TSTP Solution File: GEO257+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n012.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 02:53:20 EDT 2022

% Result   : Theorem 0.70s 1.10s
% Output   : Refutation 0.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Sat Jun 18 00:49:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.70/1.09  *** allocated 10000 integers for termspace/termends
% 0.70/1.09  *** allocated 10000 integers for clauses
% 0.70/1.09  *** allocated 10000 integers for justifications
% 0.70/1.09  Bliksem 1.12
% 0.70/1.09  
% 0.70/1.09  
% 0.70/1.09  Automatic Strategy Selection
% 0.70/1.09  
% 0.70/1.09  
% 0.70/1.09  Clauses:
% 0.70/1.09  
% 0.70/1.09  { ! unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X
% 0.70/1.09    , reverse_line( Y ) ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, reverse_line( Y ) ), 
% 0.70/1.09    unequally_directed_opposite_lines( X, Y ) }.
% 0.70/1.09  { ! right_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.09  { ! left_apart_point( X, reverse_line( Y ) ), right_apart_point( X, Y ) }.
% 0.70/1.09  { ! right_convergent_lines( X, Y ), left_convergent_lines( X, reverse_line
% 0.70/1.09    ( Y ) ) }.
% 0.70/1.09  { ! left_convergent_lines( X, reverse_line( Y ) ), right_convergent_lines( 
% 0.70/1.09    X, Y ) }.
% 0.70/1.09  { ! equally_directed_lines( X, Y ), ! unequally_directed_lines( X, Y ) }.
% 0.70/1.09  { unequally_directed_lines( X, Y ), equally_directed_lines( X, Y ) }.
% 0.70/1.09  { ! equally_directed_opposite_lines( X, Y ), ! 
% 0.70/1.09    unequally_directed_opposite_lines( X, Y ) }.
% 0.70/1.09  { unequally_directed_opposite_lines( X, Y ), 
% 0.70/1.09    equally_directed_opposite_lines( X, Y ) }.
% 0.70/1.09  { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ), 
% 0.70/1.09    right_apart_point( X, Y ) }.
% 0.70/1.09  { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.70/1.09  { ! right_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.70/1.09  { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.70/1.09  { ! convergent_lines( X, Y ), unequally_directed_opposite_lines( X, Y ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_opposite_lines( 
% 0.70/1.09    X, Y ), convergent_lines( X, Y ) }.
% 0.70/1.09  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.70/1.09  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.70/1.09  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.70/1.09  { ! alpha4( X, Y, Z ), right_apart_point( X, Z ) }.
% 0.70/1.09  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.70/1.09  { ! right_apart_point( X, Z ), ! left_apart_point( Y, Z ), alpha4( X, Y, Z
% 0.70/1.09     ) }.
% 0.70/1.09  { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.70/1.09  { ! alpha1( X, Y, Z ), right_apart_point( Y, Z ) }.
% 0.70/1.09  { ! left_apart_point( X, Z ), ! right_apart_point( Y, Z ), alpha1( X, Y, Z
% 0.70/1.09     ) }.
% 0.70/1.09  { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.70/1.09  { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.70/1.09  { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z ), before_on_line( X, Y, Z )
% 0.70/1.09     }.
% 0.70/1.09  { ! alpha2( X, Y, Z ), incident_point_and_line( Y, X ) }.
% 0.70/1.09  { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.70/1.09  { ! incident_point_and_line( Y, X ), ! alpha5( X, Y, Z ), alpha2( X, Y, Z )
% 0.70/1.09     }.
% 0.70/1.09  { ! alpha5( X, Y, Z ), incident_point_and_line( Z, X ) }.
% 0.70/1.09  { ! alpha5( X, Y, Z ), equally_directed_lines( X, line_connecting( Y, Z ) )
% 0.70/1.09     }.
% 0.70/1.09  { ! incident_point_and_line( Z, X ), ! equally_directed_lines( X, 
% 0.70/1.09    line_connecting( Y, Z ) ), alpha5( X, Y, Z ) }.
