TSTP Solution File: GEO184+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO184+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n018.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 02:52:24 EDT 2022

% Result   : Theorem 1.70s 2.10s
% Output   : Refutation 1.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEO184+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : bliksem %s
% 0.12/0.32  % Computer : n018.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % DateTime : Sat Jun 18 15:27:18 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 1.70/2.10  *** allocated 10000 integers for termspace/termends
% 1.70/2.10  *** allocated 10000 integers for clauses
% 1.70/2.10  *** allocated 10000 integers for justifications
% 1.70/2.10  Bliksem 1.12
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Automatic Strategy Selection
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Clauses:
% 1.70/2.10  
% 1.70/2.10  { ! distinct_points( X, X ) }.
% 1.70/2.10  { ! distinct_lines( X, X ) }.
% 1.70/2.10  { ! convergent_lines( X, X ) }.
% 1.70/2.10  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.70/2.10     ) }.
% 1.70/2.10  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.70/2.10     }.
% 1.70/2.10  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.70/2.10    , Z ) }.
% 1.70/2.10  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.70/2.10    , Y ) ) }.
% 1.70/2.10  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.70/2.10    , Y ) ) }.
% 1.70/2.10  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.70/2.10    , Y ), X ) }.
% 1.70/2.10  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.70/2.10    , Y ), Y ) }.
% 1.70/2.10  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.70/2.10    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.70/2.10    apart_point_and_line( Y, T ) }.
% 1.70/2.10  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 1.70/2.10    apart_point_and_line( Z, Y ) }.
% 1.70/2.10  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 1.70/2.10    apart_point_and_line( X, Z ) }.
% 1.70/2.10  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 1.70/2.10    Z ) }.
% 1.70/2.10  { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 1.70/2.10  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.70/2.10  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.70/2.10  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 1.70/2.10    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.70/2.10  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.70/2.10  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.70/2.10    , convergent_lines( Y, Z ) }.
% 1.70/2.10  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.70/2.10    , unorthogonal_lines( Y, Z ) }.
% 1.70/2.10  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.70/2.10  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.70/2.10  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.70/2.10     }.
% 1.70/2.10  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.70/2.10  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.70/2.10  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 1.70/2.10    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 1.70/2.10    unorthogonal_lines( Y, T ) }.
% 1.70/2.10  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.70/2.10  { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), ! 
% 1.70/2.10    unorthogonal_lines( X, Y ) }.
% 1.70/2.10  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.70/2.10     unorthogonal_lines( X, Y ) }.
% 1.70/2.10  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 1.70/2.10  { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.70/2.10  { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 1.70/2.10     }.
% 1.70/2.10  { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), ! 
% 1.70/2.10    convergent_lines( X, Y ) }.
% 1.70/2.10  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 1.70/2.10    line_connecting( X, Y ) ) }.
% 1.70/2.10  { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point( 
% 1.70/2.10    intersection_point( X, Y ) ) }.
% 1.70/2.10  { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 1.70/2.10  { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 1.70/2.10  { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 1.70/2.10  { distinct_points( X, Y ), equal_points( X, Y ) }.
% 1.70/2.10  { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 1.70/2.10  { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 1.70/2.10  { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 1.70/2.10  { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 1.70/2.10  { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 1.70/2.10  { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 1.70/2.10  { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.70/2.10  { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 1.70/2.10  { distinct_points( skol1, skol2 ) }.
% 1.70/2.10  { convergent_lines( skol3, skol4 ) }.
% 1.70/2.10  { incident_point_and_line( skol1, skol3 ) }.
% 1.70/2.10  { incident_point_and_line( skol2, skol3 ) }.
