TSTP Solution File: GEO170+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO170+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n017.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 02:52:12 EDT 2022

% Result   : Theorem 1.24s 1.68s
% Output   : Refutation 1.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO170+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % DateTime : Sat Jun 18 15:08:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.24/1.68  *** allocated 10000 integers for termspace/termends
% 1.24/1.68  *** allocated 10000 integers for clauses
% 1.24/1.68  *** allocated 10000 integers for justifications
% 1.24/1.68  Bliksem 1.12
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  Automatic Strategy Selection
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  Clauses:
% 1.24/1.68  
% 1.24/1.68  { ! distinct_points( X, X ) }.
% 1.24/1.68  { ! distinct_lines( X, X ) }.
% 1.24/1.68  { ! convergent_lines( X, X ) }.
% 1.24/1.68  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.24/1.68     ) }.
% 1.24/1.68  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.24/1.68     }.
% 1.24/1.68  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.24/1.68    , Z ) }.
% 1.24/1.68  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.24/1.68    , Y ) ) }.
% 1.24/1.68  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.24/1.68    , Y ) ) }.
% 1.24/1.68  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.24/1.68    , Y ), X ) }.
% 1.24/1.68  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.24/1.68    , Y ), Y ) }.
% 1.24/1.68  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.24/1.68    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.24/1.68    apart_point_and_line( Y, T ) }.
% 1.24/1.68  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 1.24/1.68    apart_point_and_line( Z, Y ) }.
% 1.24/1.68  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 1.24/1.68    apart_point_and_line( X, Z ) }.
% 1.24/1.68  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 1.24/1.68    Z ) }.
% 1.24/1.68  { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 1.24/1.68  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.24/1.68  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.24/1.68  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 1.24/1.68    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.24/1.68  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.24/1.68  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.24/1.68    , convergent_lines( Y, Z ) }.
% 1.24/1.68  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.24/1.68    , unorthogonal_lines( Y, Z ) }.
% 1.24/1.68  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.24/1.68  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.24/1.68  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.24/1.68     }.
% 1.24/1.68  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.24/1.68  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.24/1.68  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 1.24/1.68    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 1.24/1.68    unorthogonal_lines( Y, T ) }.
% 1.24/1.68  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.24/1.68  { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), ! 
% 1.24/1.68    unorthogonal_lines( X, Y ) }.
% 1.24/1.68  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.24/1.68     unorthogonal_lines( X, Y ) }.
% 1.24/1.68  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 1.24/1.68  { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.24/1.68  { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 1.24/1.68     }.
% 1.24/1.68  { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), ! 
% 1.24/1.68    convergent_lines( X, Y ) }.
% 1.24/1.68  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 1.24/1.68    line_connecting( X, Y ) ) }.
% 1.24/1.68  { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point( 
% 1.24/1.68    intersection_point( X, Y ) ) }.
% 1.24/1.68  { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 1.24/1.68  { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 1.24/1.68  { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 1.24/1.68  { distinct_points( X, Y ), equal_points( X, Y ) }.
% 1.24/1.68  { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 1.24/1.68  { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 1.24/1.68  { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 1.24/1.68  { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 1.24/1.68  { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 1.24/1.68  { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 1.24/1.68  { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.24/1.68  { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 1.24/1.68  { distinct_points( skol1, skol2 ) }.
% 1.24/1.68  { incident_point_and_line( skol1, skol3 ) }.
% 1.24/1.68  { incident_point_and_line( skol2, skol3 ) }.
