TSTP Solution File: GEO261+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO261+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n017.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  : 0s
% DateTime : Sat Jul 16 02:53:23 EDT 2022

% Result   : Theorem 0.42s 1.07s
% Output   : Refutation 0.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : GEO261+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % DateTime : Sat Jun 18 07:19:57 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.42/1.06  *** allocated 10000 integers for termspace/termends
% 0.42/1.06  *** allocated 10000 integers for clauses
% 0.42/1.06  *** allocated 10000 integers for justifications
% 0.42/1.06  Bliksem 1.12
% 0.42/1.06  
% 0.42/1.06  
% 0.42/1.06  Automatic Strategy Selection
% 0.42/1.06  
% 0.42/1.06  
% 0.42/1.06  Clauses:
% 0.42/1.06  
% 0.42/1.06  { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ), 
% 0.42/1.06    left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.06  { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.42/1.06  { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.42/1.06     }.
% 0.42/1.06  { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.06  { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.42/1.06     ) ) }.
% 0.42/1.06  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.06    reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.42/1.06  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.42/1.06  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.42/1.06  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.42/1.06  { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.06  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.42/1.06  { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ), 
% 0.42/1.06    alpha4( X, Y, Z ) }.
% 0.42/1.06  { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.42/1.06  { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.42/1.06  { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ), 
% 0.42/1.06    alpha1( X, Y, Z ) }.
% 0.42/1.06  { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.42/1.06  { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.42/1.06  { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.42/1.06     }.
% 0.42/1.06  { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.42/1.06  { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.42/1.06  { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.42/1.06  { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.42/1.06  { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.42/1.06     ) ) }.
% 0.42/1.06  { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.42/1.06    , alpha8( X, Y, Z ) }.
% 0.42/1.06  { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.42/1.06  { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.42/1.06  { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ), 
% 0.42/1.06    alpha5( X, Y ) }.
% 0.42/1.06  { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.42/1.06  { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.42/1.06  { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ), 
% 0.42/1.06    alpha2( X, Y ) }.
% 0.42/1.06  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.42/1.06     ) }.
% 0.42/1.06  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.42/1.06  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.42/1.06  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.42/1.06  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.42/1.06  { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.42/1.06    , T ) }.
% 0.42/1.06  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.42/1.06  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.42/1.06  { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.42/1.06    , T ) }.
% 0.42/1.06  { ! distinct_points( X, X ) }.
% 0.42/1.06  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.42/1.06     ) }.
% 0.42/1.06  { ! distinct_lines( X, X ) }.
% 0.42/1.06  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.42/1.06     }.
% 0.42/1.06  { ! unequally_directed_lines( X, X ) }.
% 0.42/1.06  { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ), 
% 0.42/1.06    unequally_directed_lines( Y, Z ) }.
% 0.42/1.06  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.06    reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.06  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.06    reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, 
% 0.42/1.06    reverse_line( Z ) ) }.
% 0.42/1.06  { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.06  { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.06  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.06    reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.42/1.06  { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ), 
% 0.42/1.06    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.06  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.06    reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.42/1.06    ( X, reverse_line( Y ) ) }.
% 0.42/1.07  { ! left_apart_point( X, Y ) }.
% 0.42/1.07  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.07  { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07  { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.42/1.07    line_connecting( X, Y ) ) }.
% 0.42/1.07  { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), point( 
% 0.42/1.07    intersection_point( X, Y ) ) }.
% 0.42/1.07  { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.42/1.07  { ! line( X ), line( reverse_line( X ) ) }.
% 0.42/1.07  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.42/1.07    , Y ) ) }.
% 0.42/1.07  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.42/1.07    , Y ) ) }.
% 0.42/1.07  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.07    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.42/1.07    X ) }.
% 0.42/1.07  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.07    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.42/1.07    Y ) }.
% 0.42/1.07  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.42/1.07  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.42/1.07  { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line( 
% 0.42/1.07    line_connecting( Y, X ) ) ) }.
% 0.42/1.07  { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.42/1.07  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.42/1.07    , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ), 
% 0.42/1.07    left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ), 
% 0.42/1.07    left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X, 
% 0.42/1.07    reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.42/1.07  { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point( 
% 0.42/1.07    Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.42/1.07  { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.42/1.07    , Y ) }.
% 0.42/1.07  { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ), 
% 0.42/1.07    distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.07  { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ), 
% 0.42/1.07    left_convergent_lines( X, Z ) }.
% 0.42/1.07  { between_on_line( skol4, skol2, skol5, skol3 ) }.
% 0.42/1.07  { convergent_lines( skol4, skol1 ) }.
% 0.42/1.07  { ! apart_point_and_line( skol5, skol1 ) }.
% 0.42/1.07  { ! divides_points( skol1, skol2, skol3 ) }.