% 0.70/1.09  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.70/1.09     ) }.
% 0.70/1.09  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.70/1.09  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.70/1.09  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.70/1.09  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.70/1.09  { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.70/1.09    , T ) }.
% 0.70/1.09  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.70/1.09  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.70/1.09  { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.70/1.09    , T ) }.
% 0.70/1.09  { ! distinct_points( X, X ) }.
% 0.70/1.09  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.70/1.09     ) }.
% 0.70/1.09  { ! distinct_lines( X, X ) }.
% 0.70/1.09  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.70/1.09     }.
% 0.70/1.09  { equally_directed_lines( X, X ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ), 
% 0.70/1.09    unequally_directed_lines( Y, Z ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.70/1.09    reverse_line( Y ) ), alpha7( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.70/1.09    reverse_line( Y ) ), alpha7( X, Z ), unequally_directed_lines( Y, 
% 0.70/1.09    reverse_line( Z ) ) }.
% 0.70/1.09  { ! alpha7( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.70/1.09  { ! alpha7( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.70/1.09    reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.70/1.09  { unequally_directed_lines( X, Y ), unequally_directed_lines( X, 
% 0.70/1.09    reverse_line( Y ) ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.70/1.09    reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.70/1.09    ( X, reverse_line( Y ) ) }.
% 0.70/1.09  { ! left_apart_point( X, Y ) }.
% 0.70/1.09  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.09  { ! left_convergent_lines( X, Y ) }.
% 0.70/1.09  { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.70/1.09  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.70/1.09    line_connecting( X, Y ) ) }.
% 0.70/1.09  { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.09    unequally_directed_lines( X, reverse_line( Y ) ), point( 
% 0.70/1.09    intersection_point( X, Y ) ) }.
% 0.70/1.09  { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.70/1.09  { ! line( X ), line( reverse_line( X ) ) }.
% 0.70/1.09  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.70/1.09    , Y ) ) }.
% 0.70/1.09  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.70/1.09    , Y ) ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.70/1.09    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.70/1.09    X ) }.
% 0.70/1.09  { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.70/1.09    reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ), 
% 0.70/1.09    Y ) }.
% 0.70/1.09  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.70/1.09  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.70/1.09  { ! distinct_points( X, Y ), equally_directed_lines( line_connecting( X, Y
% 0.70/1.09     ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.70/1.09  { equally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.70/1.09  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.70/1.09    , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ), 
% 0.70/1.09    left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ), 
% 0.70/1.09    left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X, 
% 0.70/1.09    reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.70/1.09  { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point( 
% 0.70/1.09    Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.70/1.09  { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.70/1.09    , Y ) }.
% 0.70/1.09  { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ), 
% 0.70/1.09    distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.70/1.09  { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ), 
% 0.70/1.09    left_convergent_lines( X, Z ) }.
% 0.70/1.09  { distinct_points( skol2, skol4 ) }.
% 0.70/1.09  { distinct_points( skol3, skol4 ) }.
% 0.70/1.09  { incident_point_and_line( skol4, skol1 ) }.
% 0.70/1.09  { left_apart_point( skol5, skol1 ) }.
% 0.70/1.09  { before_on_line( skol1, skol2, skol3 ) }.
% 0.70/1.09  { before_on_line( skol1, skol3, skol4 ) }.
% 0.70/1.09  { ! before_on_line( skol1, skol2, skol4 ) }.
