TSTP Solution File: GEO172+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO172+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n022.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 02:52:13 EDT 2022

% Result   : Theorem 2.16s 2.50s
% Output   : Refutation 2.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO172+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % DateTime : Sat Jun 18 01:26:17 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 2.16/2.50  *** allocated 10000 integers for termspace/termends
% 2.16/2.50  *** allocated 10000 integers for clauses
% 2.16/2.50  *** allocated 10000 integers for justifications
% 2.16/2.50  Bliksem 1.12
% 2.16/2.50  
% 2.16/2.50  
% 2.16/2.50  Automatic Strategy Selection
% 2.16/2.50  
% 2.16/2.50  
% 2.16/2.50  Clauses:
% 2.16/2.50  
% 2.16/2.50  { ! distinct_points( X, X ) }.
% 2.16/2.50  { ! distinct_lines( X, X ) }.
% 2.16/2.50  { ! convergent_lines( X, X ) }.
% 2.16/2.50  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 2.16/2.50     ) }.
% 2.16/2.50  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.16/2.50     }.
% 2.16/2.50  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 2.16/2.50    , Z ) }.
% 2.16/2.50  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 2.16/2.50    , Y ) ) }.
% 2.16/2.50  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 2.16/2.50    , Y ) ) }.
% 2.16/2.50  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.16/2.50    , Y ), X ) }.
% 2.16/2.50  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.16/2.50    , Y ), Y ) }.
% 2.16/2.50  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 2.16/2.50    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 2.16/2.50    apart_point_and_line( Y, T ) }.
% 2.16/2.50  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 2.16/2.50    apart_point_and_line( Z, Y ) }.
% 2.16/2.50  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 2.16/2.50    apart_point_and_line( X, Z ) }.
% 2.16/2.50  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 2.16/2.50    Z ) }.
% 2.16/2.50  { convergent_lines( skol1, skol2 ) }.
% 2.16/2.50  { ! apart_point_and_line( skol3, skol1 ) }.
% 2.16/2.50  { ! apart_point_and_line( skol3, skol2 ) }.
% 2.16/2.50  { distinct_points( skol3, intersection_point( skol1, skol2 ) ) }.
% 2.16/2.50  
% 2.16/2.50  percentage equality = 0.000000, percentage horn = 0.611111
% 2.16/2.50  This a non-horn, non-equality problem
% 2.16/2.50  
% 2.16/2.50  
% 2.16/2.50  Options Used:
% 2.16/2.50  
% 2.16/2.50  useres =            1
% 2.16/2.50  useparamod =        0
% 2.16/2.50  useeqrefl =         0
% 2.16/2.50  useeqfact =         0
% 2.16/2.50  usefactor =         1
% 2.16/2.50  usesimpsplitting =  0
% 2.16/2.50  usesimpdemod =      0
% 2.16/2.50  usesimpres =        3
% 2.16/2.50  
% 2.16/2.50  resimpinuse      =  1000
% 2.16/2.50  resimpclauses =     20000
% 2.16/2.50  substype =          standard
% 2.16/2.50  backwardsubs =      1
% 2.16/2.50  selectoldest =      5
% 2.16/2.50  
% 2.16/2.50  litorderings [0] =  split
% 2.16/2.50  litorderings [1] =  liftord
% 2.16/2.50  
% 2.16/2.50  termordering =      none
% 2.16/2.50  
% 2.16/2.50  litapriori =        1
% 2.16/2.50  termapriori =       0
% 2.16/2.50  litaposteriori =    0
% 2.16/2.50  termaposteriori =   0
% 2.16/2.50  demodaposteriori =  0
% 2.16/2.50  ordereqreflfact =   0
% 2.16/2.50  
% 2.16/2.50  litselect =         none
% 2.16/2.50  
% 2.16/2.50  maxweight =         15
% 2.16/2.50  maxdepth =          30000
% 2.16/2.50  maxlength =         115
% 2.16/2.50  maxnrvars =         195
% 2.16/2.50  excuselevel =       1
% 2.16/2.50  increasemaxweight = 1
% 2.16/2.50  
% 2.16/2.50  maxselected =       10000000
% 2.16/2.50  maxnrclauses =      10000000
% 2.16/2.50  
% 2.16/2.50  showgenerated =    0
% 2.16/2.50  showkept =         0
% 2.16/2.50  showselected =     0
% 2.16/2.50  showdeleted =      0
% 2.16/2.50  showresimp =       1
% 2.16/2.50  showstatus =       2000
% 2.16/2.50  
% 2.16/2.50  prologoutput =     0
% 2.16/2.50  nrgoals =          5000000