% 1.70/2.10  { ! equal_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  
% 1.70/2.10  percentage equality = 0.000000, percentage horn = 0.627451
% 1.70/2.10  This a non-horn, non-equality problem
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Options Used:
% 1.70/2.10  
% 1.70/2.10  useres =            1
% 1.70/2.10  useparamod =        0
% 1.70/2.10  useeqrefl =         0
% 1.70/2.10  useeqfact =         0
% 1.70/2.10  usefactor =         1
% 1.70/2.10  usesimpsplitting =  0
% 1.70/2.10  usesimpdemod =      0
% 1.70/2.10  usesimpres =        3
% 1.70/2.10  
% 1.70/2.10  resimpinuse      =  1000
% 1.70/2.10  resimpclauses =     20000
% 1.70/2.10  substype =          standard
% 1.70/2.10  backwardsubs =      1
% 1.70/2.10  selectoldest =      5
% 1.70/2.10  
% 1.70/2.10  litorderings [0] =  split
% 1.70/2.10  litorderings [1] =  liftord
% 1.70/2.10  
% 1.70/2.10  termordering =      none
% 1.70/2.10  
% 1.70/2.10  litapriori =        1
% 1.70/2.10  termapriori =       0
% 1.70/2.10  litaposteriori =    0
% 1.70/2.10  termaposteriori =   0
% 1.70/2.10  demodaposteriori =  0
% 1.70/2.10  ordereqreflfact =   0
% 1.70/2.10  
% 1.70/2.10  litselect =         none
% 1.70/2.10  
% 1.70/2.10  maxweight =         15
% 1.70/2.10  maxdepth =          30000
% 1.70/2.10  maxlength =         115
% 1.70/2.10  maxnrvars =         195
% 1.70/2.10  excuselevel =       1
% 1.70/2.10  increasemaxweight = 1
% 1.70/2.10  
% 1.70/2.10  maxselected =       10000000
% 1.70/2.10  maxnrclauses =      10000000
% 1.70/2.10  
% 1.70/2.10  showgenerated =    0
% 1.70/2.10  showkept =         0
% 1.70/2.10  showselected =     0
% 1.70/2.10  showdeleted =      0
% 1.70/2.10  showresimp =       1
% 1.70/2.10  showstatus =       2000
% 1.70/2.10  
% 1.70/2.10  prologoutput =     0
% 1.70/2.10  nrgoals =          5000000
% 1.70/2.10  totalproof =       1
% 1.70/2.10  
% 1.70/2.10  Symbols occurring in the translation:
% 1.70/2.10  
% 1.70/2.10  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.70/2.10  .  [1, 2]      (w:1, o:27, a:1, s:1, b:0), 
% 1.70/2.10  !  [4, 1]      (w:0, o:20, a:1, s:1, b:0), 
% 1.70/2.10  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.70/2.10  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.70/2.10  distinct_points  [36, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 1.70/2.10  distinct_lines  [37, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 1.70/2.10  convergent_lines  [38, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 1.70/2.10  line_connecting  [41, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 1.70/2.10  apart_point_and_line  [42, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 1.70/2.10  intersection_point  [43, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 1.70/2.10  parallel_through_point  [46, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 1.70/2.10  unorthogonal_lines  [49, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 1.70/2.10  orthogonal_through_point  [52, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 1.70/2.10  point  [54, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 1.70/2.10  line  [55, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 1.70/2.10  equal_points  [56, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 1.70/2.10  equal_lines  [57, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 1.70/2.10  parallel_lines  [58, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 1.70/2.10  incident_point_and_line  [59, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 1.70/2.10  orthogonal_lines  [60, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 1.70/2.10  alpha1  [61, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 1.70/2.10  alpha2  [62, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 1.70/2.10  skol1  [63, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 1.70/2.10  skol2  [64, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 1.70/2.10  skol3  [65, 0]      (w:1, o:18, a:1, s:1, b:0), 
% 1.70/2.10  skol4  [66, 0]      (w:1, o:19, a:1, s:1, b:0).
