TSTP Solution File: GEO197+2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n011.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 02:52:36 EDT 2022

% Result   : Theorem 25.07s 25.44s
% Output   : Refutation 25.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.12/0.34  % Computer : n011.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Sat Jun 18 09:55:08 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 25.07/25.44  *** allocated 10000 integers for termspace/termends
% 25.07/25.44  *** allocated 10000 integers for clauses
% 25.07/25.44  *** allocated 10000 integers for justifications
% 25.07/25.44  Bliksem 1.12
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  Automatic Strategy Selection
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  Clauses:
% 25.07/25.44  
% 25.07/25.44  { ! distinct_points( X, X ) }.
% 25.07/25.44  { ! distinct_lines( X, X ) }.
% 25.07/25.44  { ! convergent_lines( X, X ) }.
% 25.07/25.44  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 25.07/25.44     ) }.
% 25.07/25.44  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 25.07/25.44     }.
% 25.07/25.44  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 25.07/25.44    , Z ) }.
% 25.07/25.44  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 25.07/25.44    , Y ) ), distinct_points( Z, X ) }.
% 25.07/25.44  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 25.07/25.44    , Y ) ), distinct_points( Z, Y ) }.
% 25.07/25.44  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ), 
% 25.07/25.44    distinct_points( Z, intersection_point( X, Y ) ) }.
% 25.07/25.44  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ), 
% 25.07/25.44    distinct_points( Z, intersection_point( X, Y ) ) }.
% 25.07/25.44  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 25.07/25.44    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 25.07/25.44    apart_point_and_line( Y, T ) }.
% 25.07/25.44  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 25.07/25.44    apart_point_and_line( Z, Y ) }.
% 25.07/25.44  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 25.07/25.44    apart_point_and_line( X, Z ) }.
% 25.07/25.44  { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 25.07/25.44  { convergent_lines( skol1, skol2 ) }.
% 25.07/25.44  { convergent_lines( skol3, skol2 ) }.
% 25.07/25.44  { convergent_lines( skol1, skol3 ) }.
% 25.07/25.44  { ! apart_point_and_line( intersection_point( skol1, skol2 ), skol3 ) }.
% 25.07/25.44  { apart_point_and_line( intersection_point( skol3, skol2 ), skol1 ) }.
% 25.07/25.44  
% 25.07/25.44  percentage equality = 0.000000, percentage horn = 0.684211
% 25.07/25.44  This a non-horn, non-equality problem
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  Options Used:
% 25.07/25.44  
% 25.07/25.44  useres =            1
% 25.07/25.44  useparamod =        0
% 25.07/25.44  useeqrefl =         0
% 25.07/25.44  useeqfact =         0
% 25.07/25.44  usefactor =         1
% 25.07/25.44  usesimpsplitting =  0
% 25.07/25.44  usesimpdemod =      0
% 25.07/25.44  usesimpres =        3
% 25.07/25.44  
% 25.07/25.44  resimpinuse      =  1000
% 25.07/25.44  resimpclauses =     20000
% 25.07/25.44  substype =          standard
% 25.07/25.44  backwardsubs =      1
% 25.07/25.44  selectoldest =      5
% 25.07/25.44  
% 25.07/25.44  litorderings [0] =  split
% 25.07/25.44  litorderings [1] =  liftord
% 25.07/25.44  
% 25.07/25.44  termordering =      none
% 25.07/25.44  
% 25.07/25.44  litapriori =        1
% 25.07/25.44  termapriori =       0
% 25.07/25.44  litaposteriori =    0
% 25.07/25.44  termaposteriori =   0
% 25.07/25.44  demodaposteriori =  0
% 25.07/25.44  ordereqreflfact =   0
% 25.07/25.44  
% 25.07/25.44  litselect =         none
% 25.07/25.44  
% 25.07/25.44  maxweight =         15
% 25.07/25.44  maxdepth =          30000
% 25.07/25.44  maxlength =         115
% 25.07/25.44  maxnrvars =         195
% 25.07/25.44  excuselevel =       1
% 25.07/25.44  increasemaxweight = 1
% 25.07/25.44  
% 25.07/25.44  maxselected =       10000000
% 25.07/25.44  maxnrclauses =      10000000
% 25.07/25.44  
% 25.07/25.44  showgenerated =    0
% 25.07/25.44  showkept =         0
% 25.07/25.44  showselected =     0
% 25.07/25.44  showdeleted =      0
% 25.07/25.44  showresimp =       1
% 25.07/25.44  showstatus =       2000
% 25.07/25.44  
% 25.07/25.44  prologoutput =     0
% 25.07/25.44  nrgoals =          5000000
% 25.07/25.44  totalproof =       1
% 25.07/25.44  
% 25.07/25.44  Symbols occurring in the translation:
% 25.07/25.44  
% 25.07/25.44  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 25.07/25.44  .  [1, 2]      (w:1, o:19, a:1, s:1, b:0), 
% 25.07/25.44  !  [4, 1]      (w:0, o:14, a:1, s:1, b:0), 
% 25.07/25.44  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 25.07/25.44  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 25.07/25.44  distinct_points  [36, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 25.07/25.44  distinct_lines  [37, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 25.07/25.44  convergent_lines  [38, 2]      (w:1, o:43, a:1, s:1, b:0), 
% 25.07/25.44  line_connecting  [41, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 25.07/25.44  apart_point_and_line  [42, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 25.07/25.44  intersection_point  [43, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 25.07/25.44  skol1  [46, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 25.07/25.44  skol2  [47, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 25.07/25.44  skol3  [48, 0]      (w:1, o:13, a:1, s:1, b:0).
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  Starting Search:
% 25.07/25.44  
% 25.07/25.44  *** allocated 15000 integers for clauses
% 25.07/25.44  *** allocated 22500 integers for clauses
% 25.07/25.44  *** allocated 33750 integers for clauses
% 25.07/25.44  *** allocated 15000 integers for termspace/termends
% 25.07/25.44  Resimplifying inuse:
% 25.07/25.44  Done
% 25.07/25.44  
% 25.07/25.44  Failed to find proof!
% 25.07/25.44  maxweight =   15
% 25.07/25.44  maxnrclauses = 10000000
% 25.07/25.44  Generated: 121376
% 25.07/25.44  Kept: 885
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  The strategy used was not complete!