% 2.16/2.50  totalproof =       1
% 2.16/2.50  
% 2.16/2.50  Symbols occurring in the translation:
% 2.16/2.50  
% 2.16/2.50  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 2.16/2.50  .  [1, 2]      (w:1, o:19, a:1, s:1, b:0), 
% 2.16/2.50  !  [4, 1]      (w:0, o:14, a:1, s:1, b:0), 
% 2.16/2.50  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 2.16/2.50  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 2.16/2.50  distinct_points  [36, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 2.16/2.50  distinct_lines  [37, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 2.16/2.50  convergent_lines  [38, 2]      (w:1, o:43, a:1, s:1, b:0), 
% 2.16/2.50  line_connecting  [41, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 2.16/2.50  apart_point_and_line  [42, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 2.16/2.50  intersection_point  [43, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 2.16/2.50  skol1  [46, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 2.16/2.50  skol2  [47, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 2.16/2.50  skol3  [48, 0]      (w:1, o:13, a:1, s:1, b:0).
% 2.16/2.50  
% 2.16/2.50  
% 2.16/2.50  Starting Search:
% 2.16/2.50  
% 2.16/2.50  *** allocated 15000 integers for clauses
% 2.16/2.50  *** allocated 22500 integers for clauses
% 2.16/2.50  *** allocated 33750 integers for clauses
% 2.16/2.50  *** allocated 15000 integers for termspace/termends
% 2.16/2.50  Resimplifying inuse:
% 2.16/2.50  Done
% 2.16/2.50  
% 2.16/2.50  Failed to find proof!
% 2.16/2.50  maxweight =   15
% 2.16/2.50  maxnrclauses = 10000000
% 2.16/2.50  Generated: 128451
% 2.16/2.50  Kept: 737
% 2.16/2.50  
% 2.16/2.50  
% 2.16/2.50  The strategy used was not complete!
% 2.16/2.50  
% 2.16/2.50  Increased maxweight to 16
% 2.16/2.50  
% 2.16/2.50  Starting Search:
% 2.16/2.50  
% 2.16/2.50  *** allocated 50625 integers for clauses
% 2.16/2.50  *** allocated 22500 integers for termspace/termends
% 2.16/2.50  Resimplifying inuse:
% 2.16/2.50  Done
% 2.16/2.50  
% 2.16/2.50  *** allocated 75937 integers for clauses
% 2.16/2.50  *** allocated 33750 integers for termspace/termends
% 2.16/2.50  
% 2.16/2.50  Bliksems!, er is een bewijs:
% 2.16/2.50  % SZS status Theorem
% 2.16/2.50  % SZS output start Refutation
% 2.16/2.50  
% 2.16/2.50  (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.16/2.51  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51  (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 2.16/2.51     ), ! distinct_points( X, Y ) }.
% 2.16/2.51  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.16/2.51    , ! distinct_lines( X, Y ) }.
% 2.16/2.51  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 2.16/2.51    Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51  (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51  (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 2.16/2.51    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 2.16/2.51    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 2.16/2.51  (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 2.16/2.51    ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51  (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines( 
% 2.16/2.51    X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51  (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 2.16/2.51  (15) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, skol1 ) }.
% 2.16/2.51  (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, skol2 ) }.
% 2.16/2.51  (17) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol3, intersection_point( 
% 2.16/2.51    skol1, skol2 ) ) }.
% 2.16/2.51  (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 2.16/2.51    distinct_points( X, Y ) }.
% 2.16/2.51  (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 2.16/2.51    ( X, Y ) }.
% 2.16/2.51  (32) {G1,W6,D2,L2,V1,M1} R(5,14) { convergent_lines( skol1, X ), 
% 2.16/2.51    convergent_lines( skol2, X ) }.
% 2.16/2.51  (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.16/2.51    convergent_lines( X, Y ) }.