% 0.70/1.09  
% 0.70/1.09  percentage equality = 0.000000, percentage horn = 0.833333
% 0.70/1.09  This a non-horn, non-equality problem
% 0.70/1.09  
% 0.70/1.09  
% 0.70/1.09  Options Used:
% 0.70/1.09  
% 0.70/1.09  useres =            1
% 0.70/1.09  useparamod =        0
% 0.70/1.09  useeqrefl =         0
% 0.70/1.09  useeqfact =         0
% 0.70/1.09  usefactor =         1
% 0.70/1.09  usesimpsplitting =  0
% 0.70/1.09  usesimpdemod =      0
% 0.70/1.09  usesimpres =        3
% 0.70/1.09  
% 0.70/1.09  resimpinuse      =  1000
% 0.70/1.09  resimpclauses =     20000
% 0.70/1.09  substype =          standard
% 0.70/1.09  backwardsubs =      1
% 0.70/1.09  selectoldest =      5
% 0.70/1.09  
% 0.70/1.09  litorderings [0] =  split
% 0.70/1.09  litorderings [1] =  liftord
% 0.70/1.09  
% 0.70/1.09  termordering =      none
% 0.70/1.09  
% 0.70/1.09  litapriori =        1
% 0.70/1.09  termapriori =       0
% 0.70/1.09  litaposteriori =    0
% 0.70/1.09  termaposteriori =   0
% 0.70/1.09  demodaposteriori =  0
% 0.70/1.09  ordereqreflfact =   0
% 0.70/1.09  
% 0.70/1.09  litselect =         none
% 0.70/1.09  
% 0.70/1.09  maxweight =         15
% 0.70/1.09  maxdepth =          30000
% 0.70/1.09  maxlength =         115
% 0.70/1.09  maxnrvars =         195
% 0.70/1.09  excuselevel =       1
% 0.70/1.09  increasemaxweight = 1
% 0.70/1.09  
% 0.70/1.09  maxselected =       10000000
% 0.70/1.09  maxnrclauses =      10000000
% 0.70/1.09  
% 0.70/1.09  showgenerated =    0
% 0.70/1.09  showkept =         0
% 0.70/1.09  showselected =     0
% 0.70/1.09  showdeleted =      0
% 0.70/1.09  showresimp =       1
% 0.70/1.09  showstatus =       2000
% 0.70/1.09  
% 0.70/1.09  prologoutput =     0
% 0.70/1.09  nrgoals =          5000000
% 0.70/1.09  totalproof =       1
% 0.70/1.09  
% 0.70/1.09  Symbols occurring in the translation:
% 0.70/1.09  
% 0.70/1.09  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.70/1.09  .  [1, 2]      (w:1, o:28, a:1, s:1, b:0), 
% 0.70/1.09  !  [4, 1]      (w:0, o:20, a:1, s:1, b:0), 
% 0.70/1.09  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.70/1.09  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.70/1.09  unequally_directed_opposite_lines  [37, 2]      (w:1, o:52, a:1, s:1, b:0)
% 0.70/1.09    , 
% 0.70/1.09  reverse_line  [38, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 0.70/1.09  unequally_directed_lines  [39, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.70/1.09  right_apart_point  [40, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.70/1.09  left_apart_point  [41, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.70/1.09  right_convergent_lines  [42, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.70/1.09  left_convergent_lines  [43, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.70/1.09  equally_directed_lines  [44, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.70/1.09  equally_directed_opposite_lines  [45, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 0.70/1.09  apart_point_and_line  [48, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 0.70/1.09  convergent_lines  [50, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 0.70/1.09  divides_points  [52, 3]      (w:1, o:69, a:1, s:1, b:0), 
% 0.70/1.09  before_on_line  [53, 3]      (w:1, o:74, a:1, s:1, b:0), 
% 0.70/1.09  distinct_points  [54, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.70/1.09  incident_point_and_line  [55, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 0.70/1.09  line_connecting  [56, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.70/1.09  between_on_line  [58, 4]      (w:1, o:77, a:1, s:1, b:0), 
% 0.70/1.09  distinct_lines  [59, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.70/1.09  point  [61, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 0.70/1.09  line  [62, 1]      (w:1, o:27, a:1, s:1, b:0), 
% 0.70/1.09  intersection_point  [63, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 0.70/1.09  parallel_through_point  [64, 2]      (w:1, o:67, a:1, s:1, b:0), 
% 0.70/1.09  alpha1  [66, 3]      (w:1, o:70, a:1, s:1, b:0), 
% 0.70/1.09  alpha2  [67, 3]      (w:1, o:71, a:1, s:1, b:0), 
% 0.70/1.09  alpha3  [68, 4]      (w:1, o:75, a:1, s:1, b:0), 
% 0.70/1.09  alpha4  [69, 3]      (w:1, o:72, a:1, s:1, b:0), 
% 0.70/1.09  alpha5  [70, 3]      (w:1, o:73, a:1, s:1, b:0), 
% 0.70/1.09  alpha6  [71, 4]      (w:1, o:76, a:1, s:1, b:0), 
% 0.70/1.09  alpha7  [72, 2]      (w:1, o:68, a:1, s:1, b:0), 
% 0.70/1.09  skol1  [73, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 0.70/1.09  skol2  [74, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 0.70/1.09  skol3  [75, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 0.70/1.09  skol4  [76, 0]      (w:1, o:18, a:1, s:1, b:0), 
% 0.70/1.09  skol5  [77, 0]      (w:1, o:19, a:1, s:1, b:0).
