TSTP Solution File: GEO177+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO177+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 02:52:18 EDT 2022

% Result   : Theorem 6.54s 6.89s
% Output   : Refutation 6.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : bliksem %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % DateTime : Sat Jun 18 02:49:12 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 6.54/6.89  *** allocated 10000 integers for termspace/termends
% 6.54/6.89  *** allocated 10000 integers for clauses
% 6.54/6.89  *** allocated 10000 integers for justifications
% 6.54/6.89  Bliksem 1.12
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  Automatic Strategy Selection
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  Clauses:
% 6.54/6.89  
% 6.54/6.89  { ! distinct_points( X, X ) }.
% 6.54/6.89  { ! distinct_lines( X, X ) }.
% 6.54/6.89  { ! convergent_lines( X, X ) }.
% 6.54/6.89  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 6.54/6.89     ) }.
% 6.54/6.89  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.54/6.89     }.
% 6.54/6.89  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 6.54/6.89    , Z ) }.
% 6.54/6.89  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 6.54/6.89    , Y ) ) }.
% 6.54/6.89  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 6.54/6.89    , Y ) ) }.
% 6.54/6.89  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.54/6.89    , Y ), X ) }.
% 6.54/6.89  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.54/6.89    , Y ), Y ) }.
% 6.54/6.89  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 6.54/6.89    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 6.54/6.89    apart_point_and_line( Y, T ) }.
% 6.54/6.89  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 6.54/6.89    apart_point_and_line( Z, Y ) }.
% 6.54/6.89  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 6.54/6.89    apart_point_and_line( X, Z ) }.
% 6.54/6.89  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 6.54/6.89    Z ) }.
% 6.54/6.89  { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 6.54/6.89  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 6.54/6.89  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 6.54/6.89  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 6.54/6.89    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 6.54/6.89  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.54/6.89  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.54/6.89    , convergent_lines( Y, Z ) }.
% 6.54/6.89  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.54/6.89    , unorthogonal_lines( Y, Z ) }.
% 6.54/6.89  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 6.54/6.89  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.54/6.89  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 6.54/6.89     }.
% 6.54/6.89  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.89  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 6.54/6.89  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 6.54/6.89    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 6.54/6.89    unorthogonal_lines( Y, T ) }.
% 6.54/6.89  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.54/6.89  { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), ! 
% 6.54/6.89    unorthogonal_lines( X, Y ) }.
% 6.54/6.89  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 6.54/6.89     unorthogonal_lines( X, Y ) }.
% 6.54/6.89  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 6.54/6.89  { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 6.54/6.89  { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 6.54/6.89     }.
% 6.54/6.89  { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), ! 
% 6.54/6.89    convergent_lines( X, Y ) }.
% 6.54/6.89  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 6.54/6.89    line_connecting( X, Y ) ) }.
% 6.54/6.89  { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point( 
% 6.54/6.89    intersection_point( X, Y ) ) }.
% 6.54/6.89  { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 6.54/6.89  { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 6.54/6.89  { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 6.54/6.89  { distinct_points( X, Y ), equal_points( X, Y ) }.
% 6.54/6.89  { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 6.54/6.89  { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 6.54/6.89  { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 6.54/6.89  { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 6.54/6.89  { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.89  { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 6.54/6.89  { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.54/6.89  { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 6.54/6.89  { distinct_points( skol1, skol2 ) }.
% 6.54/6.89  { distinct_points( skol3, skol4 ) }.
% 6.54/6.89  { apart_point_and_line( skol1, line_connecting( skol3, skol4 ) ), 
% 6.54/6.89    apart_point_and_line( skol2, line_connecting( skol3, skol4 ) ) }.
% 6.54/6.89  { ! apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89  { ! apart_point_and_line( skol4, line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89  
% 6.54/6.89  percentage equality = 0.000000, percentage horn = 0.607843
% 6.54/6.89  This a non-horn, non-equality problem
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  Options Used:
% 6.54/6.89  
% 6.54/6.89  useres =            1
% 6.54/6.89  useparamod =        0
% 6.54/6.89  useeqrefl =         0
% 6.54/6.89  useeqfact =         0
% 6.54/6.89  usefactor =         1
% 6.54/6.89  usesimpsplitting =  0
% 6.54/6.89  usesimpdemod =      0
% 6.54/6.89  usesimpres =        3
% 6.54/6.89  
% 6.54/6.89  resimpinuse      =  1000
% 6.54/6.89  resimpclauses =     20000
% 6.54/6.89  substype =          standard
% 6.54/6.89  backwardsubs =      1
% 6.54/6.89  selectoldest =      5
% 6.54/6.89  
% 6.54/6.89  litorderings [0] =  split
% 6.54/6.89  litorderings [1] =  liftord
% 6.54/6.89  
% 6.54/6.89  termordering =      none
% 6.54/6.89  
% 6.54/6.89  litapriori =        1
% 6.54/6.89  termapriori =       0
% 6.54/6.89  litaposteriori =    0
% 6.54/6.89  termaposteriori =   0
% 6.54/6.89  demodaposteriori =  0
% 6.54/6.89  ordereqreflfact =   0
% 6.54/6.89  
% 6.54/6.89  litselect =         none
% 6.54/6.89  
% 6.54/6.89  maxweight =         15
% 6.54/6.89  maxdepth =          30000
% 6.54/6.89  maxlength =         115
% 6.54/6.89  maxnrvars =         195
% 6.54/6.89  excuselevel =       1
% 6.54/6.89  increasemaxweight = 1
% 6.54/6.89  
% 6.54/6.89  maxselected =       10000000
% 6.54/6.89  maxnrclauses =      10000000
% 6.54/6.89  
% 6.54/6.89  showgenerated =    0
% 6.54/6.89  showkept =         0
% 6.54/6.89  showselected =     0
% 6.54/6.89  showdeleted =      0
% 6.54/6.89  showresimp =       1
% 6.54/6.89  showstatus =       2000
% 6.54/6.89  
% 6.54/6.89  prologoutput =     0
% 6.54/6.89  nrgoals =          5000000
% 6.54/6.89  totalproof =       1
% 6.54/6.89  
% 6.54/6.89  Symbols occurring in the translation:
% 6.54/6.89  
% 6.54/6.89  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 6.54/6.89  .  [1, 2]      (w:1, o:27, a:1, s:1, b:0), 
% 6.54/6.89  !  [4, 1]      (w:0, o:20, a:1, s:1, b:0), 
% 6.54/6.89  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 6.54/6.89  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 6.54/6.89  distinct_points  [36, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 6.54/6.89  distinct_lines  [37, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 6.54/6.89  convergent_lines  [38, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 6.54/6.89  line_connecting  [41, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 6.54/6.89  apart_point_and_line  [42, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 6.54/6.89  intersection_point  [43, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 6.54/6.89  parallel_through_point  [46, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 6.54/6.89  unorthogonal_lines  [49, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 6.54/6.89  orthogonal_through_point  [52, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 6.54/6.89  point  [54, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 6.54/6.89  line  [55, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 6.54/6.89  equal_points  [56, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 6.54/6.89  equal_lines  [57, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 6.54/6.89  parallel_lines  [58, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 6.54/6.89  incident_point_and_line  [59, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 6.54/6.89  orthogonal_lines  [60, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 6.54/6.89  alpha1  [61, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 6.54/6.89  alpha2  [62, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 6.54/6.89  skol1  [63, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 6.54/6.89  skol2  [64, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 6.54/6.89  skol3  [65, 0]      (w:1, o:18, a:1, s:1, b:0), 
% 6.54/6.89  skol4  [66, 0]      (w:1, o:19, a:1, s:1, b:0).
