TSTP Solution File: GEO222+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n015.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 02:52:58 EDT 2022

% Result   : Theorem 106.39s 106.77s
% Output   : Refutation 106.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14  % Command  : bliksem %s
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % DateTime : Fri Jun 17 21:08:58 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 106.39/106.77  *** allocated 10000 integers for termspace/termends
% 106.39/106.77  *** allocated 10000 integers for clauses
% 106.39/106.77  *** allocated 10000 integers for justifications
% 106.39/106.77  Bliksem 1.12
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Automatic Strategy Selection
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Clauses:
% 106.39/106.77  
% 106.39/106.77  { ! distinct_points( X, X ) }.
% 106.39/106.77  { ! distinct_lines( X, X ) }.
% 106.39/106.77  { ! convergent_lines( X, X ) }.
% 106.39/106.77  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 106.39/106.77     ) }.
% 106.39/106.77  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 106.39/106.77     }.
% 106.39/106.77  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 106.39/106.77    , Z ) }.
% 106.39/106.77  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 106.39/106.77    , Y ) ) }.
% 106.39/106.77  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 106.39/106.77    , Y ) ) }.
% 106.39/106.77  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 106.39/106.77    , Y ), X ) }.
% 106.39/106.77  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 106.39/106.77    , Y ), Y ) }.
% 106.39/106.77  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 106.39/106.77    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 106.39/106.77    apart_point_and_line( Y, T ) }.
% 106.39/106.77  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 106.39/106.77    apart_point_and_line( Z, Y ) }.
% 106.39/106.77  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ) }.
% 106.39/106.77  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 106.39/106.77    Z ) }.
% 106.39/106.77  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 106.39/106.77  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 106.39/106.77  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 106.39/106.77    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 106.39/106.77  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 106.39/106.77  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 106.39/106.77    , convergent_lines( Y, Z ) }.
% 106.39/106.77  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 106.39/106.77    , unorthogonal_lines( Y, Z ) }.
% 106.39/106.77  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 106.39/106.77  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 106.39/106.77  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 106.39/106.77     }.
% 106.39/106.77  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 106.39/106.77  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 106.39/106.77    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 106.39/106.77    unorthogonal_lines( Y, T ) }.
% 106.39/106.77  { convergent_lines( skol2, orthogonal_through_point( 
% 106.39/106.77    orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 106.39/106.77  
% 106.39/106.77  percentage equality = 0.000000, percentage horn = 0.555556
% 106.39/106.77  This a non-horn, non-equality problem
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Options Used:
% 106.39/106.77  
% 106.39/106.77  useres =            1
% 106.39/106.77  useparamod =        0
% 106.39/106.77  useeqrefl =         0
% 106.39/106.77  useeqfact =         0
% 106.39/106.77  usefactor =         1
% 106.39/106.77  usesimpsplitting =  0
% 106.39/106.77  usesimpdemod =      0
% 106.39/106.77  usesimpres =        3
% 106.39/106.77  
% 106.39/106.77  resimpinuse      =  1000
% 106.39/106.77  resimpclauses =     20000
% 106.39/106.77  substype =          standard
% 106.39/106.77  backwardsubs =      1
% 106.39/106.77  selectoldest =      5
% 106.39/106.77  
% 106.39/106.77  litorderings [0] =  split
% 106.39/106.77  litorderings [1] =  liftord
% 106.39/106.77  
% 106.39/106.77  termordering =      none
% 106.39/106.77  
% 106.39/106.77  litapriori =        1
% 106.39/106.77  termapriori =       0
% 106.39/106.77  litaposteriori =    0
% 106.39/106.77  termaposteriori =   0
% 106.39/106.77  demodaposteriori =  0
% 106.39/106.77  ordereqreflfact =   0
% 106.39/106.77  
% 106.39/106.77  litselect =         none
% 106.39/106.77  
% 106.39/106.77  maxweight =         15
% 106.39/106.77  maxdepth =          30000
% 106.39/106.77  maxlength =         115
% 106.39/106.77  maxnrvars =         195
% 106.39/106.77  excuselevel =       1
% 106.39/106.77  increasemaxweight = 1
% 106.39/106.77  
% 106.39/106.77  maxselected =       10000000
% 106.39/106.77  maxnrclauses =      10000000
% 106.39/106.77  
% 106.39/106.77  showgenerated =    0
% 106.39/106.77  showkept =         0
% 106.39/106.77  showselected =     0
% 106.39/106.77  showdeleted =      0
% 106.39/106.77  showresimp =       1
% 106.39/106.77  showstatus =       2000
% 106.39/106.77  
% 106.39/106.77  prologoutput =     0
% 106.39/106.77  nrgoals =          5000000
% 106.39/106.77  totalproof =       1
% 106.39/106.77  
% 106.39/106.77  Symbols occurring in the translation:
% 106.39/106.77  
% 106.39/106.77  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 106.39/106.77  .  [1, 2]      (w:1, o:22, a:1, s:1, b:0), 
% 106.39/106.77  !  [4, 1]      (w:0, o:17, a:1, s:1, b:0), 
% 106.39/106.77  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 106.39/106.77  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 106.39/106.77  distinct_points  [36, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 106.39/106.77  distinct_lines  [37, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 106.39/106.77  convergent_lines  [38, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 106.39/106.77  line_connecting  [41, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 106.39/106.77  apart_point_and_line  [42, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 106.39/106.77  intersection_point  [43, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 106.39/106.77  parallel_through_point  [46, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 106.39/106.77  unorthogonal_lines  [49, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 106.39/106.77  orthogonal_through_point  [52, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 106.39/106.77  alpha1  [53, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 106.39/106.77  skol1  [54, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 106.39/106.77  skol2  [55, 0]      (w:1, o:16, a:1, s:1, b:0).
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Starting Search:
% 106.39/106.77  
% 106.39/106.77  *** allocated 15000 integers for clauses
% 106.39/106.77  *** allocated 22500 integers for clauses
% 106.39/106.77  *** allocated 33750 integers for clauses
% 106.39/106.77  *** allocated 15000 integers for termspace/termends
% 106.39/106.77  *** allocated 50625 integers for clauses
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  *** allocated 22500 integers for termspace/termends
% 106.39/106.77  *** allocated 75937 integers for clauses
% 106.39/106.77  *** allocated 33750 integers for termspace/termends
% 106.39/106.77  *** allocated 113905 integers for clauses
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  Failed to find proof!
% 106.39/106.77  maxweight =   15
% 106.39/106.77  maxnrclauses = 10000000
% 106.39/106.77  Generated: 1580008
% 106.39/106.77  Kept: 1933
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  The strategy used was not complete!
% 106.39/106.77  
% 106.39/106.77  Increased maxweight to 16
% 106.39/106.77  
% 106.39/106.77  Starting Search:
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Intermediate Status:
% 106.39/106.77  Generated:    16577
% 106.39/106.77  Kept:         2022
% 106.39/106.77  Inuse:        204
% 106.39/106.77  Deleted:      0
% 106.39/106.77  Deletedinuse: 0
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  *** allocated 50625 integers for termspace/termends
% 106.39/106.77  *** allocated 170857 integers for clauses
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  *** allocated 75937 integers for termspace/termends
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  Failed to find proof!
% 106.39/106.77  maxweight =   16
% 106.39/106.77  maxnrclauses = 10000000
% 106.39/106.77  Generated: 4889690
% 106.39/106.77  Kept: 3418
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  The strategy used was not complete!
% 106.39/106.77  
% 106.39/106.77  Increased maxweight to 17
% 106.39/106.77  
% 106.39/106.77  Starting Search:
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Intermediate Status:
% 106.39/106.77  Generated:    13877
% 106.39/106.77  Kept:         2006
% 106.39/106.77  Inuse:        166
% 106.39/106.77  Deleted:      0
% 106.39/106.77  Deletedinuse: 0
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Intermediate Status:
% 106.39/106.77  Generated:    39352
% 106.39/106.77  Kept:         4026
% 106.39/106.77  Inuse:        353
% 106.39/106.77  Deleted:      1
% 106.39/106.77  Deletedinuse: 0
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  *** allocated 256285 integers for clauses
% 106.39/106.77  *** allocated 113905 integers for termspace/termends
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Intermediate Status:
% 106.39/106.77  Generated:    7035552
% 106.39/106.77  Kept:         6049
% 106.39/106.77  Inuse:        3880
% 106.39/106.77  Deleted:      75
% 106.39/106.77  Deletedinuse: 6
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  *** allocated 384427 integers for clauses
% 106.39/106.77  *** allocated 170857 integers for termspace/termends
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Intermediate Status:
% 106.39/106.77  Generated:    14817282
% 106.39/106.77  Kept:         8729
% 106.39/106.77  Inuse:        6658
% 106.39/106.77  Deleted:      202
% 106.39/106.77  Deletedinuse: 8
% 106.39/106.77  
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  *** allocated 576640 integers for clauses
% 106.39/106.77  Resimplifying inuse:
% 106.39/106.77  Done
% 106.39/106.77  
% 106.39/106.77  *** allocated 256285 integers for termspace/termends
% 106.39/106.77  
% 106.39/106.77  Bliksems!, er is een bewijs:
% 106.39/106.77  % SZS status Theorem
% 106.39/106.77  % SZS output start Refutation
% 106.39/106.77  
% 106.39/106.77  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 106.39/106.77  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 106.39/106.77  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 106.39/106.77    , ! distinct_lines( X, Y ) }.
