TSTP Solution File: GEO222+2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n025.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 100.80s 101.23s
% Output   : Refutation 100.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % DateTime : Sat Jun 18 07:22:13 EDT 2022
% 0.17/0.33  % CPUTime  : 
% 100.80/101.23  *** allocated 10000 integers for termspace/termends
% 100.80/101.23  *** allocated 10000 integers for clauses
% 100.80/101.23  *** allocated 10000 integers for justifications
% 100.80/101.23  Bliksem 1.12
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Automatic Strategy Selection
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Clauses:
% 100.80/101.23  
% 100.80/101.23  { ! distinct_points( X, X ) }.
% 100.80/101.23  { ! distinct_lines( X, X ) }.
% 100.80/101.23  { ! convergent_lines( X, X ) }.
% 100.80/101.23  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 100.80/101.23     ) }.
% 100.80/101.23  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 100.80/101.23     }.
% 100.80/101.23  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 100.80/101.23    , Z ) }.
% 100.80/101.23  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 100.80/101.23    , Y ) ), distinct_points( Z, X ) }.
% 100.80/101.23  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 100.80/101.23    , Y ) ), distinct_points( Z, Y ) }.
% 100.80/101.23  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ) }.
% 100.80/101.23  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ) }.
% 100.80/101.23  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 100.80/101.23    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 100.80/101.23    apart_point_and_line( Y, T ) }.
% 100.80/101.23  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 100.80/101.23    apart_point_and_line( Z, Y ) }.
% 100.80/101.23  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 100.80/101.23    apart_point_and_line( X, Z ) }.
% 100.80/101.23  { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 100.80/101.23  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 100.80/101.23  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 100.80/101.23  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 100.80/101.23    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 100.80/101.23  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 100.80/101.23    , convergent_lines( Y, Z ) }.
% 100.80/101.23  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 100.80/101.23    , unorthogonal_lines( Y, Z ) }.
% 100.80/101.23  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 100.80/101.23  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 100.80/101.23     }.
% 100.80/101.23  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 100.80/101.23    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 100.80/101.23    unorthogonal_lines( Y, T ) }.
% 100.80/101.23  { convergent_lines( skol2, orthogonal_through_point( 
% 100.80/101.23    orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 100.80/101.23  
% 100.80/101.23  percentage equality = 0.000000, percentage horn = 0.592593
% 100.80/101.23  This a non-horn, non-equality problem
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Options Used:
% 100.80/101.23  
% 100.80/101.23  useres =            1
% 100.80/101.23  useparamod =        0
% 100.80/101.23  useeqrefl =         0
% 100.80/101.23  useeqfact =         0
% 100.80/101.23  usefactor =         1
% 100.80/101.23  usesimpsplitting =  0
% 100.80/101.23  usesimpdemod =      0
% 100.80/101.23  usesimpres =        3
% 100.80/101.23  
% 100.80/101.23  resimpinuse      =  1000
% 100.80/101.23  resimpclauses =     20000
% 100.80/101.23  substype =          standard
% 100.80/101.23  backwardsubs =      1
% 100.80/101.23  selectoldest =      5
% 100.80/101.23  
% 100.80/101.23  litorderings [0] =  split
% 100.80/101.23  litorderings [1] =  liftord
% 100.80/101.23  
% 100.80/101.23  termordering =      none
% 100.80/101.23  
% 100.80/101.23  litapriori =        1
% 100.80/101.23  termapriori =       0
% 100.80/101.23  litaposteriori =    0
% 100.80/101.23  termaposteriori =   0
% 100.80/101.23  demodaposteriori =  0
% 100.80/101.23  ordereqreflfact =   0