% 1.24/1.68  { ! equal_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68  
% 1.24/1.68  percentage equality = 0.000000, percentage horn = 0.620000
% 1.24/1.68  This a non-horn, non-equality problem
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  Options Used:
% 1.24/1.68  
% 1.24/1.68  useres =            1
% 1.24/1.68  useparamod =        0
% 1.24/1.68  useeqrefl =         0
% 1.24/1.68  useeqfact =         0
% 1.24/1.68  usefactor =         1
% 1.24/1.68  usesimpsplitting =  0
% 1.24/1.68  usesimpdemod =      0
% 1.24/1.68  usesimpres =        3
% 1.24/1.68  
% 1.24/1.68  resimpinuse      =  1000
% 1.24/1.68  resimpclauses =     20000
% 1.24/1.68  substype =          standard
% 1.24/1.68  backwardsubs =      1
% 1.24/1.68  selectoldest =      5
% 1.24/1.68  
% 1.24/1.68  litorderings [0] =  split
% 1.24/1.68  litorderings [1] =  liftord
% 1.24/1.68  
% 1.24/1.68  termordering =      none
% 1.24/1.68  
% 1.24/1.68  litapriori =        1
% 1.24/1.68  termapriori =       0
% 1.24/1.68  litaposteriori =    0
% 1.24/1.68  termaposteriori =   0
% 1.24/1.68  demodaposteriori =  0
% 1.24/1.68  ordereqreflfact =   0
% 1.24/1.68  
% 1.24/1.68  litselect =         none
% 1.24/1.68  
% 1.24/1.68  maxweight =         15
% 1.24/1.68  maxdepth =          30000
% 1.24/1.68  maxlength =         115
% 1.24/1.68  maxnrvars =         195
% 1.24/1.68  excuselevel =       1
% 1.24/1.68  increasemaxweight = 1
% 1.24/1.68  
% 1.24/1.68  maxselected =       10000000
% 1.24/1.68  maxnrclauses =      10000000
% 1.24/1.68  
% 1.24/1.68  showgenerated =    0
% 1.24/1.68  showkept =         0
% 1.24/1.68  showselected =     0
% 1.24/1.68  showdeleted =      0
% 1.24/1.68  showresimp =       1
% 1.24/1.68  showstatus =       2000
% 1.24/1.68  
% 1.24/1.68  prologoutput =     0
% 1.24/1.68  nrgoals =          5000000
% 1.24/1.68  totalproof =       1
% 1.24/1.68  
% 1.24/1.68  Symbols occurring in the translation:
% 1.24/1.68  
% 1.24/1.68  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.24/1.68  .  [1, 2]      (w:1, o:26, a:1, s:1, b:0), 
% 1.24/1.68  !  [4, 1]      (w:0, o:19, a:1, s:1, b:0), 
% 1.24/1.68  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.24/1.68  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.24/1.68  distinct_points  [36, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 1.24/1.68  distinct_lines  [37, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 1.24/1.68  convergent_lines  [38, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 1.24/1.68  line_connecting  [41, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 1.24/1.68  apart_point_and_line  [42, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 1.24/1.68  intersection_point  [43, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 1.24/1.68  parallel_through_point  [46, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 1.24/1.68  unorthogonal_lines  [49, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 1.24/1.68  orthogonal_through_point  [52, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 1.24/1.68  point  [54, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 1.24/1.68  line  [55, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 1.24/1.68  equal_points  [56, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 1.24/1.68  equal_lines  [57, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 1.24/1.68  parallel_lines  [58, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 1.24/1.68  incident_point_and_line  [59, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 1.24/1.68  orthogonal_lines  [60, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 1.24/1.68  alpha1  [61, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 1.24/1.68  alpha2  [62, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 1.24/1.68  skol1  [63, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 1.24/1.68  skol2  [64, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 1.24/1.68  skol3  [65, 0]      (w:1, o:18, a:1, s:1, b:0).
