tff(parallel_through_point,type,
    parallel_through_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(orthogonal_through_point,type,
    orthogonal_through_point: ( $i * $i ) > $i ).

tff(point,type,
    point: $i > $o ).

tff(line,type,
    line: $i > $o ).

tff(parallel_lines,type,
    parallel_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(unorthogonal_lines,type,
    unorthogonal_lines: ( $i * $i ) > $o ).

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

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

tff(f_62,axiom,
    ! [X] : ~ convergent_lines(X,X),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).

tff(f_438,negated_conjecture,
    ~ ! [X,Y,Z] :
        ( ( convergent_lines(X,Y)
          & convergent_lines(X,Z)
          & distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )
       => equal_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

tff(f_412,axiom,
    ! [X,Y] :
      ( equal_lines(X,Y)
    <=> ~ distinct_lines(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax2) ).

tff(f_114,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/GEO006+0.ax',cu1) ).

tff(f_86,axiom,
    ! [X,Y] :
      ( distinct_points(X,Y)
     => ~ apart_point_and_line(X,line_connecting(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).

tff(f_96,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).

tff(f_293,axiom,
    ! [L,M] :
      ~ ( ~ convergent_lines(L,M)
        & ~ unorthogonal_lines(L,M) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).

tff(f_247,axiom,
    ! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).

tff(f_133,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( distinct_lines(Y,Z)
        | convergent_lines(X,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).

tff(f_161,axiom,
    ! [X,Y] :
      ( distinct_lines(X,Y)
     => convergent_lines(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).

tff(f_427,axiom,
    ! [X,Y] :
      ( orthogonal_lines(X,Y)
    <=> ~ unorthogonal_lines(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a5) ).

tff(f_312,axiom,
    ! [L,M,N] :
      ( ( ( ~ convergent_lines(L,M)
          | ~ unorthogonal_lines(L,M) )
        & ( ~ convergent_lines(L,N)
          | ~ unorthogonal_lines(L,N) ) )
     => ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',cotno1) ).

tff(f_101,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).

tff(f_127,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_lines(Y,Z)
        | apart_point_and_line(X,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).

tff(f_250,axiom,
    ! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).

tff(f_243,axiom,
    ! [L,M,N] :
      ( ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) )
     => ( ( convergent_lines(L,N)
          & unorthogonal_lines(L,N) )
        | ( convergent_lines(M,N)
          & unorthogonal_lines(M,N) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).

tff(f_322,axiom,
    ! [L,M,N] :
      ( ( ~ unorthogonal_lines(L,M)
        & ~ unorthogonal_lines(L,N) )
     => ~ convergent_lines(M,N) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).

tff(f_68,axiom,
    ! [X,Y,Z] :
      ( distinct_points(X,Y)
     => ( distinct_points(X,Z)
        | distinct_points(Y,Z) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).

tff(c_6,plain,
    ! [X_3] : ~ convergent_lines(X_3,X_3),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_98,plain,
    convergent_lines('#skF_1','#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_438]) ).

tff(c_96,plain,
    distinct_points(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')),
    inference(cnfTransformation,[status(thm)],[f_438]) ).

tff(c_80,plain,
    ! [X_74,Y_75] :
      ( equal_lines(X_74,Y_75)
      | distinct_lines(X_74,Y_75) ),
    inference(cnfTransformation,[status(thm)],[f_412]) ).

tff(c_94,plain,
    ~ equal_lines(line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')),'#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_438]) ).

tff(c_138,plain,
    distinct_lines(line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')),'#skF_1'),
    inference(resolution,[status(thm)],[c_80,c_94]) ).

tff(c_3463,plain,
    ! [Y_384,V_385,U_386,X_387] :
      ( apart_point_and_line(Y_384,V_385)
      | apart_point_and_line(Y_384,U_386)
      | apart_point_and_line(X_387,V_385)
      | apart_point_and_line(X_387,U_386)
      | ~ distinct_lines(U_386,V_385)
      | ~ distinct_points(X_387,Y_384) ),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_42047,plain,
    ! [Y_1950,X_1951] :
      ( apart_point_and_line(Y_1950,'#skF_1')
      | apart_point_and_line(Y_1950,line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')))
      | apart_point_and_line(X_1951,'#skF_1')
      | apart_point_and_line(X_1951,line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')))
      | ~ distinct_points(X_1951,Y_1950) ),
    inference(resolution,[status(thm)],[c_138,c_3463]) ).