% 0.42/1.07  
% 0.42/1.07  percentage equality = 0.000000, percentage horn = 0.802817
% 0.42/1.07  This a non-horn, non-equality problem
% 0.42/1.07  
% 0.42/1.07  
% 0.42/1.07  Options Used:
% 0.42/1.07  
% 0.42/1.07  useres =            1
% 0.42/1.07  useparamod =        0
% 0.42/1.07  useeqrefl =         0
% 0.42/1.07  useeqfact =         0
% 0.42/1.07  usefactor =         1
% 0.42/1.07  usesimpsplitting =  0
% 0.42/1.07  usesimpdemod =      0
% 0.42/1.07  usesimpres =        3
% 0.42/1.07  
% 0.42/1.07  resimpinuse      =  1000
% 0.42/1.07  resimpclauses =     20000
% 0.42/1.07  substype =          standard
% 0.42/1.07  backwardsubs =      1
% 0.42/1.07  selectoldest =      5
% 0.42/1.07  
% 0.42/1.07  litorderings [0] =  split
% 0.42/1.07  litorderings [1] =  liftord
% 0.42/1.07  
% 0.42/1.07  termordering =      none
% 0.42/1.07  
% 0.42/1.07  litapriori =        1
% 0.42/1.07  termapriori =       0
% 0.42/1.07  litaposteriori =    0
% 0.42/1.07  termaposteriori =   0
% 0.42/1.07  demodaposteriori =  0
% 0.42/1.07  ordereqreflfact =   0
% 0.42/1.07  
% 0.42/1.07  litselect =         none
% 0.42/1.07  
% 0.42/1.07  maxweight =         15
% 0.42/1.07  maxdepth =          30000
% 0.42/1.07  maxlength =         115
% 0.42/1.07  maxnrvars =         195
% 0.42/1.07  excuselevel =       1
% 0.42/1.07  increasemaxweight = 1
% 0.42/1.07  
% 0.42/1.07  maxselected =       10000000
% 0.42/1.07  maxnrclauses =      10000000
% 0.42/1.07  
% 0.42/1.07  showgenerated =    0
% 0.42/1.07  showkept =         0
% 0.42/1.07  showselected =     0
% 0.42/1.07  showdeleted =      0
% 0.42/1.07  showresimp =       1
% 0.42/1.07  showstatus =       2000
% 0.42/1.07  
% 0.42/1.07  prologoutput =     0
% 0.42/1.07  nrgoals =          5000000
% 0.42/1.07  totalproof =       1
% 0.42/1.07  
% 0.42/1.07  Symbols occurring in the translation:
% 0.42/1.07  
% 0.42/1.07  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.42/1.07  .  [1, 2]      (w:1, o:25, a:1, s:1, b:0), 
% 0.42/1.07  !  [4, 1]      (w:0, o:17, a:1, s:1, b:0), 
% 0.42/1.07  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.42/1.07  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.42/1.07  apart_point_and_line  [37, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.42/1.07  left_apart_point  [38, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.42/1.07  reverse_line  [39, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.42/1.07  convergent_lines  [41, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 0.42/1.07  unequally_directed_lines  [42, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.42/1.07  divides_points  [44, 3]      (w:1, o:62, a:1, s:1, b:0), 
% 0.42/1.07  before_on_line  [45, 3]      (w:1, o:67, a:1, s:1, b:0), 
% 0.42/1.07  distinct_points  [46, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.42/1.07  line_connecting  [47, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.42/1.07  between_on_line  [49, 4]      (w:1, o:70, a:1, s:1, b:0), 
% 0.42/1.07  distinct_lines  [50, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.42/1.07  line  [52, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.42/1.07  left_convergent_lines  [53, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.42/1.07  point  [54, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 0.42/1.07  intersection_point  [55, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.42/1.07  parallel_through_point  [56, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.42/1.07  alpha1  [57, 3]      (w:1, o:63, a:1, s:1, b:0), 
% 0.42/1.07  alpha2  [58, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.42/1.07  alpha3  [59, 4]      (w:1, o:68, a:1, s:1, b:0), 
% 0.42/1.07  alpha4  [60, 3]      (w:1, o:64, a:1, s:1, b:0), 
% 0.42/1.07  alpha5  [61, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.42/1.07  alpha6  [62, 4]      (w:1, o:69, a:1, s:1, b:0), 
% 0.42/1.07  alpha7  [63, 3]      (w:1, o:65, a:1, s:1, b:0), 
% 0.42/1.07  alpha8  [64, 3]      (w:1, o:66, a:1, s:1, b:0), 
% 0.42/1.07  alpha9  [65, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 0.42/1.07  skol1  [66, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 0.42/1.07  skol2  [67, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 0.42/1.07  skol3  [68, 0]      (w:1, o:14, a:1, s:1, b:0), 
% 0.42/1.07  skol4  [69, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 0.42/1.07  skol5  [70, 0]      (w:1, o:16, a:1, s:1, b:0).
