TSTP Solution File: GEO252+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO252+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n019.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 02:53:17 EDT 2022

% Result   : Theorem 0.41s 1.14s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO252+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.06/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n019.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 02:06:11 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.41/1.14  *** allocated 10000 integers for termspace/termends
% 0.41/1.14  *** allocated 10000 integers for clauses
% 0.41/1.14  *** allocated 10000 integers for justifications
% 0.41/1.14  Bliksem 1.12
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Automatic Strategy Selection
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Clauses:
% 0.41/1.14  
% 0.41/1.14  { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ), 
% 0.41/1.14    left_apart_point( X, reverse_line( Y ) ) }.
% 0.41/1.14  { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.41/1.14  { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.41/1.14     }.
% 0.41/1.14  { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.41/1.14  { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.41/1.14     ) ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.41/1.14  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.41/1.14  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.41/1.14  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.41/1.14  { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.41/1.14  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.41/1.14  { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ), 
% 0.41/1.14    alpha4( X, Y, Z ) }.
% 0.41/1.14  { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.41/1.14  { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.41/1.14  { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ), 
% 0.41/1.14    alpha1( X, Y, Z ) }.
% 0.41/1.14  { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.41/1.14  { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.41/1.14  { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.41/1.14     }.
% 0.41/1.14  { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.41/1.14  { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.41/1.14  { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.41/1.14  { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.41/1.14  { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.41/1.14     ) ) }.
% 0.41/1.14  { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.41/1.14    , alpha8( X, Y, Z ) }.
% 0.41/1.14  { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.41/1.14  { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.41/1.14  { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ), 
% 0.41/1.14    alpha5( X, Y ) }.
% 0.41/1.14  { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.41/1.14  { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.41/1.14  { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ), 
% 0.41/1.14    alpha2( X, Y ) }.
% 0.41/1.14  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.41/1.14     ) }.
% 0.41/1.14  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.41/1.14  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.41/1.14  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.41/1.14  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.41/1.14  { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.41/1.14    , T ) }.
% 0.41/1.14  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.41/1.14  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.41/1.14  { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.41/1.14    , T ) }.
% 0.41/1.14  { ! distinct_points( X, X ) }.
% 0.41/1.14  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.41/1.14     ) }.
% 0.41/1.14  { ! distinct_lines( X, X ) }.
% 0.41/1.14  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.41/1.14     }.
% 0.41/1.14  { ! unequally_directed_lines( X, X ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ), 
% 0.41/1.14    unequally_directed_lines( Y, Z ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, 
% 0.41/1.14    reverse_line( Z ) ) }.
% 0.41/1.14  { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.41/1.14  { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.41/1.14  { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ), 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.41/1.14    ( X, reverse_line( Y ) ) }.
% 0.41/1.14  { ! left_apart_point( X, Y ) }.
% 0.41/1.14  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.41/1.14  { ! left_convergent_lines( X, Y ) }.
% 0.41/1.14  { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.41/1.14  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.41/1.14    line_connecting( X, Y ) ) }.
% 0.41/1.14  { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), point( 
% 0.41/1.14    intersection_point( X, Y ) ) }.
% 0.41/1.14  { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.41/1.14  { ! line( X ), line( reverse_line( X ) ) }.
% 0.41/1.14  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.41/1.14    , Y ) ) }.
% 0.41/1.14  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.41/1.14    , Y ) ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.41/1.14    X ) }.
% 0.41/1.14  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.41/1.14    Y ) }.
% 0.41/1.14  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.41/1.14  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.41/1.14  { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line( 
% 0.41/1.14    line_connecting( Y, X ) ) ) }.
% 0.41/1.14  { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.41/1.14  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.41/1.14    , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ), 
% 0.41/1.14    left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ), 
% 0.41/1.14    left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X, 
% 0.41/1.14    reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.41/1.14  { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point( 
% 0.41/1.14    Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.41/1.14  { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.41/1.14    , Y ) }.
% 0.41/1.14  { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ), 
% 0.41/1.14    distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.41/1.14  { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ), 
% 0.41/1.14    left_convergent_lines( X, Z ) }.
% 0.41/1.14  { left_apart_point( skol1, skol3 ) }.
% 0.41/1.14  { left_apart_point( skol2, reverse_line( skol3 ) ) }.
% 0.41/1.14  { ! distinct_points( skol1, skol2 ), ! left_convergent_lines( 
% 0.41/1.14    line_connecting( skol1, skol2 ), skol3 ) }.