% 2.16/2.51  (37) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol2 ), 
% 2.16/2.51    convergent_lines( skol1, X ) }.
% 2.16/2.51  (39) {G3,W6,D2,L2,V1,M1} R(37,33) { convergent_lines( X, skol1 ), 
% 2.16/2.51    convergent_lines( X, skol2 ) }.
% 2.16/2.51  (67) {G1,W15,D2,L5,V2,M3} R(10,15) { ! distinct_points( skol3, X ), ! 
% 2.16/2.51    distinct_lines( skol1, Y ), apart_point_and_line( X, skol1 ), 
% 2.16/2.51    apart_point_and_line( X, Y ), apart_point_and_line( skol3, Y ) }.
% 2.16/2.51  (98) {G1,W6,D2,L2,V1,M1} R(11,16) { distinct_points( X, skol3 ), ! 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  (100) {G2,W9,D2,L3,V2,M1} R(98,11) { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51  (127) {G2,W9,D2,L3,V3,M1} R(13,27) { ! convergent_lines( X, Y ), 
% 2.16/2.51    convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.16/2.51  (189) {G3,W12,D2,L4,V3,M1} R(100,11) { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.16/2.51    ( Z, skol2 ) }.
% 2.16/2.51  (190) {G4,W6,D2,L2,V1,M1} F(189);r(20) { distinct_points( skol3, X ), ! 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  (624) {G5,W12,D2,L4,V1,M1} R(67,190);r(0) { ! distinct_points( skol3, X ), 
% 2.16/2.51    ! distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ), 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  (790) {G6,W16,D3,L4,V1,M1} R(624,9) { ! distinct_points( skol3, 
% 2.16/2.51    intersection_point( X, skol2 ) ), ! distinct_lines( skol1, skol2 ), ! 
% 2.16/2.51    convergent_lines( X, skol2 ), apart_point_and_line( intersection_point( X
% 2.16/2.51    , skol2 ), skol1 ) }.
% 2.16/2.51  (1292) {G7,W6,D2,L2,V0,M1} R(790,8);f;r(17) { ! convergent_lines( skol1, 
% 2.16/2.51    skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51  (1293) {G8,W3,D2,L1,V0,M1} S(1292);r(14) { ! distinct_lines( skol1, skol2 )
% 2.16/2.51     }.
% 2.16/2.51  (1424) {G9,W3,D2,L1,V1,M1} R(1293,127);r(39) { convergent_lines( X, skol1 )
% 2.16/2.51     }.
% 2.16/2.51  (1443) {G10,W0,D0,L0,V0,M0} R(1424,2) {  }.
% 2.16/2.51  
% 2.16/2.51  
% 2.16/2.51  % SZS output end Refutation
% 2.16/2.51  found a proof!
% 2.16/2.51  
% 2.16/2.51  
% 2.16/2.51  Unprocessed initial clauses:
% 2.16/2.51  
% 2.16/2.51  (1445) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 2.16/2.51  (1446) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 2.16/2.51  (1447) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 2.16/2.51  (1448) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 2.16/2.51    , Z ), distinct_points( Y, Z ) }.
% 2.16/2.51  (1449) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 2.16/2.51    Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51  (1450) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 2.16/2.51    ( X, Z ), convergent_lines( Y, Z ) }.
% 2.16/2.51  (1451) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 2.16/2.51  (1452) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 2.16/2.51  (1453) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51  (1454) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51  (1455) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 2.16/2.51    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 2.16/2.51    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 2.16/2.51  (1456) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 2.16/2.51    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.16/2.51  (1457) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 2.16/2.51    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 2.16/2.51  (1458) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 2.16/2.51    , Z ), convergent_lines( X, Z ) }.
% 2.16/2.51  (1459) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 2.16/2.51  (1460) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol3, skol1 ) }.
% 2.16/2.51  (1461) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol3, skol2 ) }.
% 2.16/2.51  (1462) {G0,W5,D3,L1,V0,M1}  { distinct_points( skol3, intersection_point( 
% 2.16/2.51    skol1, skol2 ) ) }.
