TSTP Solution File: GEO193+2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO193+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n032.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 02:52:32 EDT 2022

% Result   : Theorem 24.47s 24.86s
% Output   : Refutation 24.47s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : GEO193+2 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.10  % Command  : bliksem %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % DateTime : Fri Jun 17 17:50:16 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 24.47/24.86  *** allocated 10000 integers for termspace/termends
% 24.47/24.86  *** allocated 10000 integers for clauses
% 24.47/24.86  *** allocated 10000 integers for justifications
% 24.47/24.86  Bliksem 1.12
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  Automatic Strategy Selection
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  Clauses:
% 24.47/24.86  
% 24.47/24.86  { ! distinct_points( X, X ) }.
% 24.47/24.86  { ! distinct_lines( X, X ) }.
% 24.47/24.86  { ! convergent_lines( X, X ) }.
% 24.47/24.86  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 24.47/24.86     ) }.
% 24.47/24.86  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 24.47/24.86     }.
% 24.47/24.86  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 24.47/24.86    , Z ) }.
% 24.47/24.86  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 24.47/24.86    , Y ) ), distinct_points( Z, X ) }.
% 24.47/24.86  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 24.47/24.86    , Y ) ), distinct_points( Z, Y ) }.
% 24.47/24.86  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ), 
% 24.47/24.86    distinct_points( Z, intersection_point( X, Y ) ) }.
% 24.47/24.86  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ), 
% 24.47/24.86    distinct_points( Z, intersection_point( X, Y ) ) }.
% 24.47/24.86  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 24.47/24.86    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 24.47/24.86    apart_point_and_line( Y, T ) }.
% 24.47/24.86  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 24.47/24.86    apart_point_and_line( Z, Y ) }.
% 24.47/24.86  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 24.47/24.86    apart_point_and_line( X, Z ) }.
% 24.47/24.86  { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 24.47/24.86  { convergent_lines( skol1, skol2 ) }.
% 24.47/24.86  { convergent_lines( skol3, skol2 ) }.
% 24.47/24.86  { convergent_lines( skol1, skol3 ) }.
% 24.47/24.86  { apart_point_and_line( intersection_point( skol1, skol2 ), skol3 ) }.
% 24.47/24.86  { ! apart_point_and_line( intersection_point( skol3, skol2 ), skol1 ) }.
% 24.47/24.86  
% 24.47/24.86  percentage equality = 0.000000, percentage horn = 0.684211
% 24.47/24.86  This a non-horn, non-equality problem
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  Options Used:
% 24.47/24.86  
% 24.47/24.86  useres =            1
% 24.47/24.86  useparamod =        0
% 24.47/24.86  useeqrefl =         0
% 24.47/24.86  useeqfact =         0
% 24.47/24.86  usefactor =         1
% 24.47/24.86  usesimpsplitting =  0
% 24.47/24.86  usesimpdemod =      0
% 24.47/24.86  usesimpres =        3
% 24.47/24.86  
% 24.47/24.86  resimpinuse      =  1000
% 24.47/24.86  resimpclauses =     20000
% 24.47/24.86  substype =          standard
% 24.47/24.86  backwardsubs =      1
% 24.47/24.86  selectoldest =      5
% 24.47/24.86  
% 24.47/24.86  litorderings [0] =  split
% 24.47/24.86  litorderings [1] =  liftord
% 24.47/24.86  
% 24.47/24.86  termordering =      none
% 24.47/24.86  
% 24.47/24.86  litapriori =        1
% 24.47/24.86  termapriori =       0
% 24.47/24.86  litaposteriori =    0
% 24.47/24.86  termaposteriori =   0
% 24.47/24.86  demodaposteriori =  0
% 24.47/24.86  ordereqreflfact =   0
% 24.47/24.86  
% 24.47/24.86  litselect =         none
% 24.47/24.86  
% 24.47/24.86  maxweight =         15
% 24.47/24.86  maxdepth =          30000
% 24.47/24.86  maxlength =         115
% 24.47/24.86  maxnrvars =         195
% 24.47/24.86  excuselevel =       1
% 24.47/24.86  increasemaxweight = 1
% 24.47/24.86  
% 24.47/24.86  maxselected =       10000000
% 24.47/24.86  maxnrclauses =      10000000
% 24.47/24.86  
% 24.47/24.86  showgenerated =    0
% 24.47/24.86  showkept =         0
% 24.47/24.86  showselected =     0
% 24.47/24.86  showdeleted =      0
% 24.47/24.86  showresimp =       1
% 24.47/24.86  showstatus =       2000
% 24.47/24.86  
% 24.47/24.86  prologoutput =     0
% 24.47/24.86  nrgoals =          5000000
% 24.47/24.86  totalproof =       1
% 24.47/24.86  
% 24.47/24.86  Symbols occurring in the translation:
% 24.47/24.86  
% 24.47/24.86  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 24.47/24.86  .  [1, 2]      (w:1, o:19, a:1, s:1, b:0), 
% 24.47/24.86  !  [4, 1]      (w:0, o:14, a:1, s:1, b:0), 
% 24.47/24.86  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 24.47/24.86  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 24.47/24.86  distinct_points  [36, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 24.47/24.86  distinct_lines  [37, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 24.47/24.86  convergent_lines  [38, 2]      (w:1, o:43, a:1, s:1, b:0), 
% 24.47/24.86  line_connecting  [41, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 24.47/24.86  apart_point_and_line  [42, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 24.47/24.86  intersection_point  [43, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 24.47/24.86  skol1  [46, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 24.47/24.86  skol2  [47, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 24.47/24.86  skol3  [48, 0]      (w:1, o:13, a:1, s:1, b:0).
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  Starting Search:
% 24.47/24.86  
% 24.47/24.86  *** allocated 15000 integers for clauses
% 24.47/24.86  *** allocated 22500 integers for clauses
% 24.47/24.86  *** allocated 33750 integers for clauses
% 24.47/24.86  *** allocated 15000 integers for termspace/termends
% 24.47/24.86  Resimplifying inuse:
% 24.47/24.86  Done
% 24.47/24.86  
% 24.47/24.86  Failed to find proof!
% 24.47/24.86  maxweight =   15
% 24.47/24.86  maxnrclauses = 10000000
% 24.47/24.86  Generated: 121438
% 24.47/24.86  Kept: 885
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  The strategy used was not complete!