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  Starting Search:
% 6.54/6.89  
% 6.54/6.89  *** allocated 15000 integers for clauses
% 6.54/6.89  *** allocated 22500 integers for clauses
% 6.54/6.89  *** allocated 33750 integers for clauses
% 6.54/6.89  *** allocated 15000 integers for termspace/termends
% 6.54/6.89  *** allocated 50625 integers for clauses
% 6.54/6.89  Resimplifying inuse:
% 6.54/6.89  Done
% 6.54/6.89  
% 6.54/6.89  *** allocated 22500 integers for termspace/termends
% 6.54/6.89  *** allocated 75937 integers for clauses
% 6.54/6.89  *** allocated 33750 integers for termspace/termends
% 6.54/6.89  *** allocated 113905 integers for clauses
% 6.54/6.89  
% 6.54/6.89  Intermediate Status:
% 6.54/6.89  Generated:    18654
% 6.54/6.89  Kept:         2001
% 6.54/6.89  Inuse:        314
% 6.54/6.89  Deleted:      2
% 6.54/6.89  Deletedinuse: 2
% 6.54/6.89  
% 6.54/6.89  Resimplifying inuse:
% 6.54/6.89  Done
% 6.54/6.89  
% 6.54/6.89  *** allocated 50625 integers for termspace/termends
% 6.54/6.89  *** allocated 170857 integers for clauses
% 6.54/6.89  Resimplifying inuse:
% 6.54/6.89  Done
% 6.54/6.89  
% 6.54/6.89  *** allocated 75937 integers for termspace/termends
% 6.54/6.89  
% 6.54/6.89  Intermediate Status:
% 6.54/6.89  Generated:    32063
% 6.54/6.89  Kept:         4032
% 6.54/6.89  Inuse:        475
% 6.54/6.89  Deleted:      5
% 6.54/6.89  Deletedinuse: 2
% 6.54/6.89  
% 6.54/6.89  Resimplifying inuse:
% 6.54/6.89  Done
% 6.54/6.89  
% 6.54/6.89  *** allocated 256285 integers for clauses
% 6.54/6.89  Resimplifying inuse:
% 6.54/6.89  Done
% 6.54/6.89  
% 6.54/6.89  *** allocated 113905 integers for termspace/termends
% 6.54/6.89  *** allocated 384427 integers for clauses
% 6.54/6.89  
% 6.54/6.89  Intermediate Status:
% 6.54/6.89  Generated:    64813
% 6.54/6.89  Kept:         6032
% 6.54/6.89  Inuse:        820
% 6.54/6.89  Deleted:      9
% 6.54/6.89  Deletedinuse: 3
% 6.54/6.89  
% 6.54/6.89  Resimplifying inuse:
% 6.54/6.89  Done
% 6.54/6.89  
% 6.54/6.89  Resimplifying inuse:
% 6.54/6.89  Done
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  Bliksems!, er is een bewijs:
% 6.54/6.89  % SZS status Theorem
% 6.54/6.89  % SZS output start Refutation
% 6.54/6.89  
% 6.54/6.89  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.54/6.89  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.89  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.54/6.89    , ! distinct_lines( X, Y ) }.
% 6.54/6.89  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 6.54/6.89    Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.89  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 6.54/6.89    X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.89  (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 6.54/6.89    , Y ) }.
% 6.54/6.89  (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 6.54/6.89    , X ), Y ) }.
% 6.54/6.89  (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 6.54/6.89    parallel_through_point( Y, X ) ) }.
% 6.54/6.89  (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines( 
% 6.54/6.89    X, Y ) }.
% 6.54/6.89  (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 6.54/6.89    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.54/6.89     }.
% 6.54/6.89  (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 6.54/6.89  (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 6.54/6.89    ( Y, X ), Y ) }.
% 6.54/6.89  (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 6.54/6.89    orthogonal_through_point( Y, X ) ) }.
% 6.54/6.89  (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 6.54/6.89    ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.54/6.89  (48) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line( skol1, line_connecting
% 6.54/6.89    ( skol3, skol4 ) ), apart_point_and_line( skol2, line_connecting( skol3, 
% 6.54/6.89    skol4 ) ) }.
% 6.54/6.89  (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 6.54/6.89    ( X, Y ) }.
% 6.54/6.89  (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( 
% 6.54/6.89    parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.89  (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 6.54/6.89    convergent_lines( X, Y ) }.
% 6.54/6.89  (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X, 
% 6.54/6.89    parallel_through_point( X, Y ) ) }.
% 6.54/6.89  (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ), 
% 6.54/6.89    convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.89  (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y ), 
% 6.54/6.89    convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.89  (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 6.54/6.89    orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.89  (113) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ), 
% 6.54/6.89    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.89  (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ), ! 
% 6.54/6.89    distinct_lines( Y, X ) }.
% 6.54/6.89  (138) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 6.54/6.89    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 6.54/6.89    apart_point_and_line( Z, X ) }.
% 6.54/6.89  (150) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 6.54/6.89    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89  (151) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 6.54/6.89    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89  (162) {G2,W11,D3,L3,V4,M1} R(150,12) { distinct_lines( X, 
% 6.54/6.89    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.89    apart_point_and_line( Z, T ) }.
% 6.54/6.89  (164) {G2,W11,D3,L3,V4,M1} R(151,12) { distinct_lines( X, 
% 6.54/6.89    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.89    apart_point_and_line( Z, T ) }.
% 6.54/6.89  (171) {G3,W8,D3,L2,V3,M2} R(113,69) { convergent_lines( Z, X ), 
% 6.54/6.89    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.89  (178) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ), 
% 6.54/6.89    convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 6.54/6.89    unorthogonal_lines( Y, Z ) }.
% 6.54/6.89  (184) {G4,W8,D3,L2,V3,M2} R(171,69) { convergent_lines( X, 
% 6.54/6.89    orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.89  (206) {G4,W7,D4,L1,V3,M1} R(73,15) { ! convergent_lines( X, 
% 6.54/6.89    parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.89  (216) {G5,W10,D4,L2,V4,M2} R(206,5) { ! convergent_lines( Y, X ), 
% 6.54/6.89    convergent_lines( X, parallel_through_point( parallel_through_point( Y, Z
% 6.54/6.89     ), T ) ) }.
% 6.54/6.89  (246) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X, 
% 6.54/6.89    parallel_through_point( Z, T ) ), convergent_lines( 
% 6.54/6.89    parallel_through_point( X, Y ), Z ) }.
% 6.54/6.89  (250) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z ), ! 