% 0.41/1.14  
% 0.41/1.14  percentage equality = 0.000000, percentage horn = 0.797101
% 0.41/1.14  This a non-horn, non-equality problem
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Options Used:
% 0.41/1.14  
% 0.41/1.14  useres =            1
% 0.41/1.14  useparamod =        0
% 0.41/1.14  useeqrefl =         0
% 0.41/1.14  useeqfact =         0
% 0.41/1.14  usefactor =         1
% 0.41/1.14  usesimpsplitting =  0
% 0.41/1.14  usesimpdemod =      0
% 0.41/1.14  usesimpres =        3
% 0.41/1.14  
% 0.41/1.14  resimpinuse      =  1000
% 0.41/1.14  resimpclauses =     20000
% 0.41/1.14  substype =          standard
% 0.41/1.14  backwardsubs =      1
% 0.41/1.14  selectoldest =      5
% 0.41/1.14  
% 0.41/1.14  litorderings [0] =  split
% 0.41/1.14  litorderings [1] =  liftord
% 0.41/1.14  
% 0.41/1.14  termordering =      none
% 0.41/1.14  
% 0.41/1.14  litapriori =        1
% 0.41/1.14  termapriori =       0
% 0.41/1.14  litaposteriori =    0
% 0.41/1.14  termaposteriori =   0
% 0.41/1.14  demodaposteriori =  0
% 0.41/1.14  ordereqreflfact =   0
% 0.41/1.14  
% 0.41/1.14  litselect =         none
% 0.41/1.14  
% 0.41/1.14  maxweight =         15
% 0.41/1.14  maxdepth =          30000
% 0.41/1.14  maxlength =         115
% 0.41/1.14  maxnrvars =         195
% 0.41/1.14  excuselevel =       1
% 0.41/1.14  increasemaxweight = 1
% 0.41/1.14  
% 0.41/1.14  maxselected =       10000000
% 0.41/1.14  maxnrclauses =      10000000
% 0.41/1.14  
% 0.41/1.14  showgenerated =    0
% 0.41/1.14  showkept =         0
% 0.41/1.14  showselected =     0
% 0.41/1.14  showdeleted =      0
% 0.41/1.14  showresimp =       1
% 0.41/1.14  showstatus =       2000
% 0.41/1.14  
% 0.41/1.14  prologoutput =     0
% 0.41/1.14  nrgoals =          5000000
% 0.41/1.14  totalproof =       1
% 0.41/1.14  
% 0.41/1.14  Symbols occurring in the translation:
% 0.41/1.14  
% 0.41/1.14  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.41/1.14  .  [1, 2]      (w:1, o:23, a:1, s:1, b:0), 
% 0.41/1.14  !  [4, 1]      (w:0, o:15, a:1, s:1, b:0), 
% 0.41/1.14  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.41/1.14  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.41/1.14  apart_point_and_line  [37, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 0.41/1.14  left_apart_point  [38, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.41/1.14  reverse_line  [39, 1]      (w:1, o:20, a:1, s:1, b:0), 
% 0.41/1.14  convergent_lines  [41, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.41/1.14  unequally_directed_lines  [42, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.41/1.14  divides_points  [44, 3]      (w:1, o:60, a:1, s:1, b:0), 
% 0.41/1.14  before_on_line  [45, 3]      (w:1, o:65, a:1, s:1, b:0), 
% 0.41/1.14  distinct_points  [46, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 0.41/1.14  line_connecting  [47, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.41/1.14  between_on_line  [49, 4]      (w:1, o:68, a:1, s:1, b:0), 
% 0.41/1.14  distinct_lines  [50, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.41/1.14  line  [52, 1]      (w:1, o:21, a:1, s:1, b:0), 
% 0.41/1.14  left_convergent_lines  [53, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.41/1.14  point  [54, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.41/1.14  intersection_point  [55, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.41/1.14  parallel_through_point  [56, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.41/1.14  alpha1  [57, 3]      (w:1, o:61, a:1, s:1, b:0), 
% 0.41/1.14  alpha2  [58, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.41/1.14  alpha3  [59, 4]      (w:1, o:66, a:1, s:1, b:0), 
% 0.41/1.14  alpha4  [60, 3]      (w:1, o:62, a:1, s:1, b:0), 
% 0.41/1.14  alpha5  [61, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.41/1.14  alpha6  [62, 4]      (w:1, o:67, a:1, s:1, b:0), 
% 0.41/1.14  alpha7  [63, 3]      (w:1, o:63, a:1, s:1, b:0), 
% 0.41/1.14  alpha8  [64, 3]      (w:1, o:64, a:1, s:1, b:0), 
% 0.41/1.14  alpha9  [65, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.41/1.14  skol1  [66, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 0.41/1.14  skol2  [67, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 0.41/1.14  skol3  [68, 0]      (w:1, o:14, a:1, s:1, b:0).