% 24.47/24.86  
% 24.47/24.86  Increased maxweight to 16
% 24.47/24.86  
% 24.47/24.86  Starting Search:
% 24.47/24.86  
% 24.47/24.86  *** allocated 50625 integers for clauses
% 24.47/24.86  Resimplifying inuse:
% 24.47/24.86  Done
% 24.47/24.86  
% 24.47/24.86  *** allocated 22500 integers for termspace/termends
% 24.47/24.86  Resimplifying inuse:
% 24.47/24.86  Done
% 24.47/24.86  
% 24.47/24.86  Failed to find proof!
% 24.47/24.86  maxweight =   16
% 24.47/24.86  maxnrclauses = 10000000
% 24.47/24.86  Generated: 396716
% 24.47/24.86  Kept: 1241
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  The strategy used was not complete!
% 24.47/24.86  
% 24.47/24.86  Increased maxweight to 17
% 24.47/24.86  
% 24.47/24.86  Starting Search:
% 24.47/24.86  
% 24.47/24.86  Resimplifying inuse:
% 24.47/24.86  Done
% 24.47/24.86  
% 24.47/24.86  *** allocated 75937 integers for clauses
% 24.47/24.86  *** allocated 33750 integers for termspace/termends
% 24.47/24.86  Resimplifying inuse:
% 24.47/24.86  Done
% 24.47/24.86  
% 24.47/24.86  Failed to find proof!
% 24.47/24.86  maxweight =   17
% 24.47/24.86  maxnrclauses = 10000000
% 24.47/24.86  Generated: 512820
% 24.47/24.86  Kept: 1597
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  The strategy used was not complete!
% 24.47/24.86  
% 24.47/24.86  Increased maxweight to 18
% 24.47/24.86  
% 24.47/24.86  Starting Search:
% 24.47/24.86  
% 24.47/24.86  Resimplifying inuse:
% 24.47/24.86  Done
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  Intermediate Status:
% 24.47/24.86  Generated:    125986
% 24.47/24.86  Kept:         2051
% 24.47/24.86  Inuse:        823
% 24.47/24.86  Deleted:      2
% 24.47/24.86  Deletedinuse: 0
% 24.47/24.86  
% 24.47/24.86  Resimplifying inuse:
% 24.47/24.86  Done
% 24.47/24.86  
% 24.47/24.86  *** allocated 50625 integers for termspace/termends
% 24.47/24.86  *** allocated 113905 integers for clauses
% 24.47/24.86  
% 24.47/24.86  Bliksems!, er is een bewijs:
% 24.47/24.86  % SZS status Theorem
% 24.47/24.86  % SZS output start Refutation
% 24.47/24.86  
% 24.47/24.86  (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.47/24.86  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 24.47/24.86  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 24.47/24.86  (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 24.47/24.86     ), ! distinct_points( X, Y ) }.
% 24.47/24.86  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 24.47/24.86    , ! distinct_lines( X, Y ) }.
% 24.47/24.86  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 24.47/24.86    Z ), ! convergent_lines( X, Y ) }.
% 24.47/24.86  (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 24.47/24.86    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, X ) }.
% 24.47/24.86  (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 24.47/24.86    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, Y ) }.
% 24.47/24.86  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 24.47/24.86    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 24.47/24.86    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 24.47/24.86  (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 24.47/24.86    ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.47/24.86  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 24.47/24.86    X, Z ), ! apart_point_and_line( X, Y ) }.
% 24.47/24.86  (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), distinct_lines( X
% 24.47/24.86    , Y ) }.
% 24.47/24.86  (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 24.47/24.86  (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 ) }.
% 24.47/24.86  (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 ) }.
% 24.47/24.86  (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( intersection_point( 
% 24.47/24.86    skol1, skol2 ), skol3 ) }.
% 24.47/24.86  (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( intersection_point( 
% 24.47/24.86    skol3, skol2 ), skol1 ) }.
% 24.47/24.86  (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 24.47/24.86    distinct_points( X, Y ) }.
% 24.47/24.86  (22) {G2,W9,D2,L3,V3,M3} R(21,3) { distinct_points( Z, X ), ! 
% 24.47/24.86    distinct_points( Y, Z ), distinct_points( X, Y ) }.
% 24.47/24.86  (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 24.47/24.86    ( X, Y ) }.
% 24.47/24.86  (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y ), 
% 24.47/24.86    distinct_lines( Y, X ) }.
% 24.47/24.86  (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 24.47/24.86    convergent_lines( X, Y ) }.
% 24.47/24.86  (43) {G2,W3,D2,L1,V0,M1} R(40,14) { convergent_lines( skol2, skol1 ) }.
% 24.47/24.86  (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, skol1 ) }.
% 24.47/24.86  (60) {G1,W10,D3,L2,V1,M1} R(8,17) { ! convergent_lines( skol3, X ), 
% 24.47/24.86    distinct_points( intersection_point( skol1, skol2 ), intersection_point( 
% 24.47/24.86    skol3, X ) ) }.
% 24.47/24.86  (106) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( intersection_point
% 24.47/24.86    ( skol3, skol2 ), X ), ! distinct_lines( Y, skol1 ), apart_point_and_line
% 24.47/24.86    ( X, skol1 ), apart_point_and_line( intersection_point( skol3, skol2 ), Y
% 24.47/24.86     ), apart_point_and_line( X, Y ) }.
% 24.47/24.86  (109) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( intersection_point
% 24.47/24.86    ( skol3, skol2 ), X ), ! distinct_lines( skol1, Y ), apart_point_and_line
% 24.47/24.86    ( X, skol1 ), apart_point_and_line( X, Y ), apart_point_and_line( 
% 24.47/24.86    intersection_point( skol3, skol2 ), Y ) }.
% 24.47/24.86  (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), ! 
% 24.47/24.86    convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z )
% 24.47/24.86     ), ! apart_point_and_line( X, Z ) }.
% 24.47/24.86  (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), ! 
% 24.47/24.86    convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T )
% 24.47/24.86     ), ! apart_point_and_line( X, Z ) }.
% 24.47/24.86  (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.86  (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.86  (151) {G1,W8,D3,L2,V1,M1} R(12,17) { distinct_lines( skol3, X ), 
% 24.47/24.86    apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.47/24.86  (156) {G3,W3,D2,L1,V0,M1} R(151,135);r(14) { distinct_lines( skol3, skol1 )
% 24.47/24.86     }.
% 24.47/24.86  (211) {G3,W9,D2,L3,V3,M3} R(22,21) { distinct_points( Z, X ), 
% 24.47/24.86    distinct_points( Z, Y ), ! distinct_points( X, Y ) }.
