TSTP Solution File: GEO268+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n026.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 02:53:26 EDT 2022

% Result   : Theorem 0.69s 1.10s
% Output   : Refutation 0.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n026.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 12:32:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.69/1.09  *** allocated 10000 integers for termspace/termends
% 0.69/1.09  *** allocated 10000 integers for clauses
% 0.69/1.09  *** allocated 10000 integers for justifications
% 0.69/1.09  Bliksem 1.12
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  Automatic Strategy Selection
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  Clauses:
% 0.69/1.09  
% 0.69/1.09  { ! unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X
% 0.69/1.09    , reverse_line( Y ) ) }.
% 0.69/1.09  { ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.69/1.09    unequally_directed_opposite_lines( X, Y ) }.
% 0.69/1.09  { ! right_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.69/1.09  { ! left_apart_point( X, reverse_line( Y ) ), right_apart_point( X, Y ) }.
% 0.69/1.09  { ! right_convergent_lines( X, Y ), left_convergent_lines( X, reverse_line
% 0.69/1.09    ( Y ) ) }.
% 0.69/1.09  { ! left_convergent_lines( X, reverse_line( Y ) ), right_convergent_lines( 
% 0.69/1.09    X, Y ) }.
% 0.69/1.09  { ! equally_directed_lines( X, Y ), ! unequally_directed_lines( X, Y ) }.
% 0.69/1.09  { unequally_directed_lines( X, Y ), equally_directed_lines( X, Y ) }.
% 0.69/1.09  { ! equally_directed_opposite_lines( X, Y ), ! 
% 0.69/1.09    unequally_directed_opposite_lines( X, Y ) }.
% 0.69/1.09  { unequally_directed_opposite_lines( X, Y ), 
% 0.69/1.09    equally_directed_opposite_lines( X, Y ) }.
% 0.69/1.09  { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ), 
% 0.69/1.09    right_apart_point( X, Y ) }.
% 0.69/1.09  { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.69/1.09  { ! right_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.69/1.09  { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.69/1.09  { ! convergent_lines( X, Y ), unequally_directed_opposite_lines( X, Y ) }.
% 0.69/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_opposite_lines( 
% 0.69/1.09    X, Y ), convergent_lines( X, Y ) }.
% 0.69/1.09  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.69/1.09  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.69/1.09  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.69/1.09  { ! alpha4( X, Y, Z ), right_apart_point( X, Z ) }.
% 0.69/1.09  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.69/1.09  { ! right_apart_point( X, Z ), ! left_apart_point( Y, Z ), alpha4( X, Y, Z
% 0.69/1.09     ) }.
% 0.69/1.09  { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.69/1.09  { ! alpha1( X, Y, Z ), right_apart_point( Y, Z ) }.
% 0.69/1.09  { ! left_apart_point( X, Z ), ! right_apart_point( Y, Z ), alpha1( X, Y, Z
% 0.69/1.09     ) }.
% 0.69/1.09  { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.69/1.09  { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.69/1.09  { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z ), before_on_line( X, Y, Z )
% 0.69/1.09     }.
% 0.69/1.09  { ! alpha2( X, Y, Z ), incident_point_and_line( Y, X ) }.
% 0.69/1.09  { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.69/1.09  { ! incident_point_and_line( Y, X ), ! alpha5( X, Y, Z ), alpha2( X, Y, Z )
% 0.69/1.09     }.
% 0.69/1.09  { ! alpha5( X, Y, Z ), incident_point_and_line( Z, X ) }.
% 0.69/1.09  { ! alpha5( X, Y, Z ), equally_directed_lines( X, line_connecting( Y, Z ) )
% 0.69/1.09     }.
% 0.69/1.09  { ! incident_point_and_line( Z, X ), ! equally_directed_lines( X, 
% 0.69/1.09    line_connecting( Y, Z ) ), alpha5( X, Y, Z ) }.
% 0.69/1.09  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.69/1.09     ) }.
% 0.69/1.09  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.69/1.09  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.69/1.09  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.69/1.09  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.69/1.09  { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.69/1.09    , T ) }.
% 0.69/1.09  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.69/1.09  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.69/1.09  { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.69/1.09    , T ) }.
% 0.69/1.09  { ! distinct_points( X, X ) }.
% 0.69/1.09  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.69/1.09     ) }.
% 0.69/1.09  { ! distinct_lines( X, X ) }.
% 0.69/1.09  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.69/1.09     }.
% 0.69/1.09  { equally_directed_lines( X, X ) }.
% 0.69/1.09  { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ), 
% 0.69/1.09    unequally_directed_lines( Y, Z ) }.
% 0.69/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.69/1.09    reverse_line( Y ) ), alpha7( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.69/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.69/1.09    reverse_line( Y ) ), alpha7( X, Z ), unequally_directed_lines( Y, 
% 0.69/1.09    reverse_line( Z ) ) }.
% 0.69/1.09  { ! alpha7( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.69/1.09  { ! alpha7( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.69/1.10  { unequally_directed_lines( X, Y ), unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ) }.
% 0.69/1.10  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.69/1.10    ( X, reverse_line( Y ) ) }.
% 0.69/1.10  { ! left_apart_point( X, Y ) }.