% 6.54/6.89    convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.89  (261) {G3,W8,D3,L2,V3,M2} R(250,69) { ! convergent_lines( Y, 
% 6.54/6.89    parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.89  (285) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ), 
% 6.54/6.89    unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.54/6.89  (2003) {G3,W14,D3,L4,V5,M1} R(164,12) { distinct_lines( X, 
% 6.54/6.89    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 6.54/6.89    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.89  (2005) {G4,W8,D3,L2,V3,M1} F(2003);r(58) { distinct_lines( 
% 6.54/6.89    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89  (2024) {G3,W14,D3,L4,V5,M1} R(162,12) { distinct_lines( X, 
% 6.54/6.89    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.89    ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.89  (2026) {G4,W8,D3,L2,V3,M1} F(2024);r(58) { distinct_lines( 
% 6.54/6.89    parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89  (2352) {G2,W15,D2,L5,V5,M2} R(138,12) { distinct_lines( X, Y ), 
% 6.54/6.89    distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line( T, 
% 6.54/6.89    U ), ! apart_point_and_line( T, X ) }.
% 6.54/6.89  (2356) {G3,W9,D2,L3,V3,M2} F(2352);r(58) { distinct_lines( Y, X ), ! 
% 6.54/6.89    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 6.54/6.89  (2411) {G4,W13,D3,L3,V1,M2} R(2356,48) { distinct_lines( X, line_connecting
% 6.54/6.89    ( skol3, skol4 ) ), apart_point_and_line( skol1, line_connecting( skol3, 
% 6.54/6.89    skol4 ) ), apart_point_and_line( skol2, X ) }.
% 6.54/6.89  (2738) {G5,W8,D3,L2,V3,M1} R(178,23);r(184) { convergent_lines( X, Y ), ! 
% 6.54/6.89    unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.89  (2745) {G6,W10,D3,L2,V4,M2} R(2738,285) { ! convergent_lines( 
% 6.54/6.89    orthogonal_through_point( Z, T ), X ), convergent_lines( 
% 6.54/6.89    orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.89  (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines( 
% 6.54/6.89    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.89  (3012) {G8,W9,D5,L1,V4,M1} R(2914,261) { ! convergent_lines( X, 
% 6.54/6.89    parallel_through_point( orthogonal_through_point( 
% 6.54/6.89    orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.89  (3015) {G8,W9,D5,L1,V4,M1} R(2914,74) { ! convergent_lines( 
% 6.54/6.89    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.89    parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.89  (3404) {G9,W13,D7,L1,V6,M1} R(3012,246) { ! convergent_lines( X, 
% 6.54/6.89    parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.54/6.89    ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.89    , W ) ) }.
% 6.54/6.89  (3478) {G9,W13,D7,L1,V6,M1} R(3015,216) { ! convergent_lines( X, 
% 6.54/6.89    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.89    parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.89    , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.89  (7272) {G5,W15,D3,L3,V2,M1} R(2411,2005) { distinct_lines( X, 
% 6.54/6.89    line_connecting( skol3, skol4 ) ), distinct_lines( 
% 6.54/6.89    orthogonal_through_point( Y, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.89    apart_point_and_line( skol2, X ) }.
% 6.54/6.89  (7273) {G6,W12,D3,L2,V1,M1} F(7272) { distinct_lines( 
% 6.54/6.89    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.89    apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.89  (7287) {G7,W14,D3,L2,V2,M1} R(7273,2026) { distinct_lines( 
% 6.54/6.89    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.89    distinct_lines( parallel_through_point( Y, skol2 ), 
% 6.54/6.89    orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.89  (7343) {G8,W14,D3,L2,V2,M1} R(7287,114) { convergent_lines( 
% 6.54/6.89    orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.89     ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.89    ( skol3, skol4 ) ) }.
% 6.54/6.89  (7345) {G9,W14,D3,L2,V2,M1} R(7343,114) { convergent_lines( line_connecting
% 6.54/6.89    ( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ), 
% 6.54/6.89    convergent_lines( orthogonal_through_point( X, skol1 ), 
% 6.54/6.89    parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.89  (7354) {G10,W7,D3,L1,V1,M1} R(7345,3404) { convergent_lines( 
% 6.54/6.89    line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.89     }.
% 6.54/6.89  (7355) {G11,W0,D0,L0,V0,M0} R(7354,3478) {  }.
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  % SZS output end Refutation
% 6.54/6.89  found a proof!
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  Unprocessed initial clauses:
% 6.54/6.89  
% 6.54/6.89  (7357) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 6.54/6.89  (7358) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 6.54/6.89  (7359) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 6.54/6.89  (7360) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 6.54/6.89    , Z ), distinct_points( Y, Z ) }.
% 6.54/6.89  (7361) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 6.54/6.89    Z ), distinct_lines( Y, Z ) }.
% 6.54/6.89  (7362) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 6.54/6.89    ( X, Z ), convergent_lines( Y, Z ) }.
% 6.54/6.89  (7363) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 6.54/6.89    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 6.54/6.89  (7364) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 6.54/6.89    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 6.54/6.89  (7365) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 6.54/6.89    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.54/6.89  (7366) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 6.54/6.89    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.54/6.89  (7367) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 6.54/6.89    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 6.54/6.89    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 6.54/6.89  (7368) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 6.54/6.89    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 6.54/6.89  (7369) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 6.54/6.89    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 6.54/6.89  (7370) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 6.54/6.89    , Z ), convergent_lines( X, Z ) }.
% 6.54/6.89  (7371) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), convergent_lines( X
% 6.54/6.89    , Y ) }.
% 6.54/6.89  (7372) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( Y
% 6.54/6.89    , X ), Y ) }.
% 6.54/6.89  (7373) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 6.54/6.89    parallel_through_point( Y, X ) ) }.
% 6.54/6.89  (7374) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 6.54/6.89    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 6.54/6.89    convergent_lines( X, Y ) }.
% 6.54/6.89  (7375) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 6.54/6.89    ( X, Y ) }.
% 6.54/6.89  (7376) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 6.54/6.89    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 6.54/6.89  (7377) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 6.54/6.89    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 6.54/6.89     }.
% 6.54/6.89  (7378) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y )
% 6.54/6.89     }.
% 6.54/6.89  (7379) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 6.54/6.89     }.
% 6.54/6.89  (7380) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 6.54/6.89    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 6.54/6.89  (7381) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 6.54/6.89    orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.89  (7382) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 6.54/6.89    orthogonal_through_point( Y, X ) ) }.
% 6.54/6.89  (7383) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 6.54/6.89    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 6.54/6.89    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 6.54/6.89  (7384) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 6.54/6.89    ( X, Y ) }.
% 6.54/6.89  (7385) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), convergent_lines( Z, Y ), ! 
% 6.54/6.89    convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.54/6.89  (7386) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), 
% 6.54/6.89    ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.54/6.89  (7387) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), convergent_lines( Y, X )
% 6.54/6.89     }.
% 6.54/6.89  (7388) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 6.54/6.89     }.