% 24.47/24.86  (468) {G4,W13,D3,L3,V2,M2} R(60,211) { ! convergent_lines( skol3, X ), 
% 24.47/24.86    distinct_points( Y, intersection_point( skol3, X ) ), distinct_points( Y
% 24.47/24.86    , intersection_point( skol1, skol2 ) ) }.
% 24.47/24.86  (1457) {G4,W14,D3,L4,V1,M1} R(106,135);r(156) { ! distinct_points( 
% 24.47/24.86    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 24.47/24.86    , ! convergent_lines( skol3, skol2 ), apart_point_and_line( X, skol3 )
% 24.47/24.86     }.
% 24.47/24.86  (1506) {G3,W14,D3,L4,V1,M1} R(109,136);r(15) { ! distinct_points( 
% 24.47/24.86    intersection_point( skol3, skol2 ), X ), ! distinct_lines( skol1, skol2 )
% 24.47/24.86    , apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 24.47/24.86  (1647) {G4,W18,D3,L4,V1,M1} R(1506,136) { ! distinct_points( 
% 24.47/24.86    intersection_point( skol3, skol2 ), intersection_point( X, skol2 ) ), ! 
% 24.47/24.86    distinct_lines( skol1, skol2 ), ! convergent_lines( X, skol2 ), 
% 24.47/24.86    apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 24.47/24.86  (1706) {G5,W11,D3,L3,V1,M1} S(1457);r(15) { ! distinct_points( 
% 24.47/24.86    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 24.47/24.86    , apart_point_and_line( X, skol3 ) }.
% 24.47/24.86  (1732) {G6,W15,D3,L3,V1,M1} R(1706,135) { ! distinct_points( 
% 24.47/24.86    intersection_point( skol3, skol2 ), intersection_point( skol3, X ) ), ! 
% 24.47/24.86    convergent_lines( skol3, X ), apart_point_and_line( intersection_point( 
% 24.47/24.86    skol3, X ), skol1 ) }.
% 24.47/24.86  (1766) {G7,W7,D3,L1,V0,M1} R(1732,136);f;r(45) { ! distinct_points( 
% 24.47/24.86    intersection_point( skol3, skol2 ), intersection_point( skol3, skol1 ) )
% 24.47/24.86     }.
% 24.47/24.86  (1835) {G8,W7,D3,L1,V0,M1} R(1766,468);r(45) { distinct_points( 
% 24.47/24.86    intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 ) )
% 24.47/24.86     }.
% 24.47/24.86  (2481) {G9,W6,D2,L2,V0,M1} R(1647,135);f;r(1835) { ! convergent_lines( 
% 24.47/24.86    skol1, skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 24.47/24.86  (2482) {G10,W3,D2,L1,V0,M1} S(2481);r(14) { ! distinct_lines( skol1, skol2
% 24.47/24.86     ) }.
% 24.47/24.86  (3005) {G11,W0,D0,L0,V0,M0} R(2482,29);r(43) {  }.
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  % SZS output end Refutation
% 24.47/24.86  found a proof!
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  Unprocessed initial clauses:
% 24.47/24.86  
% 24.47/24.86  (3007) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 24.47/24.86  (3008) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 24.47/24.86  (3009) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 24.47/24.86  (3010) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 24.47/24.86    , Z ), distinct_points( Y, Z ) }.
% 24.47/24.86  (3011) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 24.47/24.86    Z ), distinct_lines( Y, Z ) }.
% 24.47/24.86  (3012) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 24.47/24.86    ( X, Z ), convergent_lines( Y, Z ) }.
% 24.47/24.86  (3013) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 24.47/24.86     ) }.
% 24.47/24.86  (3014) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 24.47/24.86     ) }.
% 24.47/24.86  (3015) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 24.47/24.86    Y ) ) }.
% 24.47/24.86  (3016) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 24.47/24.86    Y ) ) }.
% 24.47/24.86  (3017) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 24.47/24.86    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 24.47/24.86    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 24.47/24.86  (3018) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 24.47/24.86    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 24.47/24.86  (3019) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 24.47/24.86    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 24.47/24.86  (3020) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), distinct_lines( X
% 24.47/24.86    , Y ) }.
% 24.47/24.86  (3021) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 24.47/24.86  (3022) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol2 ) }.
% 24.47/24.86  (3023) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol3 ) }.
% 24.47/24.86  (3024) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( intersection_point( 
% 24.47/24.86    skol1, skol2 ), skol3 ) }.
% 24.47/24.86  (3025) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( intersection_point( 
% 24.47/24.86    skol3, skol2 ), skol1 ) }.
% 24.47/24.86  
% 24.47/24.86  
% 24.47/24.86  Total Proof:
% 24.47/24.86  
% 24.47/24.86  subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.47/24.86  parent0: (3007) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 24.47/24.86  parent0: (3008) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 24.47/24.86  parent0: (3009) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 24.47/24.86    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 24.47/24.86  parent0: (3010) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), 
% 24.47/24.86    distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 2
% 24.47/24.86     1 ==> 0
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 24.47/24.86    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 24.47/24.86  parent0: (3011) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 24.47/24.86    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 2
% 24.47/24.86     1 ==> 0
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 24.47/24.86    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 24.47/24.86  parent0: (3012) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 24.47/24.86    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 2
% 24.47/24.86     1 ==> 0
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 24.47/24.86    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.47/24.86    ( Z, X ) }.
% 24.47/24.86  parent0: (3015) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 24.47/24.86    Y ) ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86     1 ==> 2
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 24.47/24.86    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.47/24.86    ( Z, Y ) }.
% 24.47/24.86  parent0: (3016) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.86    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 24.47/24.86    Y ) ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86     1 ==> 2
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 24.47/24.86    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 24.47/24.86    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 24.47/24.86    apart_point_and_line( X, Z ) }.
% 24.47/24.86  parent0: (3017) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 24.47/24.86    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 24.47/24.86    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 24.47/24.86    apart_point_and_line( Y, T ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86     T := T
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86     1 ==> 1
% 24.47/24.86     2 ==> 5
% 24.47/24.86     3 ==> 2
% 24.47/24.86     4 ==> 3
% 24.47/24.86     5 ==> 4
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 24.47/24.86    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.47/24.86  parent0: (3018) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 24.47/24.86    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 2
% 24.47/24.86     1 ==> 0
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 24.47/24.86    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 24.47/24.86  parent0: (3019) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 24.47/24.86    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 2
% 24.47/24.86     1 ==> 0
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 24.47/24.86    distinct_lines( X, Y ) }.