% 2.16/2.51  
% 2.16/2.51  
% 2.16/2.51  Total Proof:
% 2.16/2.51  
% 2.16/2.51  subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51  parent0: (1445) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.16/2.51  parent0: (1446) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51  parent0: (1447) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 2.16/2.51    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.16/2.51  parent0: (1448) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), 
% 2.16/2.51    distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := Z
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 2
% 2.16/2.51     1 ==> 0
% 2.16/2.51     2 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 2.16/2.51    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.16/2.51  parent0: (1449) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 2.16/2.51    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := Z
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 2
% 2.16/2.51     1 ==> 0
% 2.16/2.51     2 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 2.16/2.51    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51  parent0: (1450) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 2.16/2.51    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := Z
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 2
% 2.16/2.51     1 ==> 0
% 2.16/2.51     2 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51  parent0: (1453) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51  parent0: (1454) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 2.16/2.51    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 2.16/2.51    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 2.16/2.51    apart_point_and_line( X, Z ) }.
% 2.16/2.51  parent0: (1455) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 2.16/2.51    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 2.16/2.51    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 2.16/2.51    apart_point_and_line( Y, T ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := Z
% 2.16/2.51     T := T
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51     2 ==> 5
% 2.16/2.51     3 ==> 2
% 2.16/2.51     4 ==> 3
% 2.16/2.51     5 ==> 4
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.16/2.51    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51  parent0: (1456) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 2.16/2.51    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := Z
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 2
% 2.16/2.51     1 ==> 0
% 2.16/2.51     2 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 2.16/2.51    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51  parent0: (1458) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 2.16/2.51    distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := Z
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 2
% 2.16/2.51     2 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 2.16/2.51     }.
% 2.16/2.51  parent0: (1459) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (15) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, 
% 2.16/2.51    skol1 ) }.
% 2.16/2.51  parent0: (1460) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol3, skol1
% 2.16/2.51     ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, 
% 2.16/2.51    skol2 ) }.
% 2.16/2.51  parent0: (1461) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol3, skol2
% 2.16/2.51     ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (17) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol3, 
% 2.16/2.51    intersection_point( skol1, skol2 ) ) }.
% 2.16/2.51  parent0: (1462) {G0,W5,D3,L1,V0,M1}  { distinct_points( skol3, 
% 2.16/2.51    intersection_point( skol1, skol2 ) ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1538) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 2.16/2.51    distinct_points( X, Y ) }.
% 2.16/2.51  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51  parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 2.16/2.51    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 2.16/2.51    distinct_points( X, Y ) }.
% 2.16/2.51  parent0: (1538) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 2.16/2.51    distinct_points( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := Y
% 2.16/2.51     Y := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 1
% 2.16/2.51     1 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1540) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 2.16/2.51    distinct_lines( X, Y ) }.
% 2.16/2.51  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.16/2.51  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 2.16/2.51    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 2.16/2.51    distinct_lines( X, Y ) }.
% 2.16/2.51  parent0: (1540) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 2.16/2.51    distinct_lines( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := Y
% 2.16/2.51     Y := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 1
% 2.16/2.51     1 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1542) {G1,W6,D2,L2,V1,M2}  { convergent_lines( skol1, X ), 
% 2.16/2.51    convergent_lines( skol2, X ) }.
% 2.16/2.51  parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 2.16/2.51    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 2.16/2.51     }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := skol1
% 2.16/2.51     Y := skol2
% 2.16/2.51     Z := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (32) {G1,W6,D2,L2,V1,M1} R(5,14) { convergent_lines( skol1, X
% 2.16/2.51     ), convergent_lines( skol2, X ) }.
% 2.16/2.51  parent0: (1542) {G1,W6,D2,L2,V1,M2}  { convergent_lines( skol1, X ), 
% 2.16/2.51    convergent_lines( skol2, X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1543) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 2.16/2.51    convergent_lines( X, Y ) }.
% 2.16/2.51  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 2.16/2.51    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.16/2.51    convergent_lines( X, Y ) }.
% 2.16/2.51  parent0: (1543) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 2.16/2.51    convergent_lines( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := Y
% 2.16/2.51     Y := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 1
% 2.16/2.51     1 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1546) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol2 ), 
% 2.16/2.51    convergent_lines( skol1, X ) }.