% 100.80/101.23  
% 100.80/101.23  litselect =         none
% 100.80/101.23  
% 100.80/101.23  maxweight =         15
% 100.80/101.23  maxdepth =          30000
% 100.80/101.23  maxlength =         115
% 100.80/101.23  maxnrvars =         195
% 100.80/101.23  excuselevel =       1
% 100.80/101.23  increasemaxweight = 1
% 100.80/101.23  
% 100.80/101.23  maxselected =       10000000
% 100.80/101.23  maxnrclauses =      10000000
% 100.80/101.23  
% 100.80/101.23  showgenerated =    0
% 100.80/101.23  showkept =         0
% 100.80/101.23  showselected =     0
% 100.80/101.23  showdeleted =      0
% 100.80/101.23  showresimp =       1
% 100.80/101.23  showstatus =       2000
% 100.80/101.23  
% 100.80/101.23  prologoutput =     0
% 100.80/101.23  nrgoals =          5000000
% 100.80/101.23  totalproof =       1
% 100.80/101.23  
% 100.80/101.23  Symbols occurring in the translation:
% 100.80/101.23  
% 100.80/101.23  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 100.80/101.23  .  [1, 2]      (w:1, o:22, a:1, s:1, b:0), 
% 100.80/101.23  !  [4, 1]      (w:0, o:17, a:1, s:1, b:0), 
% 100.80/101.23  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 100.80/101.23  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 100.80/101.23  distinct_points  [36, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 100.80/101.23  distinct_lines  [37, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 100.80/101.23  convergent_lines  [38, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 100.80/101.23  line_connecting  [41, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 100.80/101.23  apart_point_and_line  [42, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 100.80/101.23  intersection_point  [43, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 100.80/101.23  parallel_through_point  [46, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 100.80/101.23  unorthogonal_lines  [49, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 100.80/101.23  orthogonal_through_point  [52, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 100.80/101.23  alpha1  [53, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 100.80/101.23  skol1  [54, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 100.80/101.23  skol2  [55, 0]      (w:1, o:16, a:1, s:1, b:0).
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Starting Search:
% 100.80/101.23  
% 100.80/101.23  *** allocated 15000 integers for clauses
% 100.80/101.23  *** allocated 22500 integers for clauses
% 100.80/101.23  *** allocated 33750 integers for clauses
% 100.80/101.23  *** allocated 15000 integers for termspace/termends
% 100.80/101.23  *** allocated 50625 integers for clauses
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  *** allocated 22500 integers for termspace/termends
% 100.80/101.23  *** allocated 75937 integers for clauses
% 100.80/101.23  *** allocated 33750 integers for termspace/termends
% 100.80/101.23  *** allocated 113905 integers for clauses
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  Failed to find proof!
% 100.80/101.23  maxweight =   15
% 100.80/101.23  maxnrclauses = 10000000
% 100.80/101.23  Generated: 1577221
% 100.80/101.23  Kept: 1915
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  The strategy used was not complete!
% 100.80/101.23  
% 100.80/101.23  Increased maxweight to 16
% 100.80/101.23  
% 100.80/101.23  Starting Search:
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Intermediate Status:
% 100.80/101.23  Generated:    16625
% 100.80/101.23  Kept:         2008
% 100.80/101.23  Inuse:        207
% 100.80/101.23  Deleted:      0
% 100.80/101.23  Deletedinuse: 0
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  *** allocated 50625 integers for termspace/termends
% 100.80/101.23  *** allocated 170857 integers for clauses
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  *** allocated 75937 integers for termspace/termends
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  Failed to find proof!
% 100.80/101.23  maxweight =   16
% 100.80/101.23  maxnrclauses = 10000000
% 100.80/101.23  Generated: 4885100
% 100.80/101.23  Kept: 3388
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  The strategy used was not complete!