% 24.47/24.86  parent0: (3020) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 24.47/24.86    distinct_lines( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86     1 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.47/24.86     }.
% 24.47/24.86  parent0: (3021) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 24.47/24.86     }.
% 24.47/24.86  parent0: (3022) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol2 ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 )
% 24.47/24.86     }.
% 24.47/24.86  parent0: (3023) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol3 ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 24.47/24.86    intersection_point( skol1, skol2 ), skol3 ) }.
% 24.47/24.86  parent0: (3024) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( 
% 24.47/24.86    intersection_point( skol1, skol2 ), skol3 ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( 
% 24.47/24.86    intersection_point( skol3, skol2 ), skol1 ) }.
% 24.47/24.86  parent0: (3025) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( 
% 24.47/24.86    intersection_point( skol3, skol2 ), skol1 ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  resolution: (3119) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 24.47/24.86    distinct_points( X, Y ) }.
% 24.47/24.86  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.47/24.86  parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 24.47/24.86    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86  end
% 24.47/24.86  substitution1:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := X
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 24.47/24.86    distinct_points( X, Y ) }.
% 24.47/24.86  parent0: (3119) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 24.47/24.86    distinct_points( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := Y
% 24.47/24.86     Y := X
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 1
% 24.47/24.86     1 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  resolution: (3121) {G1,W9,D2,L3,V3,M3}  { distinct_points( Y, X ), 
% 24.47/24.86    distinct_points( Z, Y ), ! distinct_points( X, Z ) }.
% 24.47/24.86  parent0[0]: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 24.47/24.86    distinct_points( X, Y ) }.
% 24.47/24.86  parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 24.47/24.86    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := Y
% 24.47/24.86     Y := X
% 24.47/24.86  end
% 24.47/24.86  substitution1:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Z
% 24.47/24.86     Z := Y
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (22) {G2,W9,D2,L3,V3,M3} R(21,3) { distinct_points( Z, X ), ! 
% 24.47/24.86    distinct_points( Y, Z ), distinct_points( X, Y ) }.
% 24.47/24.86  parent0: (3121) {G1,W9,D2,L3,V3,M3}  { distinct_points( Y, X ), 
% 24.47/24.86    distinct_points( Z, Y ), ! distinct_points( X, Z ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := Y
% 24.47/24.86     Y := X
% 24.47/24.86     Z := Z
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 2
% 24.47/24.86     1 ==> 0
% 24.47/24.86     2 ==> 1
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  resolution: (3124) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 24.47/24.86    distinct_lines( X, Y ) }.
% 24.47/24.86  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 24.47/24.86  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 24.47/24.86    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86  end
% 24.47/24.86  substitution1:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := X
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 24.47/24.86    distinct_lines( X, Y ) }.
% 24.47/24.86  parent0: (3124) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 24.47/24.86    distinct_lines( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := Y
% 24.47/24.86     Y := X
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 1
% 24.47/24.86     1 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  resolution: (3126) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 24.47/24.86    convergent_lines( X, Y ) }.
% 24.47/24.86  parent0[0]: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 24.47/24.86    distinct_lines( X, Y ) }.
% 24.47/24.86  parent1[1]: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 24.47/24.86    distinct_lines( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := Y
% 24.47/24.86     Y := X
% 24.47/24.86  end
% 24.47/24.86  substitution1:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y )
% 24.47/24.86    , distinct_lines( Y, X ) }.
% 24.47/24.86  parent0: (3126) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 24.47/24.86    convergent_lines( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.86     0 ==> 1
% 24.47/24.86     1 ==> 0
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  resolution: (3127) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 24.47/24.86    convergent_lines( X, Y ) }.
% 24.47/24.86  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 24.47/24.86  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 24.47/24.86    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := X
% 24.47/24.86  end
% 24.47/24.86  substitution1:
% 24.47/24.86     X := X
% 24.47/24.86     Y := Y
% 24.47/24.86     Z := X
% 24.47/24.86  end
% 24.47/24.86  
% 24.47/24.86  subsumption: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 24.47/24.86    convergent_lines( X, Y ) }.
% 24.47/24.86  parent0: (3127) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 24.47/24.86    convergent_lines( X, Y ) }.
% 24.47/24.86  substitution0:
% 24.47/24.86     X := Y
% 24.47/24.86     Y := X
% 24.47/24.86  end
% 24.47/24.86  permutation0:
% 24.47/24.87     0 ==> 1
% 24.47/24.87     1 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3129) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol1 )
% 24.47/24.87     }.
% 24.47/24.87  parent0[0]: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 24.47/24.87    convergent_lines( X, Y ) }.
% 24.47/24.87  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol2
% 24.47/24.87     Y := skol1
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (43) {G2,W3,D2,L1,V0,M1} R(40,14) { convergent_lines( skol2, 
% 24.47/24.87    skol1 ) }.
% 24.47/24.87  parent0: (3129) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3130) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol1 )
% 24.47/24.87     }.
% 24.47/24.87  parent0[0]: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 24.47/24.87    convergent_lines( X, Y ) }.
% 24.47/24.87  parent1[0]: (16) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol3 )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol3
% 24.47/24.87     Y := skol1
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, 
% 24.47/24.87    skol1 ) }.
% 24.47/24.87  parent0: (3130) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3131) {G1,W10,D3,L2,V1,M2}  { ! convergent_lines( skol3, X ), 
% 24.47/24.87    distinct_points( intersection_point( skol1, skol2 ), intersection_point( 
% 24.47/24.87    skol3, X ) ) }.
% 24.47/24.87  parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 24.47/24.87    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.47/24.87    ( Z, X ) }.
% 24.47/24.87  parent1[0]: (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 24.47/24.87    intersection_point( skol1, skol2 ), skol3 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol3
% 24.47/24.87     Y := X
% 24.47/24.87     Z := intersection_point( skol1, skol2 )
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (60) {G1,W10,D3,L2,V1,M1} R(8,17) { ! convergent_lines( skol3
% 24.47/24.87    , X ), distinct_points( intersection_point( skol1, skol2 ), 
% 24.47/24.87    intersection_point( skol3, X ) ) }.
% 24.47/24.87  parent0: (3131) {G1,W10,D3,L2,V1,M2}  { ! convergent_lines( skol3, X ), 
% 24.47/24.87    distinct_points( intersection_point( skol1, skol2 ), intersection_point( 
% 24.47/24.87    skol3, X ) ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3132) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( Y, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, Y ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol3, skol2 ), Y ) }.