% 2.16/2.51  parent0[0]: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.16/2.51    convergent_lines( X, Y ) }.
% 2.16/2.51  parent1[1]: (32) {G1,W6,D2,L2,V1,M1} R(5,14) { convergent_lines( skol1, X )
% 2.16/2.51    , convergent_lines( skol2, X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := skol2
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (37) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol2
% 2.16/2.51     ), convergent_lines( skol1, X ) }.
% 2.16/2.51  parent0: (1546) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol2 ), 
% 2.16/2.51    convergent_lines( skol1, X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1548) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol1 ), 
% 2.16/2.51    convergent_lines( X, skol2 ) }.
% 2.16/2.51  parent0[0]: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.16/2.51    convergent_lines( X, Y ) }.
% 2.16/2.51  parent1[1]: (37) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol2
% 2.16/2.51     ), convergent_lines( skol1, X ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := skol1
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (39) {G3,W6,D2,L2,V1,M1} R(37,33) { convergent_lines( X, skol1
% 2.16/2.51     ), convergent_lines( X, skol2 ) }.
% 2.16/2.51  parent0: (1548) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol1 ), 
% 2.16/2.51    convergent_lines( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1552) {G1,W15,D2,L5,V2,M5}  { ! distinct_points( skol3, X ), !
% 2.16/2.51     distinct_lines( skol1, Y ), apart_point_and_line( skol3, Y ), 
% 2.16/2.51    apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ) }.
% 2.16/2.51  parent0[0]: (15) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, 
% 2.16/2.51    skol1 ) }.
% 2.16/2.51  parent1[5]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 2.16/2.51    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 2.16/2.51    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 2.16/2.51    apart_point_and_line( X, Z ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := skol3
% 2.16/2.51     Y := X
% 2.16/2.51     Z := skol1
% 2.16/2.51     T := Y
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (67) {G1,W15,D2,L5,V2,M3} R(10,15) { ! distinct_points( skol3
% 2.16/2.51    , X ), ! distinct_lines( skol1, Y ), apart_point_and_line( X, skol1 ), 
% 2.16/2.51    apart_point_and_line( X, Y ), apart_point_and_line( skol3, Y ) }.
% 2.16/2.51  parent0: (1552) {G1,W15,D2,L5,V2,M5}  { ! distinct_points( skol3, X ), ! 
% 2.16/2.51    distinct_lines( skol1, Y ), apart_point_and_line( skol3, Y ), 
% 2.16/2.51    apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51     2 ==> 4
% 2.16/2.51     3 ==> 2
% 2.16/2.51     4 ==> 3
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1558) {G1,W6,D2,L2,V1,M2}  { distinct_points( X, skol3 ), ! 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0[0]: (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, 
% 2.16/2.51    skol2 ) }.
% 2.16/2.51  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.16/2.51    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51     Y := skol2
% 2.16/2.51     Z := skol3
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (98) {G1,W6,D2,L2,V1,M1} R(11,16) { distinct_points( X, skol3
% 2.16/2.51     ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0: (1558) {G1,W6,D2,L2,V1,M2}  { distinct_points( X, skol3 ), ! 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1559) {G1,W9,D2,L3,V2,M3}  { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51  parent0[1]: (98) {G1,W6,D2,L2,V1,M1} R(11,16) { distinct_points( X, skol3 )
% 2.16/2.51    , ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.16/2.51    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := Y
% 2.16/2.51     Y := skol2
% 2.16/2.51     Z := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (100) {G2,W9,D2,L3,V2,M1} R(98,11) { distinct_points( X, skol3
% 2.16/2.51     ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51  parent0: (1559) {G1,W9,D2,L3,V2,M3}  { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51     2 ==> 2
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1561) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 2.16/2.51    convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.16/2.51  parent0[0]: (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 2.16/2.51    distinct_lines( X, Y ) }.
% 2.16/2.51  parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 2.16/2.51    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := Y
% 2.16/2.51     Y := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := Z
% 2.16/2.51     Y := X
% 2.16/2.51     Z := Y
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (127) {G2,W9,D2,L3,V3,M1} R(13,27) { ! convergent_lines( X, Y
% 2.16/2.51     ), convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.16/2.51  parent0: (1561) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 2.16/2.51    convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := Y
% 2.16/2.51     Y := Z
% 2.16/2.51     Z := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 2
% 2.16/2.51     1 ==> 0
% 2.16/2.51     2 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1562) {G1,W12,D2,L4,V3,M4}  { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.16/2.51    ( Z, skol2 ) }.
