TSTP Solution File: GEO226+2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO226+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n027.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 02:53:01 EDT 2022

% Result   : Theorem 0.71s 1.12s
% Output   : Refutation 0.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO226+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n027.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 : Fri Jun 17 20:38:52 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.71/1.11  *** allocated 10000 integers for termspace/termends
% 0.71/1.11  *** allocated 10000 integers for clauses
% 0.71/1.11  *** allocated 10000 integers for justifications
% 0.71/1.11  Bliksem 1.12
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Automatic Strategy Selection
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Clauses:
% 0.71/1.11  
% 0.71/1.11  { ! distinct_points( X, X ) }.
% 0.71/1.11  { ! distinct_lines( X, X ) }.
% 0.71/1.11  { ! convergent_lines( X, X ) }.
% 0.71/1.11  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.71/1.11     ) }.
% 0.71/1.11  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.71/1.11     }.
% 0.71/1.11  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.71/1.11    , Z ) }.
% 0.71/1.11  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 0.71/1.11    , Y ) ), distinct_points( Z, X ) }.
% 0.71/1.11  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 0.71/1.11    , Y ) ), distinct_points( Z, Y ) }.
% 0.71/1.11  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ), 
% 0.71/1.11    distinct_points( Z, intersection_point( X, Y ) ) }.
% 0.71/1.11  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ), 
% 0.71/1.11    distinct_points( Z, intersection_point( X, Y ) ) }.
% 0.71/1.11  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.71/1.11    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 0.71/1.11    apart_point_and_line( Y, T ) }.
% 0.71/1.11  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 0.71/1.11    apart_point_and_line( Z, Y ) }.
% 0.71/1.11  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 0.71/1.11    apart_point_and_line( X, Z ) }.
% 0.71/1.11  { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 0.71/1.11  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.71/1.11    line_connecting( X, Y ) ) }.
% 0.71/1.11  { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point( 
% 0.71/1.11    intersection_point( X, Y ) ) }.
% 0.71/1.11  { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.71/1.11  { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.71/1.11  { line( skol1 ) }.
% 0.71/1.11  { line( skol2 ) }.
% 0.71/1.11  { convergent_lines( skol1, skol2 ) }.
% 0.71/1.11  { point( X ) }.
% 0.71/1.11  { apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 0.71/1.11  
% 0.71/1.11  percentage equality = 0.000000, percentage horn = 0.695652
% 0.71/1.11  This a non-horn, non-equality problem
% 0.71/1.11  
% 0.71/1.11  
% 0.71/1.11  Options Used:
% 0.71/1.11  
% 0.71/1.11  useres =            1
% 0.71/1.11  useparamod =        0
% 0.71/1.11  useeqrefl =         0
% 0.71/1.11  useeqfact =         0
% 0.71/1.11  usefactor =         1
% 0.71/1.11  usesimpsplitting =  0
% 0.71/1.11  usesimpdemod =      0
% 0.71/1.11  usesimpres =        3
% 0.71/1.11  
% 0.71/1.11  resimpinuse      =  1000
% 0.71/1.11  resimpclauses =     20000
% 0.71/1.11  substype =          standard
% 0.71/1.11  backwardsubs =      1
% 0.71/1.11  selectoldest =      5
% 0.71/1.11  
% 0.71/1.11  litorderings [0] =  split
% 0.71/1.11  litorderings [1] =  liftord
% 0.71/1.11  
% 0.71/1.11  termordering =      none
% 0.71/1.11  
% 0.71/1.11  litapriori =        1
% 0.71/1.11  termapriori =       0
% 0.71/1.11  litaposteriori =    0
% 0.71/1.11  termaposteriori =   0
% 0.71/1.11  demodaposteriori =  0
% 0.71/1.11  ordereqreflfact =   0
% 0.71/1.11  
% 0.71/1.11  litselect =         none
% 0.71/1.11  
% 0.71/1.11  maxweight =         15
% 0.71/1.11  maxdepth =          30000
% 0.71/1.11  maxlength =         115
% 0.71/1.11  maxnrvars =         195
% 0.71/1.11  excuselevel =       1