% 0.42/1.07  
% 0.42/1.07  
% 0.42/1.07  Starting Search:
% 0.42/1.07  
% 0.42/1.07  *** allocated 15000 integers for clauses
% 0.42/1.07  *** allocated 22500 integers for clauses
% 0.42/1.07  *** allocated 33750 integers for clauses
% 0.42/1.07  
% 0.42/1.07  Bliksems!, er is een bewijs:
% 0.42/1.07  % SZS status Theorem
% 0.42/1.07  % SZS output start Refutation
% 0.42/1.07  
% 0.42/1.07  (3) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  (4) {G0,W7,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  (5) {G0,W10,D3,L3,V2,M2} I { convergent_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.07    reverse_line( Y ) ) }.
% 0.42/1.07  (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X ) }.
% 0.42/1.07  (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ), 
% 0.42/1.07    unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07  (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines( 
% 0.42/1.07    X, reverse_line( Y ) ), left_convergent_lines( X, Y ) }.
% 0.42/1.07  (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07  (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( Y, X ), Y ) }.
% 0.42/1.07  (68) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol4, skol1 ) }.
% 0.42/1.07  (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines( Y, X ), 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  (120) {G2,W5,D3,L1,V2,M1} R(109,65) { ! unequally_directed_lines( X, 
% 0.42/1.07    parallel_through_point( X, Y ) ) }.
% 0.42/1.07  (121) {G3,W8,D3,L2,V3,M2} R(120,44) { ! unequally_directed_lines( Y, X ), 
% 0.42/1.07    unequally_directed_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.42/1.07  (136) {G4,W8,D3,L2,V3,M2} R(121,109) { unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Z ), Y ), ! unequally_directed_lines( X, Y )
% 0.42/1.07     }.
% 0.42/1.07  (174) {G5,W9,D3,L2,V3,M1} R(136,4) { ! convergent_lines( X, Z ), 
% 0.42/1.07    unequally_directed_lines( parallel_through_point( X, Y ), reverse_line( Z
% 0.42/1.07     ) ) }.
% 0.42/1.07  (176) {G5,W8,D3,L2,V3,M1} R(136,3) { ! convergent_lines( X, Z ), 
% 0.42/1.07    unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.42/1.07  (187) {G6,W8,D3,L2,V3,M2} R(176,5);r(174) { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.42/1.07  (191) {G7,W5,D3,L1,V1,M1} R(187,68) { convergent_lines( 
% 0.42/1.07    parallel_through_point( skol4, X ), skol1 ) }.
% 0.42/1.07  (192) {G8,W7,D4,L1,V2,M1} R(191,187) { convergent_lines( 
% 0.42/1.07    parallel_through_point( parallel_through_point( skol4, X ), Y ), skol1 )
% 0.42/1.07     }.
% 0.42/1.07  (410) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { ! unequally_directed_lines( X
% 0.42/1.07    , reverse_line( Y ) ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07  (436) {G6,W3,D2,L1,V2,M1} R(410,176);r(174) { ! convergent_lines( X, Z )
% 0.42/1.07     }.
% 0.42/1.07  (450) {G9,W0,D0,L0,V0,M0} R(436,192) {  }.
% 0.42/1.07  
% 0.42/1.07  
% 0.42/1.07  % SZS output end Refutation
% 0.42/1.07  found a proof!
% 0.42/1.07  
% 0.42/1.07  
% 0.42/1.07  Unprocessed initial clauses:
% 0.42/1.07  
% 0.42/1.07  (452) {G0,W10,D3,L3,V2,M3}  { ! apart_point_and_line( X, Y ), 
% 0.42/1.07    left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.07  (453) {G0,W6,D2,L2,V2,M2}  { ! left_apart_point( X, Y ), 
% 0.42/1.07    apart_point_and_line( X, Y ) }.
% 0.42/1.07  (454) {G0,W7,D3,L2,V2,M2}  { ! left_apart_point( X, reverse_line( Y ) ), 
% 0.42/1.07    apart_point_and_line( X, Y ) }.
% 0.42/1.07  (455) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  (456) {G0,W7,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  (457) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.42/1.07     ) }.
% 0.42/1.07  (458) {G0,W12,D2,L3,V3,M3}  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.42/1.07     ), alpha4( X, Y, Z ) }.
% 0.42/1.07  (459) {G0,W8,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.42/1.07     }.
% 0.42/1.07  (460) {G0,W8,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.42/1.07     }.