% 0.69/1.10  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.69/1.10  { ! left_convergent_lines( X, Y ) }.
% 0.69/1.10  { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.69/1.10    line_connecting( X, Y ) ) }.
% 0.69/1.10  { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), point( 
% 0.69/1.10    intersection_point( X, Y ) ) }.
% 0.69/1.10  { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.69/1.10  { ! line( X ), line( reverse_line( X ) ) }.
% 0.69/1.10  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.69/1.10    , Y ) ) }.
% 0.69/1.10  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.69/1.10    , Y ) ) }.
% 0.69/1.10  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.69/1.10    X ) }.
% 0.69/1.10  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.69/1.10    Y ) }.
% 0.69/1.10  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.69/1.10  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.69/1.10  { ! distinct_points( X, Y ), equally_directed_lines( line_connecting( X, Y
% 0.69/1.10     ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.69/1.10  { equally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.69/1.10  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.69/1.10    , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ), 
% 0.69/1.10    left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ), 
% 0.69/1.10    left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X, 
% 0.69/1.10    reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.69/1.10  { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point( 
% 0.69/1.10    Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.69/1.10  { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.69/1.10    , Y ) }.
% 0.69/1.10  { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ), 
% 0.69/1.10    distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.69/1.10  { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ), 
% 0.69/1.10    left_convergent_lines( X, Z ) }.
% 0.69/1.10  { alpha8( skol1, skol2 ), unequally_directed_opposite_lines( skol1, 
% 0.69/1.10    reverse_line( skol2 ) ) }.
% 0.69/1.10  { alpha8( skol1, skol2 ), ! unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  { ! alpha8( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  { ! alpha8( X, Y ), ! unequally_directed_opposite_lines( X, reverse_line( Y
% 0.69/1.10     ) ) }.
% 0.69/1.10  { ! unequally_directed_lines( X, Y ), unequally_directed_opposite_lines( X
% 0.69/1.10    , reverse_line( Y ) ), alpha8( X, Y ) }.
% 0.69/1.10  
% 0.69/1.10  percentage equality = 0.000000, percentage horn = 0.802632
% 0.69/1.10  This a non-horn, non-equality problem
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  Options Used:
% 0.69/1.10  
% 0.69/1.10  useres =            1
% 0.69/1.10  useparamod =        0
% 0.69/1.10  useeqrefl =         0
% 0.69/1.10  useeqfact =         0
% 0.69/1.10  usefactor =         1
% 0.69/1.10  usesimpsplitting =  0
% 0.69/1.10  usesimpdemod =      0
% 0.69/1.10  usesimpres =        3
% 0.69/1.10  
% 0.69/1.10  resimpinuse      =  1000
% 0.69/1.10  resimpclauses =     20000
% 0.69/1.10  substype =          standard
% 0.69/1.10  backwardsubs =      1
% 0.69/1.10  selectoldest =      5
% 0.69/1.10  
% 0.69/1.10  litorderings [0] =  split
% 0.69/1.10  litorderings [1] =  liftord
% 0.69/1.10  
% 0.69/1.10  termordering =      none
% 0.69/1.10  
% 0.69/1.10  litapriori =        1
% 0.69/1.10  termapriori =       0
% 0.69/1.10  litaposteriori =    0
% 0.69/1.10  termaposteriori =   0
% 0.69/1.10  demodaposteriori =  0
% 0.69/1.10  ordereqreflfact =   0
% 0.69/1.10  
% 0.69/1.10  litselect =         none
% 0.69/1.10  
% 0.69/1.10  maxweight =         15
% 0.69/1.10  maxdepth =          30000
% 0.69/1.10  maxlength =         115
% 0.69/1.10  maxnrvars =         195
% 0.69/1.10  excuselevel =       1
% 0.69/1.10  increasemaxweight = 1
% 0.69/1.10  
% 0.69/1.10  maxselected =       10000000
% 0.69/1.10  maxnrclauses =      10000000
% 0.69/1.10  
% 0.69/1.10  showgenerated =    0
% 0.69/1.10  showkept =         0
% 0.69/1.10  showselected =     0
% 0.69/1.10  showdeleted =      0
% 0.69/1.10  showresimp =       1
% 0.69/1.10  showstatus =       2000
% 0.69/1.10  
% 0.69/1.10  prologoutput =     0
% 0.69/1.10  nrgoals =          5000000
% 0.69/1.10  totalproof =       1
% 0.69/1.10  
% 0.69/1.10  Symbols occurring in the translation:
% 0.69/1.10  
% 0.69/1.10  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.69/1.10  .  [1, 2]      (w:1, o:24, a:1, s:1, b:0), 
% 0.69/1.10  !  [4, 1]      (w:0, o:16, a:1, s:1, b:0), 
% 0.69/1.10  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.69/1.10  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.69/1.10  unequally_directed_opposite_lines  [37, 2]      (w:1, o:48, a:1, s:1, b:0)