% 0.70/1.09  
% 0.70/1.09  
% 0.70/1.09  Starting Search:
% 0.70/1.09  
% 0.70/1.09  
% 0.70/1.09  Bliksems!, er is een bewijs:
% 0.70/1.10  % SZS status Theorem
% 0.70/1.10  % SZS output start Refutation
% 0.70/1.10  
% 0.70/1.10  (56) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.70/1.10  (74) {G1,W0,D0,L0,V0,M0} I;r(56) {  }.
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  % SZS output end Refutation
% 0.70/1.10  found a proof!
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  Unprocessed initial clauses:
% 0.70/1.10  
% 0.70/1.10  (76) {G0,W7,D3,L2,V2,M2}  { ! unequally_directed_opposite_lines( X, Y ), 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.70/1.10  (77) {G0,W7,D3,L2,V2,M2}  { ! unequally_directed_lines( X, reverse_line( Y
% 0.70/1.10     ) ), unequally_directed_opposite_lines( X, Y ) }.
% 0.70/1.10  (78) {G0,W7,D3,L2,V2,M2}  { ! right_apart_point( X, Y ), left_apart_point( 
% 0.70/1.10    X, reverse_line( Y ) ) }.
% 0.70/1.10  (79) {G0,W7,D3,L2,V2,M2}  { ! left_apart_point( X, reverse_line( Y ) ), 
% 0.70/1.10    right_apart_point( X, Y ) }.
% 0.70/1.10  (80) {G0,W7,D3,L2,V2,M2}  { ! right_convergent_lines( X, Y ), 
% 0.70/1.10    left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.70/1.10  (81) {G0,W7,D3,L2,V2,M2}  { ! left_convergent_lines( X, reverse_line( Y ) )
% 0.70/1.10    , right_convergent_lines( X, Y ) }.
% 0.70/1.10  (82) {G0,W6,D2,L2,V2,M2}  { ! equally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, Y ) }.
% 0.70/1.10  (83) {G0,W6,D2,L2,V2,M2}  { unequally_directed_lines( X, Y ), 
% 0.70/1.10    equally_directed_lines( X, Y ) }.
% 0.70/1.10  (84) {G0,W6,D2,L2,V2,M2}  { ! equally_directed_opposite_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_opposite_lines( X, Y ) }.
% 0.70/1.10  (85) {G0,W6,D2,L2,V2,M2}  { unequally_directed_opposite_lines( X, Y ), 
% 0.70/1.10    equally_directed_opposite_lines( X, Y ) }.
% 0.70/1.10  (86) {G0,W9,D2,L3,V2,M3}  { ! apart_point_and_line( X, Y ), 
% 0.70/1.10    left_apart_point( X, Y ), right_apart_point( X, Y ) }.
% 0.70/1.10  (87) {G0,W6,D2,L2,V2,M2}  { ! left_apart_point( X, Y ), 
% 0.70/1.10    apart_point_and_line( X, Y ) }.
% 0.70/1.10  (88) {G0,W6,D2,L2,V2,M2}  { ! right_apart_point( X, Y ), 
% 0.70/1.10    apart_point_and_line( X, Y ) }.