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Starting Search:
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Bliksems!, er is een bewijs:
% 0.41/1.14  % SZS status Theorem
% 0.41/1.14  % SZS output start Refutation
% 0.41/1.14  
% 0.41/1.14  (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.41/1.14  (67) {G1,W0,D0,L0,V0,M0} I;r(52) {  }.
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  % SZS output end Refutation
% 0.41/1.14  found a proof!
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Unprocessed initial clauses:
% 0.41/1.14  
% 0.41/1.14  (69) {G0,W10,D3,L3,V2,M3}  { ! apart_point_and_line( X, Y ), 
% 0.41/1.14    left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.41/1.14  (70) {G0,W6,D2,L2,V2,M2}  { ! left_apart_point( X, Y ), 
% 0.41/1.14    apart_point_and_line( X, Y ) }.
% 0.41/1.14  (71) {G0,W7,D3,L2,V2,M2}  { ! left_apart_point( X, reverse_line( Y ) ), 
% 0.41/1.14    apart_point_and_line( X, Y ) }.
% 0.41/1.14  (72) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.41/1.14    unequally_directed_lines( X, Y ) }.
% 0.41/1.14  (73) {G0,W7,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.41/1.14  (74) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.41/1.14     ) }.
% 0.41/1.14  (75) {G0,W12,D2,L3,V3,M3}  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z )
% 0.41/1.14    , alpha4( X, Y, Z ) }.
% 0.41/1.14  (76) {G0,W8,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.41/1.14     }.
% 0.41/1.14  (77) {G0,W8,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.41/1.14     }.
% 0.41/1.14  (78) {G0,W8,D3,L2,V3,M2}  { ! alpha4( X, Y, Z ), left_apart_point( X, 
% 0.41/1.14    reverse_line( Z ) ) }.
% 0.41/1.14  (79) {G0,W7,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.41/1.14     }.
% 0.41/1.14  (80) {G0,W11,D3,L3,V3,M3}  { ! left_apart_point( X, reverse_line( Z ) ), ! 
% 0.41/1.14    left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.41/1.14  (81) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.41/1.14     }.
% 0.41/1.14  (82) {G0,W8,D3,L2,V3,M2}  { ! alpha1( X, Y, Z ), left_apart_point( Y, 
% 0.41/1.14    reverse_line( Z ) ) }.
% 0.41/1.14  (83) {G0,W11,D3,L3,V3,M3}  { ! left_apart_point( X, Z ), ! left_apart_point
% 0.41/1.14    ( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.41/1.14  (84) {G0,W7,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), distinct_points( Y
% 0.41/1.14    , Z ) }.
% 0.41/1.14  (85) {G0,W8,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.41/1.14     }.
% 0.41/1.14  (86) {G0,W11,D2,L3,V3,M3}  { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z )
% 0.41/1.14    , before_on_line( X, Y, Z ) }.
% 0.41/1.14  (87) {G0,W7,D2,L2,V3,M2}  { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.41/1.14  (88) {G0,W8,D2,L2,V3,M2}  { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.41/1.14  (89) {G0,W11,D2,L3,V3,M3}  { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.41/1.14    ( X, Y, Z ) }.
% 0.41/1.14  (90) {G0,W7,D2,L2,V3,M2}  { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.41/1.14  (91) {G0,W9,D3,L2,V3,M2}  { ! alpha8( X, Y, Z ), ! unequally_directed_lines
% 0.41/1.14    ( X, line_connecting( Y, Z ) ) }.
% 0.41/1.14  (92) {G0,W12,D3,L3,V3,M3}  { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.41/1.14    , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.41/1.14  (93) {G0,W6,D2,L2,V2,M2}  { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.41/1.14     }.
% 0.41/1.14  (94) {G0,W7,D3,L2,V2,M2}  { ! alpha5( X, Y ), ! left_apart_point( Y, 
% 0.41/1.14    reverse_line( X ) ) }.