% 6.54/6.89  (7389) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 6.54/6.89    unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 6.54/6.89  (7390) {G0,W9,D2,L3,V3,M3}  { unorthogonal_lines( Z, X ), 
% 6.54/6.89    unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.54/6.89  (7391) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! 
% 6.54/6.89    distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 6.54/6.89  (7392) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), ! convergent_lines
% 6.54/6.89    ( X, Y ), point( intersection_point( X, Y ) ) }.
% 6.54/6.89  (7393) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 6.54/6.89    parallel_through_point( X, Y ) ) }.
% 6.54/6.89  (7394) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 6.54/6.89    orthogonal_through_point( X, Y ) ) }.
% 6.54/6.89  (7395) {G0,W6,D2,L2,V2,M2}  { ! equal_points( X, Y ), ! distinct_points( X
% 6.54/6.89    , Y ) }.
% 6.54/6.89  (7396) {G0,W6,D2,L2,V2,M2}  { distinct_points( X, Y ), equal_points( X, Y )
% 6.54/6.89     }.
% 6.54/6.89  (7397) {G0,W6,D2,L2,V2,M2}  { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 6.54/6.89     ) }.
% 6.54/6.89  (7398) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines( X, Y )
% 6.54/6.89     }.
% 6.54/6.89  (7399) {G0,W6,D2,L2,V2,M2}  { ! parallel_lines( X, Y ), ! convergent_lines
% 6.54/6.89    ( X, Y ) }.
% 6.54/6.89  (7400) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), parallel_lines( X, 
% 6.54/6.89    Y ) }.
% 6.54/6.89  (7401) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), ! 
% 6.54/6.89    apart_point_and_line( X, Y ) }.
% 6.54/6.89  (7402) {G0,W6,D2,L2,V2,M2}  { apart_point_and_line( X, Y ), 
% 6.54/6.89    incident_point_and_line( X, Y ) }.
% 6.54/6.89  (7403) {G0,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), ! 
% 6.54/6.89    unorthogonal_lines( X, Y ) }.
% 6.54/6.89  (7404) {G0,W6,D2,L2,V2,M2}  { unorthogonal_lines( X, Y ), orthogonal_lines
% 6.54/6.89    ( X, Y ) }.
% 6.54/6.89  (7405) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 6.54/6.89  (7406) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol3, skol4 ) }.
% 6.54/6.89  (7407) {G0,W10,D3,L2,V0,M2}  { apart_point_and_line( skol1, line_connecting
% 6.54/6.89    ( skol3, skol4 ) ), apart_point_and_line( skol2, line_connecting( skol3, 
% 6.54/6.89    skol4 ) ) }.
% 6.54/6.89  (7408) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( skol3, 
% 6.54/6.89    line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89  (7409) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( skol4, 
% 6.54/6.89    line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89  
% 6.54/6.89  
% 6.54/6.89  Total Proof:
% 6.54/6.89  
% 6.54/6.89  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.54/6.89  parent0: (7358) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 6.54/6.89  substitution0:
% 6.54/6.89     X := X
% 6.54/6.89  end
% 6.54/6.89  permutation0:
% 6.54/6.89     0 ==> 0
% 6.54/6.89  end
% 6.54/6.89  
% 6.54/6.89  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.89  parent0: (7359) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 6.54/6.89  substitution0:
% 6.54/6.89     X := X
% 6.54/6.89  end
% 6.54/6.89  permutation0:
% 6.54/6.89     0 ==> 0
% 6.54/6.89  end
% 6.54/6.89  
% 6.54/6.89  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 6.54/6.89    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.54/6.89  parent0: (7361) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 6.54/6.89    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 6.54/6.89  substitution0:
% 6.54/6.89     X := X
% 6.54/6.89     Y := Y
% 6.54/6.89     Z := Z
% 6.54/6.89  end
% 6.54/6.89  permutation0:
% 6.54/6.89     0 ==> 2
% 6.54/6.89     1 ==> 0
% 6.54/6.89     2 ==> 1
% 6.54/6.89  end
% 6.54/6.89  
% 6.54/6.89  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 6.54/6.89    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.89  parent0: (7362) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 6.54/6.89    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 6.54/6.89  substitution0:
% 6.54/6.89     X := X
% 6.54/6.89     Y := Y
% 6.54/6.89     Z := Z
% 6.54/6.89  end
% 6.54/6.89  permutation0:
% 6.54/6.89     0 ==> 2
% 6.54/6.89     1 ==> 0
% 6.54/6.89     2 ==> 1
% 6.54/6.89  end
% 6.54/6.89  
% 6.54/6.89  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.89    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.89  parent0: (7369) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 6.54/6.89    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 6.54/6.89  substitution0:
% 6.54/6.89     X := X
% 6.54/6.89     Y := Y
% 6.54/6.89     Z := Z
% 6.54/6.89  end
% 6.54/6.89  permutation0:
% 6.54/6.89     0 ==> 2
% 6.54/6.89     1 ==> 0
% 6.54/6.89     2 ==> 1
% 6.54/6.89  end
% 6.54/6.89  
% 6.54/6.89  subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 6.54/6.89    distinct_lines( X, Y ) }.
% 6.54/6.89  parent0: (7371) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), 
% 6.54/6.89    convergent_lines( X, Y ) }.
% 6.54/6.89  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent0: (7372) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 6.54/6.90    parallel_through_point( Y, X ) ) }.
% 6.54/6.90  parent0: (7373) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 6.54/6.90    parallel_through_point( Y, X ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 6.54/6.90    unorthogonal_lines( X, Y ) }.
% 6.54/6.90  parent0: (7375) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), 
% 6.54/6.90    unorthogonal_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 6.54/6.90    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.54/6.90     }.
% 6.54/6.90  parent0: (7377) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 6.54/6.90    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 6.54/6.90     }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90     2 ==> 3
% 6.54/6.90     3 ==> 2
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 6.54/6.90    alpha1( X, Y ) }.
% 6.54/6.90  parent0: (7378) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( 
% 6.54/6.90    X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 6.54/6.90    orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent0: (7381) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 6.54/6.90    orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 6.54/6.90    orthogonal_through_point( Y, X ) ) }.
% 6.54/6.90  parent0: (7382) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 6.54/6.90    orthogonal_through_point( Y, X ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), 
% 6.54/6.90    unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.54/6.90  parent0: (7390) {G0,W9,D2,L3,V3,M3}  { unorthogonal_lines( Z, X ), 
% 6.54/6.90    unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 2
% 6.54/6.90     2 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (48) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line( skol1, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90  parent0: (7407) {G0,W10,D3,L2,V0,M2}  { apart_point_and_line( skol1, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7529) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.54/6.90  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 6.54/6.90    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  parent0: (7529) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7531) {G1,W8,D3,L2,V3,M2}  { convergent_lines( Z, X ), ! 
% 6.54/6.90    convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := parallel_through_point( X, Y )
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.90  parent0: (7531) {G1,W8,D3,L2,V3,M2}  { convergent_lines( Z, X ), ! 
% 6.54/6.90    convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7533) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.90  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  parent0: (7533) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7535) {G1,W5,D3,L1,V2,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( X, Y ) ) }.