% 25.07/25.44  
% 25.07/25.44  Increased maxweight to 16
% 25.07/25.44  
% 25.07/25.44  Starting Search:
% 25.07/25.44  
% 25.07/25.44  *** allocated 50625 integers for clauses
% 25.07/25.44  Resimplifying inuse:
% 25.07/25.44  Done
% 25.07/25.44  
% 25.07/25.44  *** allocated 22500 integers for termspace/termends
% 25.07/25.44  Resimplifying inuse:
% 25.07/25.44  Done
% 25.07/25.44  
% 25.07/25.44  Failed to find proof!
% 25.07/25.44  maxweight =   16
% 25.07/25.44  maxnrclauses = 10000000
% 25.07/25.44  Generated: 396154
% 25.07/25.44  Kept: 1241
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  The strategy used was not complete!
% 25.07/25.44  
% 25.07/25.44  Increased maxweight to 17
% 25.07/25.44  
% 25.07/25.44  Starting Search:
% 25.07/25.44  
% 25.07/25.44  Resimplifying inuse:
% 25.07/25.44  Done
% 25.07/25.44  
% 25.07/25.44  *** allocated 75937 integers for clauses
% 25.07/25.44  *** allocated 33750 integers for termspace/termends
% 25.07/25.44  Resimplifying inuse:
% 25.07/25.44  Done
% 25.07/25.44  
% 25.07/25.44  Failed to find proof!
% 25.07/25.44  maxweight =   17
% 25.07/25.44  maxnrclauses = 10000000
% 25.07/25.44  Generated: 535654
% 25.07/25.44  Kept: 1637
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  The strategy used was not complete!
% 25.07/25.44  
% 25.07/25.44  Increased maxweight to 18
% 25.07/25.44  
% 25.07/25.44  Starting Search:
% 25.07/25.44  
% 25.07/25.44  Resimplifying inuse:
% 25.07/25.44  Done
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  Intermediate Status:
% 25.07/25.44  Generated:    125731
% 25.07/25.44  Kept:         2050
% 25.07/25.44  Inuse:        821
% 25.07/25.44  Deleted:      2
% 25.07/25.44  Deletedinuse: 0
% 25.07/25.44  
% 25.07/25.44  Resimplifying inuse:
% 25.07/25.44  Done
% 25.07/25.44  
% 25.07/25.44  *** allocated 50625 integers for termspace/termends
% 25.07/25.44  *** allocated 113905 integers for clauses
% 25.07/25.44  
% 25.07/25.44  Bliksems!, er is een bewijs:
% 25.07/25.44  % SZS status Theorem
% 25.07/25.44  % SZS output start Refutation
% 25.07/25.44  
% 25.07/25.44  (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 25.07/25.44  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 25.07/25.44  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 25.07/25.44  (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 25.07/25.44     ), ! distinct_points( X, Y ) }.
% 25.07/25.44  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 25.07/25.44    , ! distinct_lines( X, Y ) }.
% 25.07/25.44  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 25.07/25.44    Z ), ! convergent_lines( X, Y ) }.
% 25.07/25.44  (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 25.07/25.44    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, X ) }.
% 25.07/25.44  (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 25.07/25.44    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, Y ) }.
% 25.07/25.44  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 25.07/25.44    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 25.07/25.44    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 25.07/25.44  (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 25.07/25.44    ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.44  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 25.07/25.44    X, Z ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.44  (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), distinct_lines( X
% 25.07/25.44    , Y ) }.
% 25.07/25.44  (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 25.07/25.44  (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 ) }.
% 25.07/25.44  (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 ) }.
% 25.07/25.44  (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( intersection_point( 
% 25.07/25.44    skol1, skol2 ), skol3 ) }.
% 25.07/25.44  (18) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( intersection_point( 
% 25.07/25.44    skol3, skol2 ), skol1 ) }.
% 25.07/25.44  (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 25.07/25.44    distinct_points( X, Y ) }.
% 25.07/25.44  (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 25.07/25.44    ( X, Y ) }.
% 25.07/25.44  (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y ), 
% 25.07/25.44    distinct_lines( Y, X ) }.
% 25.07/25.44  (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 25.07/25.44    convergent_lines( X, Y ) }.
% 25.07/25.44  (44) {G2,W3,D2,L1,V0,M1} R(40,15) { convergent_lines( skol2, skol3 ) }.
% 25.07/25.44  (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, skol1 ) }.
% 25.07/25.44  (106) {G1,W19,D3,L5,V2,M3} R(10,17) { ! distinct_points( intersection_point
% 25.07/25.44    ( skol1, skol2 ), X ), ! distinct_lines( Y, skol3 ), apart_point_and_line
% 25.07/25.44    ( X, skol3 ), apart_point_and_line( intersection_point( skol1, skol2 ), Y
% 25.07/25.44     ), apart_point_and_line( X, Y ) }.
% 25.07/25.44  (109) {G1,W19,D3,L5,V2,M3} R(10,17) { ! distinct_points( intersection_point
% 25.07/25.44    ( skol1, skol2 ), X ), ! distinct_lines( skol3, Y ), apart_point_and_line
% 25.07/25.44    ( X, skol3 ), apart_point_and_line( X, Y ), apart_point_and_line( 
% 25.07/25.44    intersection_point( skol1, skol2 ), Y ) }.
% 25.07/25.44  (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), ! 
% 25.07/25.44    convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z )
% 25.07/25.44     ), ! apart_point_and_line( X, Z ) }.
% 25.07/25.44  (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), ! 
% 25.07/25.44    convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T )
% 25.07/25.44     ), ! apart_point_and_line( X, Z ) }.
% 25.07/25.44  (132) {G1,W8,D3,L2,V1,M1} R(11,18) { distinct_points( intersection_point( 
% 25.07/25.44    skol3, skol2 ), X ), apart_point_and_line( X, skol1 ) }.
% 25.07/25.44  (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.44  (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.44  (152) {G1,W8,D3,L2,V1,M1} R(12,18) { distinct_lines( skol1, X ), 
% 25.07/25.44    apart_point_and_line( intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.44  (158) {G3,W3,D2,L1,V0,M1} R(152,135);r(15) { distinct_lines( skol1, skol3 )
% 25.07/25.44     }.
