TSTP Solution File: GEO186+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n019.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 02:52:26 EDT 2022

% Result   : Theorem 2.35s 2.71s
% Output   : Refutation 2.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command  : bliksem %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Fri Jun 17 17:00:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 2.35/2.71  *** allocated 10000 integers for termspace/termends
% 2.35/2.71  *** allocated 10000 integers for clauses
% 2.35/2.71  *** allocated 10000 integers for justifications
% 2.35/2.71  Bliksem 1.12
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  Automatic Strategy Selection
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  Clauses:
% 2.35/2.71  
% 2.35/2.71  { ! distinct_points( X, X ) }.
% 2.35/2.71  { ! distinct_lines( X, X ) }.
% 2.35/2.71  { ! convergent_lines( X, X ) }.
% 2.35/2.71  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 2.35/2.71     ) }.
% 2.35/2.71  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.35/2.71     }.
% 2.35/2.71  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 2.35/2.71    , Z ) }.
% 2.35/2.71  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 2.35/2.71    , Y ) ) }.
% 2.35/2.71  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 2.35/2.71    , Y ) ) }.
% 2.35/2.71  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.35/2.71    , Y ), X ) }.
% 2.35/2.71  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.35/2.71    , Y ), Y ) }.
% 2.35/2.71  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 2.35/2.71    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 2.35/2.71    apart_point_and_line( Y, T ) }.
% 2.35/2.71  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 2.35/2.71    apart_point_and_line( Z, Y ) }.
% 2.35/2.71  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 2.35/2.71    apart_point_and_line( X, Z ) }.
% 2.35/2.71  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 2.35/2.71    Z ) }.
% 2.35/2.71  { distinct_points( skol1, skol4 ) }.
% 2.35/2.71  { convergent_lines( skol2, skol3 ) }.
% 2.35/2.71  { ! apart_point_and_line( skol1, skol2 ) }.
% 2.35/2.71  { ! apart_point_and_line( skol1, skol3 ) }.
% 2.35/2.71  { distinct_points( skol1, intersection_point( skol2, skol3 ) ) }.
% 2.35/2.71  
% 2.35/2.71  percentage equality = 0.000000, percentage horn = 0.631579
% 2.35/2.71  This a non-horn, non-equality problem
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  Options Used:
% 2.35/2.71  
% 2.35/2.71  useres =            1
% 2.35/2.71  useparamod =        0
% 2.35/2.71  useeqrefl =         0
% 2.35/2.71  useeqfact =         0
% 2.35/2.71  usefactor =         1
% 2.35/2.71  usesimpsplitting =  0
% 2.35/2.71  usesimpdemod =      0
% 2.35/2.71  usesimpres =        3
% 2.35/2.71  
% 2.35/2.71  resimpinuse      =  1000
% 2.35/2.71  resimpclauses =     20000
% 2.35/2.71  substype =          standard
% 2.35/2.71  backwardsubs =      1
% 2.35/2.71  selectoldest =      5
% 2.35/2.71  
% 2.35/2.71  litorderings [0] =  split
% 2.35/2.71  litorderings [1] =  liftord
% 2.35/2.71  
% 2.35/2.71  termordering =      none
% 2.35/2.71  
% 2.35/2.71  litapriori =        1
% 2.35/2.71  termapriori =       0
% 2.35/2.71  litaposteriori =    0
% 2.35/2.71  termaposteriori =   0
% 2.35/2.71  demodaposteriori =  0
% 2.35/2.71  ordereqreflfact =   0
% 2.35/2.71  
% 2.35/2.71  litselect =         none
% 2.35/2.71  
% 2.35/2.71  maxweight =         15
% 2.35/2.71  maxdepth =          30000
% 2.35/2.71  maxlength =         115
% 2.35/2.71  maxnrvars =         195
% 2.35/2.71  excuselevel =       1
% 2.35/2.71  increasemaxweight = 1
% 2.35/2.71  
% 2.35/2.71  maxselected =       10000000
% 2.35/2.71  maxnrclauses =      10000000
% 2.35/2.71  
% 2.35/2.71  showgenerated =    0
% 2.35/2.71  showkept =         0
% 2.35/2.71  showselected =     0
% 2.35/2.71  showdeleted =      0
% 2.35/2.71  showresimp =       1
% 2.35/2.71  showstatus =       2000
% 2.35/2.71  
% 2.35/2.71  prologoutput =     0
% 2.35/2.71  nrgoals =          5000000
% 2.35/2.71  totalproof =       1
% 2.35/2.71  
% 2.35/2.71  Symbols occurring in the translation:
% 2.35/2.71  
% 2.35/2.71  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 2.35/2.71  .  [1, 2]      (w:1, o:20, a:1, s:1, b:0), 
% 2.35/2.71  !  [4, 1]      (w:0, o:15, a:1, s:1, b:0), 
% 2.35/2.71  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 2.35/2.71  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 2.35/2.71  distinct_points  [36, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 2.35/2.71  distinct_lines  [37, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 2.35/2.71  convergent_lines  [38, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 2.35/2.71  line_connecting  [41, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 2.35/2.71  apart_point_and_line  [42, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 2.35/2.71  intersection_point  [43, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 2.35/2.71  skol1  [46, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 2.35/2.71  skol2  [47, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 2.35/2.71  skol3  [48, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 2.35/2.71  skol4  [49, 0]      (w:1, o:14, a:1, s:1, b:0).