% 0.71/1.11  increasemaxweight = 1
% 0.71/1.11  
% 0.71/1.11  maxselected =       10000000
% 0.71/1.11  maxnrclauses =      10000000
% 0.71/1.11  
% 0.71/1.11  showgenerated =    0
% 0.71/1.11  showkept =         0
% 0.71/1.11  showselected =     0
% 0.71/1.11  showdeleted =      0
% 0.71/1.11  showresimp =       1
% 0.71/1.11  showstatus =       2000
% 0.71/1.11  
% 0.71/1.11  prologoutput =     0
% 0.71/1.11  nrgoals =          5000000
% 0.71/1.11  totalproof =       1
% 0.71/1.11  
% 0.71/1.11  Symbols occurring in the translation:
% 0.71/1.11  
% 0.71/1.11  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.71/1.11  .  [1, 2]      (w:1, o:24, a:1, s:1, b:0), 
% 0.71/1.12  !  [4, 1]      (w:0, o:17, a:1, s:1, b:0), 
% 0.71/1.12  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.71/1.12  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.71/1.12  distinct_points  [36, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.71/1.12  distinct_lines  [37, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.71/1.12  convergent_lines  [38, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.71/1.12  line_connecting  [41, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 0.71/1.12  apart_point_and_line  [42, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.71/1.12  intersection_point  [43, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.71/1.12  point  [48, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.71/1.12  line  [49, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.71/1.12  parallel_through_point  [52, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.71/1.12  orthogonal_through_point  [53, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.71/1.12  skol1  [54, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 0.71/1.12  skol2  [55, 0]      (w:1, o:16, a:1, s:1, b:0).
% 0.71/1.12  
% 0.71/1.12  
% 0.71/1.12  Starting Search:
% 0.71/1.12  
% 0.71/1.12  *** allocated 15000 integers for clauses
% 0.71/1.12  
% 0.71/1.12  Bliksems!, er is een bewijs:
% 0.71/1.12  % SZS status Theorem
% 0.71/1.12  % SZS output start Refutation
% 0.71/1.12  
% 0.71/1.12  (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 0.71/1.12  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.71/1.12  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 0.71/1.12    Z ), ! convergent_lines( X, Y ) }.
% 0.71/1.12  (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 0.71/1.12    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, X ) }.
% 0.71/1.12  (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 0.71/1.12    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, Y ) }.
% 0.71/1.12  (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 0.71/1.12    ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 0.71/1.12  (20) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 0.71/1.12  (22) {G0,W6,D2,L2,V1,M1} I { apart_point_and_line( X, skol1 ), 
% 0.71/1.12    apart_point_and_line( X, skol2 ) }.
% 0.71/1.12  (46) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 0.71/1.12    convergent_lines( X, Y ) }.
% 0.71/1.12  (49) {G2,W3,D2,L1,V0,M1} R(46,20) { convergent_lines( skol2, skol1 ) }.
% 0.71/1.12  (178) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), ! 
% 0.71/1.12    convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z )
% 0.71/1.12     ), ! apart_point_and_line( X, Z ) }.
% 0.71/1.12  (179) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), ! 
% 0.71/1.12    convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T )
% 0.71/1.12     ), ! apart_point_and_line( X, Z ) }.
% 0.71/1.12  (185) {G2,W8,D3,L2,V2,M1} F(179);r(0) { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.71/1.12  (186) {G2,W8,D3,L2,V2,M1} F(178);r(0) { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.71/1.12  (188) {G3,W8,D3,L2,V1,M1} R(185,22) { ! convergent_lines( skol2, X ), 
% 0.71/1.12    apart_point_and_line( intersection_point( skol2, X ), skol1 ) }.
% 0.71/1.12  (219) {G4,W0,D0,L0,V0,M0} R(188,186);f;r(49) {  }.
% 0.71/1.12  
% 0.71/1.12  
% 0.71/1.12  % SZS output end Refutation
% 0.71/1.12  found a proof!