% 106.39/106.77  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 106.39/106.77    Z ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 106.39/106.77  (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 106.39/106.77  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 106.39/106.77    X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines( 
% 106.39/106.77    X, Z ), distinct_lines( Y, Z ) }.
% 106.39/106.77  (16) {G0,W12,D2,L4,V3,M2} I { ! distinct_lines( X, Y ), convergent_lines( X
% 106.39/106.77    , Y ), apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 106.39/106.77  (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines( 
% 106.39/106.77    X, Y ) }.
% 106.39/106.77  (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 106.39/106.77  (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 106.39/106.77     }.
% 106.39/106.77  (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 106.39/106.77  (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! alpha1( X, Y )
% 106.39/106.77     }.
% 106.39/106.77  (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 106.39/106.77    ( Y, X ), Y ) }.
% 106.39/106.77  (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 106.39/106.77    orthogonal_through_point( Y, X ) ) }.
% 106.39/106.77  (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 106.39/106.77  (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2, 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 106.39/106.77     ) ) }.
% 106.39/106.77  (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 106.39/106.77    ( X, Y ) }.
% 106.39/106.77  (35) {G2,W9,D2,L3,V3,M3} R(34,4) { distinct_lines( Z, X ), ! distinct_lines
% 106.39/106.77    ( Y, Z ), distinct_lines( X, Y ) }.
% 106.39/106.77  (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), X ) }.
% 106.39/106.77  (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), ! 
% 106.39/106.77    convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 106.39/106.77  (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  (97) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  (185) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 106.39/106.77    apart_point_and_line( Z, X ) }.
% 106.39/106.77  (194) {G1,W11,D3,L3,V3,M1} R(12,8) { distinct_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Y, Z ), ! apart_point_and_line( intersection_point( Y, 
% 106.39/106.77    Z ), X ) }.
% 106.39/106.77  (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 106.39/106.77    apart_point_and_line( Z, T ) }.
% 106.39/106.77  (215) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X, skol2 ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.77    skol2, skol1 ), skol1 ), X ) }.
% 106.39/106.77  (216) {G3,W9,D2,L3,V3,M3} R(44,43) { convergent_lines( Z, X ), 
% 106.39/106.77    convergent_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  (225) {G2,W9,D2,L3,V3,M1} R(13,34) { ! convergent_lines( X, Y ), 
% 106.39/106.77    convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 106.39/106.77  (230) {G3,W9,D2,L3,V3,M3} R(35,34) { distinct_lines( Z, X ), distinct_lines
% 106.39/106.77    ( Z, Y ), ! distinct_lines( X, Y ) }.
% 106.39/106.77  (249) {G1,W14,D3,L4,V3,M1} R(16,9) { convergent_lines( X, Y ), ! 
% 106.39/106.77    distinct_lines( X, Y ), ! convergent_lines( Z, X ), apart_point_and_line
% 106.39/106.77    ( intersection_point( Z, X ), Y ) }.
% 106.39/106.77  (268) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y ), 
% 106.39/106.77    convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  (290) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ), 
% 106.39/106.77    convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 106.39/106.77    unorthogonal_lines( Y, Z ) }.
% 106.39/106.77  (306) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ), 
% 106.39/106.77    apart_point_and_line( T, orthogonal_through_point( Y, Z ) ), 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  (307) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 106.39/106.77    unorthogonal_lines( Z, X ) }.
% 106.39/106.77  (1976) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 106.39/106.77    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 106.39/106.77  (1978) {G4,W8,D3,L2,V3,M1} F(1976);r(34) { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  (2715) {G2,W17,D3,L5,V5,M1} R(185,194) { distinct_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Y, Z ), distinct_lines( Z, T ), ! convergent_lines( T, U
% 106.39/106.77     ), ! apart_point_and_line( intersection_point( T, U ), X ) }.
% 106.39/106.77  (2741) {G3,W11,D3,L3,V3,M1} F(2715);r(34) { ! convergent_lines( Y, Z ), 
% 106.39/106.77    distinct_lines( Y, X ), ! apart_point_and_line( intersection_point( Y, Z
% 106.39/106.77     ), X ) }.
% 106.39/106.77  (3213) {G4,W8,D3,L2,V3,M1} R(268,23);r(97) { convergent_lines( Z, X ), ! 
% 106.39/106.77    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  (3217) {G5,W16,D3,L4,V4,M1} R(3213,290) { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, orthogonal_through_point( Y, T ) ), convergent_lines
% 106.39/106.77    ( Z, X ), ! unorthogonal_lines( Z, orthogonal_through_point( Y, T ) ) }.
% 106.39/106.77  (3218) {G6,W10,D3,L2,V2,M1} F(3217);r(2) { ! convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  (3219) {G7,W5,D3,L1,V2,M1} S(3218);r(46) { ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  (4619) {G4,W12,D2,L4,V3,M2} R(249,2741);f { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), distinct_lines( Z, Y ), ! distinct_lines( X, Y
% 106.39/106.77     ) }.
% 106.39/106.77  (4635) {G5,W12,D2,L4,V3,M2} R(4619,34) { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), ! distinct_lines( Y, X ), distinct_lines( Z, Y
% 106.39/106.77     ) }.
% 106.39/106.77  (4644) {G6,W12,D2,L4,V3,M2} R(4635,34) { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines( Y, X
% 106.39/106.77     ) }.
% 106.39/106.77  (4648) {G7,W15,D2,L5,V4,M3} R(4644,230) { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), distinct_lines( Y, T ), ! distinct_lines( X, T
% 106.39/106.77     ), distinct_lines( Y, Z ) }.
% 106.39/106.77  (4655) {G8,W12,D2,L4,V3,M2} F(4648) { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), ! distinct_lines( X, Z ), distinct_lines( Y, Z
% 106.39/106.77     ) }.
% 106.39/106.77  (4665) {G9,W15,D2,L5,V4,M1} R(4655,225) { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), ! convergent_lines( T, Z ), convergent_lines( T
% 106.39/106.77    , X ), distinct_lines( Y, Z ) }.
% 106.39/106.77  (4671) {G10,W9,D2,L3,V2,M1} F(4665);r(2) { ! convergent_lines( Y, X ), ! 
% 106.39/106.77    convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.77  (4692) {G11,W6,D2,L2,V2,M1} S(4671);r(43) { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  (4839) {G2,W17,D3,L3,V4,M2} R(306,23) { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.77    apart_point_and_line( T, orthogonal_through_point( X, Z ) ), 
% 106.39/106.77    apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  (4886) {G8,W17,D4,L3,V4,M2} R(307,3219) { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.77    apart_point_and_line( T, X ), apart_point_and_line( T, 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 106.39/106.77  (6002) {G3,W12,D3,L2,V3,M1} R(4839,24) { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.77    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 106.39/106.77  (6208) {G5,W14,D3,L2,V4,M2} R(6002,1978) { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), ! 
% 106.39/106.77    distinct_lines( orthogonal_through_point( X, Y ), 
% 106.39/106.77    orthogonal_through_point( X, Z ) ) }.
% 106.39/106.77  (6214) {G4,W16,D5,L2,V3,M1} R(6002,8) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.77    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  (6302) {G12,W14,D3,L2,V4,M1} R(6208,4692) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ), 
% 106.39/106.77    distinct_lines( orthogonal_through_point( X, Y ), 
% 106.39/106.77    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.77  (6357) {G13,W14,D3,L2,V4,M1} R(6302,34) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.77    distinct_lines( orthogonal_through_point( X, Z ), 
% 106.39/106.77    orthogonal_through_point( T, Y ) ) }.
% 106.39/106.77  (6916) {G14,W16,D5,L2,V3,M2} R(6214,6357) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.77    intersection_point( orthogonal_through_point( X, Y ), Z ) ) ), ! 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  (6917) {G13,W16,D5,L2,V3,M2} R(6214,6302) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.77    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ), ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  (6938) {G15,W11,D5,L1,V2,M1} R(6916,37) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.77    intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 106.39/106.77  (7062) {G16,W15,D6,L1,V0,M1} R(6938,215) { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 106.39/106.77    intersection_point( orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.77    skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ), 
% 106.39/106.77    skol2 ) }.