% 25.07/25.44  (217) {G2,W13,D3,L3,V2,M2} R(132,9) { ! convergent_lines( Y, skol1 ), 
% 25.07/25.44    distinct_points( X, intersection_point( Y, skol1 ) ), distinct_points( 
% 25.07/25.44    intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.44  (1457) {G4,W14,D3,L4,V1,M1} R(106,135);r(158) { ! distinct_points( 
% 25.07/25.44    intersection_point( skol1, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.44    , ! convergent_lines( skol1, skol2 ), apart_point_and_line( X, skol3 )
% 25.07/25.44     }.
% 25.07/25.44  (1506) {G3,W14,D3,L4,V1,M1} R(109,136);r(14) { ! distinct_points( 
% 25.07/25.44    intersection_point( skol1, skol2 ), X ), ! distinct_lines( skol3, skol2 )
% 25.07/25.44    , apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol3 ) }.
% 25.07/25.44  (1646) {G4,W18,D3,L4,V1,M1} R(1506,135) { ! distinct_points( 
% 25.07/25.44    intersection_point( skol1, skol2 ), intersection_point( skol3, X ) ), ! 
% 25.07/25.44    distinct_lines( skol3, skol2 ), ! convergent_lines( skol3, X ), 
% 25.07/25.44    apart_point_and_line( intersection_point( skol3, X ), skol2 ) }.
% 25.07/25.44  (1706) {G5,W11,D3,L3,V1,M1} S(1457);r(14) { ! distinct_points( 
% 25.07/25.44    intersection_point( skol1, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.44    , apart_point_and_line( X, skol3 ) }.
% 25.07/25.44  (1732) {G6,W15,D3,L3,V1,M1} R(1706,135) { ! distinct_points( 
% 25.07/25.44    intersection_point( skol1, skol2 ), intersection_point( skol3, X ) ), ! 
% 25.07/25.44    convergent_lines( skol3, X ), apart_point_and_line( intersection_point( 
% 25.07/25.44    skol3, X ), skol1 ) }.
% 25.07/25.44  (1766) {G7,W7,D3,L1,V0,M1} R(1732,136);f;r(45) { ! distinct_points( 
% 25.07/25.44    intersection_point( skol1, skol2 ), intersection_point( skol3, skol1 ) )
% 25.07/25.44     }.
% 25.07/25.44  (1832) {G8,W7,D3,L1,V0,M1} R(1766,217);r(45) { distinct_points( 
% 25.07/25.44    intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 ) )
% 25.07/25.44     }.
% 25.07/25.44  (1895) {G9,W7,D3,L1,V0,M1} R(1832,21) { distinct_points( intersection_point
% 25.07/25.44    ( skol1, skol2 ), intersection_point( skol3, skol2 ) ) }.
% 25.07/25.44  (2268) {G10,W6,D2,L2,V0,M1} R(1646,136);f;r(1895) { ! convergent_lines( 
% 25.07/25.44    skol3, skol2 ), ! distinct_lines( skol3, skol2 ) }.
% 25.07/25.44  (2269) {G11,W3,D2,L1,V0,M1} S(2268);r(15) { ! distinct_lines( skol3, skol2
% 25.07/25.44     ) }.
% 25.07/25.44  (2781) {G12,W0,D0,L0,V0,M0} R(2269,29);r(44) {  }.
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  % SZS output end Refutation
% 25.07/25.44  found a proof!
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  Unprocessed initial clauses:
% 25.07/25.44  
% 25.07/25.44  (2783) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 25.07/25.44  (2784) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 25.07/25.44  (2785) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 25.07/25.44  (2786) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 25.07/25.44    , Z ), distinct_points( Y, Z ) }.
% 25.07/25.44  (2787) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 25.07/25.44    Z ), distinct_lines( Y, Z ) }.
% 25.07/25.44  (2788) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 25.07/25.44    ( X, Z ), convergent_lines( Y, Z ) }.
% 25.07/25.44  (2789) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 25.07/25.44     ) }.
% 25.07/25.44  (2790) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 25.07/25.44     ) }.
% 25.07/25.44  (2791) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 25.07/25.44    Y ) ) }.
% 25.07/25.44  (2792) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 25.07/25.44    Y ) ) }.
% 25.07/25.44  (2793) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 25.07/25.44    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 25.07/25.44    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 25.07/25.44  (2794) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 25.07/25.44    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 25.07/25.44  (2795) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 25.07/25.44    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 25.07/25.44  (2796) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), distinct_lines( X
% 25.07/25.44    , Y ) }.
% 25.07/25.44  (2797) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 25.07/25.44  (2798) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol2 ) }.
% 25.07/25.44  (2799) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol3 ) }.
% 25.07/25.44  (2800) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( intersection_point( 
% 25.07/25.44    skol1, skol2 ), skol3 ) }.
% 25.07/25.44  (2801) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( intersection_point( 
% 25.07/25.44    skol3, skol2 ), skol1 ) }.
% 25.07/25.44  
% 25.07/25.44  
% 25.07/25.44  Total Proof:
% 25.07/25.44  
% 25.07/25.44  subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 25.07/25.44  parent0: (2783) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 0
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 25.07/25.44  parent0: (2784) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 0
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 25.07/25.44  parent0: (2785) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 0
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 25.07/25.44    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 25.07/25.44  parent0: (2786) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), 
% 25.07/25.44    distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44     Y := Y
% 25.07/25.44     Z := Z
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 2
% 25.07/25.44     1 ==> 0
% 25.07/25.44     2 ==> 1
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 25.07/25.44    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 25.07/25.44  parent0: (2787) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 25.07/25.44    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44     Y := Y
% 25.07/25.44     Z := Z
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 2
% 25.07/25.44     1 ==> 0
% 25.07/25.44     2 ==> 1
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 25.07/25.44    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 25.07/25.44  parent0: (2788) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 25.07/25.44    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44     Y := Y
% 25.07/25.44     Z := Z
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 2
% 25.07/25.44     1 ==> 0
% 25.07/25.44     2 ==> 1
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 25.07/25.44    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 25.07/25.44    ( Z, X ) }.