% 0.71/1.12  
% 0.71/1.12  
% 0.71/1.12  Unprocessed initial clauses:
% 0.71/1.12  
% 0.71/1.12  (221) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.71/1.12  (222) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.71/1.12  (223) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 0.71/1.12  (224) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 0.71/1.12    , Z ), distinct_points( Y, Z ) }.
% 0.71/1.12  (225) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.71/1.12     ), distinct_lines( Y, Z ) }.
% 0.71/1.12  (226) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines( 
% 0.71/1.12    X, Z ), convergent_lines( Y, Z ) }.
% 0.71/1.12  (227) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 0.71/1.12     ) }.
% 0.71/1.12  (228) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 0.71/1.12     ) }.
% 0.71/1.12  (229) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 0.71/1.12    Y ) ) }.
% 0.71/1.12  (230) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 0.71/1.12    Y ) ) }.
% 0.71/1.12  (231) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines( 
% 0.71/1.12    Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 0.71/1.12    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.71/1.12  (232) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 0.71/1.12    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.71/1.12  (233) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), distinct_lines
% 0.71/1.12    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.71/1.12  (234) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), distinct_lines( X
% 0.71/1.12    , Y ) }.
% 0.71/1.12  (235) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.71/1.12    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.71/1.12  (236) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), ! convergent_lines
% 0.71/1.12    ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.71/1.12  (237) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.71/1.12    parallel_through_point( X, Y ) ) }.
% 0.71/1.12  (238) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.71/1.12    orthogonal_through_point( X, Y ) ) }.
% 0.71/1.12  (239) {G0,W2,D2,L1,V0,M1}  { line( skol1 ) }.
% 0.71/1.12  (240) {G0,W2,D2,L1,V0,M1}  { line( skol2 ) }.
% 0.71/1.12  (241) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 0.71/1.12  (242) {G0,W2,D2,L1,V1,M1}  { point( X ) }.
% 0.71/1.12  (243) {G0,W6,D2,L2,V1,M2}  { apart_point_and_line( X, skol1 ), 
% 0.71/1.12    apart_point_and_line( X, skol2 ) }.
% 0.71/1.12  
% 0.71/1.12  
% 0.71/1.12  Total Proof:
% 0.71/1.12  
% 0.71/1.12  subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 0.71/1.12  parent0: (221) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.71/1.12  parent0: (223) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 0.71/1.12    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.71/1.12  parent0: (226) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 0.71/1.12    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 2
% 0.71/1.12     1 ==> 0
% 0.71/1.12     2 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 0.71/1.12    ( Z, X ) }.
% 0.71/1.12  parent0: (229) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 0.71/1.12    Y ) ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12     1 ==> 2
% 0.71/1.12     2 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 0.71/1.12    ( Z, Y ) }.
% 0.71/1.12  parent0: (230) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 0.71/1.12    Y ) ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12     1 ==> 2
% 0.71/1.12     2 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 0.71/1.12    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 0.71/1.12  parent0: (232) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 0.71/1.12    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 2
% 0.71/1.12     1 ==> 0
% 0.71/1.12     2 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (20) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 0.71/1.12     }.
% 0.71/1.12  parent0: (241) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (22) {G0,W6,D2,L2,V1,M1} I { apart_point_and_line( X, skol1 )
% 0.71/1.12    , apart_point_and_line( X, skol2 ) }.
% 0.71/1.12  parent0: (243) {G0,W6,D2,L2,V1,M2}  { apart_point_and_line( X, skol1 ), 
% 0.71/1.12    apart_point_and_line( X, skol2 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12     1 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (284) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 0.71/1.12    convergent_lines( X, Y ) }.
% 0.71/1.12  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.71/1.12  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 0.71/1.12    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := X
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (46) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 0.71/1.12    convergent_lines( X, Y ) }.
% 0.71/1.12  parent0: (284) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 0.71/1.12    convergent_lines( X, Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := Y
% 0.71/1.12     Y := X
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 1
% 0.71/1.12     1 ==> 0
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (286) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol1 )
% 0.71/1.12     }.