% 0.42/1.07  (461) {G0,W8,D3,L2,V3,M2}  { ! alpha4( X, Y, Z ), left_apart_point( X, 
% 0.42/1.07    reverse_line( Z ) ) }.
% 0.42/1.07  (462) {G0,W7,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.42/1.07     }.
% 0.42/1.07  (463) {G0,W11,D3,L3,V3,M3}  { ! left_apart_point( X, reverse_line( Z ) ), !
% 0.42/1.07     left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.42/1.07  (464) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.42/1.07     }.
% 0.42/1.07  (465) {G0,W8,D3,L2,V3,M2}  { ! alpha1( X, Y, Z ), left_apart_point( Y, 
% 0.42/1.07    reverse_line( Z ) ) }.
% 0.42/1.07  (466) {G0,W11,D3,L3,V3,M3}  { ! left_apart_point( X, Z ), ! 
% 0.42/1.07    left_apart_point( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.42/1.07  (467) {G0,W7,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), distinct_points( 
% 0.42/1.07    Y, Z ) }.
% 0.42/1.07  (468) {G0,W8,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.42/1.07     }.
% 0.42/1.07  (469) {G0,W11,D2,L3,V3,M3}  { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z
% 0.42/1.07     ), before_on_line( X, Y, Z ) }.
% 0.42/1.07  (470) {G0,W7,D2,L2,V3,M2}  { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.42/1.07  (471) {G0,W8,D2,L2,V3,M2}  { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.42/1.07  (472) {G0,W11,D2,L3,V3,M3}  { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.42/1.07    ( X, Y, Z ) }.
% 0.42/1.07  (473) {G0,W7,D2,L2,V3,M2}  { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.42/1.07  (474) {G0,W9,D3,L2,V3,M2}  { ! alpha8( X, Y, Z ), ! 
% 0.42/1.07    unequally_directed_lines( X, line_connecting( Y, Z ) ) }.
% 0.42/1.07  (475) {G0,W12,D3,L3,V3,M3}  { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.42/1.07    , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.42/1.07  (476) {G0,W6,D2,L2,V2,M2}  { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.42/1.07     }.
% 0.42/1.07  (477) {G0,W7,D3,L2,V2,M2}  { ! alpha5( X, Y ), ! left_apart_point( Y, 
% 0.42/1.07    reverse_line( X ) ) }.
% 0.42/1.07  (478) {G0,W10,D3,L3,V2,M3}  { left_apart_point( Y, X ), left_apart_point( Y
% 0.42/1.07    , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.42/1.07  (479) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.42/1.07     }.
% 0.42/1.07  (480) {G0,W7,D3,L2,V2,M2}  { ! alpha2( X, Y ), ! left_apart_point( Y, 
% 0.42/1.07    reverse_line( X ) ) }.
% 0.42/1.07  (481) {G0,W10,D3,L3,V2,M3}  { left_apart_point( Y, X ), left_apart_point( Y
% 0.42/1.07    , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.42/1.07  (482) {G0,W15,D2,L3,V4,M3}  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.42/1.07    , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.42/1.07  (483) {G0,W10,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.42/1.07    , Z, T ) }.
% 0.42/1.07  (484) {G0,W10,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.42/1.07    , Z, T ) }.
% 0.42/1.07  (485) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, 
% 0.42/1.07    Z ) }.
% 0.42/1.07  (486) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, 
% 0.42/1.07    Y ) }.
% 0.42/1.07  (487) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, T, Z ), ! before_on_line
% 0.42/1.07    ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.42/1.07  (488) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, 
% 0.42/1.07    Z ) }.
% 0.42/1.07  (489) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, 
% 0.42/1.07    T ) }.
% 0.42/1.07  (490) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.42/1.07    ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.42/1.07  (491) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.42/1.07  (492) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 0.42/1.07    , Z ), distinct_points( Y, Z ) }.
% 0.42/1.07  (493) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.42/1.07  (494) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.42/1.07     ), distinct_lines( Y, Z ) }.
% 0.42/1.07  (495) {G0,W3,D2,L1,V1,M1}  { ! unequally_directed_lines( X, X ) }.
% 0.42/1.07  (496) {G0,W9,D2,L3,V3,M3}  { ! unequally_directed_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.07  (497) {G0,W13,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ), 
% 0.42/1.07    unequally_directed_lines( Y, Z ) }.
% 0.42/1.07  (498) {G0,W14,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ), 
% 0.42/1.07    unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.42/1.07  (499) {G0,W6,D2,L2,V2,M2}  { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.42/1.07    , Y ) }.
% 0.42/1.07  (500) {G0,W7,D3,L2,V2,M2}  { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.42/1.07    , reverse_line( Y ) ) }.
% 0.42/1.07  (501) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.42/1.07  (502) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), 
% 0.42/1.07    unequally_directed_lines( X, Y ), unequally_directed_lines( X, 
% 0.42/1.07    reverse_line( Y ) ) }.