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  Starting Search:
% 1.24/1.68  
% 1.24/1.68  *** allocated 15000 integers for clauses
% 1.24/1.68  *** allocated 22500 integers for clauses
% 1.24/1.68  *** allocated 33750 integers for clauses
% 1.24/1.68  *** allocated 15000 integers for termspace/termends
% 1.24/1.68  *** allocated 50625 integers for clauses
% 1.24/1.68  Resimplifying inuse:
% 1.24/1.68  Done
% 1.24/1.68  
% 1.24/1.68  *** allocated 22500 integers for termspace/termends
% 1.24/1.68  *** allocated 75937 integers for clauses
% 1.24/1.68  *** allocated 33750 integers for termspace/termends
% 1.24/1.68  *** allocated 113905 integers for clauses
% 1.24/1.68  
% 1.24/1.68  Intermediate Status:
% 1.24/1.68  Generated:    14312
% 1.24/1.68  Kept:         2031
% 1.24/1.68  Inuse:        329
% 1.24/1.68  Deleted:      2
% 1.24/1.68  Deletedinuse: 2
% 1.24/1.68  
% 1.24/1.68  Resimplifying inuse:
% 1.24/1.68  Done
% 1.24/1.68  
% 1.24/1.68  *** allocated 50625 integers for termspace/termends
% 1.24/1.68  *** allocated 170857 integers for clauses
% 1.24/1.68  Resimplifying inuse:
% 1.24/1.68  Done
% 1.24/1.68  
% 1.24/1.68  *** allocated 75937 integers for termspace/termends
% 1.24/1.68  *** allocated 256285 integers for clauses
% 1.24/1.68  
% 1.24/1.68  Intermediate Status:
% 1.24/1.68  Generated:    36270
% 1.24/1.68  Kept:         4167
% 1.24/1.68  Inuse:        484
% 1.24/1.68  Deleted:      5
% 1.24/1.68  Deletedinuse: 2
% 1.24/1.68  
% 1.24/1.68  Resimplifying inuse:
% 1.24/1.68  Done
% 1.24/1.68  
% 1.24/1.68  *** allocated 113905 integers for termspace/termends
% 1.24/1.68  Resimplifying inuse:
% 1.24/1.68  Done
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  Bliksems!, er is een bewijs:
% 1.24/1.68  % SZS status Theorem
% 1.24/1.68  % SZS output start Refutation
% 1.24/1.68  
% 1.24/1.68  (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68  (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 1.24/1.68    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.24/1.68    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 1.24/1.68  (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.24/1.68     }.
% 1.24/1.68  (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), ! 
% 1.24/1.68    incident_point_and_line( X, Y ) }.
% 1.24/1.68  (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 1.24/1.68  (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, skol3 ) }.
% 1.24/1.68  (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, skol3 ) }.
% 1.24/1.68  (49) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, line_connecting( skol1, 
% 1.24/1.68    skol2 ) ) }.
% 1.24/1.68  (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line( skol1, skol3 )
% 1.24/1.68     }.
% 1.24/1.68  (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( skol2, skol3 )
% 1.24/1.68     }.
% 1.24/1.68  (75) {G1,W5,D3,L1,V0,M1} R(39,49) { distinct_lines( skol3, line_connecting
% 1.24/1.68    ( skol1, skol2 ) ) }.
% 1.24/1.68  (98) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y ), ! 
% 1.24/1.68    distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T ), 
% 1.24/1.68    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.24/1.68    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.24/1.68  (111) {G2,W14,D3,L4,V3,M2} F(98);r(7) { ! distinct_points( X, Y ), ! 
% 1.24/1.68    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 1.24/1.68     ), apart_point_and_line( X, Z ) }.
% 1.24/1.68  (2254) {G3,W11,D3,L3,V1,M1} R(111,74) { ! distinct_points( X, skol2 ), ! 
% 1.24/1.68    distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.24/1.68    apart_point_and_line( X, skol3 ) }.
% 1.24/1.68  (5466) {G4,W5,D3,L1,V0,M1} R(2254,73);r(46) { ! distinct_lines( skol3, 
% 1.24/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68  (5467) {G5,W0,D0,L0,V0,M0} S(5466);r(75) {  }.
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  % SZS output end Refutation
% 1.24/1.68  found a proof!
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  Unprocessed initial clauses:
% 1.24/1.68  
% 1.24/1.68  (5469) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 1.24/1.68  (5470) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 1.24/1.68  (5471) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 1.24/1.68  (5472) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 1.24/1.68    , Z ), distinct_points( Y, Z ) }.
% 1.24/1.68  (5473) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 1.24/1.68    Z ), distinct_lines( Y, Z ) }.