% 25.07/25.44  parent0: (2791) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 25.07/25.44    Y ) ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44     Y := Y
% 25.07/25.44     Z := Z
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 0
% 25.07/25.44     1 ==> 2
% 25.07/25.44     2 ==> 1
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 25.07/25.44    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 25.07/25.44    ( Z, Y ) }.
% 25.07/25.44  parent0: (2792) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.44    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 25.07/25.44    Y ) ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44     Y := Y
% 25.07/25.44     Z := Z
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 0
% 25.07/25.44     1 ==> 2
% 25.07/25.44     2 ==> 1
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 25.07/25.44    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 25.07/25.44    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 25.07/25.44    apart_point_and_line( X, Z ) }.
% 25.07/25.44  parent0: (2793) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 25.07/25.44    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 25.07/25.44    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 25.07/25.44    apart_point_and_line( Y, T ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44     Y := Y
% 25.07/25.44     Z := Z
% 25.07/25.44     T := T
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 0
% 25.07/25.44     1 ==> 1
% 25.07/25.44     2 ==> 5
% 25.07/25.44     3 ==> 2
% 25.07/25.44     4 ==> 3
% 25.07/25.44     5 ==> 4
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 25.07/25.44    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.44  parent0: (2794) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 25.07/25.44    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 25.07/25.44  substitution0:
% 25.07/25.44     X := X
% 25.07/25.44     Y := Y
% 25.07/25.44     Z := Z
% 25.07/25.44  end
% 25.07/25.44  permutation0:
% 25.07/25.44     0 ==> 2
% 25.07/25.44     1 ==> 0
% 25.07/25.44     2 ==> 1
% 25.07/25.44  end
% 25.07/25.44  
% 25.07/25.44  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 25.07/25.44    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.44  parent0: (2795) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 25.07/25.45    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45     Z := Z
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 2
% 25.07/25.45     1 ==> 0
% 25.07/25.45     2 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_lines( X, Y ) }.
% 25.07/25.45  parent0: (2796) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_lines( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  parent0: (2797) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  parent0: (2798) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 )
% 25.07/25.45     }.
% 25.07/25.45  parent0: (2799) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( 
% 25.07/25.45    intersection_point( skol1, skol2 ), skol3 ) }.
% 25.07/25.45  parent0: (2800) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( 
% 25.07/25.45    intersection_point( skol1, skol2 ), skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (18) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 25.07/25.45    intersection_point( skol3, skol2 ), skol1 ) }.
% 25.07/25.45  parent0: (2801) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( 
% 25.07/25.45    intersection_point( skol3, skol2 ), skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2895) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 25.07/25.45    distinct_points( X, Y ) }.
% 25.07/25.45  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 25.07/25.45  parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 25.07/25.45    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45     Z := X
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 25.07/25.45    distinct_points( X, Y ) }.
% 25.07/25.45  parent0: (2895) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 25.07/25.45    distinct_points( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := Y
% 25.07/25.45     Y := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 1
% 25.07/25.45     1 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2897) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 25.07/25.45    distinct_lines( X, Y ) }.
% 25.07/25.45  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 25.07/25.45  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 25.07/25.45    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45     Z := X
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 25.07/25.45    distinct_lines( X, Y ) }.
% 25.07/25.45  parent0: (2897) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 25.07/25.45    distinct_lines( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := Y
% 25.07/25.45     Y := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 1
% 25.07/25.45     1 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2899) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 25.07/25.45    convergent_lines( X, Y ) }.
% 25.07/25.45  parent0[0]: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 25.07/25.45    distinct_lines( X, Y ) }.
% 25.07/25.45  parent1[1]: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_lines( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := Y
% 25.07/25.45     Y := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y )
% 25.07/25.45    , distinct_lines( Y, X ) }.
% 25.07/25.45  parent0: (2899) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 25.07/25.45    convergent_lines( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 1
% 25.07/25.45     1 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2900) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 25.07/25.45    convergent_lines( X, Y ) }.
% 25.07/25.45  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 25.07/25.45  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 25.07/25.45    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45     Z := X
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 25.07/25.45    convergent_lines( X, Y ) }.
% 25.07/25.45  parent0: (2900) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 25.07/25.45    convergent_lines( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := Y
% 25.07/25.45     Y := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 1
% 25.07/25.45     1 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2902) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol3 )
% 25.07/25.45     }.
% 25.07/25.45  parent0[0]: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 25.07/25.45    convergent_lines( X, Y ) }.
% 25.07/25.45  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol2
% 25.07/25.45     Y := skol3
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (44) {G2,W3,D2,L1,V0,M1} R(40,15) { convergent_lines( skol2, 
% 25.07/25.45    skol3 ) }.
% 25.07/25.45  parent0: (2902) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2903) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol1 )
% 25.07/25.45     }.
% 25.07/25.45  parent0[0]: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 25.07/25.45    convergent_lines( X, Y ) }.
% 25.07/25.45  parent1[0]: (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol3
% 25.07/25.45     Y := skol1
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, 
% 25.07/25.45    skol1 ) }.
% 25.07/25.45  parent0: (2903) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2904) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( Y, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, Y ), apart_point_and_line( X, skol3 ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol1, skol2 ), Y ) }.
% 25.07/25.45  parent0[0]: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( 
% 25.07/25.45    intersection_point( skol1, skol2 ), skol3 ) }.
% 25.07/25.45  parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 25.07/25.45    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 25.07/25.45    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 25.07/25.45    apart_point_and_line( X, Z ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := intersection_point( skol1, skol2 )
% 25.07/25.45     Y := X
% 25.07/25.45     Z := Y
% 25.07/25.45     T := skol3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (106) {G1,W19,D3,L5,V2,M3} R(10,17) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( Y, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( 
% 25.07/25.45    intersection_point( skol1, skol2 ), Y ), apart_point_and_line( X, Y ) }.
% 25.07/25.45  parent0: (2904) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( Y, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, Y ), apart_point_and_line( X, skol3 ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol1, skol2 ), Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45     2 ==> 4
% 25.07/25.45     3 ==> 2
% 25.07/25.45     4 ==> 3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2916) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( skol3, Y ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol1, skol2 ), Y ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( X, Y ) }.
% 25.07/25.45  parent0[0]: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( 
% 25.07/25.45    intersection_point( skol1, skol2 ), skol3 ) }.