% 0.71/1.12  parent0[0]: (46) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 0.71/1.12    convergent_lines( X, Y ) }.
% 0.71/1.12  parent1[0]: (20) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 0.71/1.12     }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := skol2
% 0.71/1.12     Y := skol1
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (49) {G2,W3,D2,L1,V0,M1} R(46,20) { convergent_lines( skol2, 
% 0.71/1.12    skol1 ) }.
% 0.71/1.12  parent0: (286) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol1 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (287) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 0.71/1.12    , ! apart_point_and_line( T, Y ) }.
% 0.71/1.12  parent0[2]: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 0.71/1.12    ( Z, Y ) }.
% 0.71/1.12  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 0.71/1.12    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12     X := T
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (178) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), 
% 0.71/1.12    ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z
% 0.71/1.12     ) ), ! apart_point_and_line( X, Z ) }.
% 0.71/1.12  parent0: (287) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 0.71/1.12    , ! apart_point_and_line( T, Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := T
% 0.71/1.12     Y := Z
% 0.71/1.12     Z := Y
% 0.71/1.12     T := X
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 1
% 0.71/1.12     1 ==> 2
% 0.71/1.12     2 ==> 0
% 0.71/1.12     3 ==> 3
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (289) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 0.71/1.12    , ! apart_point_and_line( T, X ) }.
% 0.71/1.12  parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 0.71/1.12    ( Z, X ) }.
% 0.71/1.12  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 0.71/1.12    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12     X := T
% 0.71/1.12     Y := X
% 0.71/1.12     Z := Z
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (179) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), 
% 0.71/1.12    ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T
% 0.71/1.12     ) ), ! apart_point_and_line( X, Z ) }.
% 0.71/1.12  parent0: (289) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 0.71/1.12    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 0.71/1.12    , ! apart_point_and_line( T, X ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := Z
% 0.71/1.12     Y := T
% 0.71/1.12     Z := Y
% 0.71/1.12     T := X
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 1
% 0.71/1.12     1 ==> 2
% 0.71/1.12     2 ==> 0
% 0.71/1.12     3 ==> 3
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  factor: (291) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point( 
% 0.71/1.12    X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.71/1.12  parent0[0, 2]: (179) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y )
% 0.71/1.12    , ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, 
% 0.71/1.12    T ) ), ! apart_point_and_line( X, Z ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := intersection_point( X, Y )
% 0.71/1.12     Y := intersection_point( X, Y )
% 0.71/1.12     Z := X
% 0.71/1.12     T := Y
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (292) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.71/1.12  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 0.71/1.12  parent1[0]: (291) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 0.71/1.12    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 0.71/1.12    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 0.71/1.12    Y ), X ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := intersection_point( X, Y )
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (185) {G2,W8,D3,L2,V2,M1} F(179);r(0) { ! convergent_lines( X
% 0.71/1.12    , Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.71/1.12  parent0: (292) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12     1 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  factor: (293) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point( 
% 0.71/1.12    X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.71/1.12  parent0[0, 2]: (178) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y )
% 0.71/1.12    , ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, 
% 0.71/1.12    Z ) ), ! apart_point_and_line( X, Z ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := intersection_point( X, Y )
% 0.71/1.12     Y := intersection_point( X, Y )
% 0.71/1.12     Z := Y
% 0.71/1.12     T := X
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (294) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.71/1.12  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 0.71/1.12  parent1[0]: (293) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 0.71/1.12    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 0.71/1.12    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 0.71/1.12    Y ), Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := intersection_point( X, Y )
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (186) {G2,W8,D3,L2,V2,M1} F(178);r(0) { ! convergent_lines( X
% 0.71/1.12    , Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.71/1.12  parent0: (294) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.71/1.12    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12     Y := Y
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12     1 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  *** allocated 22500 integers for clauses
% 0.71/1.12  resolution: (296) {G1,W8,D3,L2,V1,M2}  { ! convergent_lines( skol2, X ), 
% 0.71/1.12    apart_point_and_line( intersection_point( skol2, X ), skol1 ) }.