% 1.24/1.68  (5474) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 1.24/1.68    ( X, Z ), convergent_lines( Y, Z ) }.
% 1.24/1.68  (5475) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68  (5476) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68  (5477) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.24/1.68  (5478) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.24/1.68  (5479) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 1.24/1.68    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 1.24/1.68    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.24/1.68  (5480) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.24/1.68    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.24/1.68  (5481) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.24/1.68    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.24/1.68  (5482) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.24/1.68    , Z ), convergent_lines( X, Z ) }.
% 1.24/1.68  (5483) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), convergent_lines( X
% 1.24/1.68    , Y ) }.
% 1.24/1.68  (5484) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( Y
% 1.24/1.68    , X ), Y ) }.
% 1.24/1.68  (5485) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 1.24/1.68    parallel_through_point( Y, X ) ) }.
% 1.24/1.68  (5486) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 1.24/1.68    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 1.24/1.68    convergent_lines( X, Y ) }.
% 1.24/1.68  (5487) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 1.24/1.68    ( X, Y ) }.
% 1.24/1.68  (5488) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 1.24/1.68    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.24/1.68  (5489) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 1.24/1.68    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.24/1.68     }.
% 1.24/1.68  (5490) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y )
% 1.24/1.68     }.
% 1.24/1.68  (5491) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 1.24/1.68     }.
% 1.24/1.68  (5492) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 1.24/1.68    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 1.24/1.68  (5493) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 1.24/1.68    orthogonal_through_point( Y, X ), Y ) }.
% 1.24/1.68  (5494) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 1.24/1.68    orthogonal_through_point( Y, X ) ) }.
% 1.24/1.68  (5495) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 1.24/1.68    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 1.24/1.68    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 1.24/1.68  (5496) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 1.24/1.68    ( X, Y ) }.
% 1.24/1.68  (5497) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), convergent_lines( Z, Y ), ! 
% 1.24/1.68    convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.24/1.68  (5498) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), 
% 1.24/1.68    ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.24/1.68  (5499) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), convergent_lines( Y, X )
% 1.24/1.68     }.
% 1.24/1.68  (5500) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 1.24/1.68     }.
% 1.24/1.68  (5501) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 1.24/1.68    unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 1.24/1.68  (5502) {G0,W9,D2,L3,V3,M3}  { unorthogonal_lines( Z, X ), 
% 1.24/1.68    unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.24/1.68  (5503) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! 
% 1.24/1.68    distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 1.24/1.68  (5504) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), ! convergent_lines
% 1.24/1.68    ( X, Y ), point( intersection_point( X, Y ) ) }.
% 1.24/1.68  (5505) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 1.24/1.68    parallel_through_point( X, Y ) ) }.
% 1.24/1.68  (5506) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 1.24/1.68    orthogonal_through_point( X, Y ) ) }.
% 1.24/1.68  (5507) {G0,W6,D2,L2,V2,M2}  { ! equal_points( X, Y ), ! distinct_points( X
% 1.24/1.68    , Y ) }.
% 1.24/1.68  (5508) {G0,W6,D2,L2,V2,M2}  { distinct_points( X, Y ), equal_points( X, Y )
% 1.24/1.68     }.
% 1.24/1.68  (5509) {G0,W6,D2,L2,V2,M2}  { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 1.24/1.68     ) }.
% 1.24/1.68  (5510) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.24/1.68     }.
% 1.24/1.68  (5511) {G0,W6,D2,L2,V2,M2}  { ! parallel_lines( X, Y ), ! convergent_lines
% 1.24/1.68    ( X, Y ) }.
% 1.24/1.68  (5512) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), parallel_lines( X, 
% 1.24/1.68    Y ) }.
% 1.24/1.68  (5513) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( X, Y ) }.
% 1.24/1.68  (5514) {G0,W6,D2,L2,V2,M2}  { apart_point_and_line( X, Y ), 
% 1.24/1.68    incident_point_and_line( X, Y ) }.
% 1.24/1.68  (5515) {G0,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), ! 
% 1.24/1.68    unorthogonal_lines( X, Y ) }.