tff(c_42071,plain,
    ( apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1')
    | apart_point_and_line(intersection_point('#skF_1','#skF_3'),line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')))
    | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1')
    | apart_point_and_line(intersection_point('#skF_1','#skF_2'),line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3'))) ),
    inference(resolution,[status(thm)],[c_96,c_42047]) ).

tff(c_42250,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3'))),
    inference(splitLeft,[status(thm)],[c_42071]) ).

tff(c_14,plain,
    ! [X_13,Y_14] :
      ( ~ apart_point_and_line(X_13,line_connecting(X_13,Y_14))
      | ~ distinct_points(X_13,Y_14) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_42433,plain,
    ~ distinct_points(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')),
    inference(resolution,[status(thm)],[c_42250,c_14]) ).

tff(c_42439,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_42433]) ).

tff(c_42440,plain,
    ( apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1')
    | apart_point_and_line(intersection_point('#skF_1','#skF_3'),line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')))
    | apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1') ),
    inference(splitRight,[status(thm)],[c_42071]) ).

tff(c_42888,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1'),
    inference(splitLeft,[status(thm)],[c_42440]) ).

tff(c_18,plain,
    ! [X_17,Y_18] :
      ( ~ apart_point_and_line(intersection_point(X_17,Y_18),X_17)
      | ~ convergent_lines(X_17,Y_18) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_42895,plain,
    ~ convergent_lines('#skF_1','#skF_3'),
    inference(resolution,[status(thm)],[c_42888,c_18]) ).

tff(c_42901,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_98,c_42895]) ).

tff(c_42903,plain,
    ~ apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1'),
    inference(splitRight,[status(thm)],[c_42440]) ).

tff(c_116,plain,
    ! [L_101,M_102] :
      ( unorthogonal_lines(L_101,M_102)
      | convergent_lines(L_101,M_102) ),
    inference(cnfTransformation,[status(thm)],[f_293]) ).

tff(c_48,plain,
    ! [L_49,A_48] : ~ unorthogonal_lines(orthogonal_through_point(L_49,A_48),L_49),
    inference(cnfTransformation,[status(thm)],[f_247]) ).

tff(c_121,plain,
    ! [M_102,A_48] : convergent_lines(orthogonal_through_point(M_102,A_48),M_102),
    inference(resolution,[status(thm)],[c_116,c_48]) ).

tff(c_190,plain,
    ! [X_141,Z_142,Y_143] :
      ( convergent_lines(X_141,Z_142)
      | distinct_lines(Y_143,Z_142)
      | ~ convergent_lines(X_141,Y_143) ),
    inference(cnfTransformation,[status(thm)],[f_133]) ).

tff(c_321,plain,
    ! [M_163,A_164,Z_165] :
      ( convergent_lines(orthogonal_through_point(M_163,A_164),Z_165)
      | distinct_lines(M_163,Z_165) ),
    inference(resolution,[status(thm)],[c_121,c_190]) ).

tff(c_333,plain,
    ! [M_166,A_167] : distinct_lines(M_166,orthogonal_through_point(M_166,A_167)),
    inference(resolution,[status(thm)],[c_321,c_6]) ).

tff(c_30,plain,
    ! [X_34,Y_35] :
      ( convergent_lines(X_34,Y_35)
      | ~ distinct_lines(X_34,Y_35) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_340,plain,
    ! [M_166,A_167] : convergent_lines(M_166,orthogonal_through_point(M_166,A_167)),
    inference(resolution,[status(thm)],[c_333,c_30]) ).

tff(c_92,plain,
    ! [X_80,Y_81] :
      ( orthogonal_lines(X_80,Y_81)
      | unorthogonal_lines(X_80,Y_81) ),
    inference(cnfTransformation,[status(thm)],[f_427]) ).