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  Starting Search:
% 2.35/2.71  
% 2.35/2.71  *** allocated 15000 integers for clauses
% 2.35/2.71  *** allocated 22500 integers for clauses
% 2.35/2.71  *** allocated 33750 integers for clauses
% 2.35/2.71  *** allocated 15000 integers for termspace/termends
% 2.35/2.71  Resimplifying inuse:
% 2.35/2.71  Done
% 2.35/2.71  
% 2.35/2.71  Failed to find proof!
% 2.35/2.71  maxweight =   15
% 2.35/2.71  maxnrclauses = 10000000
% 2.35/2.71  Generated: 136122
% 2.35/2.71  Kept: 799
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  The strategy used was not complete!
% 2.35/2.71  
% 2.35/2.71  Increased maxweight to 16
% 2.35/2.71  
% 2.35/2.71  Starting Search:
% 2.35/2.71  
% 2.35/2.71  *** allocated 50625 integers for clauses
% 2.35/2.71  *** allocated 22500 integers for termspace/termends
% 2.35/2.71  Resimplifying inuse:
% 2.35/2.71  Done
% 2.35/2.71  
% 2.35/2.71  *** allocated 75937 integers for clauses
% 2.35/2.71  *** allocated 33750 integers for termspace/termends
% 2.35/2.71  
% 2.35/2.71  Bliksems!, er is een bewijs:
% 2.35/2.71  % SZS status Theorem
% 2.35/2.71  % SZS output start Refutation
% 2.35/2.71  
% 2.35/2.71  (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.35/2.71  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.35/2.71  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.35/2.71  (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 2.35/2.71     ), ! distinct_points( X, Y ) }.
% 2.35/2.71  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.35/2.71    , ! distinct_lines( X, Y ) }.
% 2.35/2.71  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 2.35/2.71    Z ), ! convergent_lines( X, Y ) }.
% 2.35/2.71  (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.35/2.71  (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.35/2.71  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 2.35/2.71    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 2.35/2.71    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 2.35/2.71  (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 2.35/2.71    ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.35/2.71  (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines( 
% 2.35/2.71    X, Z ), distinct_lines( Y, Z ) }.
% 2.35/2.71  (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 ) }.
% 2.35/2.71  (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, skol2 ) }.
% 2.35/2.71  (17) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, skol3 ) }.
% 2.35/2.71  (18) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol1, intersection_point( 
% 2.35/2.71    skol2, skol3 ) ) }.
% 2.35/2.71  (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 2.35/2.71    distinct_points( X, Y ) }.
% 2.35/2.71  (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 2.35/2.71    ( X, Y ) }.
% 2.35/2.71  (37) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol2, X ), 
% 2.35/2.71    convergent_lines( skol3, X ) }.
% 2.35/2.71  (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.35/2.71    convergent_lines( X, Y ) }.
% 2.35/2.71  (42) {G2,W6,D2,L2,V1,M2} R(37,38) { convergent_lines( X, skol3 ), 
% 2.35/2.71    convergent_lines( skol2, X ) }.
% 2.35/2.71  (44) {G3,W6,D2,L2,V1,M1} R(42,38) { convergent_lines( X, skol2 ), 
% 2.35/2.71    convergent_lines( X, skol3 ) }.