% 2.16/2.51  parent0[2]: (100) {G2,W9,D2,L3,V2,M1} R(98,11) { distinct_points( X, skol3
% 2.16/2.51     ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.16/2.51    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := Z
% 2.16/2.51     Y := skol2
% 2.16/2.51     Z := Y
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (189) {G3,W12,D2,L4,V3,M1} R(100,11) { distinct_points( X, 
% 2.16/2.51    skol3 ), distinct_points( Y, X ), distinct_points( Z, Y ), ! 
% 2.16/2.51    apart_point_and_line( Z, skol2 ) }.
% 2.16/2.51  parent0: (1562) {G1,W12,D2,L4,V3,M4}  { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.16/2.51    ( Z, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := Y
% 2.16/2.51     Z := Z
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51     2 ==> 2
% 2.16/2.51     3 ==> 3
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  factor: (1568) {G3,W9,D2,L3,V1,M3}  { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0[0, 2]: (189) {G3,W12,D2,L4,V3,M1} R(100,11) { distinct_points( X, 
% 2.16/2.51    skol3 ), distinct_points( Y, X ), distinct_points( Z, Y ), ! 
% 2.16/2.51    apart_point_and_line( Z, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := skol3
% 2.16/2.51     Z := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1574) {G2,W9,D2,L3,V1,M3}  { distinct_points( skol3, X ), 
% 2.16/2.51    distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0[0]: (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 2.16/2.51    distinct_points( X, Y ) }.
% 2.16/2.51  parent1[0]: (1568) {G3,W9,D2,L3,V1,M3}  { distinct_points( X, skol3 ), 
% 2.16/2.51    distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := skol3
% 2.16/2.51     Y := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  factor: (1576) {G2,W6,D2,L2,V1,M2}  { distinct_points( skol3, X ), ! 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0[0, 1]: (1574) {G2,W9,D2,L3,V1,M3}  { distinct_points( skol3, X ), 
% 2.16/2.51    distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (190) {G4,W6,D2,L2,V1,M1} F(189);r(20) { distinct_points( 
% 2.16/2.51    skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0: (1576) {G2,W6,D2,L2,V1,M2}  { distinct_points( skol3, X ), ! 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1583) {G2,W15,D2,L5,V1,M5}  { distinct_points( skol3, skol3 )
% 2.16/2.51    , ! distinct_points( skol3, X ), ! distinct_lines( skol1, skol2 ), 
% 2.16/2.51    apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0[1]: (190) {G4,W6,D2,L2,V1,M1} F(189);r(20) { distinct_points( skol3
% 2.16/2.51    , X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent1[4]: (67) {G1,W15,D2,L5,V2,M3} R(10,15) { ! distinct_points( skol3, 
% 2.16/2.51    X ), ! distinct_lines( skol1, Y ), apart_point_and_line( X, skol1 ), 
% 2.16/2.51    apart_point_and_line( X, Y ), apart_point_and_line( skol3, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := skol3
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51     Y := skol2
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1584) {G1,W12,D2,L4,V1,M4}  { ! distinct_points( skol3, X ), !
% 2.16/2.51     distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ), 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51  parent1[0]: (1583) {G2,W15,D2,L5,V1,M5}  { distinct_points( skol3, skol3 )
% 2.16/2.51    , ! distinct_points( skol3, X ), ! distinct_lines( skol1, skol2 ), 
% 2.16/2.51    apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := skol3
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (624) {G5,W12,D2,L4,V1,M1} R(67,190);r(0) { ! distinct_points
% 2.16/2.51    ( skol3, X ), ! distinct_lines( skol1, skol2 ), apart_point_and_line( X, 
% 2.16/2.51    skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  parent0: (1584) {G1,W12,D2,L4,V1,M4}  { ! distinct_points( skol3, X ), ! 