% 1.24/1.68  (5516) {G0,W6,D2,L2,V2,M2}  { unorthogonal_lines( X, Y ), orthogonal_lines
% 1.24/1.68    ( X, Y ) }.
% 1.24/1.68  (5517) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 1.24/1.68  (5518) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol1, skol3 ) }.
% 1.24/1.68  (5519) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol2, skol3 ) }.
% 1.24/1.68  (5520) {G0,W5,D3,L1,V0,M1}  { ! equal_lines( skol3, line_connecting( skol1
% 1.24/1.68    , skol2 ) ) }.
% 1.24/1.68  
% 1.24/1.68  
% 1.24/1.68  Total Proof:
% 1.24/1.68  
% 1.24/1.68  subsumption: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68  parent0: (5475) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68     X := X
% 1.24/1.68     Y := Y
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68     1 ==> 1
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68  parent0: (5476) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.24/1.68    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68     X := X
% 1.24/1.68     Y := Y
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68     1 ==> 1
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 1.24/1.68    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 1.24/1.68    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 1.24/1.68    apart_point_and_line( X, Z ) }.
% 1.24/1.68  parent0: (5479) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.24/1.68    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 1.24/1.68    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.24/1.68    apart_point_and_line( Y, T ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68     X := X
% 1.24/1.68     Y := Y
% 1.24/1.68     Z := Z
% 1.24/1.68     T := T
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68     1 ==> 1
% 1.24/1.68     2 ==> 5
% 1.24/1.68     3 ==> 2
% 1.24/1.68     4 ==> 3
% 1.24/1.68     5 ==> 4
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), 
% 1.24/1.68    equal_lines( X, Y ) }.
% 1.24/1.68  parent0: (5510) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines
% 1.24/1.68    ( X, Y ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68     X := X
% 1.24/1.68     Y := Y
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68     1 ==> 1
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.24/1.68     incident_point_and_line( X, Y ) }.
% 1.24/1.68  parent0: (5513) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), !
% 1.24/1.68     apart_point_and_line( X, Y ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68     X := X
% 1.24/1.68     Y := Y
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 1
% 1.24/1.68     1 ==> 0
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.24/1.68     }.
% 1.24/1.68  parent0: (5517) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  parent0: (5518) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol1, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  parent0: (5519) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol2, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (49) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, 
% 1.24/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68  parent0: (5520) {G0,W5,D3,L1,V0,M1}  { ! equal_lines( skol3, 
% 1.24/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  resolution: (5626) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), ! 
% 1.24/1.68    incident_point_and_line( X, Y ) }.
% 1.24/1.68  parent1[0]: (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68     X := skol1
% 1.24/1.68     Y := skol3
% 1.24/1.68  end
% 1.24/1.68  substitution1:
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line( 
% 1.24/1.68    skol1, skol3 ) }.
% 1.24/1.68  parent0: (5626) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, skol3
% 1.24/1.68     ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  resolution: (5627) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol2, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), ! 
% 1.24/1.68    incident_point_and_line( X, Y ) }.
% 1.24/1.68  parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, 
% 1.24/1.68    skol3 ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68     X := skol2
% 1.24/1.68     Y := skol3
% 1.24/1.68  end
% 1.24/1.68  substitution1:
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( 
% 1.24/1.68    skol2, skol3 ) }.
% 1.24/1.68  parent0: (5627) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol2, skol3
% 1.24/1.68     ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68  end
% 1.24/1.68  permutation0:
% 1.24/1.68     0 ==> 0
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  resolution: (5628) {G1,W5,D3,L1,V0,M1}  { distinct_lines( skol3, 
% 1.24/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68  parent0[0]: (49) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, 
% 1.24/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68  parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), 
% 1.24/1.68    equal_lines( X, Y ) }.