% 25.07/25.45  parent1[5]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 25.07/25.45    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 25.07/25.45    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 25.07/25.45    apart_point_and_line( X, Z ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := intersection_point( skol1, skol2 )
% 25.07/25.45     Y := X
% 25.07/25.45     Z := skol3
% 25.07/25.45     T := Y
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (109) {G1,W19,D3,L5,V2,M3} R(10,17) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( skol3, Y ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( X, Y ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol1, skol2 ), Y ) }.
% 25.07/25.45  parent0: (2916) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( skol3, Y ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol1, skol2 ), Y ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45     2 ==> 4
% 25.07/25.45     3 ==> 2
% 25.07/25.45     4 ==> 3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2922) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 25.07/25.45    , ! apart_point_and_line( T, Y ) }.
% 25.07/25.45  parent0[2]: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 25.07/25.45    ( Z, Y ) }.
% 25.07/25.45  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 25.07/25.45    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45     Z := Z
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := T
% 25.07/25.45     Y := Y
% 25.07/25.45     Z := Z
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), 
% 25.07/25.45    ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z
% 25.07/25.45     ) ), ! apart_point_and_line( X, Z ) }.
% 25.07/25.45  parent0: (2922) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 25.07/25.45    , ! apart_point_and_line( T, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := T
% 25.07/25.45     Y := Z
% 25.07/25.45     Z := Y
% 25.07/25.45     T := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 1
% 25.07/25.45     1 ==> 2
% 25.07/25.45     2 ==> 0
% 25.07/25.45     3 ==> 3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2924) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 25.07/25.45    , ! apart_point_and_line( T, X ) }.
% 25.07/25.45  parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 25.07/25.45    ( Z, X ) }.
% 25.07/25.45  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 25.07/25.45    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45     Z := Z
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := T
% 25.07/25.45     Y := X
% 25.07/25.45     Z := Z
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), 
% 25.07/25.45    ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T
% 25.07/25.45     ) ), ! apart_point_and_line( X, Z ) }.
% 25.07/25.45  parent0: (2924) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 25.07/25.45    , ! apart_point_and_line( T, X ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := Z
% 25.07/25.45     Y := T
% 25.07/25.45     Z := Y
% 25.07/25.45     T := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 1
% 25.07/25.45     1 ==> 2
% 25.07/25.45     2 ==> 0
% 25.07/25.45     3 ==> 3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2926) {G1,W8,D3,L2,V1,M2}  { distinct_points( 
% 25.07/25.45    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.45     }.
% 25.07/25.45  parent0[2]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 25.07/25.45    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.45  parent1[0]: (18) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 25.07/25.45    intersection_point( skol3, skol2 ), skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := intersection_point( skol3, skol2 )
% 25.07/25.45     Y := skol1
% 25.07/25.45     Z := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (132) {G1,W8,D3,L2,V1,M1} R(11,18) { distinct_points( 
% 25.07/25.45    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.45     }.
% 25.07/25.45  parent0: (2926) {G1,W8,D3,L2,V1,M2}  { distinct_points( intersection_point
% 25.07/25.45    ( skol3, skol2 ), X ), apart_point_and_line( X, skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  factor: (2927) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point
% 25.07/25.45    ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 25.07/25.45    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  parent0[0, 2]: (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y )
% 25.07/25.45    , ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, 
% 25.07/25.45    T ) ), ! apart_point_and_line( X, Z ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := intersection_point( X, Y )
% 25.07/25.45     Y := intersection_point( X, Y )
% 25.07/25.45     Z := X
% 25.07/25.45     T := Y
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2928) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.45    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 25.07/25.45  parent1[0]: (2927) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 25.07/25.45    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 25.07/25.45    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 25.07/25.45    Y ), X ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := intersection_point( X, Y )
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X
% 25.07/25.45    , Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  parent0: (2928) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.45    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  factor: (2929) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point
% 25.07/25.45    ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 25.07/25.45    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.45  parent0[0, 2]: (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y )
% 25.07/25.45    , ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, 
% 25.07/25.45    Z ) ), ! apart_point_and_line( X, Z ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := intersection_point( X, Y )
% 25.07/25.45     Y := intersection_point( X, Y )
% 25.07/25.45     Z := Y
% 25.07/25.45     T := X
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2930) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.45    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.45  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 25.07/25.45  parent1[0]: (2929) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 25.07/25.45    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 25.07/25.45    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 25.07/25.45    Y ), Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := intersection_point( X, Y )
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X
% 25.07/25.45    , Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.45  parent0: (2930) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 25.07/25.45    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := Y
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2931) {G1,W8,D3,L2,V1,M2}  { distinct_lines( skol1, X ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.45  parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 25.07/25.45    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 25.07/25.45  parent1[0]: (18) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 25.07/25.45    intersection_point( skol3, skol2 ), skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := intersection_point( skol3, skol2 )
% 25.07/25.45     Y := skol1
% 25.07/25.45     Z := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (152) {G1,W8,D3,L2,V1,M1} R(12,18) { distinct_lines( skol1, X
% 25.07/25.45     ), apart_point_and_line( intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.45  parent0: (2931) {G1,W8,D3,L2,V1,M2}  { distinct_lines( skol1, X ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2932) {G2,W6,D2,L2,V0,M2}  { ! convergent_lines( skol3, skol2
% 25.07/25.45     ), distinct_lines( skol1, skol3 ) }.
% 25.07/25.45  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 25.07/25.45    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  parent1[1]: (152) {G1,W8,D3,L2,V1,M1} R(12,18) { distinct_lines( skol1, X )
% 25.07/25.45    , apart_point_and_line( intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol3
% 25.07/25.45     Y := skol2
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := skol3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2933) {G1,W3,D2,L1,V0,M1}  { distinct_lines( skol1, skol3 )
% 25.07/25.45     }.
% 25.07/25.45  parent0[0]: (2932) {G2,W6,D2,L2,V0,M2}  { ! convergent_lines( skol3, skol2
% 25.07/25.45     ), distinct_lines( skol1, skol3 ) }.
% 25.07/25.45  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (158) {G3,W3,D2,L1,V0,M1} R(152,135);r(15) { distinct_lines( 
% 25.07/25.45    skol1, skol3 ) }.