tff(c_2255,plain,
    ! [L_331,M_332,N_333] :
      ( unorthogonal_lines(L_331,M_332)
      | convergent_lines(L_331,N_333)
      | ~ unorthogonal_lines(M_332,N_333)
      | ~ convergent_lines(M_332,N_333) ),
    inference(cnfTransformation,[status(thm)],[f_312]) ).

tff(c_6312,plain,
    ! [L_499,X_500,Y_501] :
      ( unorthogonal_lines(L_499,X_500)
      | convergent_lines(L_499,Y_501)
      | ~ convergent_lines(X_500,Y_501)
      | orthogonal_lines(X_500,Y_501) ),
    inference(resolution,[status(thm)],[c_92,c_2255]) ).

tff(c_6970,plain,
    ! [Y_519,X_520] :
      ( unorthogonal_lines(Y_519,X_520)
      | ~ convergent_lines(X_520,Y_519)
      | orthogonal_lines(X_520,Y_519) ),
    inference(resolution,[status(thm)],[c_6312,c_6]) ).

tff(c_6991,plain,
    ! [X_520,A_48] :
      ( ~ convergent_lines(X_520,orthogonal_through_point(X_520,A_48))
      | orthogonal_lines(X_520,orthogonal_through_point(X_520,A_48)) ),
    inference(resolution,[status(thm)],[c_6970,c_48]) ).

tff(c_7002,plain,
    ! [X_520,A_48] : orthogonal_lines(X_520,orthogonal_through_point(X_520,A_48)),
    inference(demodulation,[status(thm),theory(equality)],[c_340,c_6991]) ).

tff(c_100,plain,
    convergent_lines('#skF_1','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_438]) ).

tff(c_199,plain,
    ! [Z_142] :
      ( convergent_lines('#skF_1',Z_142)
      | distinct_lines('#skF_2',Z_142) ),
    inference(resolution,[status(thm)],[c_100,c_190]) ).

tff(c_29774,plain,
    ! [Y_1418,Z_1419,X_1420] :
      ( apart_point_and_line(Y_1418,Z_1419)
      | apart_point_and_line(Y_1418,'#skF_2')
      | apart_point_and_line(X_1420,Z_1419)
      | apart_point_and_line(X_1420,'#skF_2')
      | ~ distinct_points(X_1420,Y_1418)
      | convergent_lines('#skF_1',Z_1419) ),
    inference(resolution,[status(thm)],[c_199,c_3463]) ).

tff(c_29792,plain,
    ! [Z_1419] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_3'),Z_1419)
      | apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2')
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_1419)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2')
      | convergent_lines('#skF_1',Z_1419) ),
    inference(resolution,[status(thm)],[c_96,c_29774]) ).

tff(c_30027,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_2'),
    inference(splitLeft,[status(thm)],[c_29792]) ).

tff(c_20,plain,
    ! [X_19,Y_20] :
      ( ~ apart_point_and_line(intersection_point(X_19,Y_20),Y_20)
      | ~ convergent_lines(X_19,Y_20) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_30096,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_30027,c_20]) ).

tff(c_30102,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_30096]) ).

tff(c_30103,plain,
    ! [Z_1419] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2')
      | apart_point_and_line(intersection_point('#skF_1','#skF_3'),Z_1419)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_1419)
      | convergent_lines('#skF_1',Z_1419) ),
    inference(splitRight,[status(thm)],[c_29792]) ).

tff(c_30240,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_2'),
    inference(splitLeft,[status(thm)],[c_30103]) ).

tff(c_26,plain,
    ! [X_28,Z_30,Y_29] :
      ( apart_point_and_line(X_28,Z_30)
      | distinct_lines(Y_29,Z_30)
      | ~ apart_point_and_line(X_28,Y_29) ),
    inference(cnfTransformation,[status(thm)],[f_127]) ).

tff(c_32319,plain,
    ! [Z_1559] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_3'),Z_1559)
      | distinct_lines('#skF_2',Z_1559) ),
    inference(resolution,[status(thm)],[c_30240,c_26]) ).

tff(c_50,plain,
    ! [A_50,L_51] : ~ apart_point_and_line(A_50,orthogonal_through_point(L_51,A_50)),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_33040,plain,
    ! [L_1584] : distinct_lines('#skF_2',orthogonal_through_point(L_1584,intersection_point('#skF_1','#skF_3'))),
    inference(resolution,[status(thm)],[c_32319,c_50]) ).