% 2.16/2.51    distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ), 
% 2.16/2.51    apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51     2 ==> 2
% 2.16/2.51     3 ==> 3
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1586) {G1,W16,D3,L4,V1,M4}  { ! convergent_lines( X, skol2 ), 
% 2.16/2.51    ! distinct_points( skol3, intersection_point( X, skol2 ) ), ! 
% 2.16/2.51    distinct_lines( skol1, skol2 ), apart_point_and_line( intersection_point
% 2.16/2.51    ( X, skol2 ), skol1 ) }.
% 2.16/2.51  parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51  parent1[3]: (624) {G5,W12,D2,L4,V1,M1} R(67,190);r(0) { ! distinct_points( 
% 2.16/2.51    skol3, X ), ! distinct_lines( skol1, skol2 ), apart_point_and_line( X, 
% 2.16/2.51    skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51     Y := skol2
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := intersection_point( X, skol2 )
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (790) {G6,W16,D3,L4,V1,M1} R(624,9) { ! distinct_points( skol3
% 2.16/2.51    , intersection_point( X, skol2 ) ), ! distinct_lines( skol1, skol2 ), ! 
% 2.16/2.51    convergent_lines( X, skol2 ), apart_point_and_line( intersection_point( X
% 2.16/2.51    , skol2 ), skol1 ) }.
% 2.16/2.51  parent0: (1586) {G1,W16,D3,L4,V1,M4}  { ! convergent_lines( X, skol2 ), ! 
% 2.16/2.51    distinct_points( skol3, intersection_point( X, skol2 ) ), ! 
% 2.16/2.51    distinct_lines( skol1, skol2 ), apart_point_and_line( intersection_point
% 2.16/2.51    ( X, skol2 ), skol1 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 2
% 2.16/2.51     1 ==> 0
% 2.16/2.51     2 ==> 1
% 2.16/2.51     3 ==> 3
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1587) {G1,W14,D3,L4,V0,M4}  { ! convergent_lines( skol1, skol2
% 2.16/2.51     ), ! distinct_points( skol3, intersection_point( skol1, skol2 ) ), ! 
% 2.16/2.51    distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, skol2 ) }.
% 2.16/2.51  parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.16/2.51    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51  parent1[3]: (790) {G6,W16,D3,L4,V1,M1} R(624,9) { ! distinct_points( skol3
% 2.16/2.51    , intersection_point( X, skol2 ) ), ! distinct_lines( skol1, skol2 ), ! 
% 2.16/2.51    convergent_lines( X, skol2 ), apart_point_and_line( intersection_point( X
% 2.16/2.51    , skol2 ), skol1 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := skol1
% 2.16/2.51     Y := skol2
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := skol1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1589) {G1,W9,D2,L3,V0,M3}  { ! convergent_lines( skol1, skol2
% 2.16/2.51     ), ! distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, skol2 )
% 2.16/2.51     }.
% 2.16/2.51  parent0[1]: (1587) {G1,W14,D3,L4,V0,M4}  { ! convergent_lines( skol1, skol2
% 2.16/2.51     ), ! distinct_points( skol3, intersection_point( skol1, skol2 ) ), ! 
% 2.16/2.51    distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, skol2 ) }.
% 2.16/2.51  parent1[0]: (17) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol3, 
% 2.16/2.51    intersection_point( skol1, skol2 ) ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  factor: (1590) {G1,W6,D2,L2,V0,M2}  { ! convergent_lines( skol1, skol2 ), !
% 2.16/2.51     distinct_lines( skol1, skol2 ) }.
% 2.16/2.51  parent0[0, 2]: (1589) {G1,W9,D2,L3,V0,M3}  { ! convergent_lines( skol1, 
% 2.16/2.51    skol2 ), ! distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, 
% 2.16/2.51    skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (1292) {G7,W6,D2,L2,V0,M1} R(790,8);f;r(17) { ! 
% 2.16/2.51    convergent_lines( skol1, skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51  parent0: (1590) {G1,W6,D2,L2,V0,M2}  { ! convergent_lines( skol1, skol2 ), 
% 2.16/2.51    ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51     1 ==> 1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1591) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol1, skol2 )
% 2.16/2.51     }.