% 0.69/1.10    , 
% 0.69/1.10  reverse_line  [38, 1]      (w:1, o:21, a:1, s:1, b:0), 
% 0.69/1.10  unequally_directed_lines  [39, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.69/1.10  right_apart_point  [40, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.69/1.10  left_apart_point  [41, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 0.69/1.10  right_convergent_lines  [42, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.69/1.10  left_convergent_lines  [43, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.69/1.10  equally_directed_lines  [44, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.69/1.10  equally_directed_opposite_lines  [45, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.69/1.10  apart_point_and_line  [48, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.69/1.10  convergent_lines  [50, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.69/1.10  divides_points  [52, 3]      (w:1, o:66, a:1, s:1, b:0), 
% 0.69/1.10  before_on_line  [53, 3]      (w:1, o:71, a:1, s:1, b:0), 
% 0.69/1.10  distinct_points  [54, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.69/1.10  incident_point_and_line  [55, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.69/1.10  line_connecting  [56, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 0.69/1.10  between_on_line  [58, 4]      (w:1, o:74, a:1, s:1, b:0), 
% 0.69/1.10  distinct_lines  [59, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.69/1.10  point  [61, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.69/1.10  line  [62, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.69/1.10  intersection_point  [63, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 0.69/1.10  parallel_through_point  [64, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 0.69/1.10  alpha1  [65, 3]      (w:1, o:67, a:1, s:1, b:0), 
% 0.69/1.10  alpha2  [66, 3]      (w:1, o:68, a:1, s:1, b:0), 
% 0.69/1.10  alpha3  [67, 4]      (w:1, o:72, a:1, s:1, b:0), 
% 0.69/1.10  alpha4  [68, 3]      (w:1, o:69, a:1, s:1, b:0), 
% 0.69/1.10  alpha5  [69, 3]      (w:1, o:70, a:1, s:1, b:0), 
% 0.69/1.10  alpha6  [70, 4]      (w:1, o:73, a:1, s:1, b:0), 
% 0.69/1.10  alpha7  [71, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 0.69/1.10  alpha8  [72, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.69/1.10  skol1  [73, 0]      (w:1, o:14, a:1, s:1, b:0), 
% 0.69/1.10  skol2  [74, 0]      (w:1, o:15, a:1, s:1, b:0).
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  Starting Search:
% 0.69/1.10  
% 0.69/1.10  *** allocated 15000 integers for clauses
% 0.69/1.10  *** allocated 22500 integers for clauses
% 0.69/1.10  
% 0.69/1.10  Bliksems!, er is een bewijs:
% 0.69/1.10  % SZS status Theorem
% 0.69/1.10  % SZS output start Refutation
% 0.69/1.10  
% 0.69/1.10  (0) {G0,W7,D3,L2,V2,M1} I { ! unequally_directed_opposite_lines( X, Y ), 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  (1) {G0,W7,D3,L2,V2,M1} I { unequally_directed_opposite_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  (54) {G0,W7,D3,L2,V2,M2} I { unequally_directed_lines( X, reverse_line( Y )
% 0.69/1.10     ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  (55) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines( 
% 0.69/1.10    X, reverse_line( Y ) ), left_convergent_lines( X, Y ) }.
% 0.69/1.10  (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y ) }.
% 0.69/1.10  (71) {G0,W7,D3,L2,V0,M1} I { unequally_directed_opposite_lines( skol1, 
% 0.69/1.10    reverse_line( skol2 ) ), alpha8( skol1, skol2 ) }.
% 0.69/1.10  (72) {G0,W6,D2,L2,V0,M1} I { ! unequally_directed_lines( skol1, skol2 ), 
% 0.69/1.10    alpha8( skol1, skol2 ) }.
% 0.69/1.10  (73) {G0,W6,D2,L2,V2,M1} I { unequally_directed_lines( X, Y ), ! alpha8( X
% 0.69/1.10    , Y ) }.
% 0.69/1.10  (74) {G0,W7,D3,L2,V2,M1} I { ! unequally_directed_opposite_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), ! alpha8( X, Y ) }.
% 0.69/1.10  (96) {G1,W7,D3,L2,V0,M1} R(74,72) { ! unequally_directed_opposite_lines( 
% 0.69/1.10    skol1, reverse_line( skol2 ) ), ! unequally_directed_lines( skol1, skol2
% 0.69/1.10     ) }.
% 0.69/1.10  (101) {G1,W6,D2,L2,V2,M1} R(54,1) { unequally_directed_opposite_lines( X, Y
% 0.69/1.10     ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  (109) {G2,W4,D3,L1,V0,M1} R(96,54);r(101) { unequally_directed_lines( skol1
% 0.69/1.10    , reverse_line( skol2 ) ) }.
% 0.69/1.10  (110) {G1,W7,D3,L2,V0,M1} R(71,73) { unequally_directed_opposite_lines( 
% 0.69/1.10    skol1, reverse_line( skol2 ) ), unequally_directed_lines( skol1, skol2 )
% 0.69/1.10     }.
% 0.69/1.10  (266) {G1,W7,D3,L2,V2,M2} S(55);r(57);r(57) { ! unequally_directed_lines( X
% 0.69/1.10    , reverse_line( Y ) ), ! unequally_directed_lines( X, Y ) }.