tff(c_33053,plain,
    ! [L_1584] : convergent_lines('#skF_2',orthogonal_through_point(L_1584,intersection_point('#skF_1','#skF_3'))),
    inference(resolution,[status(thm)],[c_33040,c_30]) ).

tff(c_1982,plain,
    ! [L_318,N_319,M_320] :
      ( unorthogonal_lines(L_318,N_319)
      | unorthogonal_lines(M_320,N_319)
      | ~ unorthogonal_lines(L_318,M_320)
      | ~ convergent_lines(L_318,M_320) ),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_5936,plain,
    ! [X_484,N_485,Y_486] :
      ( unorthogonal_lines(X_484,N_485)
      | unorthogonal_lines(Y_486,N_485)
      | ~ convergent_lines(X_484,Y_486)
      | orthogonal_lines(X_484,Y_486) ),
    inference(resolution,[status(thm)],[c_92,c_1982]) ).

tff(c_37415,plain,
    ! [X_1753,N_1754,A_1755] :
      ( unorthogonal_lines(X_1753,N_1754)
      | ~ convergent_lines(X_1753,orthogonal_through_point(N_1754,A_1755))
      | orthogonal_lines(X_1753,orthogonal_through_point(N_1754,A_1755)) ),
    inference(resolution,[status(thm)],[c_5936,c_48]) ).

tff(c_180,plain,
    ! [M_138,N_139,L_140] :
      ( ~ convergent_lines(M_138,N_139)
      | unorthogonal_lines(L_140,N_139)
      | unorthogonal_lines(L_140,M_138) ),
    inference(cnfTransformation,[status(thm)],[f_322]) ).

tff(c_349,plain,
    ! [L_173,M_174,A_175] :
      ( unorthogonal_lines(L_173,M_174)
      | unorthogonal_lines(L_173,orthogonal_through_point(M_174,A_175)) ),
    inference(resolution,[status(thm)],[c_121,c_180]) ).

tff(c_90,plain,
    ! [X_80,Y_81] :
      ( ~ unorthogonal_lines(X_80,Y_81)
      | ~ orthogonal_lines(X_80,Y_81) ),
    inference(cnfTransformation,[status(thm)],[f_427]) ).

tff(c_357,plain,
    ! [L_173,M_174,A_175] :
      ( ~ orthogonal_lines(L_173,orthogonal_through_point(M_174,A_175))
      | unorthogonal_lines(L_173,M_174) ),
    inference(resolution,[status(thm)],[c_349,c_90]) ).

tff(c_38628,plain,
    ! [X_1786,N_1787,A_1788] :
      ( unorthogonal_lines(X_1786,N_1787)
      | ~ convergent_lines(X_1786,orthogonal_through_point(N_1787,A_1788)) ),
    inference(resolution,[status(thm)],[c_37415,c_357]) ).

tff(c_39031,plain,
    ! [L_1789] : unorthogonal_lines('#skF_2',L_1789),
    inference(resolution,[status(thm)],[c_33053,c_38628]) ).

tff(c_39059,plain,
    ! [L_1790] : ~ orthogonal_lines('#skF_2',L_1790),
    inference(resolution,[status(thm)],[c_39031,c_90]) ).

tff(c_39106,plain,
    $false,
    inference(resolution,[status(thm)],[c_7002,c_39059]) ).

tff(c_121317,plain,
    ! [Z_3436] :
      ( apart_point_and_line(intersection_point('#skF_1','#skF_3'),Z_3436)
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),Z_3436)
      | convergent_lines('#skF_1',Z_3436) ),
    inference(splitRight,[status(thm)],[c_30103]) ).

tff(c_42441,plain,
    ~ apart_point_and_line(intersection_point('#skF_1','#skF_2'),line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3'))),
    inference(splitRight,[status(thm)],[c_42071]) ).

tff(c_460,plain,
    ! [Y_190,Z_191,X_192] :
      ( distinct_points(Y_190,Z_191)
      | distinct_points(X_192,Z_191)
      | ~ distinct_points(X_192,Y_190) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_463,plain,
    ! [Z_191] :
      ( distinct_points(intersection_point('#skF_1','#skF_3'),Z_191)
      | distinct_points(intersection_point('#skF_1','#skF_2'),Z_191) ),
    inference(resolution,[status(thm)],[c_96,c_460]) ).