% 2.35/2.71  (75) {G1,W15,D2,L5,V2,M3} R(10,16) { ! distinct_points( skol1, X ), ! 
% 2.35/2.71    distinct_lines( skol2, Y ), apart_point_and_line( X, skol2 ), 
% 2.35/2.71    apart_point_and_line( X, Y ), apart_point_and_line( skol1, Y ) }.
% 2.35/2.71  (106) {G1,W6,D2,L2,V1,M1} R(11,17) { distinct_points( X, skol1 ), ! 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  (108) {G2,W9,D2,L3,V2,M1} R(106,11) { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.35/2.71  (136) {G2,W9,D2,L3,V3,M1} R(13,30) { ! convergent_lines( X, Y ), 
% 2.35/2.71    convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.35/2.71  (235) {G3,W12,D2,L4,V3,M1} R(108,11) { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.35/2.71    ( Z, skol3 ) }.
% 2.35/2.71  (236) {G4,W6,D2,L2,V1,M1} F(235);r(21) { distinct_points( skol1, X ), ! 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  (686) {G5,W12,D2,L4,V1,M1} R(75,236);r(0) { ! distinct_points( skol1, X ), 
% 2.35/2.71    ! distinct_lines( skol2, skol3 ), apart_point_and_line( X, skol2 ), 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  (852) {G6,W16,D3,L4,V1,M1} R(686,9) { ! distinct_points( skol1, 
% 2.35/2.71    intersection_point( X, skol3 ) ), ! distinct_lines( skol2, skol3 ), ! 
% 2.35/2.71    convergent_lines( X, skol3 ), apart_point_and_line( intersection_point( X
% 2.35/2.71    , skol3 ), skol2 ) }.
% 2.35/2.71  (1322) {G7,W6,D2,L2,V0,M1} R(852,8);f;r(18) { ! convergent_lines( skol2, 
% 2.35/2.71    skol3 ), ! distinct_lines( skol2, skol3 ) }.
% 2.35/2.71  (1323) {G8,W3,D2,L1,V0,M1} S(1322);r(15) { ! distinct_lines( skol2, skol3 )
% 2.35/2.71     }.
% 2.35/2.71  (1452) {G9,W3,D2,L1,V1,M1} R(1323,136);r(44) { convergent_lines( X, skol2 )
% 2.35/2.71     }.
% 2.35/2.71  (1469) {G10,W0,D0,L0,V0,M0} R(1452,2) {  }.
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  % SZS output end Refutation
% 2.35/2.71  found a proof!
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  Unprocessed initial clauses:
% 2.35/2.71  
% 2.35/2.71  (1471) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 2.35/2.71  (1472) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 2.35/2.71  (1473) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 2.35/2.71  (1474) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 2.35/2.71    , Z ), distinct_points( Y, Z ) }.
% 2.35/2.71  (1475) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 2.35/2.71    Z ), distinct_lines( Y, Z ) }.
% 2.35/2.71  (1476) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 2.35/2.71    ( X, Z ), convergent_lines( Y, Z ) }.
% 2.35/2.71  (1477) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 2.35/2.71  (1478) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 2.35/2.71  (1479) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.35/2.71  (1480) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.35/2.71  (1481) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 2.35/2.71    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 2.35/2.71    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 2.35/2.71  (1482) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 2.35/2.71    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.35/2.71  (1483) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 2.35/2.71    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 2.35/2.71  (1484) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 2.35/2.71    , Z ), convergent_lines( X, Z ) }.
% 2.35/2.71  (1485) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol4 ) }.
% 2.35/2.71  (1486) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol3 ) }.
% 2.35/2.71  (1487) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, skol2 ) }.
% 2.35/2.71  (1488) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, skol3 ) }.
% 2.35/2.71  (1489) {G0,W5,D3,L1,V0,M1}  { distinct_points( skol1, intersection_point( 
% 2.35/2.71    skol2, skol3 ) ) }.