% 0.69/1.10  (313) {G2,W4,D3,L1,V0,M1} R(266,110);r(101) { 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  (315) {G3,W5,D4,L1,V0,M1} R(266,109) { ! unequally_directed_lines( skol1, 
% 0.69/1.10    reverse_line( reverse_line( skol2 ) ) ) }.
% 0.69/1.10  (385) {G4,W0,D0,L0,V0,M0} R(315,0);r(313) {  }.
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  % SZS output end Refutation
% 0.69/1.10  found a proof!
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  Unprocessed initial clauses:
% 0.69/1.10  
% 0.69/1.10  (387) {G0,W7,D3,L2,V2,M2}  { ! unequally_directed_opposite_lines( X, Y ), 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  (388) {G0,W7,D3,L2,V2,M2}  { ! unequally_directed_lines( X, reverse_line( Y
% 0.69/1.10     ) ), unequally_directed_opposite_lines( X, Y ) }.
% 0.69/1.10  (389) {G0,W7,D3,L2,V2,M2}  { ! right_apart_point( X, Y ), left_apart_point
% 0.69/1.10    ( X, reverse_line( Y ) ) }.
% 0.69/1.10  (390) {G0,W7,D3,L2,V2,M2}  { ! left_apart_point( X, reverse_line( Y ) ), 
% 0.69/1.10    right_apart_point( X, Y ) }.
% 0.69/1.10  (391) {G0,W7,D3,L2,V2,M2}  { ! right_convergent_lines( X, Y ), 
% 0.69/1.10    left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  (392) {G0,W7,D3,L2,V2,M2}  { ! left_convergent_lines( X, reverse_line( Y )
% 0.69/1.10     ), right_convergent_lines( X, Y ) }.
% 0.69/1.10  (393) {G0,W6,D2,L2,V2,M2}  { ! equally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, Y ) }.
% 0.69/1.10  (394) {G0,W6,D2,L2,V2,M2}  { unequally_directed_lines( X, Y ), 
% 0.69/1.10    equally_directed_lines( X, Y ) }.
% 0.69/1.10  (395) {G0,W6,D2,L2,V2,M2}  { ! equally_directed_opposite_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_opposite_lines( X, Y ) }.
% 0.69/1.10  (396) {G0,W6,D2,L2,V2,M2}  { unequally_directed_opposite_lines( X, Y ), 
% 0.69/1.10    equally_directed_opposite_lines( X, Y ) }.
% 0.69/1.10  (397) {G0,W9,D2,L3,V2,M3}  { ! apart_point_and_line( X, Y ), 
% 0.69/1.10    left_apart_point( X, Y ), right_apart_point( X, Y ) }.
% 0.69/1.10  (398) {G0,W6,D2,L2,V2,M2}  { ! left_apart_point( X, Y ), 
% 0.69/1.10    apart_point_and_line( X, Y ) }.
% 0.69/1.10  (399) {G0,W6,D2,L2,V2,M2}  { ! right_apart_point( X, Y ), 
% 0.69/1.10    apart_point_and_line( X, Y ) }.
% 0.69/1.10  (400) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.69/1.10    unequally_directed_lines( X, Y ) }.
% 0.69/1.10  (401) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.69/1.10    unequally_directed_opposite_lines( X, Y ) }.
% 0.69/1.10  (402) {G0,W9,D2,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_opposite_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.69/1.10  (403) {G0,W12,D2,L3,V3,M3}  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.69/1.10     ), alpha4( X, Y, Z ) }.
% 0.69/1.10  (404) {G0,W8,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.69/1.10     }.
% 0.69/1.10  (405) {G0,W8,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.69/1.10     }.
% 0.69/1.10  (406) {G0,W7,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), right_apart_point( X, Z )
% 0.69/1.10     }.
% 0.69/1.10  (407) {G0,W7,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.69/1.10     }.
% 0.69/1.10  (408) {G0,W10,D2,L3,V3,M3}  { ! right_apart_point( X, Z ), ! 
% 0.69/1.10    left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.69/1.10  (409) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.69/1.10     }.
% 0.69/1.10  (410) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), right_apart_point( Y, Z )
% 0.69/1.10     }.
% 0.69/1.10  (411) {G0,W10,D2,L3,V3,M3}  { ! left_apart_point( X, Z ), ! 
% 0.69/1.10    right_apart_point( Y, Z ), alpha1( X, Y, Z ) }.
% 0.69/1.10  (412) {G0,W7,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), distinct_points( 
% 0.69/1.10    Y, Z ) }.
% 0.69/1.10  (413) {G0,W8,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z )
% 0.69/1.10     }.
% 0.69/1.10  (414) {G0,W11,D2,L3,V3,M3}  { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z
% 0.69/1.10     ), before_on_line( X, Y, Z ) }.
% 0.69/1.10  (415) {G0,W7,D2,L2,V3,M2}  { ! alpha2( X, Y, Z ), incident_point_and_line( 
% 0.69/1.10    Y, X ) }.
% 0.69/1.10  (416) {G0,W8,D2,L2,V3,M2}  { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.69/1.10  (417) {G0,W11,D2,L3,V3,M3}  { ! incident_point_and_line( Y, X ), ! alpha5( 
% 0.69/1.10    X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.69/1.10  (418) {G0,W7,D2,L2,V3,M2}  { ! alpha5( X, Y, Z ), incident_point_and_line( 
% 0.69/1.10    Z, X ) }.