% 106.39/106.77  (7579) {G9,W10,D4,L2,V3,M1} R(4886,24) { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.77    apart_point_and_line( Z, X ) }.
% 106.39/106.77  (7631) {G10,W12,D4,L2,V4,M2} R(7579,1978) { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( T, Z ), X ), ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 106.39/106.77  (7638) {G10,W12,D4,L2,V3,M1} R(7579,9) { ! convergent_lines( Z, X ), ! 
% 106.39/106.77    distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Y
% 106.39/106.77     ), intersection_point( Z, X ) ), X ) }.
% 106.39/106.77  (9429) {G12,W12,D4,L2,V4,M1} R(7631,4692) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ), 
% 106.39/106.77    distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  (9603) {G13,W12,D4,L2,V3,M2} R(7638,9429) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( Y, Z ), 
% 106.39/106.77    intersection_point( X, Y ) ), Y ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  (9854) {G14,W12,D4,L2,V3,M2} R(9603,43) { ! convergent_lines( X, Z ), ! 
% 106.39/106.77    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.77    Y ), intersection_point( Z, X ) ), X ) }.
% 106.39/106.77  (10085) {G15,W15,D4,L3,V4,M3} R(9854,216) { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( X, Z ), 
% 106.39/106.77    intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ), ! 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  (10101) {G16,W12,D4,L2,V3,M2} F(10085) { ! convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.77    Y ), intersection_point( Z, X ) ), Z ) }.
% 106.39/106.77  (10108) {G17,W7,D4,L1,V3,M1} R(10101,6917);r(43) { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 106.39/106.77  (10305) {G18,W0,D0,L0,V0,M0} R(10108,7062) {  }.
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  % SZS output end Refutation
% 106.39/106.77  found a proof!
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Unprocessed initial clauses:
% 106.39/106.77  
% 106.39/106.77  (10307) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 106.39/106.77  (10308) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 106.39/106.77  (10309) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 106.39/106.77  (10310) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( 
% 106.39/106.77    X, Z ), distinct_points( Y, Z ) }.
% 106.39/106.77  (10311) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X
% 106.39/106.77    , Z ), distinct_lines( Y, Z ) }.
% 106.39/106.77  (10312) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 106.39/106.77    ( X, Z ), convergent_lines( Y, Z ) }.
% 106.39/106.77  (10313) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 106.39/106.77  (10314) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 106.39/106.77  (10315) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 106.39/106.77  (10316) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 106.39/106.77  (10317) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 106.39/106.77    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 106.39/106.77    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 106.39/106.77  (10318) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 106.39/106.77    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 106.39/106.77  (10319) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 106.39/106.77    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 106.39/106.77  (10320) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( 
% 106.39/106.77    Y, Z ), convergent_lines( X, Z ) }.
% 106.39/106.77  (10321) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( 
% 106.39/106.77    Y, X ), Y ) }.
% 106.39/106.77  (10322) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 106.39/106.77    parallel_through_point( Y, X ) ) }.
% 106.39/106.77  (10323) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  (10324) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 106.39/106.77    ( X, Y ) }.
% 106.39/106.77  (10325) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 106.39/106.77  (10326) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 106.39/106.77     }.
% 106.39/106.77  (10327) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y )
% 106.39/106.77     }.
% 106.39/106.77  (10328) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 106.39/106.77     }.
% 106.39/106.77  (10329) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 106.39/106.77  (10330) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 106.39/106.77    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  (10331) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 106.39/106.77    orthogonal_through_point( Y, X ) ) }.
% 106.39/106.77  (10332) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 106.39/106.77  (10333) {G0,W7,D4,L1,V0,M1}  { convergent_lines( skol2, 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 106.39/106.77     ) ) }.
% 106.39/106.77  
% 106.39/106.77  
% 106.39/106.77  Total Proof:
% 106.39/106.77  
% 106.39/106.77  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 106.39/106.77  parent0: (10308) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 106.39/106.77  parent0: (10309) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 106.39/106.77    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 106.39/106.77  parent0: (10311) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 106.39/106.77    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  parent0: (10312) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 106.39/106.77  parent0: (10315) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 106.39/106.77  parent0: (10316) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  parent0: (10319) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 106.39/106.77    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 106.39/106.77    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 106.39/106.77  parent0: (10320) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 2
% 106.39/106.77     2 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (16) {G0,W12,D2,L4,V3,M2} I { ! distinct_lines( X, Y ), 
% 106.39/106.77    convergent_lines( X, Y ), apart_point_and_line( Z, X ), 
% 106.39/106.77    apart_point_and_line( Z, Y ) }.
% 106.39/106.77  parent0: (10323) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 2
% 106.39/106.77     2 ==> 3
% 106.39/106.77     3 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  parent0: (10324) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 106.39/106.77  parent0: (10325) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 3
% 106.39/106.77     3 ==> 2
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 106.39/106.77     }.
% 106.39/106.77  parent0: (10326) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 106.39/106.77     }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 3
% 106.39/106.77     3 ==> 2
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 106.39/106.77    alpha1( X, Y ) }.
% 106.39/106.77  parent0: (10327) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines
% 106.39/106.77    ( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! 
% 106.39/106.77    alpha1( X, Y ) }.
% 106.39/106.77  parent0: (10328) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 106.39/106.77    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  parent0: (10330) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 106.39/106.77    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 106.39/106.77    orthogonal_through_point( Y, X ) ) }.
% 106.39/106.77  parent0: (10331) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 106.39/106.77    orthogonal_through_point( Y, X ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 106.39/106.77  parent0: (10332) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77     T := T
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 2
% 106.39/106.77     3 ==> 4
% 106.39/106.77     4 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2, 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 106.39/106.77     ) ) }.
% 106.39/106.77  parent0: (10333) {G0,W7,D4,L1,V0,M1}  { convergent_lines( skol2, 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 106.39/106.77     ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10467) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 106.39/106.77  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 106.39/106.77    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent0: (10467) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10469) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 106.39/106.77  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 106.39/106.77    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (35) {G2,W9,D2,L3,V3,M3} R(34,4) { distinct_lines( Z, X ), ! 
% 106.39/106.77    distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 106.39/106.77  parent0: (10469) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10472) {G1,W5,D3,L1,V2,M1}  { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), X ) }.
% 106.39/106.77  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 106.39/106.77    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := orthogonal_through_point( X, Y )
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), X ) }.
% 106.39/106.77  parent0: (10472) {G1,W5,D3,L1,V2,M1}  { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10473) {G1,W8,D3,L2,V3,M2}  { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 106.39/106.77  parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := orthogonal_through_point( X, Y )
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  parent0: (10473) {G1,W8,D3,L2,V3,M2}  { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10474) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 106.39/106.77  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  parent0: (10474) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10476) {G1,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 106.39/106.77  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 106.39/106.77     convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 106.39/106.77  parent0: (10476) {G1,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10479) {G2,W5,D3,L1,V2,M1}  { convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := orthogonal_through_point( X, Y )
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent0: (10479) {G2,W5,D3,L1,V2,M1}  { convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10480) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 106.39/106.77  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (97) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  parent0: (10480) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10482) {G1,W12,D2,L4,V4,M4}  { distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, Y ), distinct_lines( T, X ), ! 
% 106.39/106.77    apart_point_and_line( Z, T ) }.
% 106.39/106.77  parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := T
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (185) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 106.39/106.77    apart_point_and_line( Z, X ) }.
% 106.39/106.77  parent0: (10482) {G1,W12,D2,L4,V4,M4}  { distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, Y ), distinct_lines( T, X ), ! 
% 106.39/106.77    apart_point_and_line( Z, T ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := T
% 106.39/106.77     Z := Z
% 106.39/106.77     T := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 2
% 106.39/106.77     2 ==> 0
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10484) {G1,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Z, X ), ! apart_point_and_line( intersection_point( X, Y
% 106.39/106.77     ), Z ) }.
% 106.39/106.77  parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 106.39/106.77  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := intersection_point( X, Y )
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (194) {G1,W11,D3,L3,V3,M1} R(12,8) { distinct_lines( X, Y ), !
% 106.39/106.77     convergent_lines( Y, Z ), ! apart_point_and_line( intersection_point( Y
% 106.39/106.77    , Z ), X ) }.
% 106.39/106.77  parent0: (10484) {G1,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Z, X ), ! apart_point_and_line( intersection_point( X, Y
% 106.39/106.77     ), Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 2
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10485) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 106.39/106.77    orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 106.39/106.77  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 106.39/106.77    orthogonal_through_point( Y, X ) ) }.