% 0.42/1.07  (503) {G0,W14,D3,L4,V2,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines( 
% 0.42/1.07    X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  (504) {G0,W3,D2,L1,V2,M1}  { ! left_apart_point( X, Y ) }.
% 0.42/1.07  (505) {G0,W4,D3,L1,V2,M1}  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.07  (506) {G0,W3,D2,L1,V2,M1}  { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07  (507) {G0,W4,D3,L1,V2,M1}  { ! left_convergent_lines( X, reverse_line( Y )
% 0.42/1.07     ) }.
% 0.42/1.07  (508) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.42/1.07    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.42/1.07  (509) {G0,W15,D3,L5,V2,M5}  { ! line( X ), ! line( Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.07    reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.42/1.07  (510) {G0,W8,D3,L3,V2,M3}  { ! point( Y ), ! line( X ), line( 
% 0.42/1.07    parallel_through_point( X, Y ) ) }.
% 0.42/1.07  (511) {G0,W5,D3,L2,V1,M2}  { ! line( X ), line( reverse_line( X ) ) }.
% 0.42/1.07  (512) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.42/1.07    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.42/1.07  (513) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.42/1.07    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.42/1.07  (514) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.42/1.07    ( intersection_point( X, Y ), X ) }.
% 0.42/1.07  (515) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.42/1.07    ( intersection_point( X, Y ), Y ) }.
% 0.42/1.07  (516) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.42/1.07    parallel_through_point( Y, X ) ) }.
% 0.42/1.07  (517) {G0,W4,D3,L1,V1,M1}  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.42/1.07  (518) {G0,W8,D4,L1,V2,M1}  { ! unequally_directed_lines( line_connecting( X
% 0.42/1.07    , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.42/1.07  (519) {G0,W5,D3,L1,V2,M1}  { ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( Y, X ), Y ) }.
% 0.42/1.07  (520) {G0,W34,D3,L10,V4,M10}  { ! distinct_points( X, Y ), ! distinct_lines
% 0.42/1.07    ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ), 
% 0.42/1.07    left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X, 
% 0.42/1.07    reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ), 
% 0.42/1.07    left_apart_point( X, reverse_line( T ) ), left_apart_point( Y, 
% 0.42/1.07    reverse_line( T ) ) }.
% 0.42/1.07  (521) {G0,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! left_apart_point
% 0.42/1.07    ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines( 
% 0.42/1.07    line_connecting( X, Y ), Z ) }.
% 0.42/1.07  (522) {G0,W9,D2,L3,V3,M3}  { ! left_apart_point( X, Y ), distinct_points( X
% 0.42/1.07    , Z ), left_apart_point( Z, Y ) }.
% 0.42/1.07  (523) {G0,W13,D3,L4,V3,M4}  { ! left_apart_point( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ), 
% 0.42/1.07    left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.07  (524) {G0,W9,D2,L3,V3,M3}  { ! left_convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.42/1.07  (525) {G0,W5,D2,L1,V0,M1}  { between_on_line( skol4, skol2, skol5, skol3 )
% 0.42/1.07     }.
% 0.42/1.07  (526) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol4, skol1 ) }.
% 0.42/1.07  (527) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol5, skol1 ) }.
% 0.42/1.07  (528) {G0,W4,D2,L1,V0,M1}  { ! divides_points( skol1, skol2, skol3 ) }.
% 0.42/1.07  
% 0.42/1.07  
% 0.42/1.07  Total Proof:
% 0.42/1.07  
% 0.42/1.07  subsumption: (3) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  parent0: (455) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07     1 ==> 1
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (4) {G0,W7,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  parent0: (456) {G0,W7,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07     1 ==> 1
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (5) {G0,W10,D3,L3,V2,M2} I { convergent_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.07    reverse_line( Y ) ) }.
% 0.42/1.07  parent0: (457) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), 
% 0.42/1.07    ! unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, 
% 0.42/1.07    Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 1
% 0.42/1.07     1 ==> 2
% 0.42/1.07     2 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X
% 0.42/1.07     ) }.
% 0.42/1.07  parent0: (495) {G0,W3,D2,L1,V1,M1}  { ! unequally_directed_lines( X, X )
% 0.42/1.07     }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z )
% 0.42/1.07    , unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y )
% 0.42/1.07     }.
% 0.42/1.07  parent0: (496) {G0,W9,D2,L3,V3,M3}  { ! unequally_directed_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 2
% 0.42/1.07     1 ==> 0
% 0.42/1.07     2 ==> 1
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.42/1.07     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.42/1.07    left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X, 
% 0.42/1.07    Y ) }.