% 0.69/1.10  (419) {G0,W9,D3,L2,V3,M2}  { ! alpha5( X, Y, Z ), equally_directed_lines( X
% 0.69/1.10    , line_connecting( Y, Z ) ) }.
% 0.69/1.10  (420) {G0,W12,D3,L3,V3,M3}  { ! incident_point_and_line( Z, X ), ! 
% 0.69/1.10    equally_directed_lines( X, line_connecting( Y, Z ) ), alpha5( X, Y, Z )
% 0.69/1.10     }.
% 0.69/1.10  (421) {G0,W15,D2,L3,V4,M3}  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.69/1.10    , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.69/1.10  (422) {G0,W10,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.69/1.10    , Z, T ) }.
% 0.69/1.10  (423) {G0,W10,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.69/1.10    , Z, T ) }.
% 0.69/1.10  (424) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, 
% 0.69/1.10    Z ) }.
% 0.69/1.10  (425) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, 
% 0.69/1.10    Y ) }.
% 0.69/1.10  (426) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, T, Z ), ! before_on_line
% 0.69/1.10    ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.69/1.10  (427) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, 
% 0.69/1.10    Z ) }.
% 0.69/1.10  (428) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, 
% 0.69/1.10    T ) }.
% 0.69/1.10  (429) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.69/1.10    ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.69/1.10  (430) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.69/1.10  (431) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 0.69/1.10    , Z ), distinct_points( Y, Z ) }.
% 0.69/1.10  (432) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.69/1.10  (433) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.69/1.10     ), distinct_lines( Y, Z ) }.
% 0.69/1.10  (434) {G0,W3,D2,L1,V1,M1}  { equally_directed_lines( X, X ) }.
% 0.69/1.10  (435) {G0,W9,D2,L3,V3,M3}  { ! unequally_directed_lines( X, Y ), 
% 0.69/1.10    unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.69/1.10  (436) {G0,W13,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ), 
% 0.69/1.10    unequally_directed_lines( Y, Z ) }.
% 0.69/1.10  (437) {G0,W14,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ), 
% 0.69/1.10    unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.69/1.10  (438) {G0,W6,D2,L2,V2,M2}  { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.69/1.10    , Y ) }.
% 0.69/1.10  (439) {G0,W7,D3,L2,V2,M2}  { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.69/1.10    , reverse_line( Y ) ) }.
% 0.69/1.10  (440) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.69/1.10  (441) {G0,W7,D3,L2,V2,M2}  { unequally_directed_lines( X, Y ), 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  (442) {G0,W14,D3,L4,V2,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines( 
% 0.69/1.10    X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  (443) {G0,W3,D2,L1,V2,M1}  { ! left_apart_point( X, Y ) }.
% 0.69/1.10  (444) {G0,W4,D3,L1,V2,M1}  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.69/1.10  (445) {G0,W3,D2,L1,V2,M1}  { ! left_convergent_lines( X, Y ) }.
% 0.69/1.10  (446) {G0,W4,D3,L1,V2,M1}  { ! left_convergent_lines( X, reverse_line( Y )
% 0.69/1.10     ) }.
% 0.69/1.10  (447) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.69/1.10    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.69/1.10  (448) {G0,W15,D3,L5,V2,M5}  { ! line( X ), ! line( Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.69/1.10  (449) {G0,W8,D3,L3,V2,M3}  { ! point( Y ), ! line( X ), line( 
% 0.69/1.10    parallel_through_point( X, Y ) ) }.
% 0.69/1.10  (450) {G0,W5,D3,L2,V1,M2}  { ! line( X ), line( reverse_line( X ) ) }.
% 0.69/1.10  (451) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.69/1.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.69/1.10  (452) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.69/1.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.69/1.10  (453) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.69/1.10    ( intersection_point( X, Y ), X ) }.
% 0.69/1.10  (454) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.69/1.10    ( intersection_point( X, Y ), Y ) }.
% 0.69/1.10  (455) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.69/1.10    parallel_through_point( Y, X ) ) }.
% 0.69/1.10  (456) {G0,W4,D3,L1,V1,M1}  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.69/1.10  (457) {G0,W11,D4,L2,V2,M2}  { ! distinct_points( X, Y ), 
% 0.69/1.10    equally_directed_lines( line_connecting( X, Y ), reverse_line( 
% 0.69/1.10    line_connecting( Y, X ) ) ) }.
% 0.69/1.10  (458) {G0,W5,D3,L1,V2,M1}  { equally_directed_lines( parallel_through_point
% 0.69/1.10    ( Y, X ), Y ) }.
% 0.69/1.10  (459) {G0,W34,D3,L10,V4,M10}  { ! distinct_points( X, Y ), ! distinct_lines
% 0.69/1.10    ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ), 
% 0.69/1.10    left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X, 
% 0.69/1.10    reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ), 
% 0.69/1.10    left_apart_point( X, reverse_line( T ) ), left_apart_point( Y, 
% 0.69/1.10    reverse_line( T ) ) }.