% 106.39/106.77  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := orthogonal_through_point( Y, X )
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  parent0: (10485) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 106.39/106.77    orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10486) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 106.39/106.77    apart_point_and_line( Z, T ) }.
% 106.39/106.77  parent0[1]: (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := T
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 106.39/106.77    apart_point_and_line( Z, T ) }.
% 106.39/106.77  parent0: (10486) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 106.39/106.77    apart_point_and_line( Z, T ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77     T := T
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 2
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10488) {G1,W10,D4,L2,V1,M2}  { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 106.39/106.77     ), X ), convergent_lines( X, skol2 ) }.
% 106.39/106.77  parent0[1]: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), ! 
% 106.39/106.77    convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2, 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 106.39/106.77     ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := skol2
% 106.39/106.77     Z := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 106.39/106.77    , skol1 )
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (215) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X, 
% 106.39/106.77    skol2 ), convergent_lines( orthogonal_through_point( 
% 106.39/106.77    orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 106.39/106.77  parent0: (10488) {G1,W10,D4,L2,V1,M2}  { convergent_lines( 
% 106.39/106.77    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 106.39/106.77     ), X ), convergent_lines( X, skol2 ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10491) {G2,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), ! 
% 106.39/106.77    convergent_lines( Z, X ), convergent_lines( Y, Z ) }.
% 106.39/106.77  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.77    convergent_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), ! 
% 106.39/106.77    convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (216) {G3,W9,D2,L3,V3,M3} R(44,43) { convergent_lines( Z, X )
% 106.39/106.77    , convergent_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  parent0: (10491) {G2,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), ! 
% 106.39/106.77    convergent_lines( Z, X ), convergent_lines( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 2
% 106.39/106.77     2 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10495) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 106.39/106.77    convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 106.39/106.77  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 106.39/106.77    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (225) {G2,W9,D2,L3,V3,M1} R(13,34) { ! convergent_lines( X, Y
% 106.39/106.77     ), convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 106.39/106.77  parent0: (10495) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 106.39/106.77    convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10498) {G2,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 106.39/106.77    distinct_lines( Z, X ), distinct_lines( Y, Z ) }.
% 106.39/106.77  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (35) {G2,W9,D2,L3,V3,M3} R(34,4) { distinct_lines( Z, X ), ! 
% 106.39/106.77    distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (230) {G3,W9,D2,L3,V3,M3} R(35,34) { distinct_lines( Z, X ), 
% 106.39/106.77    distinct_lines( Z, Y ), ! distinct_lines( X, Y ) }.
% 106.39/106.77  parent0: (10498) {G2,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), ! 
% 106.39/106.77    distinct_lines( Z, X ), distinct_lines( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 2
% 106.39/106.77     2 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10503) {G1,W14,D3,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    distinct_lines( Y, Z ), convergent_lines( Y, Z ), apart_point_and_line( 
% 106.39/106.77    intersection_point( X, Y ), Z ) }.
% 106.39/106.77  parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 106.39/106.77  parent1[2]: (16) {G0,W12,D2,L4,V3,M2} I { ! distinct_lines( X, Y ), 
% 106.39/106.77    convergent_lines( X, Y ), apart_point_and_line( Z, X ), 
% 106.39/106.77    apart_point_and_line( Z, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := intersection_point( X, Y )
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (249) {G1,W14,D3,L4,V3,M1} R(16,9) { convergent_lines( X, Y )
% 106.39/106.77    , ! distinct_lines( X, Y ), ! convergent_lines( Z, X ), 
% 106.39/106.77    apart_point_and_line( intersection_point( Z, X ), Y ) }.
% 106.39/106.77  parent0: (10503) {G1,W14,D3,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    distinct_lines( Y, Z ), convergent_lines( Y, Z ), apart_point_and_line( 
% 106.39/106.77    intersection_point( X, Y ), Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 0
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10507) {G1,W12,D2,L4,V3,M4}  { unorthogonal_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 106.39/106.77    ( Z, Y ) }.
% 106.39/106.77  parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! 
% 106.39/106.77    alpha1( X, Y ) }.
% 106.39/106.77  parent1[3]: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (268) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 106.39/106.77     ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  parent0: (10507) {G1,W12,D2,L4,V3,M4}  { unorthogonal_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 106.39/106.77    ( Z, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 3
% 106.39/106.77     3 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10509) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 106.39/106.77    unorthogonal_lines( Z, Y ) }.
% 106.39/106.77  parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 106.39/106.77    ( X, Y ) }.
% 106.39/106.77  parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 106.39/106.77     }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (290) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 106.39/106.77     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 106.39/106.77    unorthogonal_lines( Y, Z ) }.
% 106.39/106.77  parent0: (10509) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 106.39/106.77    unorthogonal_lines( Z, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 2
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10510) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( Z, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 106.39/106.77    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 106.39/106.77    unorthogonal_lines( Z, X ) }.
% 106.39/106.77  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 106.39/106.77    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  parent1[3]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := orthogonal_through_point( X, Y )
% 106.39/106.77     Z := T
% 106.39/106.77     T := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (306) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ), 
% 106.39/106.77    apart_point_and_line( T, orthogonal_through_point( Y, Z ) ), 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  parent0: (10510) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( Z, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 106.39/106.77    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 106.39/106.77    unorthogonal_lines( Z, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77     T := T
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 2
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10514) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 106.39/106.77    unorthogonal_lines( Z, X ) }.
% 106.39/106.77  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 106.39/106.77    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  parent1[4]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 106.39/106.77    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 106.39/106.77    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := orthogonal_through_point( X, Y )
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := T
% 106.39/106.77     T := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (307) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 106.39/106.77    unorthogonal_lines( Z, X ) }.
% 106.39/106.77  parent0: (10514) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 106.39/106.77    unorthogonal_lines( Z, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77     T := T
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 2
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10516) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 106.39/106.77    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 106.39/106.77  parent0[2]: (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 106.39/106.77    apart_point_and_line( Z, T ) }.
% 106.39/106.77  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 106.39/106.77    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77     T := T
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := U
% 106.39/106.77     Z := T
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (1976) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 106.39/106.77    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 106.39/106.77  parent0: (10516) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 106.39/106.77    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77     T := T
% 106.39/106.77     U := U
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 2
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  factor: (10522) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  parent0[0, 2]: (1976) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 106.39/106.77    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77     T := orthogonal_through_point( Y, Z )
% 106.39/106.77     U := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10528) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (10522) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 106.39/106.77    orthogonal_through_point( Y, Z ) ), distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := orthogonal_through_point( Y, Z )
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  factor: (10530) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 106.39/106.77  parent0[0, 1]: (10528) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (1978) {G4,W8,D3,L2,V3,M1} F(1976);r(34) { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.77  parent0: (10530) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10532) {G2,W17,D3,L5,V5,M5}  { distinct_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Y, Z ), distinct_lines( T, U ), distinct_lines( U, X )
% 106.39/106.77    , ! apart_point_and_line( intersection_point( Y, Z ), T ) }.
% 106.39/106.77  parent0[2]: (194) {G1,W11,D3,L3,V3,M1} R(12,8) { distinct_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Y, Z ), ! apart_point_and_line( intersection_point( Y, 
% 106.39/106.77    Z ), X ) }.
% 106.39/106.77  parent1[2]: (185) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 106.39/106.77    apart_point_and_line( Z, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := T
% 106.39/106.77     Y := U
% 106.39/106.77     Z := intersection_point( Y, Z )
% 106.39/106.77     T := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (2715) {G2,W17,D3,L5,V5,M1} R(185,194) { distinct_lines( X, Y
% 106.39/106.77     ), distinct_lines( Y, Z ), distinct_lines( Z, T ), ! convergent_lines( T
% 106.39/106.77    , U ), ! apart_point_and_line( intersection_point( T, U ), X ) }.