% 100.80/101.23  
% 100.80/101.23  Increased maxweight to 17
% 100.80/101.23  
% 100.80/101.23  Starting Search:
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Intermediate Status:
% 100.80/101.23  Generated:    13805
% 100.80/101.23  Kept:         2016
% 100.80/101.23  Inuse:        169
% 100.80/101.23  Deleted:      0
% 100.80/101.23  Deletedinuse: 0
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Intermediate Status:
% 100.80/101.23  Generated:    40532
% 100.80/101.23  Kept:         4073
% 100.80/101.23  Inuse:        371
% 100.80/101.23  Deleted:      1
% 100.80/101.23  Deletedinuse: 0
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  *** allocated 256285 integers for clauses
% 100.80/101.23  *** allocated 113905 integers for termspace/termends
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Intermediate Status:
% 100.80/101.23  Generated:    7002702
% 100.80/101.23  Kept:         6073
% 100.80/101.23  Inuse:        3788
% 100.80/101.23  Deleted:      59
% 100.80/101.23  Deletedinuse: 4
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  *** allocated 384427 integers for clauses
% 100.80/101.23  *** allocated 170857 integers for termspace/termends
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Intermediate Status:
% 100.80/101.23  Generated:    14440928
% 100.80/101.23  Kept:         8419
% 100.80/101.23  Inuse:        6289
% 100.80/101.23  Deleted:      196
% 100.80/101.23  Deletedinuse: 5
% 100.80/101.23  
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  *** allocated 576640 integers for clauses
% 100.80/101.23  Resimplifying inuse:
% 100.80/101.23  Done
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Bliksems!, er is een bewijs:
% 100.80/101.23  % SZS status Theorem
% 100.80/101.23  % SZS output start Refutation
% 100.80/101.23  
% 100.80/101.23  (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 100.80/101.23  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 100.80/101.23    , ! distinct_lines( X, Y ) }.
% 100.80/101.23  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 100.80/101.23    Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23  (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 100.80/101.23    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 100.80/101.23    , intersection_point( X, Y ) ), ! apart_point_and_line( Z, Y ) }.
% 100.80/101.23  (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 100.80/101.23    ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 100.80/101.23    X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), distinct_lines( X
% 100.80/101.23    , Y ) }.
% 100.80/101.23  (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines( 
% 100.80/101.23    X, Y ) }.
% 100.80/101.23  (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 100.80/101.23  (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 100.80/101.23     }.
% 100.80/101.23  (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 100.80/101.23  (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! alpha1( X, Y )
% 100.80/101.23     }.
% 100.80/101.23  (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 100.80/101.23    ( Y, X ), Y ) }.
% 100.80/101.23  (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 100.80/101.23    orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23  (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 100.80/101.23    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 100.80/101.23    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23  (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2, 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ) ) }.
% 100.80/101.23  (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 100.80/101.23    ( X, Y ) }.
% 100.80/101.23  (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23  (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), ! 
% 100.80/101.23    convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 100.80/101.23  (45) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), ! 
% 100.80/101.23    convergent_lines( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23  (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  (99) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  (165) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), ! 
% 100.80/101.23    convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z )
% 100.80/101.23     ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  (166) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), ! 
% 100.80/101.23    convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T )
% 100.80/101.23     ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  (173) {G2,W8,D3,L2,V2,M1} F(166);r(0) { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23  (174) {G2,W8,D3,L2,V2,M1} F(165);r(0) { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23  (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 100.80/101.23    apart_point_and_line( Z, T ) }.
% 100.80/101.23  (241) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y ), 
% 100.80/101.23    convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  (249) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ), 
% 100.80/101.23    convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 100.80/101.23    unorthogonal_lines( Y, Z ) }.
% 100.80/101.23  (265) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X, skol2 ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( orthogonal_through_point( 
% 100.80/101.23    skol2, skol1 ), skol1 ), X ) }.
% 100.80/101.23  (293) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ), 
% 100.80/101.23    apart_point_and_line( T, orthogonal_through_point( Y, Z ) ), 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  (294) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 100.80/101.23    unorthogonal_lines( Z, X ) }.
% 100.80/101.23  (2023) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 100.80/101.23    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23  (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  (3187) {G4,W8,D3,L2,V3,M1} R(241,23);r(99) { convergent_lines( Z, X ), ! 
% 100.80/101.23    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  (3191) {G5,W16,D3,L4,V4,M1} R(3187,249) { convergent_lines( X, Y ), ! 
% 100.80/101.23    convergent_lines( Z, orthogonal_through_point( Y, T ) ), convergent_lines
% 100.80/101.23    ( Z, X ), ! unorthogonal_lines( Z, orthogonal_through_point( Y, T ) ) }.