% 0.69/1.10  (460) {G0,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! left_apart_point
% 0.69/1.10    ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines( 
% 0.69/1.10    line_connecting( X, Y ), Z ) }.
% 0.69/1.10  (461) {G0,W9,D2,L3,V3,M3}  { ! left_apart_point( X, Y ), distinct_points( X
% 0.69/1.10    , Z ), left_apart_point( Z, Y ) }.
% 0.69/1.10  (462) {G0,W13,D3,L4,V3,M4}  { ! left_apart_point( X, Y ), ! 
% 0.69/1.10    unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ), 
% 0.69/1.10    left_apart_point( X, reverse_line( Z ) ) }.
% 0.69/1.10  (463) {G0,W9,D2,L3,V3,M3}  { ! left_convergent_lines( X, Y ), 
% 0.69/1.10    unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.69/1.10  (464) {G0,W7,D3,L2,V0,M2}  { alpha8( skol1, skol2 ), 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  (465) {G0,W6,D2,L2,V0,M2}  { alpha8( skol1, skol2 ), ! 
% 0.69/1.10    unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  (466) {G0,W6,D2,L2,V2,M2}  { ! alpha8( X, Y ), unequally_directed_lines( X
% 0.69/1.10    , Y ) }.
% 0.69/1.10  (467) {G0,W7,D3,L2,V2,M2}  { ! alpha8( X, Y ), ! 
% 0.69/1.10    unequally_directed_opposite_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  (468) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), 
% 0.69/1.10    unequally_directed_opposite_lines( X, reverse_line( Y ) ), alpha8( X, Y )
% 0.69/1.10     }.
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  Total Proof:
% 0.69/1.10  
% 0.69/1.10  subsumption: (0) {G0,W7,D3,L2,V2,M1} I { ! 
% 0.69/1.10    unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ) }.
% 0.69/1.10  parent0: (387) {G0,W7,D3,L2,V2,M2}  { ! unequally_directed_opposite_lines( 
% 0.69/1.10    X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10     1 ==> 1
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (1) {G0,W7,D3,L2,V2,M1} I { unequally_directed_opposite_lines
% 0.69/1.10    ( X, Y ), ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  parent0: (388) {G0,W7,D3,L2,V2,M2}  { ! unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), unequally_directed_opposite_lines( X, Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (54) {G0,W7,D3,L2,V2,M2} I { unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  parent0: (441) {G0,W7,D3,L2,V2,M2}  { unequally_directed_lines( X, Y ), 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (55) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.69/1.10     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.69/1.10    left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X, 
% 0.69/1.10    Y ) }.
% 0.69/1.10  parent0: (442) {G0,W14,D3,L4,V2,M4}  { ! unequally_directed_lines( X, Y ), 
% 0.69/1.10    ! unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines
% 0.69/1.10    ( X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10     1 ==> 1
% 0.69/1.10     2 ==> 3
% 0.69/1.10     3 ==> 2
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.69/1.10     }.
% 0.69/1.10  parent0: (445) {G0,W3,D2,L1,V2,M1}  { ! left_convergent_lines( X, Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  *** allocated 33750 integers for clauses
% 0.69/1.10  subsumption: (71) {G0,W7,D3,L2,V0,M1} I { unequally_directed_opposite_lines
% 0.69/1.10    ( skol1, reverse_line( skol2 ) ), alpha8( skol1, skol2 ) }.
% 0.69/1.10  parent0: (464) {G0,W7,D3,L2,V0,M2}  { alpha8( skol1, skol2 ), 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (72) {G0,W6,D2,L2,V0,M1} I { ! unequally_directed_lines( skol1
% 0.69/1.10    , skol2 ), alpha8( skol1, skol2 ) }.
% 0.69/1.10  parent0: (465) {G0,W6,D2,L2,V0,M2}  { alpha8( skol1, skol2 ), ! 
% 0.69/1.10    unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (73) {G0,W6,D2,L2,V2,M1} I { unequally_directed_lines( X, Y )
% 0.69/1.10    , ! alpha8( X, Y ) }.
% 0.69/1.10  parent0: (466) {G0,W6,D2,L2,V2,M2}  { ! alpha8( X, Y ), 
% 0.69/1.10    unequally_directed_lines( X, Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (74) {G0,W7,D3,L2,V2,M1} I { ! 
% 0.69/1.10    unequally_directed_opposite_lines( X, reverse_line( Y ) ), ! alpha8( X, Y
% 0.69/1.10     ) }.
% 0.69/1.10  parent0: (467) {G0,W7,D3,L2,V2,M2}  { ! alpha8( X, Y ), ! 
% 0.69/1.10    unequally_directed_opposite_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (616) {G1,W7,D3,L2,V0,M2}  { ! 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), ! 
% 0.69/1.10    unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  parent0[1]: (74) {G0,W7,D3,L2,V2,M1} I { ! 
% 0.69/1.10    unequally_directed_opposite_lines( X, reverse_line( Y ) ), ! alpha8( X, Y
% 0.69/1.10     ) }.
% 0.69/1.10  parent1[1]: (72) {G0,W6,D2,L2,V0,M1} I { ! unequally_directed_lines( skol1
% 0.69/1.10    , skol2 ), alpha8( skol1, skol2 ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := skol2
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (96) {G1,W7,D3,L2,V0,M1} R(74,72) { ! 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), ! 