% 24.47/24.87  parent0[0]: (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( 
% 24.47/24.87    intersection_point( skol3, skol2 ), skol1 ) }.
% 24.47/24.87  parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 24.47/24.87    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 24.47/24.87    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 24.47/24.87    apart_point_and_line( X, Z ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := intersection_point( skol3, skol2 )
% 24.47/24.87     Y := X
% 24.47/24.87     Z := Y
% 24.47/24.87     T := skol1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (106) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( Y, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( 
% 24.47/24.87    intersection_point( skol3, skol2 ), Y ), apart_point_and_line( X, Y ) }.
% 24.47/24.87  parent0: (3132) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( Y, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, Y ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol3, skol2 ), Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87     2 ==> 4
% 24.47/24.87     3 ==> 2
% 24.47/24.87     4 ==> 3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3144) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( skol1, Y ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol3, skol2 ), Y ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ) }.
% 24.47/24.87  parent0[0]: (18) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( 
% 24.47/24.87    intersection_point( skol3, skol2 ), skol1 ) }.
% 24.47/24.87  parent1[5]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 24.47/24.87    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 24.47/24.87    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 24.47/24.87    apart_point_and_line( X, Z ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := intersection_point( skol3, skol2 )
% 24.47/24.87     Y := X
% 24.47/24.87     Z := skol1
% 24.47/24.87     T := Y
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (109) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( skol1, Y ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol3, skol2 ), Y ) }.
% 24.47/24.87  parent0: (3144) {G1,W19,D3,L5,V2,M5}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( skol1, Y ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol3, skol2 ), Y ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87     2 ==> 4
% 24.47/24.87     3 ==> 2
% 24.47/24.87     4 ==> 3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3150) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 24.47/24.87    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.47/24.87    , ! apart_point_and_line( T, Y ) }.
% 24.47/24.87  parent0[2]: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 24.47/24.87    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.47/24.87    ( Z, Y ) }.
% 24.47/24.87  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 24.47/24.87    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87     Z := Z
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := T
% 24.47/24.87     Y := Y
% 24.47/24.87     Z := Z
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), 
% 24.47/24.87    ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z
% 24.47/24.87     ) ), ! apart_point_and_line( X, Z ) }.
% 24.47/24.87  parent0: (3150) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 24.47/24.87    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.47/24.87    , ! apart_point_and_line( T, Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := T
% 24.47/24.87     Y := Z
% 24.47/24.87     Z := Y
% 24.47/24.87     T := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 1
% 24.47/24.87     1 ==> 2
% 24.47/24.87     2 ==> 0
% 24.47/24.87     3 ==> 3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3152) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 24.47/24.87    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.47/24.87    , ! apart_point_and_line( T, X ) }.
% 24.47/24.87  parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 24.47/24.87    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 24.47/24.87    ( Z, X ) }.
% 24.47/24.87  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 24.47/24.87    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87     Z := Z
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := T
% 24.47/24.87     Y := X
% 24.47/24.87     Z := Z
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), 
% 24.47/24.87    ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T
% 24.47/24.87     ) ), ! apart_point_and_line( X, Z ) }.
% 24.47/24.87  parent0: (3152) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 24.47/24.87    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 24.47/24.87    , ! apart_point_and_line( T, X ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := Z
% 24.47/24.87     Y := T
% 24.47/24.87     Z := Y
% 24.47/24.87     T := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 1
% 24.47/24.87     1 ==> 2
% 24.47/24.87     2 ==> 0
% 24.47/24.87     3 ==> 3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  factor: (3154) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point
% 24.47/24.87    ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 24.47/24.87    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  parent0[0, 2]: (128) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y )
% 24.47/24.87    , ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, 
% 24.47/24.87    T ) ), ! apart_point_and_line( X, Z ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := intersection_point( X, Y )
% 24.47/24.87     Y := intersection_point( X, Y )
% 24.47/24.87     Z := X
% 24.47/24.87     T := Y
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3155) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.87    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.47/24.87  parent1[0]: (3154) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 24.47/24.87    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 24.47/24.87    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 24.47/24.87    Y ), X ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := intersection_point( X, Y )
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X
% 24.47/24.87    , Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  parent0: (3155) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.87    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  factor: (3156) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point
% 24.47/24.87    ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 24.47/24.87    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.87  parent0[0, 2]: (127) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y )
% 24.47/24.87    , ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, 
% 24.47/24.87    Z ) ), ! apart_point_and_line( X, Z ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := intersection_point( X, Y )
% 24.47/24.87     Y := intersection_point( X, Y )
% 24.47/24.87     Z := Y
% 24.47/24.87     T := X
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3157) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.87    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.87  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 24.47/24.87  parent1[0]: (3156) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 24.47/24.87    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 24.47/24.87    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 24.47/24.87    Y ), Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := intersection_point( X, Y )
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X
% 24.47/24.87    , Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.87  parent0: (3157) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 24.47/24.87    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87     Y := Y
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3158) {G1,W8,D3,L2,V1,M2}  { distinct_lines( skol3, X ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.47/24.87  parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 24.47/24.87    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 24.47/24.87  parent1[0]: (17) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 24.47/24.87    intersection_point( skol1, skol2 ), skol3 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := intersection_point( skol1, skol2 )
% 24.47/24.87     Y := skol3
% 24.47/24.87     Z := X
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (151) {G1,W8,D3,L2,V1,M1} R(12,17) { distinct_lines( skol3, X
% 24.47/24.87     ), apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.47/24.87  parent0: (3158) {G1,W8,D3,L2,V1,M2}  { distinct_lines( skol3, X ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3159) {G2,W6,D2,L2,V0,M2}  { ! convergent_lines( skol1, skol2
% 24.47/24.87     ), distinct_lines( skol3, skol1 ) }.
% 24.47/24.87  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 24.47/24.87    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  parent1[1]: (151) {G1,W8,D3,L2,V1,M1} R(12,17) { distinct_lines( skol3, X )
% 24.47/24.87    , apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol1
% 24.47/24.87     Y := skol2
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := skol1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3160) {G1,W3,D2,L1,V0,M1}  { distinct_lines( skol3, skol1 )
% 24.47/24.87     }.
% 24.47/24.87  parent0[0]: (3159) {G2,W6,D2,L2,V0,M2}  { ! convergent_lines( skol1, skol2
% 24.47/24.87     ), distinct_lines( skol3, skol1 ) }.
% 24.47/24.87  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (156) {G3,W3,D2,L1,V0,M1} R(151,135);r(14) { distinct_lines( 
% 24.47/24.87    skol3, skol1 ) }.