% 106.39/106.77  parent0: (10532) {G2,W17,D3,L5,V5,M5}  { distinct_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Y, Z ), distinct_lines( T, U ), distinct_lines( U, X )
% 106.39/106.77    , ! apart_point_and_line( intersection_point( Y, Z ), T ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := T
% 106.39/106.77     Z := U
% 106.39/106.77     T := X
% 106.39/106.77     U := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 2
% 106.39/106.77     1 ==> 3
% 106.39/106.77     2 ==> 0
% 106.39/106.77     3 ==> 1
% 106.39/106.77     4 ==> 4
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  factor: (10538) {G2,W14,D3,L4,V3,M4}  { distinct_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Y, X ), ! convergent_lines( Y, Z ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 106.39/106.77  parent0[0, 2]: (2715) {G2,W17,D3,L5,V5,M1} R(185,194) { distinct_lines( X, 
% 106.39/106.77    Y ), distinct_lines( Y, Z ), distinct_lines( Z, T ), ! convergent_lines( 
% 106.39/106.77    T, U ), ! apart_point_and_line( intersection_point( T, U ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := X
% 106.39/106.77     T := Y
% 106.39/106.77     U := Z
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10544) {G2,W14,D3,L4,V3,M4}  { distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( Y, X ), ! convergent_lines( Y, Z ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 106.39/106.77  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent1[0]: (10538) {G2,W14,D3,L4,V3,M4}  { distinct_lines( X, Y ), 
% 106.39/106.77    distinct_lines( Y, X ), ! convergent_lines( Y, Z ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  factor: (10546) {G2,W11,D3,L3,V3,M3}  { distinct_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( X, Z ), ! apart_point_and_line( intersection_point( X, 
% 106.39/106.77    Z ), Y ) }.
% 106.39/106.77  parent0[0, 1]: (10544) {G2,W14,D3,L4,V3,M4}  { distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( Y, X ), ! convergent_lines( Y, Z ), ! 
% 106.39/106.77    apart_point_and_line( intersection_point( Y, Z ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (2741) {G3,W11,D3,L3,V3,M1} F(2715);r(34) { ! convergent_lines
% 106.39/106.77    ( Y, Z ), distinct_lines( Y, X ), ! apart_point_and_line( 
% 106.39/106.77    intersection_point( Y, Z ), X ) }.
% 106.39/106.77  parent0: (10546) {G2,W11,D3,L3,V3,M3}  { distinct_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( X, Z ), ! apart_point_and_line( intersection_point( X, 
% 106.39/106.77    Z ), Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 0
% 106.39/106.77     2 ==> 2
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10548) {G1,W13,D3,L3,V3,M3}  { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), ! 
% 106.39/106.77    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 106.39/106.77    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.77  parent1[2]: (268) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 106.39/106.77     ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), ! 
% 106.39/106.77    unorthogonal_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := orthogonal_through_point( X, Y )
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10550) {G2,W11,D3,L3,V3,M3}  { convergent_lines( Z, X ), ! 
% 106.39/106.77    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ), 
% 106.39/106.77    convergent_lines( Z, X ) }.
% 106.39/106.77  parent0[0]: (10548) {G1,W13,D3,L3,V3,M3}  { ! convergent_lines( 
% 106.39/106.77    orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), ! 
% 106.39/106.77    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  parent1[1]: (97) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ), 
% 106.39/106.77    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  factor: (10551) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 106.39/106.77  parent0[0, 2]: (10550) {G2,W11,D3,L3,V3,M3}  { convergent_lines( Z, X ), ! 
% 106.39/106.77    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ), 
% 106.39/106.77    convergent_lines( Z, X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (3213) {G4,W8,D3,L2,V3,M1} R(268,23);r(97) { convergent_lines
% 106.39/106.77    ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  parent0: (10551) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10552) {G2,W16,D3,L4,V4,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 106.39/106.77    ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 106.39/106.77  parent0[1]: (3213) {G4,W8,D3,L2,V3,M1} R(268,23);r(97) { convergent_lines( 
% 106.39/106.77    Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.77  parent1[3]: (290) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 106.39/106.77     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 106.39/106.77    unorthogonal_lines( Y, Z ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := T
% 106.39/106.77     Y := orthogonal_through_point( Y, Z )
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (3217) {G5,W16,D3,L4,V4,M1} R(3213,290) { convergent_lines( X
% 106.39/106.77    , Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ), 
% 106.39/106.77    convergent_lines( Z, X ), ! unorthogonal_lines( Z, 
% 106.39/106.77    orthogonal_through_point( Y, T ) ) }.
% 106.39/106.77  parent0: (10552) {G2,W16,D3,L4,V4,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 106.39/106.77    ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := T
% 106.39/106.77     T := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 2
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  factor: (10554) {G5,W13,D3,L3,V2,M3}  { convergent_lines( X, X ), ! 
% 106.39/106.77    convergent_lines( X, orthogonal_through_point( X, Y ) ), ! 
% 106.39/106.77    unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent0[0, 2]: (3217) {G5,W16,D3,L4,V4,M1} R(3213,290) { convergent_lines( 
% 106.39/106.77    X, Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ), 
% 106.39/106.77    convergent_lines( Z, X ), ! unorthogonal_lines( Z, 
% 106.39/106.77    orthogonal_through_point( Y, T ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := X
% 106.39/106.77     Z := X
% 106.39/106.77     T := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10555) {G1,W10,D3,L2,V2,M2}  { ! convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 106.39/106.77  parent1[0]: (10554) {G5,W13,D3,L3,V2,M3}  { convergent_lines( X, X ), ! 
% 106.39/106.77    convergent_lines( X, orthogonal_through_point( X, Y ) ), ! 
% 106.39/106.77    unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (3218) {G6,W10,D3,L2,V2,M1} F(3217);r(2) { ! convergent_lines
% 106.39/106.77    ( X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent0: (10555) {G1,W10,D3,L2,V2,M2}  { ! convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10556) {G3,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent0[0]: (3218) {G6,W10,D3,L2,V2,M1} F(3217);r(2) { ! convergent_lines( 
% 106.39/106.77    X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent1[0]: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (3219) {G7,W5,D3,L1,V2,M1} S(3218);r(46) { ! 
% 106.39/106.77    unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  parent0: (10556) {G3,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( X, 
% 106.39/106.77    orthogonal_through_point( X, Y ) ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10560) {G2,W15,D2,L5,V3,M5}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 106.39/106.77     ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  parent0[2]: (2741) {G3,W11,D3,L3,V3,M1} F(2715);r(34) { ! convergent_lines
% 106.39/106.77    ( Y, Z ), distinct_lines( Y, X ), ! apart_point_and_line( 
% 106.39/106.77    intersection_point( Y, Z ), X ) }.
% 106.39/106.77  parent1[3]: (249) {G1,W14,D3,L4,V3,M1} R(16,9) { convergent_lines( X, Y ), 
% 106.39/106.77    ! distinct_lines( X, Y ), ! convergent_lines( Z, X ), 
% 106.39/106.77    apart_point_and_line( intersection_point( Z, X ), Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := Y
% 106.39/106.77     Y := Z
% 106.39/106.77     Z := X
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  factor: (10561) {G2,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 106.39/106.77     ) }.
% 106.39/106.77  parent0[0, 4]: (10560) {G2,W15,D2,L5,V3,M5}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 106.39/106.77     ), ! convergent_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (4619) {G4,W12,D2,L4,V3,M2} R(249,2741);f { convergent_lines( 
% 106.39/106.77    X, Y ), ! convergent_lines( Z, X ), distinct_lines( Z, Y ), ! 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent0: (10561) {G2,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), 
% 106.39/106.77    distinct_lines( X, Z ), convergent_lines( Y, Z ), ! distinct_lines( Y, Z
% 106.39/106.77     ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := Z
% 106.39/106.77     Y := X
% 106.39/106.77     Z := Y
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 1
% 106.39/106.77     1 ==> 2
% 106.39/106.77     2 ==> 0
% 106.39/106.77     3 ==> 3
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10562) {G2,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), distinct_lines( Z, Y ), ! distinct_lines( Y, X
% 106.39/106.77     ) }.
% 106.39/106.77  parent0[3]: (4619) {G4,W12,D2,L4,V3,M2} R(249,2741);f { convergent_lines( X
% 106.39/106.77    , Y ), ! convergent_lines( Z, X ), distinct_lines( Z, Y ), ! 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  parent1[1]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.77    distinct_lines( X, Y ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  substitution1:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  subsumption: (4635) {G5,W12,D2,L4,V3,M2} R(4619,34) { convergent_lines( X, 
% 106.39/106.77    Y ), ! convergent_lines( Z, X ), ! distinct_lines( Y, X ), distinct_lines
% 106.39/106.77    ( Z, Y ) }.
% 106.39/106.77  parent0: (10562) {G2,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.77    convergent_lines( Z, X ), distinct_lines( Z, Y ), ! distinct_lines( Y, X
% 106.39/106.77     ) }.
% 106.39/106.77  substitution0:
% 106.39/106.77     X := X
% 106.39/106.77     Y := Y
% 106.39/106.77     Z := Z
% 106.39/106.77  end
% 106.39/106.77  permutation0:
% 106.39/106.77     0 ==> 0
% 106.39/106.77     1 ==> 1
% 106.39/106.77     2 ==> 3
% 106.39/106.77     3 ==> 2
% 106.39/106.77  end
% 106.39/106.77  
% 106.39/106.77  resolution: (10564) {G2,W12,D2,L4,V3,M4}  { distinct_lines( Y, X ), 
% 106.39/106.77    convergent_lines( Z, Y ), ! convergent_lines( X, Z ), ! distinct_lines( Y
% 106.39/106.77    , Z ) }.