% 1.24/1.68  substitution0:
% 1.24/1.68  end
% 1.24/1.68  substitution1:
% 1.24/1.68     X := skol3
% 1.24/1.68     Y := line_connecting( skol1, skol2 )
% 1.24/1.68  end
% 1.24/1.68  
% 1.24/1.68  subsumption: (75) {G1,W5,D3,L1,V0,M1} R(39,49) { distinct_lines( skol3, 
% 1.24/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  parent0: (5628) {G1,W5,D3,L1,V0,M1}  { distinct_lines( skol3, 
% 1.31/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68  end
% 1.31/1.68  permutation0:
% 1.31/1.68     0 ==> 0
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  resolution: (5629) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.31/1.68    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.31/1.68    , Y ) ), apart_point_and_line( X, T ) }.
% 1.31/1.68  parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.31/1.68    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.31/1.68  parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 1.31/1.68    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 1.31/1.68    apart_point_and_line( X, Z ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68     X := X
% 1.31/1.68     Y := Y
% 1.31/1.68  end
% 1.31/1.68  substitution1:
% 1.31/1.68     X := X
% 1.31/1.68     Y := Z
% 1.31/1.68     Z := T
% 1.31/1.68     T := line_connecting( X, Y )
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  subsumption: (98) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y )
% 1.31/1.68    , ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T
% 1.31/1.68     ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.31/1.68    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.31/1.68  parent0: (5629) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.31/1.68    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.31/1.68    , Y ) ), apart_point_and_line( X, T ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68     X := X
% 1.31/1.68     Y := T
% 1.31/1.68     Z := Y
% 1.31/1.68     T := Z
% 1.31/1.68  end
% 1.31/1.68  permutation0:
% 1.31/1.68     0 ==> 2
% 1.31/1.68     1 ==> 0
% 1.31/1.68     2 ==> 1
% 1.31/1.68     3 ==> 4
% 1.31/1.68     4 ==> 5
% 1.31/1.68     5 ==> 3
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  factor: (5645) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68     ), apart_point_and_line( Y, Z ), apart_point_and_line( Y, 
% 1.31/1.68    line_connecting( X, Y ) ) }.
% 1.31/1.68  parent0[0, 2]: (98) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y
% 1.31/1.68     ), ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X
% 1.31/1.68    , T ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.31/1.68    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68     X := X
% 1.31/1.68     Y := Y
% 1.31/1.68     Z := Z
% 1.31/1.68     T := Y
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  resolution: (5652) {G1,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 1.31/1.68    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68  parent0[1]: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.31/1.68    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.31/1.68  parent1[4]: (5645) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68     ), apart_point_and_line( Y, Z ), apart_point_and_line( Y, 
% 1.31/1.68    line_connecting( X, Y ) ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68     X := X
% 1.31/1.68     Y := Y
% 1.31/1.68  end
% 1.31/1.68  substitution1:
% 1.31/1.68     X := X
% 1.31/1.68     Y := Y
% 1.31/1.68     Z := Z
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  factor: (5653) {G1,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68     ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68  parent0[0, 1]: (5652) {G1,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 1.31/1.68    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68     X := X
% 1.31/1.68     Y := Y
% 1.31/1.68     Z := Z
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  subsumption: (111) {G2,W14,D3,L4,V3,M2} F(98);r(7) { ! distinct_points( X, 
% 1.31/1.68    Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.31/1.68    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.31/1.68  parent0: (5653) {G1,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 1.31/1.68    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68     ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68     X := X
% 1.31/1.68     Y := Y
% 1.31/1.68     Z := Z
% 1.31/1.68  end
% 1.31/1.68  permutation0:
% 1.31/1.68     0 ==> 0
% 1.31/1.68     1 ==> 1
% 1.31/1.68     2 ==> 3
% 1.31/1.68     3 ==> 2
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  resolution: (5655) {G2,W11,D3,L3,V1,M3}  { ! distinct_points( X, skol2 ), !
% 1.31/1.68     distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.31/1.68    apart_point_and_line( X, skol3 ) }.
% 1.31/1.68  parent0[0]: (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( 
% 1.31/1.68    skol2, skol3 ) }.