% 100.80/101.23  (3192) {G6,W10,D3,L2,V2,M1} F(3191);r(2) { ! convergent_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  (3193) {G7,W5,D3,L1,V2,M1} S(3192);r(46) { ! unorthogonal_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  (4903) {G2,W17,D3,L3,V4,M2} R(293,23) { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.23    apart_point_and_line( T, orthogonal_through_point( X, Z ) ), 
% 100.80/101.23    apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  (4904) {G8,W17,D4,L3,V4,M2} R(294,3193) { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.23    apart_point_and_line( T, X ), apart_point_and_line( T, 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 100.80/101.23  (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.23    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.23  (6026) {G5,W14,D3,L2,V4,M2} R(5820,2025) { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), ! 
% 100.80/101.23    distinct_lines( orthogonal_through_point( X, Y ), 
% 100.80/101.23    orthogonal_through_point( X, Z ) ) }.
% 100.80/101.23  (6029) {G4,W16,D5,L2,V3,M1} R(5820,174) { ! convergent_lines( Y, 
% 100.80/101.23    orthogonal_through_point( X, Z ) ), ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, intersection_point( Y, 
% 100.80/101.23    orthogonal_through_point( X, Z ) ) ), orthogonal_through_point( X, Z ) )
% 100.80/101.23     }.
% 100.80/101.23  (6122) {G6,W14,D3,L2,V4,M1} R(6026,13) { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ), 
% 100.80/101.23    distinct_lines( orthogonal_through_point( X, Y ), 
% 100.80/101.23    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.23  (6167) {G7,W14,D3,L2,V4,M1} R(6122,34) { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.23    distinct_lines( orthogonal_through_point( X, Z ), 
% 100.80/101.23    orthogonal_through_point( T, Y ) ) }.
% 100.80/101.23  (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), orthogonal_through_point( Y, 
% 100.80/101.23    intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), ! 
% 100.80/101.23    convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.23  (6725) {G9,W11,D5,L1,V2,M1} R(6706,46) { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.23    intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.23  (6726) {G9,W16,D5,L2,V3,M2} R(6706,43) { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.23    intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.23  (6852) {G10,W15,D6,L1,V0,M1} R(6725,265) { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.23    intersection_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ) ) ), skol2 ) }.
% 100.80/101.23  (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.23    apart_point_and_line( Z, X ) }.
% 100.80/101.23  (7325) {G10,W12,D4,L2,V4,M2} R(7277,2025) { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( T, Z ), X ), ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.23  (7329) {G10,W12,D4,L2,V3,M1} R(7277,173) { ! convergent_lines( X, Z ), ! 
% 100.80/101.23    distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Y
% 100.80/101.23     ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.23  (9130) {G11,W12,D4,L2,V4,M1} R(7325,13) { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ), 
% 100.80/101.23    distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  (9294) {G12,W12,D4,L2,V3,M2} R(7329,9130) { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( X, Z ), 
% 100.80/101.23    intersection_point( X, Y ) ), X ), ! convergent_lines( X, Y ) }.
% 100.80/101.23  (9544) {G13,W12,D4,L2,V3,M2} R(9294,43) { ! convergent_lines( Z, X ), ! 
% 100.80/101.23    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 100.80/101.23    Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.23  (9775) {G14,W15,D4,L3,V4,M3} R(9544,45) { convergent_lines( Z, 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( Y, T ), 
% 100.80/101.23    intersection_point( Y, X ) ) ), ! convergent_lines( Z, Y ), ! 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  (9792) {G15,W12,D4,L2,V3,M2} F(9775) { ! convergent_lines( X, Y ), 
% 100.80/101.23    convergent_lines( X, orthogonal_through_point( orthogonal_through_point( 
% 100.80/101.23    Y, Z ), intersection_point( Y, X ) ) ) }.
% 100.80/101.23  (9799) {G16,W7,D4,L1,V3,M1} R(9792,6726);f { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.23  (9996) {G17,W0,D0,L0,V0,M0} R(9799,6852) {  }.
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  % SZS output end Refutation
% 100.80/101.23  found a proof!
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Unprocessed initial clauses:
% 100.80/101.23  
% 100.80/101.23  (9998) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 100.80/101.23  (9999) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 100.80/101.23  (10000) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 100.80/101.23  (10001) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( 
% 100.80/101.23    X, Z ), distinct_points( Y, Z ) }.