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Starting Search:
% 1.70/2.10  
% 1.70/2.10  *** allocated 15000 integers for clauses
% 1.70/2.10  *** allocated 22500 integers for clauses
% 1.70/2.10  *** allocated 33750 integers for clauses
% 1.70/2.10  *** allocated 15000 integers for termspace/termends
% 1.70/2.10  *** allocated 50625 integers for clauses
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  *** allocated 22500 integers for termspace/termends
% 1.70/2.10  *** allocated 75937 integers for clauses
% 1.70/2.10  *** allocated 33750 integers for termspace/termends
% 1.70/2.10  *** allocated 113905 integers for clauses
% 1.70/2.10  
% 1.70/2.10  Intermediate Status:
% 1.70/2.10  Generated:    13862
% 1.70/2.10  Kept:         2007
% 1.70/2.10  Inuse:        348
% 1.70/2.10  Deleted:      2
% 1.70/2.10  Deletedinuse: 1
% 1.70/2.10  
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  *** allocated 50625 integers for termspace/termends
% 1.70/2.10  *** allocated 170857 integers for clauses
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  *** allocated 75937 integers for termspace/termends
% 1.70/2.10  *** allocated 256285 integers for clauses
% 1.70/2.10  
% 1.70/2.10  Intermediate Status:
% 1.70/2.10  Generated:    29015
% 1.70/2.10  Kept:         4084
% 1.70/2.10  Inuse:        540
% 1.70/2.10  Deleted:      5
% 1.70/2.10  Deletedinuse: 1
% 1.70/2.10  
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  *** allocated 113905 integers for termspace/termends
% 1.70/2.10  *** allocated 384427 integers for clauses
% 1.70/2.10  
% 1.70/2.10  Intermediate Status:
% 1.70/2.10  Generated:    37494
% 1.70/2.10  Kept:         6145
% 1.70/2.10  Inuse:        588
% 1.70/2.10  Deleted:      6
% 1.70/2.10  Deletedinuse: 2
% 1.70/2.10  
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  *** allocated 170857 integers for termspace/termends
% 1.70/2.10  
% 1.70/2.10  Intermediate Status:
% 1.70/2.10  Generated:    57803
% 1.70/2.10  Kept:         8159
% 1.70/2.10  Inuse:        684
% 1.70/2.10  Deleted:      6
% 1.70/2.10  Deletedinuse: 2
% 1.70/2.10  
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  Resimplifying inuse:
% 1.70/2.10  Done
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Bliksems!, er is een bewijs:
% 1.70/2.10  % SZS status Theorem
% 1.70/2.10  % SZS output start Refutation
% 1.70/2.10  
% 1.70/2.10  (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10  (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 1.70/2.10    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.70/2.10    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 1.70/2.10  (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.70/2.10     }.
% 1.70/2.10  (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), ! 
% 1.70/2.10    incident_point_and_line( X, Y ) }.
% 1.70/2.10  (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 1.70/2.10  (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, skol3 ) }.
% 1.70/2.10  (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, skol3 ) }.
% 1.70/2.10  (50) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, line_connecting( skol1, 
% 1.70/2.10    skol2 ) ) }.
% 1.70/2.10  (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( skol1, skol3 )
% 1.70/2.10     }.
% 1.70/2.10  (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line( skol2, skol3 )
% 1.70/2.10     }.
% 1.70/2.10  (78) {G1,W5,D3,L1,V0,M1} R(39,50) { distinct_lines( skol3, line_connecting
% 1.70/2.10    ( skol1, skol2 ) ) }.
% 1.70/2.10  (101) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T ), 
% 1.70/2.10    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.70/2.10  (114) {G2,W14,D3,L4,V3,M2} F(101);r(7) { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 1.70/2.10     ), apart_point_and_line( X, Z ) }.
% 1.70/2.10  (1989) {G3,W11,D3,L3,V1,M1} R(114,77) { ! distinct_points( X, skol2 ), ! 
% 1.70/2.10    distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.70/2.10    apart_point_and_line( X, skol3 ) }.
% 1.70/2.10  (9258) {G4,W5,D3,L1,V0,M1} R(1989,76);r(46) { ! distinct_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  (9259) {G5,W0,D0,L0,V0,M0} S(9258);r(78) {  }.
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  % SZS output end Refutation
% 1.70/2.10  found a proof!
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Unprocessed initial clauses:
% 1.70/2.10  
% 1.70/2.10  (9261) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 1.70/2.10  (9262) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 1.70/2.10  (9263) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 1.70/2.10  (9264) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 1.70/2.10    , Z ), distinct_points( Y, Z ) }.
% 1.70/2.10  (9265) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 1.70/2.10    Z ), distinct_lines( Y, Z ) }.
% 1.70/2.10  (9266) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 1.70/2.10    ( X, Z ), convergent_lines( Y, Z ) }.
% 1.70/2.10  (9267) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10  (9268) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10  (9269) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.70/2.10  (9270) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.70/2.10  (9271) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 1.70/2.10    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 1.70/2.10    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.70/2.10  (9272) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.70/2.10    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.70/2.10  (9273) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.70/2.10    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.70/2.10  (9274) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.70/2.10    , Z ), convergent_lines( X, Z ) }.