% 6.54/6.90  parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent1[1]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := parallel_through_point( X, Y )
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( X, Y ) ) }.
% 6.54/6.90  parent0: (7535) {G1,W5,D3,L1,V2,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( X, Y ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7536) {G1,W8,D3,L2,V3,M2}  { convergent_lines( Z, 
% 6.54/6.90    parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 6.54/6.90  parent0[0]: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( X, Y ) ) }.
% 6.54/6.90  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := parallel_through_point( X, Y )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X )
% 6.54/6.90    , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90  parent0: (7536) {G1,W8,D3,L2,V3,M2}  { convergent_lines( Z, 
% 6.54/6.90    parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7539) {G1,W8,D3,L2,V3,M2}  { convergent_lines( Z, 
% 6.54/6.90    parallel_through_point( X, Y ) ), ! convergent_lines( Z, X ) }.
% 6.54/6.90  parent0[0]: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( X, Y ) ) }.
% 6.54/6.90  parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := X
% 6.54/6.90     Z := parallel_through_point( X, Y )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y )
% 6.54/6.90    , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90  parent0: (7539) {G1,W8,D3,L2,V3,M2}  { convergent_lines( Z, 
% 6.54/6.90    parallel_through_point( X, Y ) ), ! convergent_lines( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7540) {G1,W5,D3,L1,V2,M1}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 6.54/6.90    orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 6.54/6.90    unorthogonal_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := orthogonal_through_point( X, Y )
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90  parent0: (7540) {G1,W5,D3,L1,V2,M1}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7541) {G1,W8,D3,L2,V3,M2}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 6.54/6.90  parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90  parent1[0]: (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( X, Y )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (113) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent0: (7541) {G1,W8,D3,L2,V3,M2}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7542) {G1,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    distinct_lines( Y, X ) }.
% 6.54/6.90  parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  parent1[1]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y )
% 6.54/6.90    , ! distinct_lines( Y, X ) }.
% 6.54/6.90  parent0: (7542) {G1,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    distinct_lines( Y, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7543) {G1,W12,D2,L4,V4,M4}  { distinct_lines( X, Y ), 
% 6.54/6.90    apart_point_and_line( Z, Y ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := T
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (138) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 6.54/6.90    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 6.54/6.90    apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0: (7543) {G1,W12,D2,L4,V4,M4}  { distinct_lines( X, Y ), 
% 6.54/6.90    apart_point_and_line( Z, Y ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := T
% 6.54/6.90     Z := Z
% 6.54/6.90     T := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 2
% 6.54/6.90     2 ==> 0
% 6.54/6.90     3 ==> 3
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7545) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 6.54/6.90    parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90  parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 6.54/6.90    parallel_through_point( Y, X ) ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := parallel_through_point( Y, X )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (150) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0: (7545) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 6.54/6.90    parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7546) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 6.54/6.90    orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 6.54/6.90    orthogonal_through_point( Y, X ) ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := orthogonal_through_point( Y, X )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (151) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0: (7546) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 6.54/6.90    orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7547) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  parent0[1]: (150) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := T
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (162) {G2,W11,D3,L3,V4,M1} R(150,12) { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  parent0: (7547) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90     2 ==> 2
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7549) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  parent0[1]: (151) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := T
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (164) {G2,W11,D3,L3,V4,M1} R(151,12) { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  parent0: (7549) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90     2 ==> 2
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7551) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 6.54/6.90  parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  parent1[0]: (113) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (171) {G3,W8,D3,L2,V3,M2} R(113,69) { convergent_lines( Z, X )
% 6.54/6.90    , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent0: (7551) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7554) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 6.54/6.90    unorthogonal_lines( Z, Y ) }.
% 6.54/6.90  parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 6.54/6.90    ( X, Y ) }.
% 6.54/6.90  parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 6.54/6.90    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.54/6.90     }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (178) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 6.54/6.90     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 6.54/6.90    unorthogonal_lines( Y, Z ) }.
% 6.54/6.90  parent0: (7554) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 6.54/6.90    unorthogonal_lines( Z, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90     2 ==> 2
% 6.54/6.90     3 ==> 3
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7556) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Z, 
% 6.54/6.90    orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 6.54/6.90  parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  parent1[1]: (171) {G3,W8,D3,L2,V3,M2} R(113,69) { convergent_lines( Z, X )
% 6.54/6.90    , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := orthogonal_through_point( X, Y )
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (184) {G4,W8,D3,L2,V3,M2} R(171,69) { convergent_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90  parent0: (7556) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Z, 
% 6.54/6.90    orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7557) {G1,W7,D4,L1,V3,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90  parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent1[1]: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := parallel_through_point( X, Y )
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := parallel_through_point( parallel_through_point( X, Y ), Z )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (206) {G4,W7,D4,L1,V3,M1} R(73,15) { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90  parent0: (7557) {G1,W7,D4,L1,V3,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7558) {G1,W10,D4,L2,V4,M2}  { convergent_lines( T, 
% 6.54/6.90    parallel_through_point( parallel_through_point( X, Y ), Z ) ), ! 
% 6.54/6.90    convergent_lines( X, T ) }.
% 6.54/6.90  parent0[0]: (206) {G4,W7,D4,L1,V3,M1} R(73,15) { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 6.54/6.90    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := T
% 6.54/6.90     Z := parallel_through_point( parallel_through_point( X, Y ), Z )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (216) {G5,W10,D4,L2,V4,M2} R(206,5) { ! convergent_lines( Y, X
% 6.54/6.90     ), convergent_lines( X, parallel_through_point( parallel_through_point( 
% 6.54/6.90    Y, Z ), T ) ) }.
% 6.54/6.90  parent0: (7558) {G1,W10,D4,L2,V4,M2}  { convergent_lines( T, 
% 6.54/6.90    parallel_through_point( parallel_through_point( X, Y ), Z ) ), ! 
% 6.54/6.90    convergent_lines( X, T ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := T
% 6.54/6.90     T := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7560) {G2,W10,D3,L2,V4,M2}  { convergent_lines( 
% 6.54/6.90    parallel_through_point( Z, T ), X ), ! convergent_lines( Z, 
% 6.54/6.90    parallel_through_point( X, Y ) ) }.
% 6.54/6.90  parent0[0]: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.90  parent1[1]: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := parallel_through_point( Z, T )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := parallel_through_point( X, Y )
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := T
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (246) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( Z, T ) ), convergent_lines( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent0: (7560) {G2,W10,D3,L2,V4,M2}  { convergent_lines( 
% 6.54/6.90    parallel_through_point( Z, T ), X ), ! convergent_lines( Z, 
% 6.54/6.90    parallel_through_point( X, Y ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := T
% 6.54/6.90     Z := X
% 6.54/6.90     T := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7562) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), ! 
% 6.54/6.90    convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 6.54/6.90  parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  parent1[1]: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (250) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z )
% 6.54/6.90    , ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent0: (7562) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), ! 