% 25.07/25.45  parent0: (2933) {G1,W3,D2,L1,V0,M1}  { distinct_lines( skol1, skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2934) {G1,W13,D3,L3,V2,M3}  { ! convergent_lines( X, skol1 ), 
% 25.07/25.45    distinct_points( Y, intersection_point( X, skol1 ) ), distinct_points( 
% 25.07/25.45    intersection_point( skol3, skol2 ), Y ) }.
% 25.07/25.45  parent0[2]: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 25.07/25.45    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 25.07/25.45    ( Z, Y ) }.
% 25.07/25.45  parent1[1]: (132) {G1,W8,D3,L2,V1,M1} R(11,18) { distinct_points( 
% 25.07/25.45    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45     Y := skol1
% 25.07/25.45     Z := Y
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := Y
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (217) {G2,W13,D3,L3,V2,M2} R(132,9) { ! convergent_lines( Y, 
% 25.07/25.45    skol1 ), distinct_points( X, intersection_point( Y, skol1 ) ), 
% 25.07/25.45    distinct_points( intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.45  parent0: (2934) {G1,W13,D3,L3,V2,M3}  { ! convergent_lines( X, skol1 ), 
% 25.07/25.45    distinct_points( Y, intersection_point( X, skol1 ) ), distinct_points( 
% 25.07/25.45    intersection_point( skol3, skol2 ), Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := Y
% 25.07/25.45     Y := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45     2 ==> 2
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2936) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol1, skol2
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), X ), ! 
% 25.07/25.45    distinct_lines( skol1, skol3 ), apart_point_and_line( X, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, skol1 ) }.
% 25.07/25.45  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 25.07/25.45    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  parent1[3]: (106) {G1,W19,D3,L5,V2,M3} R(10,17) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( Y, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( 
% 25.07/25.45    intersection_point( skol1, skol2 ), Y ), apart_point_and_line( X, Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol1
% 25.07/25.45     Y := skol2
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := skol1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2938) {G3,W14,D3,L4,V1,M4}  { ! convergent_lines( skol1, skol2
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), X ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( X, skol1 ) }.
% 25.07/25.45  parent0[2]: (2936) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol1, skol2
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), X ), ! 
% 25.07/25.45    distinct_lines( skol1, skol3 ), apart_point_and_line( X, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, skol1 ) }.
% 25.07/25.45  parent1[0]: (158) {G3,W3,D2,L1,V0,M1} R(152,135);r(15) { distinct_lines( 
% 25.07/25.45    skol1, skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1457) {G4,W14,D3,L4,V1,M1} R(106,135);r(158) { ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), X ), 
% 25.07/25.45    apart_point_and_line( X, skol1 ), ! convergent_lines( skol1, skol2 ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  parent0: (2938) {G3,W14,D3,L4,V1,M4}  { ! convergent_lines( skol1, skol2 )
% 25.07/25.45    , ! distinct_points( intersection_point( skol1, skol2 ), X ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( X, skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 2
% 25.07/25.45     1 ==> 0
% 25.07/25.45     2 ==> 3
% 25.07/25.45     3 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2941) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol1, skol2
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), X ), ! 
% 25.07/25.45    distinct_lines( skol3, skol2 ), apart_point_and_line( X, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, skol2 ) }.
% 25.07/25.45  parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, 
% 25.07/25.45    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.45  parent1[4]: (109) {G1,W19,D3,L5,V2,M3} R(10,17) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( skol3, Y ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ), apart_point_and_line( X, Y ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol1, skol2 ), Y ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol1
% 25.07/25.45     Y := skol2
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := X
% 25.07/25.45     Y := skol2
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2942) {G1,W14,D3,L4,V1,M4}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( skol3, skol2 )
% 25.07/25.45    , apart_point_and_line( X, skol3 ), apart_point_and_line( X, skol2 ) }.
% 25.07/25.45  parent0[0]: (2941) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol1, skol2
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), X ), ! 
% 25.07/25.45    distinct_lines( skol3, skol2 ), apart_point_and_line( X, skol3 ), 
% 25.07/25.45    apart_point_and_line( X, skol2 ) }.
% 25.07/25.45  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1506) {G3,W14,D3,L4,V1,M1} R(109,136);r(14) { ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), X ), ! 
% 25.07/25.45    distinct_lines( skol3, skol2 ), apart_point_and_line( X, skol2 ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  parent0: (2942) {G1,W14,D3,L4,V1,M4}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), ! distinct_lines( skol3, skol2 )
% 25.07/25.45    , apart_point_and_line( X, skol3 ), apart_point_and_line( X, skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45     2 ==> 3
% 25.07/25.45     3 ==> 2
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2944) {G3,W18,D3,L4,V1,M4}  { ! convergent_lines( skol3, X ), 
% 25.07/25.45    ! distinct_points( intersection_point( skol1, skol2 ), intersection_point
% 25.07/25.45    ( skol3, X ) ), ! distinct_lines( skol3, skol2 ), apart_point_and_line( 
% 25.07/25.45    intersection_point( skol3, X ), skol2 ) }.
% 25.07/25.45  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 25.07/25.45    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  parent1[3]: (1506) {G3,W14,D3,L4,V1,M1} R(109,136);r(14) { ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), X ), ! 
% 25.07/25.45    distinct_lines( skol3, skol2 ), apart_point_and_line( X, skol2 ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol3
% 25.07/25.45     Y := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := intersection_point( skol3, X )
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1646) {G4,W18,D3,L4,V1,M1} R(1506,135) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, X ) ), ! 
% 25.07/25.45    distinct_lines( skol3, skol2 ), ! convergent_lines( skol3, X ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol3, X ), skol2 ) }.