% 2.16/2.51  parent0[0]: (1292) {G7,W6,D2,L2,V0,M1} R(790,8);f;r(17) { ! 
% 2.16/2.51    convergent_lines( skol1, skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 2.16/2.51     }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (1293) {G8,W3,D2,L1,V0,M1} S(1292);r(14) { ! distinct_lines( 
% 2.16/2.51    skol1, skol2 ) }.
% 2.16/2.51  parent0: (1591) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1592) {G3,W6,D2,L2,V1,M2}  { ! convergent_lines( X, skol2 ), 
% 2.16/2.51    convergent_lines( X, skol1 ) }.
% 2.16/2.51  parent0[0]: (1293) {G8,W3,D2,L1,V0,M1} S(1292);r(14) { ! distinct_lines( 
% 2.16/2.51    skol1, skol2 ) }.
% 2.16/2.51  parent1[2]: (127) {G2,W9,D2,L3,V3,M1} R(13,27) { ! convergent_lines( X, Y )
% 2.16/2.51    , convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51     Y := skol2
% 2.16/2.51     Z := skol1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1593) {G4,W6,D2,L2,V1,M2}  { convergent_lines( X, skol1 ), 
% 2.16/2.51    convergent_lines( X, skol1 ) }.
% 2.16/2.51  parent0[0]: (1592) {G3,W6,D2,L2,V1,M2}  { ! convergent_lines( X, skol2 ), 
% 2.16/2.51    convergent_lines( X, skol1 ) }.
% 2.16/2.51  parent1[1]: (39) {G3,W6,D2,L2,V1,M1} R(37,33) { convergent_lines( X, skol1
% 2.16/2.51     ), convergent_lines( X, skol2 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  factor: (1594) {G4,W3,D2,L1,V1,M1}  { convergent_lines( X, skol1 ) }.
% 2.16/2.51  parent0[0, 1]: (1593) {G4,W6,D2,L2,V1,M2}  { convergent_lines( X, skol1 ), 
% 2.16/2.51    convergent_lines( X, skol1 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (1424) {G9,W3,D2,L1,V1,M1} R(1293,127);r(39) { 
% 2.16/2.51    convergent_lines( X, skol1 ) }.
% 2.16/2.51  parent0: (1594) {G4,W3,D2,L1,V1,M1}  { convergent_lines( X, skol1 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := X
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51     0 ==> 0
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  resolution: (1595) {G1,W0,D0,L0,V0,M0}  {  }.
% 2.16/2.51  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51  parent1[0]: (1424) {G9,W3,D2,L1,V1,M1} R(1293,127);r(39) { convergent_lines
% 2.16/2.51    ( X, skol1 ) }.
% 2.16/2.51  substitution0:
% 2.16/2.51     X := skol1
% 2.16/2.51  end
% 2.16/2.51  substitution1:
% 2.16/2.51     X := skol1
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  subsumption: (1443) {G10,W0,D0,L0,V0,M0} R(1424,2) {  }.
% 2.16/2.51  parent0: (1595) {G1,W0,D0,L0,V0,M0}  {  }.
% 2.16/2.51  substitution0:
% 2.16/2.51  end
% 2.16/2.51  permutation0:
% 2.16/2.51  end
% 2.16/2.51  
% 2.16/2.51  Proof check complete!
% 2.16/2.51  
% 2.16/2.51  Memory use:
% 2.16/2.51  
% 2.16/2.51  space for terms:        22582
% 2.16/2.51  space for clauses:      52008
% 2.16/2.51  
% 2.16/2.51  
% 2.16/2.51  clauses generated:      174364
% 2.16/2.51  clauses kept:           1444
% 2.16/2.51  clauses selected:       990
% 2.16/2.51  clauses deleted:        9
% 2.16/2.51  clauses inuse deleted:  0
% 2.16/2.51  
% 2.16/2.51  subsentry:          185274
% 2.16/2.51  literals s-matched: 117776
% 2.16/2.51  literals matched:   117741
% 2.16/2.51  full subsumption:   69246
% 2.16/2.51  
% 2.16/2.51  checksum:           -10310973
% 2.16/2.51  
% 2.16/2.51  
% 2.16/2.51  Bliksem ended
%------------------------------------------------------------------------------