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  Total Proof:
% 2.35/2.71  
% 2.35/2.71  subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.35/2.71  parent0: (1471) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.35/2.71  parent0: (1472) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.35/2.71  parent0: (1473) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 2.35/2.71    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.35/2.71  parent0: (1474) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), 
% 2.35/2.71    distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := Z
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 2
% 2.35/2.71     1 ==> 0
% 2.35/2.71     2 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 2.35/2.71    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.35/2.71  parent0: (1475) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 2.35/2.71    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := Z
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 2
% 2.35/2.71     1 ==> 0
% 2.35/2.71     2 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 2.35/2.71    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.35/2.71  parent0: (1476) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 2.35/2.71    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := Z
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 2
% 2.35/2.71     1 ==> 0
% 2.35/2.71     2 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.35/2.71  parent0: (1479) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.35/2.71  parent0: (1480) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 2.35/2.71    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 2.35/2.71    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 2.35/2.71    apart_point_and_line( X, Z ) }.
% 2.35/2.71  parent0: (1481) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 2.35/2.71    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 2.35/2.71    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 2.35/2.71    apart_point_and_line( Y, T ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := Z
% 2.35/2.71     T := T
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71     2 ==> 5
% 2.35/2.71     3 ==> 2
% 2.35/2.71     4 ==> 3
% 2.35/2.71     5 ==> 4
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.35/2.71    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.35/2.71  parent0: (1482) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 2.35/2.71    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := Z
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 2
% 2.35/2.71     1 ==> 0
% 2.35/2.71     2 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 2.35/2.71    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.35/2.71  parent0: (1484) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 2.35/2.71    distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := Z
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 2
% 2.35/2.71     2 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 2.35/2.71     }.
% 2.35/2.71  parent0: (1486) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, 
% 2.35/2.71    skol2 ) }.
% 2.35/2.71  parent0: (1487) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, skol2
% 2.35/2.71     ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (17) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, 
% 2.35/2.71    skol3 ) }.
% 2.35/2.71  parent0: (1488) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, skol3
% 2.35/2.71     ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (18) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol1, 
% 2.35/2.71    intersection_point( skol2, skol3 ) ) }.
% 2.35/2.71  parent0: (1489) {G0,W5,D3,L1,V0,M1}  { distinct_points( skol1, 
% 2.35/2.71    intersection_point( skol2, skol3 ) ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1565) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 2.35/2.71    distinct_points( X, Y ) }.
% 2.35/2.71  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.35/2.71  parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 2.35/2.71    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 2.35/2.71    distinct_points( X, Y ) }.
% 2.35/2.71  parent0: (1565) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 2.35/2.71    distinct_points( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := Y
% 2.35/2.71     Y := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 1
% 2.35/2.71     1 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1567) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 2.35/2.71    distinct_lines( X, Y ) }.
% 2.35/2.71  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.35/2.71  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 2.35/2.71    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 2.35/2.71    distinct_lines( X, Y ) }.
% 2.35/2.71  parent0: (1567) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 2.35/2.71    distinct_lines( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := Y
% 2.35/2.71     Y := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 1
% 2.35/2.71     1 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1569) {G1,W6,D2,L2,V1,M2}  { convergent_lines( skol2, X ), 
% 2.35/2.71    convergent_lines( skol3, X ) }.
% 2.35/2.71  parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 2.35/2.71    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.35/2.71  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 2.35/2.71     }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := skol2
% 2.35/2.71     Y := skol3
% 2.35/2.71     Z := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (37) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol2, X
% 2.35/2.71     ), convergent_lines( skol3, X ) }.
% 2.35/2.71  parent0: (1569) {G1,W6,D2,L2,V1,M2}  { convergent_lines( skol2, X ), 
% 2.35/2.71    convergent_lines( skol3, X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1570) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 2.35/2.71    convergent_lines( X, Y ) }.
% 2.35/2.71  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.35/2.71  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 2.35/2.71    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.35/2.71    convergent_lines( X, Y ) }.
% 2.35/2.71  parent0: (1570) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 2.35/2.71    convergent_lines( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := Y
% 2.35/2.71     Y := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 1
% 2.35/2.71     1 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1573) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol3 ), 
% 2.35/2.71    convergent_lines( skol2, X ) }.
% 2.35/2.71  parent0[0]: (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.35/2.71    convergent_lines( X, Y ) }.
% 2.35/2.71  parent1[1]: (37) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol2, X )
% 2.35/2.71    , convergent_lines( skol3, X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := skol3
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (42) {G2,W6,D2,L2,V1,M2} R(37,38) { convergent_lines( X, skol3
% 2.35/2.71     ), convergent_lines( skol2, X ) }.