% 25.07/25.45  parent0: (2944) {G3,W18,D3,L4,V1,M4}  { ! convergent_lines( skol3, X ), ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), intersection_point( 
% 25.07/25.45    skol3, X ) ), ! distinct_lines( skol3, skol2 ), apart_point_and_line( 
% 25.07/25.45    intersection_point( skol3, X ), skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 2
% 25.07/25.45     1 ==> 0
% 25.07/25.45     2 ==> 1
% 25.07/25.45     3 ==> 3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2945) {G1,W11,D3,L3,V1,M3}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.45    , apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  parent0[2]: (1457) {G4,W14,D3,L4,V1,M1} R(106,135);r(158) { ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), X ), 
% 25.07/25.45    apart_point_and_line( X, skol1 ), ! convergent_lines( skol1, skol2 ), 
% 25.07/25.45    apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1706) {G5,W11,D3,L3,V1,M1} S(1457);r(14) { ! distinct_points
% 25.07/25.45    ( intersection_point( skol1, skol2 ), X ), apart_point_and_line( X, skol1
% 25.07/25.45     ), apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  parent0: (2945) {G1,W11,D3,L3,V1,M3}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.45    , apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45     2 ==> 2
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2947) {G3,W15,D3,L3,V1,M3}  { ! convergent_lines( skol3, X ), 
% 25.07/25.45    ! distinct_points( intersection_point( skol1, skol2 ), intersection_point
% 25.07/25.45    ( skol3, X ) ), apart_point_and_line( intersection_point( skol3, X ), 
% 25.07/25.45    skol1 ) }.
% 25.07/25.45  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 25.07/25.45    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 25.07/25.45  parent1[2]: (1706) {G5,W11,D3,L3,V1,M1} S(1457);r(14) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), X ), apart_point_and_line( X, skol1 )
% 25.07/25.45    , apart_point_and_line( X, skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol3
% 25.07/25.45     Y := X
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := intersection_point( skol3, X )
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1732) {G6,W15,D3,L3,V1,M1} R(1706,135) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, X ) ), ! 
% 25.07/25.45    convergent_lines( skol3, X ), apart_point_and_line( intersection_point( 
% 25.07/25.45    skol3, X ), skol1 ) }.
% 25.07/25.45  parent0: (2947) {G3,W15,D3,L3,V1,M3}  { ! convergent_lines( skol3, X ), ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), intersection_point( 
% 25.07/25.45    skol3, X ) ), apart_point_and_line( intersection_point( skol3, X ), skol1
% 25.07/25.45     ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := X
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 1
% 25.07/25.45     1 ==> 0
% 25.07/25.45     2 ==> 2
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2948) {G3,W13,D3,L3,V0,M3}  { ! convergent_lines( skol3, skol1
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), 
% 25.07/25.45    intersection_point( skol3, skol1 ) ), ! convergent_lines( skol3, skol1 )
% 25.07/25.45     }.
% 25.07/25.45  parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, 
% 25.07/25.45    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.45  parent1[2]: (1732) {G6,W15,D3,L3,V1,M1} R(1706,135) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, X ) ), ! 
% 25.07/25.45    convergent_lines( skol3, X ), apart_point_and_line( intersection_point( 
% 25.07/25.45    skol3, X ), skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol3
% 25.07/25.45     Y := skol1
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := skol1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  factor: (2949) {G3,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1 ), 
% 25.07/25.45    ! distinct_points( intersection_point( skol1, skol2 ), intersection_point
% 25.07/25.45    ( skol3, skol1 ) ) }.
% 25.07/25.45  parent0[0, 2]: (2948) {G3,W13,D3,L3,V0,M3}  { ! convergent_lines( skol3, 
% 25.07/25.45    skol1 ), ! distinct_points( intersection_point( skol1, skol2 ), 
% 25.07/25.45    intersection_point( skol3, skol1 ) ), ! convergent_lines( skol3, skol1 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2951) {G3,W7,D3,L1,V0,M1}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, skol1 ) )
% 25.07/25.45     }.
% 25.07/25.45  parent0[0]: (2949) {G3,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), 
% 25.07/25.45    intersection_point( skol3, skol1 ) ) }.
% 25.07/25.45  parent1[0]: (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, 
% 25.07/25.45    skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1766) {G7,W7,D3,L1,V0,M1} R(1732,136);f;r(45) { ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), intersection_point( 
% 25.07/25.45    skol3, skol1 ) ) }.
% 25.07/25.45  parent0: (2951) {G3,W7,D3,L1,V0,M1}  { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, skol1 ) )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2952) {G3,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1
% 25.07/25.45     ), distinct_points( intersection_point( skol3, skol2 ), 
% 25.07/25.45    intersection_point( skol1, skol2 ) ) }.
% 25.07/25.45  parent0[0]: (1766) {G7,W7,D3,L1,V0,M1} R(1732,136);f;r(45) { ! 
% 25.07/25.45    distinct_points( intersection_point( skol1, skol2 ), intersection_point( 
% 25.07/25.45    skol3, skol1 ) ) }.
% 25.07/25.45  parent1[1]: (217) {G2,W13,D3,L3,V2,M2} R(132,9) { ! convergent_lines( Y, 
% 25.07/25.45    skol1 ), distinct_points( X, intersection_point( Y, skol1 ) ), 
% 25.07/25.45    distinct_points( intersection_point( skol3, skol2 ), X ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := intersection_point( skol1, skol2 )
% 25.07/25.45     Y := skol3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2953) {G3,W7,D3,L1,V0,M1}  { distinct_points( 
% 25.07/25.45    intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 ) )
% 25.07/25.45     }.
% 25.07/25.45  parent0[0]: (2952) {G3,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1
% 25.07/25.45     ), distinct_points( intersection_point( skol3, skol2 ), 
% 25.07/25.45    intersection_point( skol1, skol2 ) ) }.
% 25.07/25.45  parent1[0]: (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, 
% 25.07/25.45    skol1 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1832) {G8,W7,D3,L1,V0,M1} R(1766,217);r(45) { distinct_points
% 25.07/25.45    ( intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 )
% 25.07/25.45     ) }.
% 25.07/25.45  parent0: (2953) {G3,W7,D3,L1,V0,M1}  { distinct_points( intersection_point
% 25.07/25.45    ( skol3, skol2 ), intersection_point( skol1, skol2 ) ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2954) {G2,W7,D3,L1,V0,M1}  { distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, skol2 ) )
% 25.07/25.45     }.
% 25.07/25.45  parent0[0]: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 25.07/25.45    distinct_points( X, Y ) }.