% 106.39/106.77  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.78    distinct_lines( X, Y ) }.
% 106.39/106.78  parent1[3]: (4635) {G5,W12,D2,L4,V3,M2} R(4619,34) { convergent_lines( X, Y
% 106.39/106.78     ), ! convergent_lines( Z, X ), ! distinct_lines( Y, X ), distinct_lines
% 106.39/106.78    ( Z, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4644) {G6,W12,D2,L4,V3,M2} R(4635,34) { convergent_lines( X, 
% 106.39/106.78    Y ), ! convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines
% 106.39/106.78    ( Y, X ) }.
% 106.39/106.78  parent0: (10564) {G2,W12,D2,L4,V3,M4}  { distinct_lines( Y, X ), 
% 106.39/106.78    convergent_lines( Z, Y ), ! convergent_lines( X, Z ), ! distinct_lines( Y
% 106.39/106.78    , Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := X
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 2
% 106.39/106.78     1 ==> 0
% 106.39/106.78     2 ==> 1
% 106.39/106.78     3 ==> 3
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10565) {G4,W15,D2,L5,V4,M5}  { convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( Z, X ), distinct_lines( Y, Z ), distinct_lines( Y, T )
% 106.39/106.78    , ! distinct_lines( X, T ) }.
% 106.39/106.78  parent0[3]: (4644) {G6,W12,D2,L4,V3,M2} R(4635,34) { convergent_lines( X, Y
% 106.39/106.78     ), ! convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines
% 106.39/106.78    ( Y, X ) }.
% 106.39/106.78  parent1[0]: (230) {G3,W9,D2,L3,V3,M3} R(35,34) { distinct_lines( Z, X ), 
% 106.39/106.78    distinct_lines( Z, Y ), ! distinct_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := T
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4648) {G7,W15,D2,L5,V4,M3} R(4644,230) { convergent_lines( X
% 106.39/106.78    , Y ), ! convergent_lines( Z, X ), distinct_lines( Y, T ), ! 
% 106.39/106.78    distinct_lines( X, T ), distinct_lines( Y, Z ) }.
% 106.39/106.78  parent0: (10565) {G4,W15,D2,L5,V4,M5}  { convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( Z, X ), distinct_lines( Y, Z ), distinct_lines( Y, T )
% 106.39/106.78    , ! distinct_lines( X, T ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78     2 ==> 4
% 106.39/106.78     3 ==> 2
% 106.39/106.78     4 ==> 3
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  factor: (10569) {G7,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines( X, Z
% 106.39/106.78     ) }.
% 106.39/106.78  parent0[2, 4]: (4648) {G7,W15,D2,L5,V4,M3} R(4644,230) { convergent_lines( 
% 106.39/106.78    X, Y ), ! convergent_lines( Z, X ), distinct_lines( Y, T ), ! 
% 106.39/106.78    distinct_lines( X, T ), distinct_lines( Y, Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := Z
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4655) {G8,W12,D2,L4,V3,M2} F(4648) { convergent_lines( X, Y )
% 106.39/106.78    , ! convergent_lines( Z, X ), ! distinct_lines( X, Z ), distinct_lines( Y
% 106.39/106.78    , Z ) }.
% 106.39/106.78  parent0: (10569) {G7,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( Z, X ), distinct_lines( Y, Z ), ! distinct_lines( X, Z
% 106.39/106.78     ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78     2 ==> 3
% 106.39/106.78     3 ==> 2
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10571) {G3,W15,D2,L5,V4,M5}  { convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( Z, X ), distinct_lines( Y, Z ), ! convergent_lines( T, 
% 106.39/106.78    Z ), convergent_lines( T, X ) }.
% 106.39/106.78  parent0[2]: (4655) {G8,W12,D2,L4,V3,M2} F(4648) { convergent_lines( X, Y )
% 106.39/106.78    , ! convergent_lines( Z, X ), ! distinct_lines( X, Z ), distinct_lines( Y
% 106.39/106.78    , Z ) }.
% 106.39/106.78  parent1[2]: (225) {G2,W9,D2,L3,V3,M1} R(13,34) { ! convergent_lines( X, Y )
% 106.39/106.78    , convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := T
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4665) {G9,W15,D2,L5,V4,M1} R(4655,225) { convergent_lines( X
% 106.39/106.78    , Y ), ! convergent_lines( Z, X ), ! convergent_lines( T, Z ), 
% 106.39/106.78    convergent_lines( T, X ), distinct_lines( Y, Z ) }.
% 106.39/106.78  parent0: (10571) {G3,W15,D2,L5,V4,M5}  { convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( Z, X ), distinct_lines( Y, Z ), ! convergent_lines( T, 
% 106.39/106.78    Z ), convergent_lines( T, X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78     2 ==> 4
% 106.39/106.78     3 ==> 2
% 106.39/106.78     4 ==> 3
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  factor: (10576) {G9,W12,D2,L4,V2,M4}  { convergent_lines( X, X ), ! 
% 106.39/106.78    convergent_lines( Y, X ), ! convergent_lines( X, Y ), distinct_lines( X, 
% 106.39/106.78    Y ) }.
% 106.39/106.78  parent0[0, 3]: (4665) {G9,W15,D2,L5,V4,M1} R(4655,225) { convergent_lines( 
% 106.39/106.78    X, Y ), ! convergent_lines( Z, X ), ! convergent_lines( T, Z ), 
% 106.39/106.78    convergent_lines( T, X ), distinct_lines( Y, Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Y
% 106.39/106.78     T := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10579) {G1,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 106.39/106.78    convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.78  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 106.39/106.78  parent1[0]: (10576) {G9,W12,D2,L4,V2,M4}  { convergent_lines( X, X ), ! 
% 106.39/106.78    convergent_lines( Y, X ), ! convergent_lines( X, Y ), distinct_lines( X, 
% 106.39/106.78    Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4671) {G10,W9,D2,L3,V2,M1} F(4665);r(2) { ! convergent_lines
% 106.39/106.78    ( Y, X ), ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.78  parent0: (10579) {G1,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 106.39/106.78    convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78     2 ==> 2
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10583) {G2,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), 
% 106.39/106.78    distinct_lines( Y, X ), ! convergent_lines( Y, X ) }.
% 106.39/106.78  parent0[0]: (4671) {G10,W9,D2,L3,V2,M1} F(4665);r(2) { ! convergent_lines( 
% 106.39/106.78    Y, X ), ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.78  parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.78    convergent_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  factor: (10585) {G2,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 106.39/106.78    distinct_lines( X, Y ) }.
% 106.39/106.78  parent0[0, 2]: (10583) {G2,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), 
% 106.39/106.78    distinct_lines( Y, X ), ! convergent_lines( Y, X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4692) {G11,W6,D2,L2,V2,M1} S(4671);r(43) { ! convergent_lines
% 106.39/106.78    ( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.78  parent0: (10585) {G2,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 106.39/106.78    distinct_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10587) {G1,W17,D3,L3,V4,M3}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 106.39/106.78  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 106.39/106.78    orthogonal_through_point( Y, X ), Y ) }.
% 106.39/106.78  parent1[3]: (306) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X, 
% 106.39/106.78    orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( Y, Z ) ), 
% 106.39/106.78    unorthogonal_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := orthogonal_through_point( X, Y )
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4839) {G2,W17,D3,L3,V4,M2} R(306,23) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  parent0: (10587) {G1,W17,D3,L3,V4,M3}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 2
% 106.39/106.78     2 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10589) {G2,W17,D4,L3,V4,M3}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 106.39/106.78  parent0[0]: (3219) {G7,W5,D3,L1,V2,M1} S(3218);r(46) { ! unorthogonal_lines
% 106.39/106.78    ( X, orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  parent1[3]: (307) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 106.39/106.78    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 106.39/106.78    unorthogonal_lines( Z, X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := orthogonal_through_point( X, Y )
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := X
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (4886) {G8,W17,D4,L3,V4,M2} R(307,3219) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.78    apart_point_and_line( T, X ), apart_point_and_line( T, 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 106.39/106.78  parent0: (10589) {G2,W17,D4,L3,V4,M3}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 2
% 106.39/106.78     2 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10591) {G1,W12,D3,L2,V3,M2}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ), 
% 106.39/106.78    apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 106.39/106.78  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 106.39/106.78    orthogonal_through_point( Y, X ) ) }.