% 0.69/1.10    unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  parent0: (616) {G1,W7,D3,L2,V0,M2}  { ! unequally_directed_opposite_lines( 
% 0.69/1.10    skol1, reverse_line( skol2 ) ), ! unequally_directed_lines( skol1, skol2
% 0.69/1.10     ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10     1 ==> 1
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (617) {G1,W6,D2,L2,V2,M2}  { unequally_directed_opposite_lines
% 0.69/1.10    ( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  parent0[1]: (1) {G0,W7,D3,L2,V2,M1} I { unequally_directed_opposite_lines( 
% 0.69/1.10    X, Y ), ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  parent1[0]: (54) {G0,W7,D3,L2,V2,M2} I { unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (101) {G1,W6,D2,L2,V2,M1} R(54,1) { 
% 0.69/1.10    unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X, Y
% 0.69/1.10     ) }.
% 0.69/1.10  parent0: (617) {G1,W6,D2,L2,V2,M2}  { unequally_directed_opposite_lines( X
% 0.69/1.10    , Y ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10     1 ==> 1
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (619) {G1,W8,D3,L2,V0,M2}  { ! 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), 
% 0.69/1.10    unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0[1]: (96) {G1,W7,D3,L2,V0,M1} R(74,72) { ! 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), ! 
% 0.69/1.10    unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  parent1[1]: (54) {G0,W7,D3,L2,V2,M2} I { unequally_directed_lines( X, 
% 0.69/1.10    reverse_line( Y ) ), unequally_directed_lines( X, Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := skol2
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (620) {G2,W8,D3,L2,V0,M2}  { unequally_directed_lines( skol1, 
% 0.69/1.10    reverse_line( skol2 ) ), unequally_directed_lines( skol1, reverse_line( 
% 0.69/1.10    skol2 ) ) }.
% 0.69/1.10  parent0[0]: (619) {G1,W8,D3,L2,V0,M2}  { ! 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), 
% 0.69/1.10    unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent1[0]: (101) {G1,W6,D2,L2,V2,M1} R(54,1) { 
% 0.69/1.10    unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X, Y
% 0.69/1.10     ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := reverse_line( skol2 )
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  factor: (621) {G2,W4,D3,L1,V0,M1}  { unequally_directed_lines( skol1, 
% 0.69/1.10    reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0[0, 1]: (620) {G2,W8,D3,L2,V0,M2}  { unequally_directed_lines( skol1
% 0.69/1.10    , reverse_line( skol2 ) ), unequally_directed_lines( skol1, reverse_line
% 0.69/1.10    ( skol2 ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (109) {G2,W4,D3,L1,V0,M1} R(96,54);r(101) { 
% 0.69/1.10    unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0: (621) {G2,W4,D3,L1,V0,M1}  { unequally_directed_lines( skol1, 
% 0.69/1.10    reverse_line( skol2 ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (622) {G1,W7,D3,L2,V0,M2}  { unequally_directed_lines( skol1, 
% 0.69/1.10    skol2 ), unequally_directed_opposite_lines( skol1, reverse_line( skol2 )
% 0.69/1.10     ) }.
% 0.69/1.10  parent0[1]: (73) {G0,W6,D2,L2,V2,M1} I { unequally_directed_lines( X, Y ), 
% 0.69/1.10    ! alpha8( X, Y ) }.
% 0.69/1.10  parent1[1]: (71) {G0,W7,D3,L2,V0,M1} I { unequally_directed_opposite_lines
% 0.69/1.10    ( skol1, reverse_line( skol2 ) ), alpha8( skol1, skol2 ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := skol2
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (110) {G1,W7,D3,L2,V0,M1} R(71,73) { 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), 
% 0.69/1.10    unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  parent0: (622) {G1,W7,D3,L2,V0,M2}  { unequally_directed_lines( skol1, 
% 0.69/1.10    skol2 ), unequally_directed_opposite_lines( skol1, reverse_line( skol2 )
% 0.69/1.10     ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (623) {G1,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y
% 0.69/1.10     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.69/1.10    left_convergent_lines( X, Y ) }.
% 0.69/1.10  parent0[0]: (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.69/1.10     }.
% 0.69/1.10  parent1[2]: (55) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.69/1.10     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.69/1.10    left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X, 
% 0.69/1.10    Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := reverse_line( Y )
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (625) {G1,W7,D3,L2,V2,M2}  { ! unequally_directed_lines( X, Y )
% 0.69/1.10    , ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  parent0[0]: (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.69/1.10     }.
% 0.69/1.10  parent1[2]: (623) {G1,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y
% 0.69/1.10     ), ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.69/1.10    left_convergent_lines( X, Y ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (266) {G1,W7,D3,L2,V2,M2} S(55);r(57);r(57) { ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), ! 
% 0.69/1.10    unequally_directed_lines( X, Y ) }.
% 0.69/1.10  parent0: (625) {G1,W7,D3,L2,V2,M2}  { ! unequally_directed_lines( X, Y ), !