% 0.42/1.07  parent0: (503) {G0,W14,D3,L4,V2,M4}  { ! unequally_directed_lines( X, Y ), 
% 0.42/1.07    ! unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines
% 0.42/1.07    ( X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07     1 ==> 1
% 0.42/1.07     2 ==> 3
% 0.42/1.07     3 ==> 2
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.07     }.
% 0.42/1.07  parent0: (506) {G0,W3,D2,L1,V2,M1}  { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( Y, X ), Y ) }.
% 0.42/1.07  parent0: (519) {G0,W5,D3,L1,V2,M1}  { ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( Y, X ), Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (68) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol4, skol1 )
% 0.42/1.07     }.
% 0.42/1.07  parent0: (526) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol4, skol1 ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (592) {G1,W6,D2,L2,V2,M2}  { unequally_directed_lines( Y, X ), 
% 0.42/1.07    ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07  parent0[0]: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X )
% 0.42/1.07     }.
% 0.42/1.07  parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ), 
% 0.42/1.07    unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := X
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! 
% 0.42/1.07    unequally_directed_lines( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07  parent0: (592) {G1,W6,D2,L2,V2,M2}  { unequally_directed_lines( Y, X ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := Y
% 0.42/1.07     Y := X
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 1
% 0.42/1.07     1 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (594) {G1,W5,D3,L1,V2,M1}  { ! unequally_directed_lines( X, 
% 0.42/1.07    parallel_through_point( X, Y ) ) }.
% 0.42/1.07  parent0[0]: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( Y, X ), Y ) }.
% 0.42/1.07  parent1[1]: (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.42/1.07    ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := Y
% 0.42/1.07     Y := X
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := parallel_through_point( X, Y )
% 0.42/1.07     Y := X
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (120) {G2,W5,D3,L1,V2,M1} R(109,65) { ! 
% 0.42/1.07    unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.42/1.07  parent0: (594) {G1,W5,D3,L1,V2,M1}  { ! unequally_directed_lines( X, 
% 0.42/1.07    parallel_through_point( X, Y ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (595) {G1,W8,D3,L2,V3,M2}  { unequally_directed_lines( Z, 
% 0.42/1.07    parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.42/1.07  parent0[0]: (120) {G2,W5,D3,L1,V2,M1} R(109,65) { ! 
% 0.42/1.07    unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.42/1.07  parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ), 
% 0.42/1.07    unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Z
% 0.42/1.07     Z := parallel_through_point( X, Y )
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (121) {G3,W8,D3,L2,V3,M2} R(120,44) { ! 
% 0.42/1.07    unequally_directed_lines( Y, X ), unequally_directed_lines( X, 
% 0.42/1.07    parallel_through_point( Y, Z ) ) }.
% 0.42/1.07  parent0: (595) {G1,W8,D3,L2,V3,M2}  { unequally_directed_lines( Z, 
% 0.42/1.07    parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := Y
% 0.42/1.07     Y := Z
% 0.42/1.07     Z := X
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 1
% 0.42/1.07     1 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (598) {G2,W8,D3,L2,V3,M2}  { unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( Y, Z ), X ), ! unequally_directed_lines( Y, X )
% 0.42/1.07     }.
% 0.42/1.07  parent0[0]: (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.42/1.07    ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07  parent1[1]: (121) {G3,W8,D3,L2,V3,M2} R(120,44) { ! 
% 0.42/1.07    unequally_directed_lines( Y, X ), unequally_directed_lines( X, 
% 0.42/1.07    parallel_through_point( Y, Z ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := parallel_through_point( Y, Z )
% 0.42/1.07     Y := X
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (136) {G4,W8,D3,L2,V3,M2} R(121,109) { 
% 0.42/1.07    unequally_directed_lines( parallel_through_point( X, Z ), Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  parent0: (598) {G2,W8,D3,L2,V3,M2}  { unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( Y, Z ), X ), ! unequally_directed_lines( Y, X )
% 0.42/1.07     }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := Y
% 0.42/1.07     Y := X
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07     1 ==> 1
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (599) {G1,W9,D3,L2,V3,M2}  { unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines( 
% 0.42/1.07    X, Z ) }.
% 0.42/1.07  parent0[1]: (136) {G4,W8,D3,L2,V3,M2} R(121,109) { unequally_directed_lines
% 0.42/1.07    ( parallel_through_point( X, Z ), Y ), ! unequally_directed_lines( X, Y )
% 0.42/1.07     }.
% 0.42/1.07  parent1[1]: (4) {G0,W7,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := reverse_line( Z )
% 0.42/1.07     Z := Y
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (174) {G5,W9,D3,L2,V3,M1} R(136,4) { ! convergent_lines( X, Z
% 0.42/1.07     ), unequally_directed_lines( parallel_through_point( X, Y ), 
% 0.42/1.07    reverse_line( Z ) ) }.