% 100.80/101.23  (10002) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X
% 100.80/101.23    , Z ), distinct_lines( Y, Z ) }.
% 100.80/101.23  (10003) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 100.80/101.23    ( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23  (10004) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 100.80/101.23     ) }.
% 100.80/101.23  (10005) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 100.80/101.23     ) }.
% 100.80/101.23  (10006) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 100.80/101.23    Y ) ) }.
% 100.80/101.23  (10007) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 100.80/101.23    Y ) ) }.
% 100.80/101.23  (10008) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 100.80/101.23    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 100.80/101.23    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 100.80/101.23  (10009) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 100.80/101.23    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 100.80/101.23  (10010) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 100.80/101.23    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 100.80/101.23  (10011) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), distinct_lines( 
% 100.80/101.23    X, Y ) }.
% 100.80/101.23  (10012) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( 
% 100.80/101.23    Y, X ), Y ) }.
% 100.80/101.23  (10013) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 100.80/101.23    parallel_through_point( Y, X ) ) }.
% 100.80/101.23  (10014) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 100.80/101.23    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  (10015) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 100.80/101.23    ( X, Y ) }.
% 100.80/101.23  (10016) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23  (10017) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 100.80/101.23     }.
% 100.80/101.23  (10018) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y )
% 100.80/101.23     }.
% 100.80/101.23  (10019) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 100.80/101.23     }.
% 100.80/101.23  (10020) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 100.80/101.23  (10021) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 100.80/101.23    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  (10022) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 100.80/101.23    orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23  (10023) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 100.80/101.23    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 100.80/101.23    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 100.80/101.23  (10024) {G0,W7,D4,L1,V0,M1}  { convergent_lines( skol2, 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ) ) }.
% 100.80/101.23  
% 100.80/101.23  
% 100.80/101.23  Total Proof:
% 100.80/101.23  
% 100.80/101.23  subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23  parent0: (9998) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 100.80/101.23  parent0: (9999) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23  parent0: (10000) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 100.80/101.23    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 100.80/101.23  parent0: (10002) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 100.80/101.23    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 2
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23  parent0: (10003) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 100.80/101.23    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 2
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23    ( Z, X ) }.
% 100.80/101.23  parent0: (10006) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 100.80/101.23    Y ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 2
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23    ( Z, Y ) }.
% 100.80/101.23  parent0: (10007) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 100.80/101.23    Y ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 2
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 100.80/101.23    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  parent0: (10009) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 100.80/101.23    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 2
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 100.80/101.23    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  parent0: (10010) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 100.80/101.23    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 2
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_lines( X, Y ) }.
% 100.80/101.23  parent0: (10011) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  parent0: (10015) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 100.80/101.23  parent0: (10016) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 3
% 100.80/101.23     3 ==> 2
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 100.80/101.23     }.
% 100.80/101.23  parent0: (10017) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 100.80/101.23     }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 3
% 100.80/101.23     3 ==> 2
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 100.80/101.23    alpha1( X, Y ) }.
% 100.80/101.23  parent0: (10018) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines
% 100.80/101.23    ( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! 
% 100.80/101.23    alpha1( X, Y ) }.
% 100.80/101.23  parent0: (10019) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 100.80/101.23    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  parent0: (10021) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 100.80/101.23    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 100.80/101.23    orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23  parent0: (10022) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 100.80/101.23    orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 100.80/101.23    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 100.80/101.23    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23  parent0: (10023) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 100.80/101.23    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 100.80/101.23    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23     T := T
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 2
% 100.80/101.23     3 ==> 4
% 100.80/101.23     4 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2, 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ) ) }.
% 100.80/101.23  parent0: (10024) {G0,W7,D4,L1,V0,M1}  { convergent_lines( skol2, 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10157) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 100.80/101.23    distinct_lines( X, Y ) }.
% 100.80/101.23  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 100.80/101.23  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 100.80/101.23    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 100.80/101.23    distinct_lines( X, Y ) }.