% 0.69/1.10     unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := X
% 0.69/1.10     Y := Y
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 1
% 0.69/1.10     1 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (626) {G2,W8,D3,L2,V0,M2}  { ! unequally_directed_lines( skol1
% 0.69/1.10    , reverse_line( skol2 ) ), unequally_directed_opposite_lines( skol1, 
% 0.69/1.10    reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0[1]: (266) {G1,W7,D3,L2,V2,M2} S(55);r(57);r(57) { ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), ! 
% 0.69/1.10    unequally_directed_lines( X, Y ) }.
% 0.69/1.10  parent1[1]: (110) {G1,W7,D3,L2,V0,M1} R(71,73) { 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), 
% 0.69/1.10    unequally_directed_lines( skol1, skol2 ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := skol2
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (627) {G2,W8,D3,L2,V0,M2}  { unequally_directed_opposite_lines
% 0.69/1.10    ( skol1, reverse_line( skol2 ) ), unequally_directed_opposite_lines( 
% 0.69/1.10    skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0[0]: (626) {G2,W8,D3,L2,V0,M2}  { ! unequally_directed_lines( skol1
% 0.69/1.10    , reverse_line( skol2 ) ), unequally_directed_opposite_lines( skol1, 
% 0.69/1.10    reverse_line( skol2 ) ) }.
% 0.69/1.10  parent1[1]: (101) {G1,W6,D2,L2,V2,M1} R(54,1) { 
% 0.69/1.10    unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X, Y
% 0.69/1.10     ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := reverse_line( skol2 )
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  factor: (628) {G2,W4,D3,L1,V0,M1}  { unequally_directed_opposite_lines( 
% 0.69/1.10    skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0[0, 1]: (627) {G2,W8,D3,L2,V0,M2}  { 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ), 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (313) {G2,W4,D3,L1,V0,M1} R(266,110);r(101) { 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0: (628) {G2,W4,D3,L1,V0,M1}  { unequally_directed_opposite_lines( 
% 0.69/1.10    skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (630) {G2,W5,D4,L1,V0,M1}  { ! unequally_directed_lines( skol1
% 0.69/1.10    , reverse_line( reverse_line( skol2 ) ) ) }.
% 0.69/1.10  parent0[1]: (266) {G1,W7,D3,L2,V2,M2} S(55);r(57);r(57) { ! 
% 0.69/1.10    unequally_directed_lines( X, reverse_line( Y ) ), ! 
% 0.69/1.10    unequally_directed_lines( X, Y ) }.
% 0.69/1.10  parent1[0]: (109) {G2,W4,D3,L1,V0,M1} R(96,54);r(101) { 
% 0.69/1.10    unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := reverse_line( skol2 )
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (315) {G3,W5,D4,L1,V0,M1} R(266,109) { ! 
% 0.69/1.10    unequally_directed_lines( skol1, reverse_line( reverse_line( skol2 ) ) )
% 0.69/1.10     }.
% 0.69/1.10  parent0: (630) {G2,W5,D4,L1,V0,M1}  { ! unequally_directed_lines( skol1, 
% 0.69/1.10    reverse_line( reverse_line( skol2 ) ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10     0 ==> 0
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (631) {G1,W4,D3,L1,V0,M1}  { ! 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent0[0]: (315) {G3,W5,D4,L1,V0,M1} R(266,109) { ! 
% 0.69/1.10    unequally_directed_lines( skol1, reverse_line( reverse_line( skol2 ) ) )
% 0.69/1.10     }.
% 0.69/1.10  parent1[1]: (0) {G0,W7,D3,L2,V2,M1} I { ! unequally_directed_opposite_lines
% 0.69/1.10    ( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10     X := skol1
% 0.69/1.10     Y := reverse_line( skol2 )
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  resolution: (632) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.69/1.10  parent0[0]: (631) {G1,W4,D3,L1,V0,M1}  { ! 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  parent1[0]: (313) {G2,W4,D3,L1,V0,M1} R(266,110);r(101) { 
% 0.69/1.10    unequally_directed_opposite_lines( skol1, reverse_line( skol2 ) ) }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  substitution1:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  subsumption: (385) {G4,W0,D0,L0,V0,M0} R(315,0);r(313) {  }.
% 0.69/1.10  parent0: (632) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.69/1.10  substitution0:
% 0.69/1.10  end
% 0.69/1.10  permutation0:
% 0.69/1.10  end
% 0.69/1.10  
% 0.69/1.10  Proof check complete!
% 0.69/1.10  
% 0.69/1.10  Memory use:
% 0.69/1.10  
% 0.69/1.10  space for terms:        5217
% 0.69/1.10  space for clauses:      19931
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  clauses generated:      997
% 0.69/1.10  clauses kept:           386
% 0.69/1.10  clauses selected:       153
% 0.69/1.10  clauses deleted:        25
% 0.69/1.10  clauses inuse deleted:  0
% 0.69/1.10  
% 0.69/1.10  subsentry:          4973
% 0.69/1.10  literals s-matched: 2580
% 0.69/1.10  literals matched:   2380
% 0.69/1.10  full subsumption:   696
% 0.69/1.10  
% 0.69/1.10  checksum:           -1853296204
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  Bliksem ended
%------------------------------------------------------------------------------