% 0.70/1.10  (89) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.70/1.10    unequally_directed_lines( X, Y ) }.
% 0.70/1.10  (90) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 0.70/1.10    unequally_directed_opposite_lines( X, Y ) }.
% 0.70/1.10  (91) {G0,W9,D2,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_opposite_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.70/1.10  (92) {G0,W12,D2,L3,V3,M3}  { ! divides_points( Z, X, Y ), alpha1( X, Y, Z )
% 0.70/1.10    , alpha4( X, Y, Z ) }.
% 0.70/1.10  (93) {G0,W8,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.70/1.10     }.
% 0.70/1.10  (94) {G0,W8,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.70/1.10     }.
% 0.70/1.10  (95) {G0,W7,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), right_apart_point( X, Z )
% 0.70/1.10     }.
% 0.70/1.10  (96) {G0,W7,D2,L2,V3,M2}  { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.70/1.10     }.
% 0.70/1.10  (97) {G0,W10,D2,L3,V3,M3}  { ! right_apart_point( X, Z ), ! 
% 0.70/1.10    left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.70/1.10  (98) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.70/1.10     }.
% 0.70/1.10  (99) {G0,W7,D2,L2,V3,M2}  { ! alpha1( X, Y, Z ), right_apart_point( Y, Z )
% 0.70/1.10     }.
% 0.70/1.10  (100) {G0,W10,D2,L3,V3,M3}  { ! left_apart_point( X, Z ), ! 
% 0.70/1.10    right_apart_point( Y, Z ), alpha1( X, Y, Z ) }.
% 0.70/1.10  (101) {G0,W7,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), distinct_points( 
% 0.70/1.10    Y, Z ) }.
% 0.70/1.10  (102) {G0,W8,D2,L2,V3,M2}  { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z )
% 0.70/1.10     }.
% 0.70/1.10  (103) {G0,W11,D2,L3,V3,M3}  { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z
% 0.70/1.10     ), before_on_line( X, Y, Z ) }.
% 0.70/1.10  (104) {G0,W7,D2,L2,V3,M2}  { ! alpha2( X, Y, Z ), incident_point_and_line( 
% 0.70/1.10    Y, X ) }.
% 0.70/1.10  (105) {G0,W8,D2,L2,V3,M2}  { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.70/1.10  (106) {G0,W11,D2,L3,V3,M3}  { ! incident_point_and_line( Y, X ), ! alpha5( 
% 0.70/1.10    X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.70/1.10  (107) {G0,W7,D2,L2,V3,M2}  { ! alpha5( X, Y, Z ), incident_point_and_line( 
% 0.70/1.10    Z, X ) }.
% 0.70/1.10  (108) {G0,W9,D3,L2,V3,M2}  { ! alpha5( X, Y, Z ), equally_directed_lines( X
% 0.70/1.10    , line_connecting( Y, Z ) ) }.
% 0.70/1.10  (109) {G0,W12,D3,L3,V3,M3}  { ! incident_point_and_line( Z, X ), ! 
% 0.70/1.10    equally_directed_lines( X, line_connecting( Y, Z ) ), alpha5( X, Y, Z )
% 0.70/1.10     }.
% 0.70/1.10  (110) {G0,W15,D2,L3,V4,M3}  { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.70/1.10    , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.70/1.10  (111) {G0,W10,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.70/1.10    , Z, T ) }.
% 0.70/1.10  (112) {G0,W10,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.70/1.10    , Z, T ) }.
% 0.70/1.10  (113) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, T, 
% 0.70/1.10    Z ) }.
% 0.70/1.10  (114) {G0,W9,D2,L2,V4,M2}  { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, 
% 0.70/1.10    Y ) }.
% 0.70/1.10  (115) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, T, Z ), ! before_on_line
% 0.70/1.10    ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.70/1.10  (116) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, 
% 0.70/1.10    Z ) }.