% 1.70/2.10  (9275) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), convergent_lines( X
% 1.70/2.10    , Y ) }.
% 1.70/2.10  (9276) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( Y
% 1.70/2.10    , X ), Y ) }.
% 1.70/2.10  (9277) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 1.70/2.10    parallel_through_point( Y, X ) ) }.
% 1.70/2.10  (9278) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 1.70/2.10    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 1.70/2.10    convergent_lines( X, Y ) }.
% 1.70/2.10  (9279) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 1.70/2.10    ( X, Y ) }.
% 1.70/2.10  (9280) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 1.70/2.10    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.70/2.10  (9281) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 1.70/2.10    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.70/2.10     }.
% 1.70/2.10  (9282) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y )
% 1.70/2.10     }.
% 1.70/2.10  (9283) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 1.70/2.10     }.
% 1.70/2.10  (9284) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 1.70/2.10    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 1.70/2.10  (9285) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 1.70/2.10    orthogonal_through_point( Y, X ), Y ) }.
% 1.70/2.10  (9286) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 1.70/2.10    orthogonal_through_point( Y, X ) ) }.
% 1.70/2.10  (9287) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 1.70/2.10    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 1.70/2.10    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 1.70/2.10  (9288) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 1.70/2.10    ( X, Y ) }.
% 1.70/2.10  (9289) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), convergent_lines( Z, Y ), ! 
% 1.70/2.10    convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.70/2.10  (9290) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), 
% 1.70/2.10    ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.70/2.10  (9291) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), convergent_lines( Y, X )
% 1.70/2.10     }.
% 1.70/2.10  (9292) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 1.70/2.10     }.
% 1.70/2.10  (9293) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 1.70/2.10    unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 1.70/2.10  (9294) {G0,W9,D2,L3,V3,M3}  { unorthogonal_lines( Z, X ), 
% 1.70/2.10    unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.70/2.10  (9295) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! 
% 1.70/2.10    distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 1.70/2.10  (9296) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), ! convergent_lines
% 1.70/2.10    ( X, Y ), point( intersection_point( X, Y ) ) }.
% 1.70/2.10  (9297) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 1.70/2.10    parallel_through_point( X, Y ) ) }.
% 1.70/2.10  (9298) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 1.70/2.10    orthogonal_through_point( X, Y ) ) }.
% 1.70/2.10  (9299) {G0,W6,D2,L2,V2,M2}  { ! equal_points( X, Y ), ! distinct_points( X
% 1.70/2.10    , Y ) }.
% 1.70/2.10  (9300) {G0,W6,D2,L2,V2,M2}  { distinct_points( X, Y ), equal_points( X, Y )
% 1.70/2.10     }.
% 1.70/2.10  (9301) {G0,W6,D2,L2,V2,M2}  { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 1.70/2.10     ) }.
% 1.70/2.10  (9302) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.70/2.10     }.
% 1.70/2.10  (9303) {G0,W6,D2,L2,V2,M2}  { ! parallel_lines( X, Y ), ! convergent_lines
% 1.70/2.10    ( X, Y ) }.
% 1.70/2.10  (9304) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), parallel_lines( X, 
% 1.70/2.10    Y ) }.
% 1.70/2.10  (9305) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( X, Y ) }.
% 1.70/2.10  (9306) {G0,W6,D2,L2,V2,M2}  { apart_point_and_line( X, Y ), 
% 1.70/2.10    incident_point_and_line( X, Y ) }.
% 1.70/2.10  (9307) {G0,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), ! 
% 1.70/2.10    unorthogonal_lines( X, Y ) }.
% 1.70/2.10  (9308) {G0,W6,D2,L2,V2,M2}  { unorthogonal_lines( X, Y ), orthogonal_lines
% 1.70/2.10    ( X, Y ) }.
% 1.70/2.10  (9309) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 1.70/2.10  (9310) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol4 ) }.
% 1.70/2.10  (9311) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol1, skol3 ) }.
% 1.70/2.10  (9312) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol2, skol3 ) }.
% 1.70/2.10  (9313) {G0,W5,D3,L1,V0,M1}  { ! equal_lines( skol3, line_connecting( skol1
% 1.70/2.10    , skol2 ) ) }.