% 2.35/2.71  parent0: (1573) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol3 ), 
% 2.35/2.71    convergent_lines( skol2, X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1575) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol2 ), 
% 2.35/2.71    convergent_lines( X, skol3 ) }.
% 2.35/2.71  parent0[0]: (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 2.35/2.71    convergent_lines( X, Y ) }.
% 2.35/2.71  parent1[1]: (42) {G2,W6,D2,L2,V1,M2} R(37,38) { convergent_lines( X, skol3
% 2.35/2.71     ), convergent_lines( skol2, X ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := skol2
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (44) {G3,W6,D2,L2,V1,M1} R(42,38) { convergent_lines( X, skol2
% 2.35/2.71     ), convergent_lines( X, skol3 ) }.
% 2.35/2.71  parent0: (1575) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol2 ), 
% 2.35/2.71    convergent_lines( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1579) {G1,W15,D2,L5,V2,M5}  { ! distinct_points( skol1, X ), !
% 2.35/2.71     distinct_lines( skol2, Y ), apart_point_and_line( skol1, Y ), 
% 2.35/2.71    apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ) }.
% 2.35/2.71  parent0[0]: (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, 
% 2.35/2.71    skol2 ) }.
% 2.35/2.71  parent1[5]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 2.35/2.71    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 2.35/2.71    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 2.35/2.71    apart_point_and_line( X, Z ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := skol1
% 2.35/2.71     Y := X
% 2.35/2.71     Z := skol2
% 2.35/2.71     T := Y
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (75) {G1,W15,D2,L5,V2,M3} R(10,16) { ! distinct_points( skol1
% 2.35/2.71    , X ), ! distinct_lines( skol2, Y ), apart_point_and_line( X, skol2 ), 
% 2.35/2.71    apart_point_and_line( X, Y ), apart_point_and_line( skol1, Y ) }.
% 2.35/2.71  parent0: (1579) {G1,W15,D2,L5,V2,M5}  { ! distinct_points( skol1, X ), ! 
% 2.35/2.71    distinct_lines( skol2, Y ), apart_point_and_line( skol1, Y ), 
% 2.35/2.71    apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71     2 ==> 4
% 2.35/2.71     3 ==> 2
% 2.35/2.71     4 ==> 3
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1585) {G1,W6,D2,L2,V1,M2}  { distinct_points( X, skol1 ), ! 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0[0]: (17) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, 
% 2.35/2.71    skol3 ) }.
% 2.35/2.71  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.35/2.71    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71     Y := skol3
% 2.35/2.71     Z := skol1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (106) {G1,W6,D2,L2,V1,M1} R(11,17) { distinct_points( X, skol1
% 2.35/2.71     ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0: (1585) {G1,W6,D2,L2,V1,M2}  { distinct_points( X, skol1 ), ! 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1586) {G1,W9,D2,L3,V2,M3}  { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.35/2.71  parent0[1]: (106) {G1,W6,D2,L2,V1,M1} R(11,17) { distinct_points( X, skol1
% 2.35/2.71     ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.35/2.71    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := Y
% 2.35/2.71     Y := skol3
% 2.35/2.71     Z := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (108) {G2,W9,D2,L3,V2,M1} R(106,11) { distinct_points( X, 
% 2.35/2.71    skol1 ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.35/2.71  parent0: (1586) {G1,W9,D2,L3,V2,M3}  { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71     2 ==> 2
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1588) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 2.35/2.71    convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.35/2.71  parent0[0]: (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 2.35/2.71    distinct_lines( X, Y ) }.
% 2.35/2.71  parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 2.35/2.71    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := Y
% 2.35/2.71     Y := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := Z
% 2.35/2.71     Y := X
% 2.35/2.71     Z := Y
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (136) {G2,W9,D2,L3,V3,M1} R(13,30) { ! convergent_lines( X, Y
% 2.35/2.71     ), convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.35/2.71  parent0: (1588) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 2.35/2.71    convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := Y
% 2.35/2.71     Y := Z
% 2.35/2.71     Z := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 2
% 2.35/2.71     1 ==> 0
% 2.35/2.71     2 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1589) {G1,W12,D2,L4,V3,M4}  { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.35/2.71    ( Z, skol3 ) }.