% 24.47/24.87  parent0: (3160) {G1,W3,D2,L1,V0,M1}  { distinct_lines( skol3, skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3163) {G2,W9,D2,L3,V3,M3}  { distinct_points( Y, X ), ! 
% 24.47/24.87    distinct_points( Z, X ), distinct_points( Y, Z ) }.
% 24.47/24.87  parent0[0]: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 24.47/24.87    distinct_points( X, Y ) }.
% 24.47/24.87  parent1[0]: (22) {G2,W9,D2,L3,V3,M3} R(21,3) { distinct_points( Z, X ), ! 
% 24.47/24.87    distinct_points( Y, Z ), distinct_points( X, Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := Y
% 24.47/24.87     Y := X
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := Y
% 24.47/24.87     Y := Z
% 24.47/24.87     Z := X
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (211) {G3,W9,D2,L3,V3,M3} R(22,21) { distinct_points( Z, X ), 
% 24.47/24.87    distinct_points( Z, Y ), ! distinct_points( X, Y ) }.
% 24.47/24.87  parent0: (3163) {G2,W9,D2,L3,V3,M3}  { distinct_points( Y, X ), ! 
% 24.47/24.87    distinct_points( Z, X ), distinct_points( Y, Z ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := Y
% 24.47/24.87     Y := Z
% 24.47/24.87     Z := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 1
% 24.47/24.87     1 ==> 2
% 24.47/24.87     2 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3167) {G2,W13,D3,L3,V2,M3}  { distinct_points( X, 
% 24.47/24.87    intersection_point( skol1, skol2 ) ), distinct_points( X, 
% 24.47/24.87    intersection_point( skol3, Y ) ), ! convergent_lines( skol3, Y ) }.
% 24.47/24.87  parent0[2]: (211) {G3,W9,D2,L3,V3,M3} R(22,21) { distinct_points( Z, X ), 
% 24.47/24.87    distinct_points( Z, Y ), ! distinct_points( X, Y ) }.
% 24.47/24.87  parent1[1]: (60) {G1,W10,D3,L2,V1,M1} R(8,17) { ! convergent_lines( skol3, 
% 24.47/24.87    X ), distinct_points( intersection_point( skol1, skol2 ), 
% 24.47/24.87    intersection_point( skol3, X ) ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := intersection_point( skol1, skol2 )
% 24.47/24.87     Y := intersection_point( skol3, Y )
% 24.47/24.87     Z := X
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := Y
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (468) {G4,W13,D3,L3,V2,M2} R(60,211) { ! convergent_lines( 
% 24.47/24.87    skol3, X ), distinct_points( Y, intersection_point( skol3, X ) ), 
% 24.47/24.87    distinct_points( Y, intersection_point( skol1, skol2 ) ) }.
% 24.47/24.87  parent0: (3167) {G2,W13,D3,L3,V2,M3}  { distinct_points( X, 
% 24.47/24.87    intersection_point( skol1, skol2 ) ), distinct_points( X, 
% 24.47/24.87    intersection_point( skol3, Y ) ), ! convergent_lines( skol3, Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := Y
% 24.47/24.87     Y := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 2
% 24.47/24.87     1 ==> 1
% 24.47/24.87     2 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3169) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol3, skol2
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), X ), ! 
% 24.47/24.87    distinct_lines( skol3, skol1 ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 24.47/24.87    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  parent1[3]: (106) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( Y, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( 
% 24.47/24.87    intersection_point( skol3, skol2 ), Y ), apart_point_and_line( X, Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol3
% 24.47/24.87     Y := skol2
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := X
% 24.47/24.87     Y := skol3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3171) {G3,W14,D3,L4,V1,M4}  { ! convergent_lines( skol3, skol2
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), X ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  parent0[2]: (3169) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol3, skol2
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), X ), ! 
% 24.47/24.87    distinct_lines( skol3, skol1 ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  parent1[0]: (156) {G3,W3,D2,L1,V0,M1} R(151,135);r(14) { distinct_lines( 
% 24.47/24.87    skol3, skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (1457) {G4,W14,D3,L4,V1,M1} R(106,135);r(156) { ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), X ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), ! convergent_lines( skol3, skol2 ), 
% 24.47/24.87    apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  parent0: (3171) {G3,W14,D3,L4,V1,M4}  { ! convergent_lines( skol3, skol2 )
% 24.47/24.87    , ! distinct_points( intersection_point( skol3, skol2 ), X ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 2
% 24.47/24.87     1 ==> 0
% 24.47/24.87     2 ==> 1
% 24.47/24.87     3 ==> 3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3174) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol3, skol2
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), X ), ! 
% 24.47/24.87    distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol2 ) }.
% 24.47/24.87  parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, 
% 24.47/24.87    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.87  parent1[4]: (109) {G1,W19,D3,L5,V2,M3} R(10,18) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( skol1, Y ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ), 
% 24.47/24.87    apart_point_and_line( intersection_point( skol3, skol2 ), Y ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol3
% 24.47/24.87     Y := skol2
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := X
% 24.47/24.87     Y := skol2
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3175) {G1,W14,D3,L4,V1,M4}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( skol1, skol2 )
% 24.47/24.87    , apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 24.47/24.87  parent0[0]: (3174) {G2,W17,D3,L5,V1,M5}  { ! convergent_lines( skol3, skol2
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), X ), ! 
% 24.47/24.87    distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol2 ) }.
% 24.47/24.87  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (1506) {G3,W14,D3,L4,V1,M1} R(109,136);r(15) { ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), X ), ! 
% 24.47/24.87    distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol2 ) }.
% 24.47/24.87  parent0: (3175) {G1,W14,D3,L4,V1,M4}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), ! distinct_lines( skol1, skol2 )
% 24.47/24.87    , apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87     2 ==> 2
% 24.47/24.87     3 ==> 3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3177) {G3,W18,D3,L4,V1,M4}  { ! convergent_lines( X, skol2 ), 
% 24.47/24.87    ! distinct_points( intersection_point( skol3, skol2 ), intersection_point
% 24.47/24.87    ( X, skol2 ) ), ! distinct_lines( skol1, skol2 ), apart_point_and_line( 
% 24.47/24.87    intersection_point( X, skol2 ), skol1 ) }.
% 24.47/24.87  parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, 
% 24.47/24.87    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.87  parent1[3]: (1506) {G3,W14,D3,L4,V1,M1} R(109,136);r(15) { ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), X ), ! 