% 0.71/1.12  parent0[1]: (185) {G2,W8,D3,L2,V2,M1} F(179);r(0) { ! convergent_lines( X, 
% 0.71/1.12    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.71/1.12  parent1[1]: (22) {G0,W6,D2,L2,V1,M1} I { apart_point_and_line( X, skol1 ), 
% 0.71/1.12    apart_point_and_line( X, skol2 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := skol2
% 0.71/1.12     Y := X
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12     X := intersection_point( skol2, X )
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (188) {G3,W8,D3,L2,V1,M1} R(185,22) { ! convergent_lines( 
% 0.71/1.12    skol2, X ), apart_point_and_line( intersection_point( skol2, X ), skol1 )
% 0.71/1.12     }.
% 0.71/1.12  parent0: (296) {G1,W8,D3,L2,V1,M2}  { ! convergent_lines( skol2, X ), 
% 0.71/1.12    apart_point_and_line( intersection_point( skol2, X ), skol1 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := X
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12     0 ==> 0
% 0.71/1.12     1 ==> 1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (297) {G3,W6,D2,L2,V0,M2}  { ! convergent_lines( skol2, skol1 )
% 0.71/1.12    , ! convergent_lines( skol2, skol1 ) }.
% 0.71/1.12  parent0[1]: (186) {G2,W8,D3,L2,V2,M1} F(178);r(0) { ! convergent_lines( X, 
% 0.71/1.12    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.71/1.12  parent1[1]: (188) {G3,W8,D3,L2,V1,M1} R(185,22) { ! convergent_lines( skol2
% 0.71/1.12    , X ), apart_point_and_line( intersection_point( skol2, X ), skol1 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12     X := skol2
% 0.71/1.12     Y := skol1
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12     X := skol1
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  factor: (298) {G3,W3,D2,L1,V0,M1}  { ! convergent_lines( skol2, skol1 ) }.
% 0.71/1.12  parent0[0, 1]: (297) {G3,W6,D2,L2,V0,M2}  { ! convergent_lines( skol2, 
% 0.71/1.12    skol1 ), ! convergent_lines( skol2, skol1 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  resolution: (300) {G3,W0,D0,L0,V0,M0}  {  }.
% 0.71/1.12  parent0[0]: (298) {G3,W3,D2,L1,V0,M1}  { ! convergent_lines( skol2, skol1 )
% 0.71/1.12     }.
% 0.71/1.12  parent1[0]: (49) {G2,W3,D2,L1,V0,M1} R(46,20) { convergent_lines( skol2, 
% 0.71/1.12    skol1 ) }.
% 0.71/1.12  substitution0:
% 0.71/1.12  end
% 0.71/1.12  substitution1:
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  subsumption: (219) {G4,W0,D0,L0,V0,M0} R(188,186);f;r(49) {  }.
% 0.71/1.12  parent0: (300) {G3,W0,D0,L0,V0,M0}  {  }.
% 0.71/1.12  substitution0:
% 0.71/1.12  end
% 0.71/1.12  permutation0:
% 0.71/1.12  end
% 0.71/1.12  
% 0.71/1.12  Proof check complete!
% 0.71/1.12  
% 0.71/1.12  Memory use:
% 0.71/1.12  
% 0.71/1.12  space for terms:        3144
% 0.71/1.12  space for clauses:      13339
% 0.71/1.12  
% 0.71/1.12  
% 0.71/1.12  clauses generated:      487
% 0.71/1.12  clauses kept:           220
% 0.71/1.12  clauses selected:       62
% 0.71/1.12  clauses deleted:        3
% 0.71/1.12  clauses inuse deleted:  0
% 0.71/1.12  
% 0.71/1.12  subsentry:          878
% 0.71/1.12  literals s-matched: 787
% 0.71/1.12  literals matched:   772
% 0.71/1.12  full subsumption:   277
% 0.71/1.12  
% 0.71/1.12  checksum:           485851174
% 0.71/1.12  
% 0.71/1.12  
% 0.71/1.12  Bliksem ended
%------------------------------------------------------------------------------