% 25.07/25.45  parent1[0]: (1832) {G8,W7,D3,L1,V0,M1} R(1766,217);r(45) { distinct_points
% 25.07/25.45    ( intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 )
% 25.07/25.45     ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := intersection_point( skol1, skol2 )
% 25.07/25.45     Y := intersection_point( skol3, skol2 )
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (1895) {G9,W7,D3,L1,V0,M1} R(1832,21) { distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, skol2 ) )
% 25.07/25.45     }.
% 25.07/25.45  parent0: (2954) {G2,W7,D3,L1,V0,M1}  { distinct_points( intersection_point
% 25.07/25.45    ( skol1, skol2 ), intersection_point( skol3, skol2 ) ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2955) {G3,W16,D3,L4,V0,M4}  { ! convergent_lines( skol3, skol2
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), 
% 25.07/25.45    intersection_point( skol3, skol2 ) ), ! distinct_lines( skol3, skol2 ), !
% 25.07/25.45     convergent_lines( skol3, skol2 ) }.
% 25.07/25.45  parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, 
% 25.07/25.45    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 25.07/25.45  parent1[3]: (1646) {G4,W18,D3,L4,V1,M1} R(1506,135) { ! distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, X ) ), ! 
% 25.07/25.45    distinct_lines( skol3, skol2 ), ! convergent_lines( skol3, X ), 
% 25.07/25.45    apart_point_and_line( intersection_point( skol3, X ), skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45     X := skol3
% 25.07/25.45     Y := skol2
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := skol2
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2957) {G4,W9,D2,L3,V0,M3}  { ! convergent_lines( skol3, skol2
% 25.07/25.45     ), ! distinct_lines( skol3, skol2 ), ! convergent_lines( skol3, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  parent0[1]: (2955) {G3,W16,D3,L4,V0,M4}  { ! convergent_lines( skol3, skol2
% 25.07/25.45     ), ! distinct_points( intersection_point( skol1, skol2 ), 
% 25.07/25.45    intersection_point( skol3, skol2 ) ), ! distinct_lines( skol3, skol2 ), !
% 25.07/25.45     convergent_lines( skol3, skol2 ) }.
% 25.07/25.45  parent1[0]: (1895) {G9,W7,D3,L1,V0,M1} R(1832,21) { distinct_points( 
% 25.07/25.45    intersection_point( skol1, skol2 ), intersection_point( skol3, skol2 ) )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  factor: (2958) {G4,W6,D2,L2,V0,M2}  { ! convergent_lines( skol3, skol2 ), !
% 25.07/25.45     distinct_lines( skol3, skol2 ) }.
% 25.07/25.45  parent0[0, 2]: (2957) {G4,W9,D2,L3,V0,M3}  { ! convergent_lines( skol3, 
% 25.07/25.45    skol2 ), ! distinct_lines( skol3, skol2 ), ! convergent_lines( skol3, 
% 25.07/25.45    skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (2268) {G10,W6,D2,L2,V0,M1} R(1646,136);f;r(1895) { ! 
% 25.07/25.45    convergent_lines( skol3, skol2 ), ! distinct_lines( skol3, skol2 ) }.
% 25.07/25.45  parent0: (2958) {G4,W6,D2,L2,V0,M2}  { ! convergent_lines( skol3, skol2 ), 
% 25.07/25.45    ! distinct_lines( skol3, skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45     1 ==> 1
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2959) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol3, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  parent0[0]: (2268) {G10,W6,D2,L2,V0,M1} R(1646,136);f;r(1895) { ! 
% 25.07/25.45    convergent_lines( skol3, skol2 ), ! distinct_lines( skol3, skol2 ) }.
% 25.07/25.45  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 25.07/25.45     }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (2269) {G11,W3,D2,L1,V0,M1} S(2268);r(15) { ! distinct_lines( 
% 25.07/25.45    skol3, skol2 ) }.
% 25.07/25.45  parent0: (2959) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol3, skol2 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45     0 ==> 0
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2960) {G3,W3,D2,L1,V0,M1}  { ! convergent_lines( skol2, skol3
% 25.07/25.45     ) }.
% 25.07/25.45  parent0[0]: (2269) {G11,W3,D2,L1,V0,M1} S(2268);r(15) { ! distinct_lines( 
% 25.07/25.45    skol3, skol2 ) }.
% 25.07/25.45  parent1[1]: (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y )
% 25.07/25.45    , distinct_lines( Y, X ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45     X := skol2
% 25.07/25.45     Y := skol3
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  resolution: (2961) {G3,W0,D0,L0,V0,M0}  {  }.
% 25.07/25.45  parent0[0]: (2960) {G3,W3,D2,L1,V0,M1}  { ! convergent_lines( skol2, skol3
% 25.07/25.45     ) }.
% 25.07/25.45  parent1[0]: (44) {G2,W3,D2,L1,V0,M1} R(40,15) { convergent_lines( skol2, 
% 25.07/25.45    skol3 ) }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  substitution1:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  subsumption: (2781) {G12,W0,D0,L0,V0,M0} R(2269,29);r(44) {  }.
% 25.07/25.45  parent0: (2961) {G3,W0,D0,L0,V0,M0}  {  }.
% 25.07/25.45  substitution0:
% 25.07/25.45  end
% 25.07/25.45  permutation0:
% 25.07/25.45  end
% 25.07/25.45  
% 25.07/25.45  Proof check complete!
% 25.07/25.45  
% 25.07/25.45  Memory use:
% 25.07/25.45  
% 25.07/25.45  space for terms:        44795
% 25.07/25.45  space for clauses:      97518
% 25.07/25.45  
% 25.07/25.45  
% 25.07/25.45  clauses generated:      909518
% 25.07/25.45  clauses kept:           2782
% 25.07/25.45  clauses selected:       2180
% 25.07/25.45  clauses deleted:        8
% 25.07/25.45  clauses inuse deleted:  0
% 25.07/25.45  
% 25.07/25.45  subsentry:          3953130
% 25.07/25.45  literals s-matched: 1469108
% 25.07/25.45  literals matched:   1469063
% 25.07/25.45  full subsumption:   1312503
% 25.07/25.45  
% 25.07/25.45  checksum:           1589058766
% 25.07/25.45  
% 25.07/25.45  
% 25.07/25.45  Bliksem ended
%------------------------------------------------------------------------------