% 24.47/24.87    distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ), 
% 24.47/24.87    apart_point_and_line( X, skol2 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87     Y := skol2
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := intersection_point( X, skol2 )
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (1647) {G4,W18,D3,L4,V1,M1} R(1506,136) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), intersection_point( X, skol2 ) ), ! 
% 24.47/24.87    distinct_lines( skol1, skol2 ), ! convergent_lines( X, skol2 ), 
% 24.47/24.87    apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 24.47/24.87  parent0: (3177) {G3,W18,D3,L4,V1,M4}  { ! convergent_lines( X, skol2 ), ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), intersection_point( 
% 24.47/24.87    X, skol2 ) ), ! distinct_lines( skol1, skol2 ), apart_point_and_line( 
% 24.47/24.87    intersection_point( X, skol2 ), skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 2
% 24.47/24.87     1 ==> 0
% 24.47/24.87     2 ==> 1
% 24.47/24.87     3 ==> 3
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3178) {G1,W11,D3,L3,V1,M3}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 24.47/24.87    , apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  parent0[2]: (1457) {G4,W14,D3,L4,V1,M1} R(106,135);r(156) { ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), X ), 
% 24.47/24.87    apart_point_and_line( X, skol1 ), ! convergent_lines( skol3, skol2 ), 
% 24.47/24.87    apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol2 )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (1706) {G5,W11,D3,L3,V1,M1} S(1457);r(15) { ! distinct_points
% 24.47/24.87    ( intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1
% 24.47/24.87     ), apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  parent0: (3178) {G1,W11,D3,L3,V1,M3}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 24.47/24.87    , apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87     2 ==> 2
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3180) {G3,W15,D3,L3,V1,M3}  { ! convergent_lines( skol3, X ), 
% 24.47/24.87    ! distinct_points( intersection_point( skol3, skol2 ), intersection_point
% 24.47/24.87    ( skol3, X ) ), apart_point_and_line( intersection_point( skol3, X ), 
% 24.47/24.87    skol1 ) }.
% 24.47/24.87  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 24.47/24.87    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  parent1[2]: (1706) {G5,W11,D3,L3,V1,M1} S(1457);r(15) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), X ), apart_point_and_line( X, skol1 )
% 24.47/24.87    , apart_point_and_line( X, skol3 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol3
% 24.47/24.87     Y := X
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := intersection_point( skol3, X )
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (1732) {G6,W15,D3,L3,V1,M1} R(1706,135) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), intersection_point( skol3, X ) ), ! 
% 24.47/24.87    convergent_lines( skol3, X ), apart_point_and_line( intersection_point( 
% 24.47/24.87    skol3, X ), skol1 ) }.
% 24.47/24.87  parent0: (3180) {G3,W15,D3,L3,V1,M3}  { ! convergent_lines( skol3, X ), ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), intersection_point( 
% 24.47/24.87    skol3, X ) ), apart_point_and_line( intersection_point( skol3, X ), skol1
% 24.47/24.87     ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := X
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 1
% 24.47/24.87     1 ==> 0
% 24.47/24.87     2 ==> 2
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3181) {G3,W13,D3,L3,V0,M3}  { ! convergent_lines( skol3, skol1
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), 
% 24.47/24.87    intersection_point( skol3, skol1 ) ), ! convergent_lines( skol3, skol1 )
% 24.47/24.87     }.
% 24.47/24.87  parent0[1]: (136) {G2,W8,D3,L2,V2,M1} F(127);r(0) { ! convergent_lines( X, 
% 24.47/24.87    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 24.47/24.87  parent1[2]: (1732) {G6,W15,D3,L3,V1,M1} R(1706,135) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), intersection_point( skol3, X ) ), ! 
% 24.47/24.87    convergent_lines( skol3, X ), apart_point_and_line( intersection_point( 
% 24.47/24.87    skol3, X ), skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol3
% 24.47/24.87     Y := skol1
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := skol1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  factor: (3182) {G3,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1 ), 
% 24.47/24.87    ! distinct_points( intersection_point( skol3, skol2 ), intersection_point
% 24.47/24.87    ( skol3, skol1 ) ) }.
% 24.47/24.87  parent0[0, 2]: (3181) {G3,W13,D3,L3,V0,M3}  { ! convergent_lines( skol3, 
% 24.47/24.87    skol1 ), ! distinct_points( intersection_point( skol3, skol2 ), 
% 24.47/24.87    intersection_point( skol3, skol1 ) ), ! convergent_lines( skol3, skol1 )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3184) {G3,W7,D3,L1,V0,M1}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), intersection_point( skol3, skol1 ) )
% 24.47/24.87     }.
% 24.47/24.87  parent0[0]: (3182) {G3,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), 
% 24.47/24.87    intersection_point( skol3, skol1 ) ) }.
% 24.47/24.87  parent1[0]: (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, 
% 24.47/24.87    skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (1766) {G7,W7,D3,L1,V0,M1} R(1732,136);f;r(45) { ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), intersection_point( 
% 24.47/24.87    skol3, skol1 ) ) }.
% 24.47/24.87  parent0: (3184) {G3,W7,D3,L1,V0,M1}  { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), intersection_point( skol3, skol1 ) )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3185) {G5,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1
% 24.47/24.87     ), distinct_points( intersection_point( skol3, skol2 ), 
% 24.47/24.87    intersection_point( skol1, skol2 ) ) }.
% 24.47/24.87  parent0[0]: (1766) {G7,W7,D3,L1,V0,M1} R(1732,136);f;r(45) { ! 
% 24.47/24.87    distinct_points( intersection_point( skol3, skol2 ), intersection_point( 
% 24.47/24.87    skol3, skol1 ) ) }.
% 24.47/24.87  parent1[1]: (468) {G4,W13,D3,L3,V2,M2} R(60,211) { ! convergent_lines( 
% 24.47/24.87    skol3, X ), distinct_points( Y, intersection_point( skol3, X ) ), 
% 24.47/24.87    distinct_points( Y, intersection_point( skol1, skol2 ) ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := skol1
% 24.47/24.87     Y := intersection_point( skol3, skol2 )
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3186) {G3,W7,D3,L1,V0,M1}  { distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 ) )
% 24.47/24.87     }.
% 24.47/24.87  parent0[0]: (3185) {G5,W10,D3,L2,V0,M2}  { ! convergent_lines( skol3, skol1
% 24.47/24.87     ), distinct_points( intersection_point( skol3, skol2 ), 
% 24.47/24.87    intersection_point( skol1, skol2 ) ) }.