% 0.42/1.07  parent0: (599) {G1,W9,D3,L2,V3,M2}  { unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines( 
% 0.42/1.07    X, Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 1
% 0.42/1.07     1 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (600) {G1,W8,D3,L2,V3,M2}  { unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.42/1.07  parent0[1]: (136) {G4,W8,D3,L2,V3,M2} R(121,109) { unequally_directed_lines
% 0.42/1.07    ( parallel_through_point( X, Z ), Y ), ! unequally_directed_lines( X, Y )
% 0.42/1.07     }.
% 0.42/1.07  parent1[1]: (3) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Z
% 0.42/1.07     Z := Y
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (176) {G5,W8,D3,L2,V3,M1} R(136,3) { ! convergent_lines( X, Z
% 0.42/1.07     ), unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.42/1.07  parent0: (600) {G1,W8,D3,L2,V3,M2}  { unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 1
% 0.42/1.07     1 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (602) {G1,W14,D3,L3,V3,M3}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines( 
% 0.42/1.07    X, Z ) }.
% 0.42/1.07  parent0[1]: (5) {G0,W10,D3,L3,V2,M2} I { convergent_lines( X, Y ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.42/1.07    reverse_line( Y ) ) }.
% 0.42/1.07  parent1[1]: (176) {G5,W8,D3,L2,V3,M1} R(136,3) { ! convergent_lines( X, Z )
% 0.42/1.07    , unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := parallel_through_point( X, Y )
% 0.42/1.07     Y := Z
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (604) {G2,W11,D3,L3,V3,M3}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ), ! 
% 0.42/1.07    convergent_lines( X, Z ) }.
% 0.42/1.07  parent0[1]: (602) {G1,W14,D3,L3,V3,M3}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines( 
% 0.42/1.07    X, Z ) }.
% 0.42/1.07  parent1[1]: (174) {G5,W9,D3,L2,V3,M1} R(136,4) { ! convergent_lines( X, Z )
% 0.42/1.07    , unequally_directed_lines( parallel_through_point( X, Y ), reverse_line
% 0.42/1.07    ( Z ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  factor: (605) {G2,W8,D3,L2,V3,M2}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.42/1.07  parent0[1, 2]: (604) {G2,W11,D3,L3,V3,M3}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ), ! 
% 0.42/1.07    convergent_lines( X, Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (187) {G6,W8,D3,L2,V3,M2} R(176,5);r(174) { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.42/1.07  parent0: (605) {G2,W8,D3,L2,V3,M2}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Z
% 0.42/1.07     Z := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07     1 ==> 1
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (606) {G1,W5,D3,L1,V1,M1}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( skol4, X ), skol1 ) }.
% 0.42/1.07  parent0[1]: (187) {G6,W8,D3,L2,V3,M2} R(176,5);r(174) { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.42/1.07  parent1[0]: (68) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol4, skol1 )
% 0.42/1.07     }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := skol4
% 0.42/1.07     Y := skol1
% 0.42/1.07     Z := X
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (191) {G7,W5,D3,L1,V1,M1} R(187,68) { convergent_lines( 
% 0.42/1.07    parallel_through_point( skol4, X ), skol1 ) }.
% 0.42/1.07  parent0: (606) {G1,W5,D3,L1,V1,M1}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( skol4, X ), skol1 ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (607) {G7,W7,D4,L1,V2,M1}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( parallel_through_point( skol4, X ), Y ), skol1 )
% 0.42/1.07     }.
% 0.42/1.07  parent0[1]: (187) {G6,W8,D3,L2,V3,M2} R(176,5);r(174) { convergent_lines( 
% 0.42/1.07    parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.42/1.07  parent1[0]: (191) {G7,W5,D3,L1,V1,M1} R(187,68) { convergent_lines( 
% 0.42/1.07    parallel_through_point( skol4, X ), skol1 ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := parallel_through_point( skol4, X )
% 0.42/1.07     Y := skol1
% 0.42/1.07     Z := Y
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (192) {G8,W7,D4,L1,V2,M1} R(191,187) { convergent_lines( 
% 0.42/1.07    parallel_through_point( parallel_through_point( skol4, X ), Y ), skol1 )
% 0.42/1.07     }.
% 0.42/1.07  parent0: (607) {G7,W7,D4,L1,V2,M1}  { convergent_lines( 
% 0.42/1.07    parallel_through_point( parallel_through_point( skol4, X ), Y ), skol1 )
% 0.42/1.07     }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (608) {G1,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y
% 0.42/1.07     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.42/1.07    left_convergent_lines( X, Y ) }.
% 0.42/1.07  parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.07     }.