% 6.54/6.90    convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7563) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 6.54/6.90  parent0[1]: (250) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z ), 
% 6.54/6.90    ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent1[1]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := parallel_through_point( X, Z )
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (261) {G3,W8,D3,L2,V3,M2} R(250,69) { ! convergent_lines( Y, 
% 6.54/6.90    parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90  parent0: (7563) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7565) {G1,W8,D3,L2,V3,M2}  { ! convergent_lines( Z, X ), 
% 6.54/6.90    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 6.54/6.90    orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), 
% 6.54/6.90    unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := X
% 6.54/6.90     Z := orthogonal_through_point( X, Y )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (285) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 6.54/6.90     ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.54/6.90  parent0: (7565) {G1,W8,D3,L2,V3,M2}  { ! convergent_lines( Z, X ), 
% 6.54/6.90    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7566) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 6.54/6.90    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  parent0[2]: (164) {G2,W11,D3,L3,V4,M1} R(151,12) { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := U
% 6.54/6.90     Z := T
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2003) {G3,W14,D3,L4,V5,M1} R(164,12) { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 6.54/6.90    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  parent0: (7566) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 6.54/6.90    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90     U := U
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90     2 ==> 2
% 6.54/6.90     3 ==> 3
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7572) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0[0, 2]: (2003) {G3,W14,D3,L4,V5,M1} R(164,12) { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 6.54/6.90    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := orthogonal_through_point( Y, Z )
% 6.54/6.90     U := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7578) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0[0]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  parent1[0]: (7572) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( Y, Z )
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7580) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90  parent0[0, 1]: (7578) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2005) {G4,W8,D3,L2,V3,M1} F(2003);r(58) { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0: (7580) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7582) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90    ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  parent0[2]: (162) {G2,W11,D3,L3,V4,M1} R(150,12) { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 6.54/6.90    apart_point_and_line( Z, T ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := U
% 6.54/6.90     Z := T
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2024) {G3,W14,D3,L4,V5,M1} R(162,12) { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90    ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  parent0: (7582) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90    ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90     U := U
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90     2 ==> 2
% 6.54/6.90     3 ==> 3
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7588) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 6.54/6.90    ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0[0, 2]: (2024) {G3,W14,D3,L4,V5,M1} R(162,12) { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90    ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := parallel_through_point( Y, Z )
% 6.54/6.90     U := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7594) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), distinct_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0[0]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  parent1[0]: (7588) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 6.54/6.90    parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 6.54/6.90    ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := parallel_through_point( Y, Z )
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7596) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90  parent0[0, 1]: (7594) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), distinct_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2026) {G4,W8,D3,L2,V3,M1} F(2024);r(58) { distinct_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0: (7596) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7598) {G1,W15,D2,L5,V5,M5}  { distinct_lines( X, Y ), 
% 6.54/6.90    distinct_lines( Y, Z ), apart_point_and_line( T, Z ), distinct_lines( U, 
% 6.54/6.90    X ), ! apart_point_and_line( T, U ) }.
% 6.54/6.90  parent0[3]: (138) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 6.54/6.90    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 6.54/6.90    apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 6.54/6.90    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := T
% 6.54/6.90     T := Z
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := T
% 6.54/6.90     Y := U
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2352) {G2,W15,D2,L5,V5,M2} R(138,12) { distinct_lines( X, Y )
% 6.54/6.90    , distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line( T
% 6.54/6.90    , U ), ! apart_point_and_line( T, X ) }.
% 6.54/6.90  parent0: (7598) {G1,W15,D2,L5,V5,M5}  { distinct_lines( X, Y ), 
% 6.54/6.90    distinct_lines( Y, Z ), apart_point_and_line( T, Z ), distinct_lines( U, 
% 6.54/6.90    X ), ! apart_point_and_line( T, U ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := U
% 6.54/6.90     T := T
% 6.54/6.90     U := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 2
% 6.54/6.90     2 ==> 3
% 6.54/6.90     3 ==> 0
% 6.54/6.90     4 ==> 4
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7604) {G2,W12,D2,L4,V3,M4}  { distinct_lines( X, Y ), 
% 6.54/6.90    distinct_lines( Y, X ), apart_point_and_line( Z, Y ), ! 
% 6.54/6.90    apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0[0, 2]: (2352) {G2,W15,D2,L5,V5,M2} R(138,12) { distinct_lines( X, Y
% 6.54/6.90     ), distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line
% 6.54/6.90    ( T, U ), ! apart_point_and_line( T, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := X
% 6.54/6.90     T := Z
% 6.54/6.90     U := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7610) {G2,W12,D2,L4,V3,M4}  { distinct_lines( Y, X ), 
% 6.54/6.90    distinct_lines( Y, X ), apart_point_and_line( Z, Y ), ! 
% 6.54/6.90    apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent0[0]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 6.54/6.90    distinct_lines( X, Y ) }.
% 6.54/6.90  parent1[0]: (7604) {G2,W12,D2,L4,V3,M4}  { distinct_lines( X, Y ), 
% 6.54/6.90    distinct_lines( Y, X ), apart_point_and_line( Z, Y ), ! 
% 6.54/6.90    apart_point_and_line( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7612) {G2,W9,D2,L3,V3,M3}  { distinct_lines( X, Y ), 
% 6.54/6.90    apart_point_and_line( Z, X ), ! apart_point_and_line( Z, Y ) }.
% 6.54/6.90  parent0[0, 1]: (7610) {G2,W12,D2,L4,V3,M4}  { distinct_lines( Y, X ), 
% 6.54/6.90    distinct_lines( Y, X ), apart_point_and_line( Z, Y ), ! 
% 6.54/6.90    apart_point_and_line( Z, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2356) {G3,W9,D2,L3,V3,M2} F(2352);r(58) { distinct_lines( Y, 
% 6.54/6.90    X ), ! apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 6.54/6.90  parent0: (7612) {G2,W9,D2,L3,V3,M3}  { distinct_lines( X, Y ), 
% 6.54/6.90    apart_point_and_line( Z, X ), ! apart_point_and_line( Z, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 2
% 6.54/6.90     2 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7615) {G1,W13,D3,L3,V1,M3}  { distinct_lines( X, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, X ), 
% 6.54/6.90    apart_point_and_line( skol1, line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90  parent0[1]: (2356) {G3,W9,D2,L3,V3,M2} F(2352);r(58) { distinct_lines( Y, X
% 6.54/6.90     ), ! apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 6.54/6.90  parent1[1]: (48) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line( skol1, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := line_connecting( skol3, skol4 )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := skol2
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2411) {G4,W13,D3,L3,V1,M2} R(2356,48) { distinct_lines( X, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol1, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, X ) }.
% 6.54/6.90  parent0: (7615) {G1,W13,D3,L3,V1,M3}  { distinct_lines( X, line_connecting
% 6.54/6.90    ( skol3, skol4 ) ), apart_point_and_line( skol2, X ), 
% 6.54/6.90    apart_point_and_line( skol1, line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 2
% 6.54/6.90     2 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7616) {G1,W13,D3,L3,V3,M3}  { ! convergent_lines( Z, 
% 6.54/6.90    orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), ! 