% 0.41/1.14  (95) {G0,W10,D3,L3,V2,M3}  { left_apart_point( Y, X ), left_apart_point( Y
% 0.41/1.14    , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.41/1.14  (96) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.41/1.14     }.
% 0.41/1.14  (97) {G0,W7,D3,L2,V2,M2}  { ! alpha2( X, Y ), ! left_apart_point( Y, 
% 0.41/1.14    reverse_line( X ) ) }.
% 0.41/1.14  (98) {G0,W10,D3,L3,V2,M3}  { left_apart_point( Y, X ), left_apart_point( Y
% 0.41/1.14    , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.41/1.14  (99) {G0,W15,D2,L3,V4,M3}  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.41/1.14    , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.41/1.14  (100) {G0,W10,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.41/1.14    , Z, T ) }.
% 0.41/1.14  (101) {G0,W10,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.41/1.14    , Z, T ) }.
% 0.41/1.14  (102) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, 
% 0.41/1.14    Z ) }.
% 0.41/1.14  (103) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, 
% 0.41/1.14    Y ) }.
% 0.41/1.14  (104) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, T, Z ), ! before_on_line
% 0.41/1.14    ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.41/1.14  (105) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, 
% 0.41/1.14    Z ) }.
% 0.41/1.14  (106) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, 
% 0.41/1.14    T ) }.
% 0.41/1.14  (107) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.41/1.14    ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.41/1.14  (108) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.41/1.14  (109) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 0.41/1.14    , Z ), distinct_points( Y, Z ) }.
% 0.41/1.14  (110) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.41/1.14  (111) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.41/1.14     ), distinct_lines( Y, Z ) }.
% 0.41/1.14  (112) {G0,W3,D2,L1,V1,M1}  { ! unequally_directed_lines( X, X ) }.
% 0.41/1.14  (113) {G0,W9,D2,L3,V3,M3}  { ! unequally_directed_lines( X, Y ), 
% 0.41/1.14    unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.41/1.14  (114) {G0,W13,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ), 
% 0.41/1.14    unequally_directed_lines( Y, Z ) }.
% 0.41/1.14  (115) {G0,W14,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ), 
% 0.41/1.14    unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.41/1.14  (116) {G0,W6,D2,L2,V2,M2}  { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.41/1.14    , Y ) }.
% 0.41/1.14  (117) {G0,W7,D3,L2,V2,M2}  { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.41/1.14    , reverse_line( Y ) ) }.
% 0.41/1.14  (118) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.41/1.14  (119) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), 
% 0.41/1.14    unequally_directed_lines( X, Y ), unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ) }.
% 0.41/1.14  (120) {G0,W14,D3,L4,V2,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines( 
% 0.41/1.14    X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.41/1.14  (121) {G0,W3,D2,L1,V2,M1}  { ! left_apart_point( X, Y ) }.
% 0.41/1.14  (122) {G0,W4,D3,L1,V2,M1}  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.41/1.14  (123) {G0,W3,D2,L1,V2,M1}  { ! left_convergent_lines( X, Y ) }.
% 0.41/1.14  (124) {G0,W4,D3,L1,V2,M1}  { ! left_convergent_lines( X, reverse_line( Y )
% 0.41/1.14     ) }.
% 0.41/1.14  (125) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.41/1.14    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.41/1.14  (126) {G0,W15,D3,L5,V2,M5}  { ! line( X ), ! line( Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.41/1.14    reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.41/1.14  (127) {G0,W8,D3,L3,V2,M3}  { ! point( Y ), ! line( X ), line( 
% 0.41/1.14    parallel_through_point( X, Y ) ) }.
% 0.41/1.14  (128) {G0,W5,D3,L2,V1,M2}  { ! line( X ), line( reverse_line( X ) ) }.
% 0.41/1.14  (129) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.41/1.14    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.41/1.14  (130) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.41/1.14    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.41/1.14  (131) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.41/1.14    ( intersection_point( X, Y ), X ) }.
% 0.41/1.14  (132) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.41/1.14    ( intersection_point( X, Y ), Y ) }.
% 0.41/1.14  (133) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.41/1.14    parallel_through_point( Y, X ) ) }.