% 0.70/1.10  (117) {G0,W9,D2,L2,V4,M2}  { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, 
% 0.70/1.10    T ) }.
% 0.70/1.10  (118) {G0,W13,D2,L3,V4,M3}  { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.70/1.10    ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.70/1.10  (119) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.70/1.10  (120) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 0.70/1.10    , Z ), distinct_points( Y, Z ) }.
% 0.70/1.10  (121) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.70/1.10  (122) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.70/1.10     ), distinct_lines( Y, Z ) }.
% 0.70/1.10  (123) {G0,W3,D2,L1,V1,M1}  { equally_directed_lines( X, X ) }.
% 0.70/1.10  (124) {G0,W9,D2,L3,V3,M3}  { ! unequally_directed_lines( X, Y ), 
% 0.70/1.10    unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.70/1.10  (125) {G0,W13,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ), 
% 0.70/1.10    unequally_directed_lines( Y, Z ) }.
% 0.70/1.10  (126) {G0,W14,D3,L4,V3,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ), 
% 0.70/1.10    unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.70/1.10  (127) {G0,W6,D2,L2,V2,M2}  { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.70/1.10    , Y ) }.
% 0.70/1.10  (128) {G0,W7,D3,L2,V2,M2}  { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.70/1.10    , reverse_line( Y ) ) }.
% 0.70/1.10  (129) {G0,W10,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.70/1.10  (130) {G0,W7,D3,L2,V2,M2}  { unequally_directed_lines( X, Y ), 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.70/1.10  (131) {G0,W14,D3,L4,V2,M4}  { ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines( 
% 0.70/1.10    X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.70/1.10  (132) {G0,W3,D2,L1,V2,M1}  { ! left_apart_point( X, Y ) }.
% 0.70/1.10  (133) {G0,W4,D3,L1,V2,M1}  { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.10  (134) {G0,W3,D2,L1,V2,M1}  { ! left_convergent_lines( X, Y ) }.
% 0.70/1.10  (135) {G0,W4,D3,L1,V2,M1}  { ! left_convergent_lines( X, reverse_line( Y )
% 0.70/1.10     ) }.
% 0.70/1.10  (136) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.70/1.10    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.70/1.10  (137) {G0,W15,D3,L5,V2,M5}  { ! line( X ), ! line( Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, Y ), ! unequally_directed_lines( X, 
% 0.70/1.10    reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.70/1.10  (138) {G0,W8,D3,L3,V2,M3}  { ! point( Y ), ! line( X ), line( 
% 0.70/1.10    parallel_through_point( X, Y ) ) }.
% 0.70/1.10  (139) {G0,W5,D3,L2,V1,M2}  { ! line( X ), line( reverse_line( X ) ) }.
% 0.70/1.10  (140) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.70/1.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.70/1.10  (141) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.70/1.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.70/1.10  (142) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.70/1.10    ( intersection_point( X, Y ), X ) }.
% 0.70/1.10  (143) {G0,W12,D3,L3,V2,M3}  { ! unequally_directed_lines( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.70/1.10    ( intersection_point( X, Y ), Y ) }.
% 0.70/1.10  (144) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.70/1.10    parallel_through_point( Y, X ) ) }.
% 0.70/1.10  (145) {G0,W4,D3,L1,V1,M1}  { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.70/1.10  (146) {G0,W11,D4,L2,V2,M2}  { ! distinct_points( X, Y ), 
% 0.70/1.10    equally_directed_lines( line_connecting( X, Y ), reverse_line( 
% 0.70/1.10    line_connecting( Y, X ) ) ) }.
% 0.70/1.10  (147) {G0,W5,D3,L1,V2,M1}  { equally_directed_lines( parallel_through_point
% 0.70/1.10    ( Y, X ), Y ) }.
% 0.70/1.10  (148) {G0,W34,D3,L10,V4,M10}  { ! distinct_points( X, Y ), ! distinct_lines
% 0.70/1.10    ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ), 
% 0.70/1.10    left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X, 
% 0.70/1.10    reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ), 
% 0.70/1.10    left_apart_point( X, reverse_line( T ) ), left_apart_point( Y, 
% 0.70/1.10    reverse_line( T ) ) }.