% 24.47/24.87  parent1[0]: (45) {G2,W3,D2,L1,V0,M1} R(40,16) { convergent_lines( skol3, 
% 24.47/24.87    skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (1835) {G8,W7,D3,L1,V0,M1} R(1766,468);r(45) { distinct_points
% 24.47/24.87    ( intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 )
% 24.47/24.87     ) }.
% 24.47/24.87  parent0: (3186) {G3,W7,D3,L1,V0,M1}  { distinct_points( intersection_point
% 24.47/24.87    ( skol3, skol2 ), intersection_point( skol1, skol2 ) ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3187) {G3,W16,D3,L4,V0,M4}  { ! convergent_lines( skol1, skol2
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), 
% 24.47/24.87    intersection_point( skol1, skol2 ) ), ! distinct_lines( skol1, skol2 ), !
% 24.47/24.87     convergent_lines( skol1, skol2 ) }.
% 24.47/24.87  parent0[1]: (135) {G2,W8,D3,L2,V2,M1} F(128);r(0) { ! convergent_lines( X, 
% 24.47/24.87    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 24.47/24.87  parent1[3]: (1647) {G4,W18,D3,L4,V1,M1} R(1506,136) { ! distinct_points( 
% 24.47/24.87    intersection_point( skol3, skol2 ), intersection_point( X, skol2 ) ), ! 
% 24.47/24.87    distinct_lines( skol1, skol2 ), ! convergent_lines( X, skol2 ), 
% 24.47/24.87    apart_point_and_line( intersection_point( X, skol2 ), skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87     X := skol1
% 24.47/24.87     Y := skol2
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := skol1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3189) {G4,W9,D2,L3,V0,M3}  { ! convergent_lines( skol1, skol2
% 24.47/24.87     ), ! distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, skol2 )
% 24.47/24.87     }.
% 24.47/24.87  parent0[1]: (3187) {G3,W16,D3,L4,V0,M4}  { ! convergent_lines( skol1, skol2
% 24.47/24.87     ), ! distinct_points( intersection_point( skol3, skol2 ), 
% 24.47/24.87    intersection_point( skol1, skol2 ) ), ! distinct_lines( skol1, skol2 ), !
% 24.47/24.87     convergent_lines( skol1, skol2 ) }.
% 24.47/24.87  parent1[0]: (1835) {G8,W7,D3,L1,V0,M1} R(1766,468);r(45) { distinct_points
% 24.47/24.87    ( intersection_point( skol3, skol2 ), intersection_point( skol1, skol2 )
% 24.47/24.87     ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  factor: (3190) {G4,W6,D2,L2,V0,M2}  { ! convergent_lines( skol1, skol2 ), !
% 24.47/24.87     distinct_lines( skol1, skol2 ) }.
% 24.47/24.87  parent0[0, 2]: (3189) {G4,W9,D2,L3,V0,M3}  { ! convergent_lines( skol1, 
% 24.47/24.87    skol2 ), ! distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, 
% 24.47/24.87    skol2 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (2481) {G9,W6,D2,L2,V0,M1} R(1647,135);f;r(1835) { ! 
% 24.47/24.87    convergent_lines( skol1, skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 24.47/24.87  parent0: (3190) {G4,W6,D2,L2,V0,M2}  { ! convergent_lines( skol1, skol2 ), 
% 24.47/24.87    ! distinct_lines( skol1, skol2 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87     1 ==> 1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3191) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol1, skol2 )
% 24.47/24.87     }.
% 24.47/24.87  parent0[0]: (2481) {G9,W6,D2,L2,V0,M1} R(1647,135);f;r(1835) { ! 
% 24.47/24.87    convergent_lines( skol1, skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 24.47/24.87  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 24.47/24.87     }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (2482) {G10,W3,D2,L1,V0,M1} S(2481);r(14) { ! distinct_lines( 
% 24.47/24.87    skol1, skol2 ) }.
% 24.47/24.87  parent0: (3191) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol1, skol2 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87     0 ==> 0
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3192) {G3,W3,D2,L1,V0,M1}  { ! convergent_lines( skol2, skol1
% 24.47/24.87     ) }.
% 24.47/24.87  parent0[0]: (2482) {G10,W3,D2,L1,V0,M1} S(2481);r(14) { ! distinct_lines( 
% 24.47/24.87    skol1, skol2 ) }.
% 24.47/24.87  parent1[1]: (29) {G2,W6,D2,L2,V2,M1} R(13,26) { ! convergent_lines( X, Y )
% 24.47/24.87    , distinct_lines( Y, X ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87     X := skol2
% 24.47/24.87     Y := skol1
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  resolution: (3193) {G3,W0,D0,L0,V0,M0}  {  }.
% 24.47/24.87  parent0[0]: (3192) {G3,W3,D2,L1,V0,M1}  { ! convergent_lines( skol2, skol1
% 24.47/24.87     ) }.
% 24.47/24.87  parent1[0]: (43) {G2,W3,D2,L1,V0,M1} R(40,14) { convergent_lines( skol2, 
% 24.47/24.87    skol1 ) }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  substitution1:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  subsumption: (3005) {G11,W0,D0,L0,V0,M0} R(2482,29);r(43) {  }.
% 24.47/24.87  parent0: (3193) {G3,W0,D0,L0,V0,M0}  {  }.
% 24.47/24.87  substitution0:
% 24.47/24.87  end
% 24.47/24.87  permutation0:
% 24.47/24.87  end
% 24.47/24.87  
% 24.47/24.87  Proof check complete!
% 24.47/24.87  
% 24.47/24.87  Memory use:
% 24.47/24.87  
% 24.47/24.87  space for terms:        47864
% 24.47/24.87  space for clauses:      106019
% 24.47/24.87  
% 24.47/24.87  
% 24.47/24.87  clauses generated:      884793
% 24.47/24.87  clauses kept:           3006
% 24.47/24.87  clauses selected:       2143
% 24.47/24.87  clauses deleted:        10
% 24.47/24.87  clauses inuse deleted:  0
% 24.47/24.87  
% 24.47/24.87  subsentry:          3998631
% 24.47/24.87  literals s-matched: 1476619
% 24.47/24.87  literals matched:   1476574
% 24.47/24.87  full subsumption:   1317697
% 24.47/24.87  
% 24.47/24.87  checksum:           -1589453843
% 24.47/24.87  
% 24.47/24.87  
% 24.47/24.87  Bliksem ended
%------------------------------------------------------------------------------