% 2.35/2.71  parent0[2]: (108) {G2,W9,D2,L3,V2,M1} R(106,11) { distinct_points( X, skol1
% 2.35/2.71     ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.35/2.71  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 2.35/2.71    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := Z
% 2.35/2.71     Y := skol3
% 2.35/2.71     Z := Y
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (235) {G3,W12,D2,L4,V3,M1} R(108,11) { distinct_points( X, 
% 2.35/2.71    skol1 ), distinct_points( Y, X ), distinct_points( Z, Y ), ! 
% 2.35/2.71    apart_point_and_line( Z, skol3 ) }.
% 2.35/2.71  parent0: (1589) {G1,W12,D2,L4,V3,M4}  { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.35/2.71    ( Z, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := Y
% 2.35/2.71     Z := Z
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71     2 ==> 2
% 2.35/2.71     3 ==> 3
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  factor: (1595) {G3,W9,D2,L3,V1,M3}  { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0[0, 2]: (235) {G3,W12,D2,L4,V3,M1} R(108,11) { distinct_points( X, 
% 2.35/2.71    skol1 ), distinct_points( Y, X ), distinct_points( Z, Y ), ! 
% 2.35/2.71    apart_point_and_line( Z, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := skol1
% 2.35/2.71     Z := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1601) {G2,W9,D2,L3,V1,M3}  { distinct_points( skol1, X ), 
% 2.35/2.71    distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0[0]: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 2.35/2.71    distinct_points( X, Y ) }.
% 2.35/2.71  parent1[0]: (1595) {G3,W9,D2,L3,V1,M3}  { distinct_points( X, skol1 ), 
% 2.35/2.71    distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := skol1
% 2.35/2.71     Y := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  factor: (1603) {G2,W6,D2,L2,V1,M2}  { distinct_points( skol1, X ), ! 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0[0, 1]: (1601) {G2,W9,D2,L3,V1,M3}  { distinct_points( skol1, X ), 
% 2.35/2.71    distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (236) {G4,W6,D2,L2,V1,M1} F(235);r(21) { distinct_points( 
% 2.35/2.71    skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0: (1603) {G2,W6,D2,L2,V1,M2}  { distinct_points( skol1, X ), ! 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1610) {G2,W15,D2,L5,V1,M5}  { distinct_points( skol1, skol1 )
% 2.35/2.71    , ! distinct_points( skol1, X ), ! distinct_lines( skol2, skol3 ), 
% 2.35/2.71    apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0[1]: (236) {G4,W6,D2,L2,V1,M1} F(235);r(21) { distinct_points( skol1
% 2.35/2.71    , X ), ! apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent1[4]: (75) {G1,W15,D2,L5,V2,M3} R(10,16) { ! distinct_points( skol1, 
% 2.35/2.71    X ), ! distinct_lines( skol2, Y ), apart_point_and_line( X, skol2 ), 
% 2.35/2.71    apart_point_and_line( X, Y ), apart_point_and_line( skol1, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := skol1
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71     Y := skol3
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1611) {G1,W12,D2,L4,V1,M4}  { ! distinct_points( skol1, X ), !
% 2.35/2.71     distinct_lines( skol2, skol3 ), apart_point_and_line( X, skol2 ), 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.35/2.71  parent1[0]: (1610) {G2,W15,D2,L5,V1,M5}  { distinct_points( skol1, skol1 )
% 2.35/2.71    , ! distinct_points( skol1, X ), ! distinct_lines( skol2, skol3 ), 
% 2.35/2.71    apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := skol1
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (686) {G5,W12,D2,L4,V1,M1} R(75,236);r(0) { ! distinct_points
% 2.35/2.71    ( skol1, X ), ! distinct_lines( skol2, skol3 ), apart_point_and_line( X, 
% 2.35/2.71    skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  parent0: (1611) {G1,W12,D2,L4,V1,M4}  { ! distinct_points( skol1, X ), ! 
% 2.35/2.71    distinct_lines( skol2, skol3 ), apart_point_and_line( X, skol2 ), 
% 2.35/2.71    apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71     2 ==> 2
% 2.35/2.71     3 ==> 3
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1613) {G1,W16,D3,L4,V1,M4}  { ! convergent_lines( X, skol3 ), 
% 2.35/2.71    ! distinct_points( skol1, intersection_point( X, skol3 ) ), ! 