% 106.39/106.78  parent1[2]: (4839) {G2,W17,D3,L3,V4,M2} R(306,23) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Z
% 106.39/106.78     T := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6002) {G3,W12,D3,L2,V3,M1} R(4839,24) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 106.39/106.78  parent0: (10591) {G1,W12,D3,L2,V3,M2}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ), 
% 106.39/106.78    apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10593) {G4,W14,D3,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 106.39/106.78    distinct_lines( orthogonal_through_point( Z, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  parent0[1]: (1978) {G4,W8,D3,L2,V3,M1} F(1976);r(34) { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.78  parent1[1]: (6002) {G3,W12,D3,L2,V3,M1} R(4839,24) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := orthogonal_through_point( Z, T )
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := T
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6208) {G5,W14,D3,L2,V4,M2} R(6002,1978) { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), ! 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Y ), 
% 106.39/106.78    orthogonal_through_point( X, Z ) ) }.
% 106.39/106.78  parent0: (10593) {G4,W14,D3,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 106.39/106.78    distinct_lines( orthogonal_through_point( Z, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := T
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := X
% 106.39/106.78     T := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10594) {G1,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.78    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.78    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 106.39/106.78  parent1[1]: (6002) {G3,W12,D3,L2,V3,M1} R(4839,24) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := orthogonal_through_point( X, Y )
% 106.39/106.78     Y := Z
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := intersection_point( orthogonal_through_point( X, Y ), Z )
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6214) {G4,W16,D5,L2,V3,M1} R(6002,8) { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.78    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  parent0: (10594) {G1,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.78    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10595) {G6,W14,D3,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( Z, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  parent0[1]: (6208) {G5,W14,D3,L2,V4,M2} R(6002,1978) { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), ! 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Y ), 
% 106.39/106.78    orthogonal_through_point( X, Z ) ) }.
% 106.39/106.78  parent1[1]: (4692) {G11,W6,D2,L2,V2,M1} S(4671);r(43) { ! convergent_lines
% 106.39/106.78    ( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := T
% 106.39/106.78     T := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := orthogonal_through_point( Z, Y )
% 106.39/106.78     Y := orthogonal_through_point( Z, T )
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6302) {G12,W14,D3,L2,V4,M1} R(6208,4692) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ), 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  parent0: (10595) {G6,W14,D3,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( Z, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10596) {G2,W14,D3,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( Z, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 106.39/106.78    distinct_lines( X, Y ) }.
% 106.39/106.78  parent1[1]: (6302) {G12,W14,D3,L2,V4,M1} R(6208,4692) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ), 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := orthogonal_through_point( Z, T )
% 106.39/106.78     Y := orthogonal_through_point( X, Y )
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6357) {G13,W14,D3,L2,V4,M1} R(6302,34) { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Z ), 
% 106.39/106.78    orthogonal_through_point( T, Y ) ) }.
% 106.39/106.78  parent0: (10596) {G2,W14,D3,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( Z, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := T
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := X
% 106.39/106.78     T := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10597) {G5,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), Z ) ) ) }.
% 106.39/106.78  parent0[1]: (6214) {G4,W16,D5,L2,V3,M1} R(6002,8) { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.78    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  parent1[1]: (6357) {G13,W14,D3,L2,V4,M1} R(6302,34) { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Z ), 
% 106.39/106.78    orthogonal_through_point( T, Y ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := intersection_point( orthogonal_through_point( X, Y ), Z )
% 106.39/106.78     T := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6916) {G14,W16,D5,L2,V3,M2} R(6214,6357) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), Z ) ) ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.78  parent0: (10597) {G5,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), Z ) ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10598) {G5,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.78    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  parent0[1]: (6214) {G4,W16,D5,L2,V3,M1} R(6002,8) { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.78    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  parent1[1]: (6302) {G12,W14,D3,L2,V4,M1} R(6208,4692) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ), 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Y ), 
% 106.39/106.78    orthogonal_through_point( Z, T ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := intersection_point( orthogonal_through_point( X, Y ), Z )
% 106.39/106.78     Z := X
% 106.39/106.78     T := Y
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6917) {G13,W16,D5,L2,V3,M2} R(6214,6302) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( X, intersection_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ) ), orthogonal_through_point( X, Y )
% 106.39/106.78     ), ! convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.78  parent0: (10598) {G5,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, intersection_point( orthogonal_through_point
% 106.39/106.78    ( X, Y ), Z ) ), orthogonal_through_point( X, Y ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10599) {G2,W11,D5,L1,V2,M1}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 106.39/106.78  parent0[1]: (6916) {G14,W16,D5,L2,V3,M2} R(6214,6357) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), Z ) ) ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.78  parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (6938) {G15,W11,D5,L1,V2,M1} R(6916,37) { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 106.39/106.78  parent0: (10599) {G2,W11,D5,L1,V2,M1}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10600) {G4,W15,D6,L1,V0,M1}  { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 106.39/106.78    intersection_point( orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.78    skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ), 
% 106.39/106.78    skol2 ) }.
% 106.39/106.78  parent0[0]: (6938) {G15,W11,D5,L1,V2,M1} R(6916,37) { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 106.39/106.78    intersection_point( orthogonal_through_point( X, Y ), X ) ) ) }.
% 106.39/106.78  parent1[1]: (215) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X, 
% 106.39/106.78    skol2 ), convergent_lines( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := orthogonal_through_point( skol2, skol1 )
% 106.39/106.78     Y := skol1
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 106.39/106.78    , intersection_point( orthogonal_through_point( orthogonal_through_point
% 106.39/106.78    ( skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) )
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (7062) {G16,W15,D6,L1,V0,M1} R(6938,215) { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 106.39/106.78    intersection_point( orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.78    skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ), 
% 106.39/106.78    skol2 ) }.
% 106.39/106.78  parent0: (10600) {G4,W15,D6,L1,V0,M1}  { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 106.39/106.78    intersection_point( orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.78    skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ), 
% 106.39/106.78    skol2 ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10602) {G1,W10,D4,L2,V3,M2}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ), 
% 106.39/106.78    apart_point_and_line( X, Y ) }.
% 106.39/106.78  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 106.39/106.78    orthogonal_through_point( Y, X ) ) }.
% 106.39/106.78  parent1[2]: (4886) {G8,W17,D4,L3,V4,M2} R(307,3219) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.78    apart_point_and_line( T, X ), apart_point_and_line( T, 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := orthogonal_through_point( Y, Z )
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := X
% 106.39/106.78     T := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (7579) {G9,W10,D4,L2,V3,M1} R(4886,24) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.78    apart_point_and_line( Z, X ) }.
% 106.39/106.78  parent0: (10602) {G1,W10,D4,L2,V3,M2}  { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ), 
% 106.39/106.78    apart_point_and_line( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10604) {G5,W12,D4,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 106.39/106.78  parent0[1]: (1978) {G4,W8,D3,L2,V3,M1} F(1976);r(34) { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 106.39/106.78  parent1[1]: (7579) {G9,W10,D4,L2,V3,M1} R(4886,24) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.78    apart_point_and_line( Z, X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := T
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (7631) {G10,W12,D4,L2,V4,M2} R(7579,1978) { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( T, Z ), X ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 106.39/106.78  parent0: (10604) {G5,W12,D4,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := T
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := X
% 106.39/106.78     T := Y
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10605) {G1,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.78    distinct_lines( orthogonal_through_point( orthogonal_through_point( Y, Z
% 106.39/106.78     ), intersection_point( X, Y ) ), Y ) }.
% 106.39/106.78  parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), ! 
% 106.39/106.78    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 106.39/106.78  parent1[1]: (7579) {G9,W10,D4,L2,V3,M1} R(4886,24) { ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 106.39/106.78    apart_point_and_line( Z, X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := intersection_point( X, Y )
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (7638) {G10,W12,D4,L2,V3,M1} R(7579,9) { ! convergent_lines( Z
% 106.39/106.78    , X ), ! distinct_lines( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 106.39/106.78  parent0: (10605) {G1,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.78    distinct_lines( orthogonal_through_point( orthogonal_through_point( Y, Z
% 106.39/106.78     ), intersection_point( X, Y ) ), Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78     1 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10606) {G11,W12,D4,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 106.39/106.78  parent0[1]: (7631) {G10,W12,D4,L2,V4,M2} R(7579,1978) { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( T, Z ), X ), ! distinct_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 106.39/106.78  parent1[1]: (4692) {G11,W6,D2,L2,V2,M1} S(4671);r(43) { ! convergent_lines
% 106.39/106.78    ( X, Y ), distinct_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := T
% 106.39/106.78     Z := Y
% 106.39/106.78     T := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := orthogonal_through_point( orthogonal_through_point( Z, T ), Y )
% 106.39/106.78     Y := Z
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (9429) {G12,W12,D4,L2,V4,M1} R(7631,4692) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ), 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.78  parent0: (10606) {G11,W12,D4,L2,V4,M2}  { distinct_lines( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10607) {G11,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( Y, 
% 106.39/106.78    T ), intersection_point( X, Y ) ), Y ) }.