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Total Proof:
% 1.70/2.10  
% 1.70/2.10  subsumption: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10  parent0: (9267) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10     1 ==> 1
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10  parent0: (9268) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10     1 ==> 1
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 1.70/2.10    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 1.70/2.10    apart_point_and_line( X, Z ) }.
% 1.70/2.10  parent0: (9271) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 1.70/2.10    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.70/2.10    apart_point_and_line( Y, T ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10     Z := Z
% 1.70/2.10     T := T
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10     1 ==> 1
% 1.70/2.10     2 ==> 5
% 1.70/2.10     3 ==> 2
% 1.70/2.10     4 ==> 3
% 1.70/2.10     5 ==> 4
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), 
% 1.70/2.10    equal_lines( X, Y ) }.
% 1.70/2.10  parent0: (9302) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines
% 1.70/2.10    ( X, Y ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10     1 ==> 1
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.70/2.10     incident_point_and_line( X, Y ) }.
% 1.70/2.10  parent0: (9305) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), !
% 1.70/2.10     apart_point_and_line( X, Y ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 1
% 1.70/2.10     1 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.70/2.10     }.
% 1.70/2.10  parent0: (9309) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  parent0: (9311) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol1, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  parent0: (9312) {G0,W3,D2,L1,V0,M1}  { incident_point_and_line( skol2, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (50) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent0: (9313) {G0,W5,D3,L1,V0,M1}  { ! equal_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9419) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), ! 
% 1.70/2.10    incident_point_and_line( X, Y ) }.
% 1.70/2.10  parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := skol1
% 1.70/2.10     Y := skol3
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( 
% 1.70/2.10    skol1, skol3 ) }.
% 1.70/2.10  parent0: (9419) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, skol3
% 1.70/2.10     ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9420) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol2, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), ! 
% 1.70/2.10    incident_point_and_line( X, Y ) }.
% 1.70/2.10  parent1[0]: (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, 
% 1.70/2.10    skol3 ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := skol2
% 1.70/2.10     Y := skol3
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line( 
% 1.70/2.10    skol2, skol3 ) }.
% 1.70/2.10  parent0: (9420) {G1,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol2, skol3
% 1.70/2.10     ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9421) {G1,W5,D3,L1,V0,M1}  { distinct_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent0[0]: (50) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), 
% 1.70/2.10    equal_lines( X, Y ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10     X := skol3
% 1.70/2.10     Y := line_connecting( skol1, skol2 )
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (78) {G1,W5,D3,L1,V0,M1} R(39,50) { distinct_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent0: (9421) {G1,W5,D3,L1,V0,M1}  { distinct_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9422) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.70/2.10    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.70/2.10    , Y ) ), apart_point_and_line( X, T ) }.
% 1.70/2.10  parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.70/2.10  parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 1.70/2.10    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 1.70/2.10    apart_point_and_line( X, Z ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Z
% 1.70/2.10     Z := T
% 1.70/2.10     T := line_connecting( X, Y )
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (101) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y )
% 1.70/2.10    , ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T
% 1.70/2.10     ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.70/2.10  parent0: (9422) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.70/2.10    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.70/2.10    , Y ) ), apart_point_and_line( X, T ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := T
% 1.70/2.10     Z := Y
% 1.70/2.10     T := Z
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 2
% 1.70/2.10     1 ==> 0
% 1.70/2.10     2 ==> 1
% 1.70/2.10     3 ==> 4
% 1.70/2.10     4 ==> 5
% 1.70/2.10     5 ==> 3
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  factor: (9438) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10     ), apart_point_and_line( Y, Z ), apart_point_and_line( Y, 
% 1.70/2.10    line_connecting( X, Y ) ) }.
% 1.70/2.10  parent0[0, 2]: (101) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y
% 1.70/2.10     ), ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X
% 1.70/2.10    , T ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10     Z := Z
% 1.70/2.10     T := Y
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9445) {G1,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 1.70/2.10    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10  parent0[1]: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.70/2.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.70/2.10  parent1[4]: (9438) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10     ), apart_point_and_line( Y, Z ), apart_point_and_line( Y, 
% 1.70/2.10    line_connecting( X, Y ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10     Z := Z
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  factor: (9446) {G1,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10     ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10  parent0[0, 1]: (9445) {G1,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 1.70/2.10    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10     Z := Z
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (114) {G2,W14,D3,L4,V3,M2} F(101);r(7) { ! distinct_points( X
% 1.70/2.10    , Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 1.70/2.10    apart_point_and_line( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.70/2.10  parent0: (9446) {G1,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 1.70/2.10    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.70/2.10     ), apart_point_and_line( Y, Z ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10     Y := Y
% 1.70/2.10     Z := Z
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10     1 ==> 1
% 1.70/2.10     2 ==> 3
% 1.70/2.10     3 ==> 2
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9448) {G2,W11,D3,L3,V1,M3}  { ! distinct_points( X, skol2 ), !