% 2.35/2.71    distinct_lines( skol2, skol3 ), apart_point_and_line( intersection_point
% 2.35/2.71    ( X, skol3 ), skol2 ) }.
% 2.35/2.71  parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.35/2.71  parent1[3]: (686) {G5,W12,D2,L4,V1,M1} R(75,236);r(0) { ! distinct_points( 
% 2.35/2.71    skol1, X ), ! distinct_lines( skol2, skol3 ), apart_point_and_line( X, 
% 2.35/2.71    skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71     Y := skol3
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := intersection_point( X, skol3 )
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (852) {G6,W16,D3,L4,V1,M1} R(686,9) { ! distinct_points( skol1
% 2.35/2.71    , intersection_point( X, skol3 ) ), ! distinct_lines( skol2, skol3 ), ! 
% 2.35/2.71    convergent_lines( X, skol3 ), apart_point_and_line( intersection_point( X
% 2.35/2.71    , skol3 ), skol2 ) }.
% 2.35/2.71  parent0: (1613) {G1,W16,D3,L4,V1,M4}  { ! convergent_lines( X, skol3 ), ! 
% 2.35/2.71    distinct_points( skol1, intersection_point( X, skol3 ) ), ! 
% 2.35/2.71    distinct_lines( skol2, skol3 ), apart_point_and_line( intersection_point
% 2.35/2.71    ( X, skol3 ), skol2 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 2
% 2.35/2.71     1 ==> 0
% 2.35/2.71     2 ==> 1
% 2.35/2.71     3 ==> 3
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1614) {G1,W14,D3,L4,V0,M4}  { ! convergent_lines( skol2, skol3
% 2.35/2.71     ), ! distinct_points( skol1, intersection_point( skol2, skol3 ) ), ! 
% 2.35/2.71    distinct_lines( skol2, skol3 ), ! convergent_lines( skol2, skol3 ) }.
% 2.35/2.71  parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 2.35/2.71    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.35/2.71  parent1[3]: (852) {G6,W16,D3,L4,V1,M1} R(686,9) { ! distinct_points( skol1
% 2.35/2.71    , intersection_point( X, skol3 ) ), ! distinct_lines( skol2, skol3 ), ! 
% 2.35/2.71    convergent_lines( X, skol3 ), apart_point_and_line( intersection_point( X
% 2.35/2.71    , skol3 ), skol2 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := skol2
% 2.35/2.71     Y := skol3
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := skol2
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1616) {G1,W9,D2,L3,V0,M3}  { ! convergent_lines( skol2, skol3
% 2.35/2.71     ), ! distinct_lines( skol2, skol3 ), ! convergent_lines( skol2, skol3 )
% 2.35/2.71     }.
% 2.35/2.71  parent0[1]: (1614) {G1,W14,D3,L4,V0,M4}  { ! convergent_lines( skol2, skol3
% 2.35/2.71     ), ! distinct_points( skol1, intersection_point( skol2, skol3 ) ), ! 
% 2.35/2.71    distinct_lines( skol2, skol3 ), ! convergent_lines( skol2, skol3 ) }.
% 2.35/2.71  parent1[0]: (18) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol1, 
% 2.35/2.71    intersection_point( skol2, skol3 ) ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  factor: (1617) {G1,W6,D2,L2,V0,M2}  { ! convergent_lines( skol2, skol3 ), !
% 2.35/2.71     distinct_lines( skol2, skol3 ) }.
% 2.35/2.71  parent0[0, 2]: (1616) {G1,W9,D2,L3,V0,M3}  { ! convergent_lines( skol2, 
% 2.35/2.71    skol3 ), ! distinct_lines( skol2, skol3 ), ! convergent_lines( skol2, 
% 2.35/2.71    skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (1322) {G7,W6,D2,L2,V0,M1} R(852,8);f;r(18) { ! 
% 2.35/2.71    convergent_lines( skol2, skol3 ), ! distinct_lines( skol2, skol3 ) }.
% 2.35/2.71  parent0: (1617) {G1,W6,D2,L2,V0,M2}  { ! convergent_lines( skol2, skol3 ), 
% 2.35/2.71    ! distinct_lines( skol2, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71     1 ==> 1
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1618) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol2, skol3 )
% 2.35/2.71     }.