% 0.42/1.07  parent1[2]: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.42/1.07     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.42/1.07    left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X, 
% 0.42/1.07    Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := reverse_line( Y )
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (610) {G1,W7,D3,L2,V2,M2}  { ! unequally_directed_lines( X, Y )
% 0.42/1.07    , ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.07     }.
% 0.42/1.07  parent1[2]: (608) {G1,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y
% 0.42/1.07     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.42/1.07    left_convergent_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (410) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  parent0: (610) {G1,W7,D3,L2,V2,M2}  { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07     unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 1
% 0.42/1.07     1 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (612) {G2,W9,D3,L2,V3,M2}  { ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines( 
% 0.42/1.07    X, Z ) }.
% 0.42/1.07  parent0[1]: (410) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { ! 
% 0.42/1.07    unequally_directed_lines( X, reverse_line( Y ) ), ! 
% 0.42/1.07    unequally_directed_lines( X, Y ) }.
% 0.42/1.07  parent1[1]: (176) {G5,W8,D3,L2,V3,M1} R(136,3) { ! convergent_lines( X, Z )
% 0.42/1.07    , unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := parallel_through_point( X, Y )
% 0.42/1.07     Y := Z
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (613) {G3,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Z ), ! 
% 0.42/1.07    convergent_lines( X, Z ) }.
% 0.42/1.07  parent0[0]: (612) {G2,W9,D3,L2,V3,M2}  { ! unequally_directed_lines( 
% 0.42/1.07    parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines( 
% 0.42/1.07    X, Z ) }.
% 0.42/1.07  parent1[1]: (174) {G5,W9,D3,L2,V3,M1} R(136,4) { ! convergent_lines( X, Z )
% 0.42/1.07    , unequally_directed_lines( parallel_through_point( X, Y ), reverse_line
% 0.42/1.07    ( Z ) ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07     Z := Z
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  factor: (614) {G3,W3,D2,L1,V2,M1}  { ! convergent_lines( X, Y ) }.
% 0.42/1.07  parent0[0, 1]: (613) {G3,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Z ), ! 
% 0.42/1.07    convergent_lines( X, Z ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Z
% 0.42/1.07     Z := Y
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (436) {G6,W3,D2,L1,V2,M1} R(410,176);r(174) { ! 
% 0.42/1.07    convergent_lines( X, Z ) }.
% 0.42/1.07  parent0: (614) {G3,W3,D2,L1,V2,M1}  { ! convergent_lines( X, Y ) }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Z
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07     0 ==> 0
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  resolution: (615) {G7,W0,D0,L0,V0,M0}  {  }.
% 0.42/1.07  parent0[0]: (436) {G6,W3,D2,L1,V2,M1} R(410,176);r(174) { ! 
% 0.42/1.07    convergent_lines( X, Z ) }.
% 0.42/1.07  parent1[0]: (192) {G8,W7,D4,L1,V2,M1} R(191,187) { convergent_lines( 
% 0.42/1.07    parallel_through_point( parallel_through_point( skol4, X ), Y ), skol1 )
% 0.42/1.07     }.
% 0.42/1.07  substitution0:
% 0.42/1.07     X := parallel_through_point( parallel_through_point( skol4, X ), Y )
% 0.42/1.07     Y := Z
% 0.42/1.07     Z := skol1
% 0.42/1.07  end
% 0.42/1.07  substitution1:
% 0.42/1.07     X := X
% 0.42/1.07     Y := Y
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  subsumption: (450) {G9,W0,D0,L0,V0,M0} R(436,192) {  }.
% 0.42/1.07  parent0: (615) {G7,W0,D0,L0,V0,M0}  {  }.
% 0.42/1.07  substitution0:
% 0.42/1.07  end
% 0.42/1.07  permutation0:
% 0.42/1.07  end
% 0.42/1.07  
% 0.42/1.07  Proof check complete!
% 0.42/1.07  
% 0.42/1.07  Memory use:
% 0.42/1.07  
% 0.42/1.07  space for terms:        6575
% 0.42/1.07  space for clauses:      22822
% 0.42/1.07  
% 0.42/1.07  
% 0.42/1.07  clauses generated:      1257
% 0.42/1.07  clauses kept:           451
% 0.42/1.07  clauses selected:       125
% 0.42/1.07  clauses deleted:        23
% 0.42/1.07  clauses inuse deleted:  0
% 0.42/1.07  
% 0.42/1.07  subsentry:          6444
% 0.42/1.07  literals s-matched: 3517
% 0.42/1.07  literals matched:   3467
% 0.42/1.07  full subsumption:   871
% 0.42/1.07  
% 0.42/1.07  checksum:           826645408
% 0.42/1.07  
% 0.42/1.07  
% 0.42/1.07  Bliksem ended
%------------------------------------------------------------------------------