% 100.80/101.23  parent0: (10157) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 100.80/101.23    distinct_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10159) {G1,W5,D3,L1,V2,M1}  { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 100.80/101.23    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := orthogonal_through_point( X, Y )
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23  parent0: (10159) {G1,W5,D3,L1,V2,M1}  { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10160) {G1,W8,D3,L2,V3,M2}  { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 100.80/101.23  parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23  parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := orthogonal_through_point( X, Y )
% 100.80/101.23     Y := X
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  parent0: (10160) {G1,W8,D3,L2,V3,M2}  { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10161) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  parent0: (10161) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10163) {G1,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 100.80/101.23  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.23     convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 100.80/101.23  parent0: (10163) {G1,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 2
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10167) {G1,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( Z, Y ), ! convergent_lines( Z, X ) }.
% 100.80/101.23  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := X
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (45) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.23     convergent_lines( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23  parent0: (10167) {G1,W9,D2,L3,V3,M3}  { convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( Z, Y ), ! convergent_lines( Z, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 2
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10169) {G2,W5,D3,L1,V2,M1}  { convergent_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := orthogonal_through_point( X, Y )
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  parent0: (10169) {G2,W5,D3,L1,V2,M1}  { convergent_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10170) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 100.80/101.23  parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( X, Y ) }.
% 100.80/101.23  parent1[0]: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (99) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  parent0: (10170) {G2,W8,D3,L2,V3,M2}  { convergent_lines( Y, X ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10172) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23    , ! apart_point_and_line( T, Y ) }.
% 100.80/101.23  parent0[2]: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23    ( Z, Y ) }.
% 100.80/101.23  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 100.80/101.23    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := T
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (165) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), 
% 100.80/101.23    ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z
% 100.80/101.23     ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  parent0: (10172) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23    , ! apart_point_and_line( T, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := T
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23     T := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 2
% 100.80/101.23     2 ==> 0
% 100.80/101.23     3 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10174) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23    , ! apart_point_and_line( T, X ) }.
% 100.80/101.23  parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23    ( Z, X ) }.
% 100.80/101.23  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 100.80/101.23    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := T
% 100.80/101.23     Y := X
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (166) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), 
% 100.80/101.23    ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T
% 100.80/101.23     ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  parent0: (10174) {G1,W14,D3,L4,V4,M4}  { ! convergent_lines( X, Y ), 
% 100.80/101.23    distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23    , ! apart_point_and_line( T, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := T
% 100.80/101.23     Z := Y
% 100.80/101.23     T := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 2
% 100.80/101.23     2 ==> 0
% 100.80/101.23     3 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  factor: (10176) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point
% 100.80/101.23    ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23  parent0[0, 2]: (166) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y )
% 100.80/101.23    , ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, 
% 100.80/101.23    T ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := intersection_point( X, Y )
% 100.80/101.23     Y := intersection_point( X, Y )
% 100.80/101.23     Z := X
% 100.80/101.23     T := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10177) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23  parent1[0]: (10176) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 100.80/101.23    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 100.80/101.23    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 100.80/101.23    Y ), X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := intersection_point( X, Y )
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (173) {G2,W8,D3,L2,V2,M1} F(166);r(0) { ! convergent_lines( X
% 100.80/101.23    , Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23  parent0: (10177) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  factor: (10178) {G1,W15,D3,L3,V2,M3}  { distinct_points( intersection_point
% 100.80/101.23    ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23  parent0[0, 2]: (165) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y )
% 100.80/101.23    , ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, 
% 100.80/101.23    Z ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := intersection_point( X, Y )
% 100.80/101.23     Y := intersection_point( X, Y )
% 100.80/101.23     Z := Y
% 100.80/101.23     T := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10179) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23  parent1[0]: (10178) {G1,W15,D3,L3,V2,M3}  { distinct_points( 
% 100.80/101.23    intersection_point( X, Y ), intersection_point( X, Y ) ), ! 