% 2.35/2.71  parent0[0]: (1322) {G7,W6,D2,L2,V0,M1} R(852,8);f;r(18) { ! 
% 2.35/2.71    convergent_lines( skol2, skol3 ), ! distinct_lines( skol2, skol3 ) }.
% 2.35/2.71  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 2.35/2.71     }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (1323) {G8,W3,D2,L1,V0,M1} S(1322);r(15) { ! distinct_lines( 
% 2.35/2.71    skol2, skol3 ) }.
% 2.35/2.71  parent0: (1618) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol2, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1619) {G3,W6,D2,L2,V1,M2}  { ! convergent_lines( X, skol3 ), 
% 2.35/2.71    convergent_lines( X, skol2 ) }.
% 2.35/2.71  parent0[0]: (1323) {G8,W3,D2,L1,V0,M1} S(1322);r(15) { ! distinct_lines( 
% 2.35/2.71    skol2, skol3 ) }.
% 2.35/2.71  parent1[2]: (136) {G2,W9,D2,L3,V3,M1} R(13,30) { ! convergent_lines( X, Y )
% 2.35/2.71    , convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71     Y := skol3
% 2.35/2.71     Z := skol2
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1620) {G4,W6,D2,L2,V1,M2}  { convergent_lines( X, skol2 ), 
% 2.35/2.71    convergent_lines( X, skol2 ) }.
% 2.35/2.71  parent0[0]: (1619) {G3,W6,D2,L2,V1,M2}  { ! convergent_lines( X, skol3 ), 
% 2.35/2.71    convergent_lines( X, skol2 ) }.
% 2.35/2.71  parent1[1]: (44) {G3,W6,D2,L2,V1,M1} R(42,38) { convergent_lines( X, skol2
% 2.35/2.71     ), convergent_lines( X, skol3 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  factor: (1621) {G4,W3,D2,L1,V1,M1}  { convergent_lines( X, skol2 ) }.
% 2.35/2.71  parent0[0, 1]: (1620) {G4,W6,D2,L2,V1,M2}  { convergent_lines( X, skol2 ), 
% 2.35/2.71    convergent_lines( X, skol2 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (1452) {G9,W3,D2,L1,V1,M1} R(1323,136);r(44) { 
% 2.35/2.71    convergent_lines( X, skol2 ) }.
% 2.35/2.71  parent0: (1621) {G4,W3,D2,L1,V1,M1}  { convergent_lines( X, skol2 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := X
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71     0 ==> 0
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  resolution: (1622) {G1,W0,D0,L0,V0,M0}  {  }.
% 2.35/2.71  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.35/2.71  parent1[0]: (1452) {G9,W3,D2,L1,V1,M1} R(1323,136);r(44) { convergent_lines
% 2.35/2.71    ( X, skol2 ) }.
% 2.35/2.71  substitution0:
% 2.35/2.71     X := skol2
% 2.35/2.71  end
% 2.35/2.71  substitution1:
% 2.35/2.71     X := skol2
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  subsumption: (1469) {G10,W0,D0,L0,V0,M0} R(1452,2) {  }.
% 2.35/2.71  parent0: (1622) {G1,W0,D0,L0,V0,M0}  {  }.
% 2.35/2.71  substitution0:
% 2.35/2.71  end
% 2.35/2.71  permutation0:
% 2.35/2.71  end
% 2.35/2.71  
% 2.35/2.71  Proof check complete!
% 2.35/2.71  
% 2.35/2.71  Memory use:
% 2.35/2.71  
% 2.35/2.71  space for terms:        22778
% 2.35/2.71  space for clauses:      52991
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  clauses generated:      176585
% 2.35/2.71  clauses kept:           1470
% 2.35/2.71  clauses selected:       1025
% 2.35/2.71  clauses deleted:        9
% 2.35/2.71  clauses inuse deleted:  0
% 2.35/2.71  
% 2.35/2.71  subsentry:          191902
% 2.35/2.71  literals s-matched: 122235
% 2.35/2.71  literals matched:   122200
% 2.35/2.71  full subsumption:   75865
% 2.35/2.71  
% 2.35/2.71  checksum:           -1742010343
% 2.35/2.71  
% 2.35/2.71  
% 2.35/2.71  Bliksem ended
%------------------------------------------------------------------------------