% 1.31/1.68  parent1[2]: (111) {G2,W14,D3,L4,V3,M2} F(98);r(7) { ! distinct_points( X, Y
% 1.31/1.68     ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.31/1.68    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68  end
% 1.31/1.68  substitution1:
% 1.31/1.68     X := X
% 1.31/1.68     Y := skol2
% 1.31/1.68     Z := skol3
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  subsumption: (2254) {G3,W11,D3,L3,V1,M1} R(111,74) { ! distinct_points( X, 
% 1.31/1.68    skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.31/1.68    apart_point_and_line( X, skol3 ) }.
% 1.31/1.68  parent0: (5655) {G2,W11,D3,L3,V1,M3}  { ! distinct_points( X, skol2 ), ! 
% 1.31/1.68    distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.31/1.68    apart_point_and_line( X, skol3 ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68     X := X
% 1.31/1.68  end
% 1.31/1.68  permutation0:
% 1.31/1.68     0 ==> 0
% 1.31/1.68     1 ==> 1
% 1.31/1.68     2 ==> 2
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  resolution: (5657) {G2,W8,D3,L2,V0,M2}  { ! distinct_points( skol1, skol2 )
% 1.31/1.68    , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  parent0[0]: (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line( 
% 1.31/1.68    skol1, skol3 ) }.
% 1.31/1.68  parent1[2]: (2254) {G3,W11,D3,L3,V1,M1} R(111,74) { ! distinct_points( X, 
% 1.31/1.68    skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.31/1.68    apart_point_and_line( X, skol3 ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68  end
% 1.31/1.68  substitution1:
% 1.31/1.68     X := skol1
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  resolution: (5658) {G1,W5,D3,L1,V0,M1}  { ! distinct_lines( skol3, 
% 1.31/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  parent0[0]: (5657) {G2,W8,D3,L2,V0,M2}  { ! distinct_points( skol1, skol2 )
% 1.31/1.68    , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.31/1.68     }.
% 1.31/1.68  substitution0:
% 1.31/1.68  end
% 1.31/1.68  substitution1:
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  subsumption: (5466) {G4,W5,D3,L1,V0,M1} R(2254,73);r(46) { ! distinct_lines
% 1.31/1.68    ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  parent0: (5658) {G1,W5,D3,L1,V0,M1}  { ! distinct_lines( skol3, 
% 1.31/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68  end
% 1.31/1.68  permutation0:
% 1.31/1.68     0 ==> 0
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  resolution: (5659) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.31/1.68  parent0[0]: (5466) {G4,W5,D3,L1,V0,M1} R(2254,73);r(46) { ! distinct_lines
% 1.31/1.68    ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  parent1[0]: (75) {G1,W5,D3,L1,V0,M1} R(39,49) { distinct_lines( skol3, 
% 1.31/1.68    line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68  substitution0:
% 1.31/1.68  end
% 1.31/1.68  substitution1:
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  subsumption: (5467) {G5,W0,D0,L0,V0,M0} S(5466);r(75) {  }.
% 1.31/1.68  parent0: (5659) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.31/1.68  substitution0:
% 1.31/1.68  end
% 1.31/1.68  permutation0:
% 1.31/1.68  end
% 1.31/1.68  
% 1.31/1.68  Proof check complete!
% 1.31/1.68  
% 1.31/1.68  Memory use:
% 1.31/1.68  
% 1.31/1.68  space for terms:        78881
% 1.31/1.68  space for clauses:      227328
% 1.31/1.68  
% 1.31/1.68  
% 1.31/1.68  clauses generated:      49673
% 1.31/1.68  clauses kept:           5468
% 1.31/1.68  clauses selected:       614
% 1.31/1.68  clauses deleted:        7
% 1.31/1.68  clauses inuse deleted:  3
% 1.31/1.68  
% 1.31/1.68  subsentry:          1017977
% 1.31/1.68  literals s-matched: 404706
% 1.31/1.68  literals matched:   404265
% 1.31/1.68  full subsumption:   248508
% 1.31/1.68  
% 1.31/1.68  checksum:           629294311
% 1.31/1.68  
% 1.31/1.68  
% 1.31/1.68  Bliksem ended
%------------------------------------------------------------------------------