% 6.54/6.90    unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 6.54/6.90  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 6.54/6.90    orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90  parent1[3]: (178) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 6.54/6.90     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 6.54/6.90    unorthogonal_lines( Y, Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Z
% 6.54/6.90     Y := orthogonal_through_point( X, Y )
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7617) {G2,W11,D3,L3,V3,M3}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  parent0[0]: (7616) {G1,W13,D3,L3,V3,M3}  { ! convergent_lines( Z, 
% 6.54/6.90    orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), ! 
% 6.54/6.90    unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 6.54/6.90  parent1[0]: (184) {G4,W8,D3,L2,V3,M2} R(171,69) { convergent_lines( X, 
% 6.54/6.90    orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := X
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7618) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90  parent0[0, 2]: (7617) {G2,W11,D3,L3,V3,M3}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ), 
% 6.54/6.90    convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2738) {G5,W8,D3,L2,V3,M1} R(178,23);r(184) { convergent_lines
% 6.54/6.90    ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90  parent0: (7618) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 6.54/6.90    unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7619) {G2,W10,D3,L2,V4,M2}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( Z, T ), X ) }.
% 6.54/6.90  parent0[1]: (2738) {G5,W8,D3,L2,V3,M1} R(178,23);r(184) { convergent_lines
% 6.54/6.90    ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90  parent1[1]: (285) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 6.54/6.90    , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( X, Y )
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := T
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := orthogonal_through_point( Z, T )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2745) {G6,W10,D3,L2,V4,M2} R(2738,285) { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( Z, T ), X ), convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  parent0: (7619) {G2,W10,D3,L2,V4,M2}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( Z, T ), X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7620) {G1,W7,D4,L1,V3,M1}  { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.90  parent1[1]: (2745) {G6,W10,D3,L2,V4,M2} R(2738,285) { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( Z, T ), X ), convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( X, Y )
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := orthogonal_through_point( X, Y )
% 6.54/6.90     T := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90  parent0: (7620) {G1,W7,D4,L1,V3,M1}  { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7621) {G4,W9,D5,L1,V4,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( orthogonal_through_point( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90  parent0[0]: (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90  parent1[1]: (261) {G3,W8,D3,L2,V3,M2} R(250,69) { ! convergent_lines( Y, 
% 6.54/6.90    parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := T
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (3012) {G8,W9,D5,L1,V4,M1} R(2914,261) { ! convergent_lines( X
% 6.54/6.90    , parallel_through_point( orthogonal_through_point( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90  parent0: (7621) {G4,W9,D5,L1,V4,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( orthogonal_through_point( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7622) {G4,W9,D5,L1,V4,M1}  { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90  parent0[0]: (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90  parent1[1]: (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y ), 
% 6.54/6.90    convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := parallel_through_point( X, Y )
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := T
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), T )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (3015) {G8,W9,D5,L1,V4,M1} R(2914,74) { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90  parent0: (7622) {G4,W9,D5,L1,V4,M1}  { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7623) {G5,W13,D7,L1,V6,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.54/6.90    ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.90    , W ) ) }.
% 6.54/6.90  parent0[0]: (3012) {G8,W9,D5,L1,V4,M1} R(2914,261) { ! convergent_lines( X
% 6.54/6.90    , parallel_through_point( orthogonal_through_point( 
% 6.54/6.90    orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90  parent1[1]: (246) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( Z, T ) ), convergent_lines( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := parallel_through_point( X, Y )
% 6.54/6.90     Y := Z
% 6.54/6.90     Z := T
% 6.54/6.90     T := U
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := parallel_through_point( orthogonal_through_point( 
% 6.54/6.90    orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.90     T := W
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (3404) {G9,W13,D7,L1,V6,M1} R(3012,246) { ! convergent_lines( 
% 6.54/6.90    X, parallel_through_point( parallel_through_point( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90  parent0: (7623) {G5,W13,D7,L1,V6,M1}  { ! convergent_lines( X, 
% 6.54/6.90    parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.54/6.90    ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.90    , W ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90     U := U
% 6.54/6.90     W := W
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7624) {G6,W13,D7,L1,V6,M1}  { ! convergent_lines( X, 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90    , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90  parent0[0]: (3015) {G8,W9,D5,L1,V4,M1} R(2914,74) { ! convergent_lines( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90  parent1[1]: (216) {G5,W10,D4,L2,V4,M2} R(206,5) { ! convergent_lines( Y, X
% 6.54/6.90     ), convergent_lines( X, parallel_through_point( parallel_through_point( 
% 6.54/6.90    Y, Z ), T ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := parallel_through_point( parallel_through_point( X, Y ), Z )
% 6.54/6.90     Y := T
% 6.54/6.90     Z := U
% 6.54/6.90     T := W
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90    , Y ), Z ), T ), U ), W )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90     T := Z
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (3478) {G9,W13,D7,L1,V6,M1} R(3015,216) { ! convergent_lines( 
% 6.54/6.90    X, orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90    , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90  parent0: (7624) {G6,W13,D7,L1,V6,M1}  { ! convergent_lines( X, 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90    , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90     U := U
% 6.54/6.90     W := W
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7625) {G5,W15,D3,L3,V2,M3}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    distinct_lines( Y, line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, Y ) }.
% 6.54/6.90  parent0[1]: (2005) {G4,W8,D3,L2,V3,M1} F(2003);r(58) { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent1[1]: (2411) {G4,W13,D3,L3,V1,M2} R(2356,48) { distinct_lines( X, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol1, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := line_connecting( skol3, skol4 )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := skol1
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (7272) {G5,W15,D3,L3,V2,M1} R(2411,2005) { distinct_lines( X, 
% 6.54/6.90    line_connecting( skol3, skol4 ) ), distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, X ) }.
% 6.54/6.90  parent0: (7625) {G5,W15,D3,L3,V2,M3}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    distinct_lines( Y, line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, Y ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90     2 ==> 2
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  factor: (7628) {G5,W12,D3,L2,V1,M2}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90  parent0[0, 1]: (7272) {G5,W15,D3,L3,V2,M1} R(2411,2005) { distinct_lines( X
% 6.54/6.90    , line_connecting( skol3, skol4 ) ), distinct_lines( 
% 6.54/6.90    orthogonal_through_point( Y, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, X ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( X, skol1 )
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (7273) {G6,W12,D3,L2,V1,M1} F(7272) { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90  parent0: (7628) {G5,W12,D3,L2,V1,M2}  { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7629) {G5,W14,D3,L2,V2,M2}  { distinct_lines( 
% 6.54/6.90    parallel_through_point( X, skol2 ), orthogonal_through_point( Y, skol1 )
% 6.54/6.90     ), distinct_lines( orthogonal_through_point( Y, skol1 ), line_connecting
% 6.54/6.90    ( skol3, skol4 ) ) }.