% 1.70/2.10     distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.70/2.10    apart_point_and_line( X, skol3 ) }.
% 1.70/2.10  parent0[0]: (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line( 
% 1.70/2.10    skol2, skol3 ) }.
% 1.70/2.10  parent1[2]: (114) {G2,W14,D3,L4,V3,M2} F(101);r(7) { ! distinct_points( X, 
% 1.70/2.10    Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.70/2.10    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10     X := X
% 1.70/2.10     Y := skol2
% 1.70/2.10     Z := skol3
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (1989) {G3,W11,D3,L3,V1,M1} R(114,77) { ! distinct_points( X, 
% 1.70/2.10    skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.70/2.10    apart_point_and_line( X, skol3 ) }.
% 1.70/2.10  parent0: (9448) {G2,W11,D3,L3,V1,M3}  { ! distinct_points( X, skol2 ), ! 
% 1.70/2.10    distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.70/2.10    apart_point_and_line( X, skol3 ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10     X := X
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10     1 ==> 1
% 1.70/2.10     2 ==> 2
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9450) {G2,W8,D3,L2,V0,M2}  { ! distinct_points( skol1, skol2 )
% 1.70/2.10    , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent0[0]: (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( 
% 1.70/2.10    skol1, skol3 ) }.
% 1.70/2.10  parent1[2]: (1989) {G3,W11,D3,L3,V1,M1} R(114,77) { ! distinct_points( X, 
% 1.70/2.10    skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ), 
% 1.70/2.10    apart_point_and_line( X, skol3 ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10     X := skol1
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9451) {G1,W5,D3,L1,V0,M1}  { ! distinct_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent0[0]: (9450) {G2,W8,D3,L2,V0,M2}  { ! distinct_points( skol1, skol2 )
% 1.70/2.10    , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.70/2.10     }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (9258) {G4,W5,D3,L1,V0,M1} R(1989,76);r(46) { ! distinct_lines
% 1.70/2.10    ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent0: (9451) {G1,W5,D3,L1,V0,M1}  { ! distinct_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10     0 ==> 0
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  resolution: (9452) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.70/2.10  parent0[0]: (9258) {G4,W5,D3,L1,V0,M1} R(1989,76);r(46) { ! distinct_lines
% 1.70/2.10    ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  parent1[0]: (78) {G1,W5,D3,L1,V0,M1} R(39,50) { distinct_lines( skol3, 
% 1.70/2.10    line_connecting( skol1, skol2 ) ) }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  substitution1:
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  subsumption: (9259) {G5,W0,D0,L0,V0,M0} S(9258);r(78) {  }.
% 1.70/2.10  parent0: (9452) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.70/2.10  substitution0:
% 1.70/2.10  end
% 1.70/2.10  permutation0:
% 1.70/2.10  end
% 1.70/2.10  
% 1.70/2.10  Proof check complete!
% 1.70/2.10  
% 1.70/2.10  Memory use:
% 1.70/2.10  
% 1.70/2.10  space for terms:        131361
% 1.70/2.10  space for clauses:      379646
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  clauses generated:      83057
% 1.70/2.10  clauses kept:           9260
% 1.70/2.10  clauses selected:       855
% 1.70/2.10  clauses deleted:        7
% 1.70/2.10  clauses inuse deleted:  2
% 1.70/2.10  
% 1.70/2.10  subsentry:          1778350
% 1.70/2.10  literals s-matched: 686979
% 1.70/2.10  literals matched:   686482
% 1.70/2.10  full subsumption:   396802
% 1.70/2.10  
% 1.70/2.10  checksum:           1262685345
% 1.70/2.10  
% 1.70/2.10  
% 1.70/2.10  Bliksem ended
%------------------------------------------------------------------------------