% 0.41/1.14  (134) {G0,W4,D3,L1,V1,M1}  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.41/1.14  (135) {G0,W8,D4,L1,V2,M1}  { ! unequally_directed_lines( line_connecting( X
% 0.41/1.14    , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.41/1.14  (136) {G0,W5,D3,L1,V2,M1}  { ! unequally_directed_lines( 
% 0.41/1.14    parallel_through_point( Y, X ), Y ) }.
% 0.41/1.14  (137) {G0,W34,D3,L10,V4,M10}  { ! distinct_points( X, Y ), ! distinct_lines
% 0.41/1.14    ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ), 
% 0.41/1.14    left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X, 
% 0.41/1.14    reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ), 
% 0.41/1.14    left_apart_point( X, reverse_line( T ) ), left_apart_point( Y, 
% 0.41/1.14    reverse_line( T ) ) }.
% 0.41/1.14  (138) {G0,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! left_apart_point
% 0.41/1.14    ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines( 
% 0.41/1.14    line_connecting( X, Y ), Z ) }.
% 0.41/1.14  (139) {G0,W9,D2,L3,V3,M3}  { ! left_apart_point( X, Y ), distinct_points( X
% 0.41/1.14    , Z ), left_apart_point( Z, Y ) }.
% 0.41/1.14  (140) {G0,W13,D3,L4,V3,M4}  { ! left_apart_point( X, Y ), ! 
% 0.41/1.14    unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ), 
% 0.41/1.14    left_apart_point( X, reverse_line( Z ) ) }.
% 0.41/1.14  (141) {G0,W9,D2,L3,V3,M3}  { ! left_convergent_lines( X, Y ), 
% 0.41/1.14    unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.41/1.14  (142) {G0,W3,D2,L1,V0,M1}  { left_apart_point( skol1, skol3 ) }.
% 0.41/1.14  (143) {G0,W4,D3,L1,V0,M1}  { left_apart_point( skol2, reverse_line( skol3 )
% 0.41/1.14     ) }.
% 0.41/1.14  (144) {G0,W8,D3,L2,V0,M2}  { ! distinct_points( skol1, skol2 ), ! 
% 0.41/1.14    left_convergent_lines( line_connecting( skol1, skol2 ), skol3 ) }.
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Total Proof:
% 0.41/1.14  
% 0.41/1.14  subsumption: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.41/1.14  parent0: (121) {G0,W3,D2,L1,V2,M1}  { ! left_apart_point( X, Y ) }.
% 0.41/1.14  substitution0:
% 0.41/1.14     X := X
% 0.41/1.14     Y := Y
% 0.41/1.14  end
% 0.41/1.14  permutation0:
% 0.41/1.14     0 ==> 0
% 0.41/1.14  end
% 0.41/1.14  
% 0.41/1.14  resolution: (498) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.41/1.14  parent0[0]: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.41/1.14  parent1[0]: (142) {G0,W3,D2,L1,V0,M1}  { left_apart_point( skol1, skol3 )
% 0.41/1.14     }.
% 0.41/1.14  substitution0:
% 0.41/1.14     X := skol1
% 0.41/1.14     Y := skol3
% 0.41/1.14  end
% 0.41/1.14  substitution1:
% 0.41/1.14  end
% 0.41/1.14  
% 0.41/1.14  subsumption: (67) {G1,W0,D0,L0,V0,M0} I;r(52) {  }.
% 0.41/1.14  parent0: (498) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.41/1.14  substitution0:
% 0.41/1.14  end
% 0.41/1.14  permutation0:
% 0.41/1.14  end
% 0.41/1.14  
% 0.41/1.14  Proof check complete!
% 0.41/1.14  
% 0.41/1.14  Memory use:
% 0.41/1.14  
% 0.41/1.14  space for terms:        2335
% 0.41/1.14  space for clauses:      3955
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  clauses generated:      74
% 0.41/1.14  clauses kept:           68
% 0.41/1.14  clauses selected:       0
% 0.41/1.14  clauses deleted:        0
% 0.41/1.14  clauses inuse deleted:  0
% 0.41/1.14  
% 0.41/1.14  subsentry:          2480
% 0.41/1.14  literals s-matched: 1296
% 0.41/1.14  literals matched:   947
% 0.41/1.14  full subsumption:   439
% 0.41/1.14  
% 0.41/1.14  checksum:           888056716
% 0.41/1.14  
% 0.41/1.14  
% 0.41/1.14  Bliksem ended
%------------------------------------------------------------------------------