% 6.54/6.90  parent0[1]: (2026) {G4,W8,D3,L2,V3,M1} F(2024);r(58) { distinct_lines( 
% 6.54/6.90    parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90  parent1[1]: (7273) {G6,W12,D3,L2,V1,M1} F(7272) { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( Y, skol1 )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := skol2
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (7287) {G7,W14,D3,L2,V2,M1} R(7273,2026) { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    distinct_lines( parallel_through_point( Y, skol2 ), 
% 6.54/6.90    orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90  parent0: (7629) {G5,W14,D3,L2,V2,M2}  { distinct_lines( 
% 6.54/6.90    parallel_through_point( X, skol2 ), orthogonal_through_point( Y, skol1 )
% 6.54/6.90     ), distinct_lines( orthogonal_through_point( Y, skol1 ), line_connecting
% 6.54/6.90    ( skol3, skol4 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := Y
% 6.54/6.90     Y := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 1
% 6.54/6.90     1 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7631) {G3,W14,D3,L2,V2,M2}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90     ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90    ( skol3, skol4 ) ) }.
% 6.54/6.90  parent0[1]: (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ), 
% 6.54/6.90    ! distinct_lines( Y, X ) }.
% 6.54/6.90  parent1[1]: (7287) {G7,W14,D3,L2,V2,M1} R(7273,2026) { distinct_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ), 
% 6.54/6.90    distinct_lines( parallel_through_point( Y, skol2 ), 
% 6.54/6.90    orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( X, skol1 )
% 6.54/6.90     Y := parallel_through_point( Y, skol2 )
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (7343) {G8,W14,D3,L2,V2,M1} R(7287,114) { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90     ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90    ( skol3, skol4 ) ) }.
% 6.54/6.90  parent0: (7631) {G3,W14,D3,L2,V2,M2}  { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90     ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90    ( skol3, skol4 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7632) {G3,W14,D3,L2,V2,M2}  { convergent_lines( 
% 6.54/6.90    line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ), 
% 6.54/6.90    convergent_lines( orthogonal_through_point( X, skol1 ), 
% 6.54/6.90    parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.90  parent0[1]: (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ), 
% 6.54/6.90    ! distinct_lines( Y, X ) }.
% 6.54/6.90  parent1[1]: (7343) {G8,W14,D3,L2,V2,M1} R(7287,114) { convergent_lines( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90     ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90    ( skol3, skol4 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := line_connecting( skol3, skol4 )
% 6.54/6.90     Y := orthogonal_through_point( X, skol1 )
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (7345) {G9,W14,D3,L2,V2,M1} R(7343,114) { convergent_lines( 
% 6.54/6.90    line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ), 
% 6.54/6.90    convergent_lines( orthogonal_through_point( X, skol1 ), 
% 6.54/6.90    parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.90  parent0: (7632) {G3,W14,D3,L2,V2,M2}  { convergent_lines( line_connecting( 
% 6.54/6.90    skol3, skol4 ), orthogonal_through_point( X, skol1 ) ), convergent_lines
% 6.54/6.90    ( orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2
% 6.54/6.90     ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90     Y := Y
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90     1 ==> 1
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7633) {G10,W7,D3,L1,V1,M1}  { convergent_lines( 
% 6.54/6.90    line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.90     }.
% 6.54/6.90  parent0[0]: (3404) {G9,W13,D7,L1,V6,M1} R(3012,246) { ! convergent_lines( X
% 6.54/6.90    , parallel_through_point( parallel_through_point( 
% 6.54/6.90    orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( X, Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90  parent1[1]: (7345) {G9,W14,D3,L2,V2,M1} R(7343,114) { convergent_lines( 
% 6.54/6.90    line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ), 
% 6.54/6.90    convergent_lines( orthogonal_through_point( X, skol1 ), 
% 6.54/6.90    parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := orthogonal_through_point( X, skol1 )
% 6.54/6.90     Y := Y
% 6.54/6.90     Z := Z
% 6.54/6.90     T := T
% 6.54/6.90     U := U
% 6.54/6.90     W := skol2
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := X
% 6.54/6.90     Y := parallel_through_point( orthogonal_through_point( 
% 6.54/6.90    orthogonal_through_point( parallel_through_point( 
% 6.54/6.90    orthogonal_through_point( X, skol1 ), Y ), Z ), T ), U )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (7354) {G10,W7,D3,L1,V1,M1} R(7345,3404) { convergent_lines( 
% 6.54/6.90    line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.90     }.
% 6.54/6.90  parent0: (7633) {G10,W7,D3,L1,V1,M1}  { convergent_lines( line_connecting( 
% 6.54/6.90    skol3, skol4 ), orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := X
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90     0 ==> 0
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  resolution: (7634) {G10,W0,D0,L0,V0,M0}  {  }.
% 6.54/6.90  parent0[0]: (3478) {G9,W13,D7,L1,V6,M1} R(3015,216) { ! convergent_lines( X
% 6.54/6.90    , orthogonal_through_point( orthogonal_through_point( 
% 6.54/6.90    parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90    , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90  parent1[0]: (7354) {G10,W7,D3,L1,V1,M1} R(7345,3404) { convergent_lines( 
% 6.54/6.90    line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.90     }.
% 6.54/6.90  substitution0:
% 6.54/6.90     X := line_connecting( skol3, skol4 )
% 6.54/6.90     Y := X
% 6.54/6.90     Z := Y
% 6.54/6.90     T := Z
% 6.54/6.90     U := T
% 6.54/6.90     W := skol1
% 6.54/6.90  end
% 6.54/6.90  substitution1:
% 6.54/6.90     X := orthogonal_through_point( parallel_through_point( 
% 6.54/6.90    parallel_through_point( parallel_through_point( line_connecting( skol3, 
% 6.54/6.90    skol4 ), X ), Y ), Z ), T )
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  subsumption: (7355) {G11,W0,D0,L0,V0,M0} R(7354,3478) {  }.
% 6.54/6.90  parent0: (7634) {G10,W0,D0,L0,V0,M0}  {  }.
% 6.54/6.90  substitution0:
% 6.54/6.90  end
% 6.54/6.90  permutation0:
% 6.54/6.90  end
% 6.54/6.90  
% 6.54/6.90  Proof check complete!
% 6.54/6.90  
% 6.54/6.90  Memory use:
% 6.54/6.90  
% 6.54/6.90  space for terms:        107037
% 6.54/6.90  space for clauses:      322898
% 6.54/6.90  
% 6.54/6.90  
% 6.54/6.90  clauses generated:      1159821
% 6.54/6.90  clauses kept:           7356
% 6.54/6.90  clauses selected:       3124
% 6.54/6.90  clauses deleted:        81
% 6.54/6.90  clauses inuse deleted:  3
% 6.54/6.90  
% 6.54/6.90  subsentry:          8619761
% 6.54/6.90  literals s-matched: 3438184
% 6.54/6.90  literals matched:   3437674
% 6.54/6.90  full subsumption:   2423971
% 6.54/6.90  
% 6.54/6.90  checksum:           1592567474
% 6.54/6.90  
% 6.54/6.90  
% 6.54/6.90  Bliksem ended
%------------------------------------------------------------------------------