% 0.70/1.10  (149) {G0,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! left_apart_point
% 0.70/1.10    ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines( 
% 0.70/1.10    line_connecting( X, Y ), Z ) }.
% 0.70/1.10  (150) {G0,W9,D2,L3,V3,M3}  { ! left_apart_point( X, Y ), distinct_points( X
% 0.70/1.10    , Z ), left_apart_point( Z, Y ) }.
% 0.70/1.10  (151) {G0,W13,D3,L4,V3,M4}  { ! left_apart_point( X, Y ), ! 
% 0.70/1.10    unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ), 
% 0.70/1.10    left_apart_point( X, reverse_line( Z ) ) }.
% 0.70/1.10  (152) {G0,W9,D2,L3,V3,M3}  { ! left_convergent_lines( X, Y ), 
% 0.70/1.10    unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.70/1.10  (153) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol2, skol4 ) }.
% 0.70/1.10  (154) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol3, skol4 ) }.
% 0.70/1.10  (155) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol4, skol1 ) }.
% 0.70/1.10  (156) {G0,W3,D2,L1,V0,M1}  { left_apart_point( skol5, skol1 ) }.
% 0.70/1.10  (157) {G0,W4,D2,L1,V0,M1}  { before_on_line( skol1, skol2, skol3 ) }.
% 0.70/1.10  (158) {G0,W4,D2,L1,V0,M1}  { before_on_line( skol1, skol3, skol4 ) }.
% 0.70/1.10  (159) {G0,W4,D2,L1,V0,M1}  { ! before_on_line( skol1, skol2, skol4 ) }.
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  Total Proof:
% 0.70/1.10  
% 0.70/1.10  subsumption: (56) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.70/1.10  parent0: (132) {G0,W3,D2,L1,V2,M1}  { ! left_apart_point( X, Y ) }.
% 0.70/1.10  substitution0:
% 0.70/1.10     X := X
% 0.70/1.10     Y := Y
% 0.70/1.10  end
% 0.70/1.10  permutation0:
% 0.70/1.10     0 ==> 0
% 0.70/1.10  end
% 0.70/1.10  
% 0.70/1.10  resolution: (505) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.70/1.10  parent0[0]: (56) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.70/1.10  parent1[0]: (156) {G0,W3,D2,L1,V0,M1}  { left_apart_point( skol5, skol1 )
% 0.70/1.10     }.
% 0.70/1.10  substitution0:
% 0.70/1.10     X := skol5
% 0.70/1.10     Y := skol1
% 0.70/1.10  end
% 0.70/1.10  substitution1:
% 0.70/1.10  end
% 0.70/1.10  
% 0.70/1.10  subsumption: (74) {G1,W0,D0,L0,V0,M0} I;r(56) {  }.
% 0.70/1.10  parent0: (505) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.70/1.10  substitution0:
% 0.70/1.10  end
% 0.70/1.10  permutation0:
% 0.70/1.10  end
% 0.70/1.10  
% 0.70/1.10  Proof check complete!
% 0.70/1.10  
% 0.70/1.10  Memory use:
% 0.70/1.10  
% 0.70/1.10  space for terms:        2440
% 0.70/1.10  space for clauses:      4444
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  clauses generated:      81
% 0.70/1.10  clauses kept:           75
% 0.70/1.10  clauses selected:       0
% 0.70/1.10  clauses deleted:        0
% 0.70/1.10  clauses inuse deleted:  0
% 0.70/1.10  
% 0.70/1.10  subsentry:          2472
% 0.70/1.10  literals s-matched: 1291
% 0.70/1.10  literals matched:   942
% 0.70/1.10  full subsumption:   439
% 0.70/1.10  
% 0.70/1.10  checksum:           967774581
% 0.70/1.10  
% 0.70/1.10  
% 0.70/1.10  Bliksem ended
%------------------------------------------------------------------------------