tff(c_42070,plain,
    ! [Z_191] :
      ( apart_point_and_line(Z_191,'#skF_1')
      | apart_point_and_line(Z_191,line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')))
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1')
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')))
      | distinct_points(intersection_point('#skF_1','#skF_3'),Z_191) ),
    inference(resolution,[status(thm)],[c_463,c_42047]) ).

tff(c_43062,plain,
    ! [Z_191] :
      ( apart_point_and_line(Z_191,'#skF_1')
      | apart_point_and_line(Z_191,line_connecting(intersection_point('#skF_1','#skF_2'),intersection_point('#skF_1','#skF_3')))
      | apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1')
      | distinct_points(intersection_point('#skF_1','#skF_3'),Z_191) ),
    inference(negUnitSimplification,[status(thm)],[c_42441,c_42070]) ).

tff(c_43063,plain,
    apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1'),
    inference(splitLeft,[status(thm)],[c_43062]) ).

tff(c_43070,plain,
    ~ convergent_lines('#skF_1','#skF_2'),
    inference(resolution,[status(thm)],[c_43063,c_18]) ).

tff(c_43076,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_43070]) ).

tff(c_43078,plain,
    ~ apart_point_and_line(intersection_point('#skF_1','#skF_2'),'#skF_1'),
    inference(splitRight,[status(thm)],[c_43062]) ).

tff(c_121320,plain,
    ( apart_point_and_line(intersection_point('#skF_1','#skF_3'),'#skF_1')
    | convergent_lines('#skF_1','#skF_1') ),
    inference(resolution,[status(thm)],[c_121317,c_43078]) ).

tff(c_121361,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6,c_42903,c_121320]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO203+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % 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
% 0.13/0.32  % Computer : n032.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Fri Aug  4 00:22:36 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 47.08/35.29  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.08/35.30  
% 47.08/35.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 47.08/35.34  
% 47.08/35.34  Inference rules
% 47.08/35.34  ----------------------
% 47.08/35.34  #Ref     : 0
% 47.08/35.34  #Sup     : 30839
% 47.08/35.34  #Fact    : 478
% 47.08/35.34  #Define  : 0
% 47.08/35.34  #Split   : 42
% 47.08/35.34  #Chain   : 0
% 47.08/35.34  #Close   : 0
% 47.08/35.34  
% 47.08/35.34  Ordering : KBO
% 47.08/35.34  
% 47.08/35.34  Simplification rules
% 47.08/35.34  ----------------------
% 47.08/35.34  #Subsume      : 2693
% 47.08/35.34  #Demod        : 3083
% 47.08/35.34  #Tautology    : 1647
% 47.08/35.34  #SimpNegUnit  : 197
% 47.08/35.34  #BackRed      : 3
% 47.08/35.34  
% 47.08/35.34  #Partial instantiations: 0
% 47.08/35.34  #Strategies tried      : 1
% 47.08/35.34  
% 47.08/35.34  Timing (in seconds)
% 47.08/35.34  ----------------------
% 47.08/35.35  Preprocessing        : 0.56
% 47.08/35.35  Parsing              : 0.31
% 47.08/35.35  CNF conversion       : 0.04
% 47.08/35.35  Main loop            : 33.74
% 47.08/35.35  Inferencing          : 4.14
% 47.08/35.35  Reduction            : 9.36
% 47.08/35.35  Demodulation         : 6.95
% 47.08/35.35  BG Simplification    : 0.21
% 47.08/35.35  Subsumption          : 17.80
% 47.08/35.35  Abstraction          : 0.26
% 47.08/35.35  MUC search           : 0.00
% 47.08/35.35  Cooper               : 0.00
% 47.08/35.35  Total                : 34.37
% 47.08/35.35  Index Insertion      : 0.00
% 47.08/35.35  Index Deletion       : 0.00
% 47.08/35.35  Index Matching       : 0.00
% 47.08/35.35  BG Taut test         : 0.00
%------------------------------------------------------------------------------