% 106.39/106.78  parent0[1]: (7638) {G10,W12,D4,L2,V3,M1} R(7579,9) { ! convergent_lines( Z
% 106.39/106.78    , X ), ! distinct_lines( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 106.39/106.78  parent1[1]: (9429) {G12,W12,D4,L2,V4,M1} R(7631,4692) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ), 
% 106.39/106.78    distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Y
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := orthogonal_through_point( Y, Z )
% 106.39/106.78     Y := intersection_point( X, Y )
% 106.39/106.78     Z := Y
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (9603) {G13,W12,D4,L2,V3,M2} R(7638,9429) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( orthogonal_through_point( Y, Z ), 
% 106.39/106.78    intersection_point( X, Y ) ), Y ), ! convergent_lines( X, Y ) }.
% 106.39/106.78  parent0: (10607) {G11,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( Y, 
% 106.39/106.78    T ), intersection_point( X, Y ) ), Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := T
% 106.39/106.78     T := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10609) {G2,W12,D4,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), 
% 106.39/106.78    intersection_point( Z, X ) ), X ), ! convergent_lines( X, Z ) }.
% 106.39/106.78  parent0[1]: (9603) {G13,W12,D4,L2,V3,M2} R(7638,9429) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( orthogonal_through_point( Y, Z ), 
% 106.39/106.78    intersection_point( X, Y ) ), Y ), ! convergent_lines( X, Y ) }.
% 106.39/106.78  parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.78    convergent_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := X
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := Z
% 106.39/106.78     Y := X
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (9854) {G14,W12,D4,L2,V3,M2} R(9603,43) { ! convergent_lines( 
% 106.39/106.78    X, Z ), ! convergent_lines( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 106.39/106.78  parent0: (10609) {G2,W12,D4,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), 
% 106.39/106.78    intersection_point( Z, X ) ), X ), ! convergent_lines( X, Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10612) {G4,W15,D4,L3,V4,M3}  { ! convergent_lines( X, Y ), 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.78    Z ), intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ) }.
% 106.39/106.78  parent0[1]: (9854) {G14,W12,D4,L2,V3,M2} R(9603,43) { ! convergent_lines( X
% 106.39/106.78    , Z ), ! convergent_lines( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), X ) }.
% 106.39/106.78  parent1[0]: (216) {G3,W9,D2,L3,V3,M3} R(44,43) { convergent_lines( Z, X ), 
% 106.39/106.78    convergent_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := Y
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := T
% 106.39/106.78     Z := orthogonal_through_point( orthogonal_through_point( X, Z ), 
% 106.39/106.78    intersection_point( Y, X ) )
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (10085) {G15,W15,D4,L3,V4,M3} R(9854,216) { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Z ), 
% 106.39/106.78    intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ), ! 
% 106.39/106.78    convergent_lines( X, Y ) }.
% 106.39/106.78  parent0: (10612) {G4,W15,D4,L3,V4,M3}  { ! convergent_lines( X, Y ), 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.78    Z ), intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78     T := T
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 2
% 106.39/106.78     1 ==> 0
% 106.39/106.78     2 ==> 1
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  factor: (10616) {G15,W12,D4,L2,V3,M2}  { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), 
% 106.39/106.78    intersection_point( Z, X ) ), Z ), ! convergent_lines( X, Z ) }.
% 106.39/106.78  parent0[1, 2]: (10085) {G15,W15,D4,L3,V4,M3} R(9854,216) { convergent_lines
% 106.39/106.78    ( orthogonal_through_point( orthogonal_through_point( X, Z ), 
% 106.39/106.78    intersection_point( Y, X ) ), T ), ! convergent_lines( X, T ), ! 
% 106.39/106.78    convergent_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := Y
% 106.39/106.78     T := Z
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (10101) {G16,W12,D4,L2,V3,M2} F(10085) { ! convergent_lines( X
% 106.39/106.78    , Z ), convergent_lines( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), Z ) }.
% 106.39/106.78  parent0: (10616) {G15,W12,D4,L2,V3,M2}  { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), 
% 106.39/106.78    intersection_point( Z, X ) ), Z ), ! convergent_lines( X, Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 1
% 106.39/106.78     1 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10617) {G14,W14,D4,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), ! 
% 106.39/106.78    convergent_lines( X, orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.78    X, Y ), Z ) ) }.
% 106.39/106.78  parent0[0]: (6917) {G13,W16,D5,L2,V3,M2} R(6214,6302) { ! convergent_lines
% 106.39/106.78    ( orthogonal_through_point( X, intersection_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), Z ) ), orthogonal_through_point( X, Y )
% 106.39/106.78     ), ! convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 106.39/106.78  parent1[1]: (10101) {G16,W12,D4,L2,V3,M2} F(10085) { ! convergent_lines( X
% 106.39/106.78    , Z ), convergent_lines( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( X, Y ), intersection_point( Z, X ) ), Z ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := orthogonal_through_point( X, Y )
% 106.39/106.78     Y := Z
% 106.39/106.78     Z := X
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10620) {G2,W14,D4,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.78    Y ), Z ), X ) }.
% 106.39/106.78  parent0[1]: (10617) {G14,W14,D4,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), ! 
% 106.39/106.78    convergent_lines( X, orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.78    X, Y ), Z ) ) }.
% 106.39/106.78  parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 106.39/106.78    convergent_lines( X, Y ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78     X := X
% 106.39/106.78     Y := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  factor: (10622) {G2,W7,D4,L1,V3,M1}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 106.39/106.78  parent0[0, 1]: (10620) {G2,W14,D4,L2,V3,M2}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.78    Y ), Z ), X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (10108) {G17,W7,D4,L1,V3,M1} R(10101,6917);r(43) { ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.78    Y ), Z ), X ) }.
% 106.39/106.78  parent0: (10622) {G2,W7,D4,L1,V3,M1}  { ! convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := X
% 106.39/106.78     Y := Y
% 106.39/106.78     Z := Z
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78     0 ==> 0
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  resolution: (10623) {G17,W0,D0,L0,V0,M0}  {  }.
% 106.39/106.78  parent0[0]: (10108) {G17,W7,D4,L1,V3,M1} R(10101,6917);r(43) { ! 
% 106.39/106.78    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 106.39/106.78    Y ), Z ), X ) }.
% 106.39/106.78  parent1[0]: (7062) {G16,W15,D6,L1,V0,M1} R(6938,215) { convergent_lines( 
% 106.39/106.78    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 106.39/106.78    intersection_point( orthogonal_through_point( orthogonal_through_point( 
% 106.39/106.78    skol2, skol1 ), skol1 ), orthogonal_through_point( skol2, skol1 ) ) ), 
% 106.39/106.78    skol2 ) }.
% 106.39/106.78  substitution0:
% 106.39/106.78     X := skol2
% 106.39/106.78     Y := skol1
% 106.39/106.78     Z := intersection_point( orthogonal_through_point( 
% 106.39/106.78    orthogonal_through_point( skol2, skol1 ), skol1 ), 
% 106.39/106.78    orthogonal_through_point( skol2, skol1 ) )
% 106.39/106.78  end
% 106.39/106.78  substitution1:
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  subsumption: (10305) {G18,W0,D0,L0,V0,M0} R(10108,7062) {  }.
% 106.39/106.78  parent0: (10623) {G17,W0,D0,L0,V0,M0}  {  }.
% 106.39/106.78  substitution0:
% 106.39/106.78  end
% 106.39/106.78  permutation0:
% 106.39/106.78  end
% 106.39/106.78  
% 106.39/106.78  Proof check complete!
% 106.39/106.78  
% 106.39/106.78  Memory use:
% 106.39/106.78  
% 106.39/106.78  space for terms:        172014
% 106.39/106.78  space for clauses:      464524
% 106.39/106.78  
% 106.39/106.78  
% 106.39/106.78  clauses generated:      15059949
% 106.39/106.78  clauses kept:           10306
% 106.39/106.78  clauses selected:       6723
% 106.39/106.78  clauses deleted:        204
% 106.39/106.78  clauses inuse deleted:  9
% 106.39/106.78  
% 106.39/106.78  subsentry:          73126118
% 106.39/106.78  literals s-matched: 21705524
% 106.39/106.78  literals matched:   21702102
% 106.39/106.78  full subsumption:   14263308
% 106.39/106.78  
% 106.39/106.78  checksum:           264594850
% 106.39/106.78  
% 106.39/106.78  
% 106.39/106.78  Bliksem ended
%------------------------------------------------------------------------------