% 100.80/101.23    convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X, 
% 100.80/101.23    Y ), Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := intersection_point( X, Y )
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (174) {G2,W8,D3,L2,V2,M1} F(165);r(0) { ! convergent_lines( X
% 100.80/101.23    , Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23  parent0: (10179) {G1,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10180) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 100.80/101.23    orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 100.80/101.23    orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 100.80/101.23    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := orthogonal_through_point( Y, X )
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  parent0: (10180) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 100.80/101.23    orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10181) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 100.80/101.23    apart_point_and_line( Z, T ) }.
% 100.80/101.23  parent0[1]: (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 100.80/101.23    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := T
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 100.80/101.23    apart_point_and_line( Z, T ) }.
% 100.80/101.23  parent0: (10181) {G1,W11,D3,L3,V4,M3}  { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 100.80/101.23    apart_point_and_line( Z, T ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23     T := T
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 2
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10184) {G1,W12,D2,L4,V3,M4}  { unorthogonal_lines( X, Y ), ! 
% 100.80/101.23    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 100.80/101.23    ( Z, Y ) }.
% 100.80/101.23  parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! 
% 100.80/101.23    alpha1( X, Y ) }.
% 100.80/101.23  parent1[3]: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (241) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 100.80/101.23     ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  parent0: (10184) {G1,W12,D2,L4,V3,M4}  { unorthogonal_lines( X, Y ), ! 
% 100.80/101.23    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 100.80/101.23    ( Z, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 2
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 3
% 100.80/101.23     3 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10186) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 100.80/101.23    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 100.80/101.23    unorthogonal_lines( Z, Y ) }.
% 100.80/101.23  parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 100.80/101.23    ( X, Y ) }.
% 100.80/101.23  parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 100.80/101.23     }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (249) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 100.80/101.23     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 100.80/101.23    unorthogonal_lines( Y, Z ) }.
% 100.80/101.23  parent0: (10186) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 100.80/101.23    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 100.80/101.23    unorthogonal_lines( Z, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 0
% 100.80/101.23     2 ==> 2
% 100.80/101.23     3 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10187) {G1,W10,D4,L2,V1,M2}  { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ), X ), convergent_lines( X, skol2 ) }.
% 100.80/101.23  parent0[1]: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), ! 
% 100.80/101.23    convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 100.80/101.23  parent1[0]: (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2, 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := skol2
% 100.80/101.23     Z := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 100.80/101.23    , skol1 )
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (265) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X, 
% 100.80/101.23    skol2 ), convergent_lines( orthogonal_through_point( 
% 100.80/101.23    orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 100.80/101.23  parent0: (10187) {G1,W10,D4,L2,V1,M2}  { convergent_lines( 
% 100.80/101.23    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23     ), X ), convergent_lines( X, skol2 ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 1
% 100.80/101.23     1 ==> 0
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10188) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( Z, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 100.80/101.23    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 100.80/101.23    unorthogonal_lines( Z, X ) }.
% 100.80/101.23  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 100.80/101.23    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  parent1[3]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 100.80/101.23    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 100.80/101.23    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := orthogonal_through_point( X, Y )
% 100.80/101.23     Z := T
% 100.80/101.23     T := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (293) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ), 
% 100.80/101.23    apart_point_and_line( T, orthogonal_through_point( Y, Z ) ), 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  parent0: (10188) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( Z, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 100.80/101.23    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 100.80/101.23    unorthogonal_lines( Z, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := X
% 100.80/101.23     T := T
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 2
% 100.80/101.23     3 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10192) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 100.80/101.23    unorthogonal_lines( Z, X ) }.
% 100.80/101.23  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 100.80/101.23    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  parent1[4]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 100.80/101.23    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 100.80/101.23    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := orthogonal_through_point( X, Y )
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := T
% 100.80/101.23     T := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (294) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 100.80/101.23    unorthogonal_lines( Z, X ) }.
% 100.80/101.23  parent0: (10192) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 100.80/101.23    unorthogonal_lines( Z, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23     T := T
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 2
% 100.80/101.23     3 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10194) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 100.80/101.23    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23  parent0[2]: (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), ! 
% 100.80/101.23    apart_point_and_line( Z, T ) }.
% 100.80/101.23  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 100.80/101.23    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23     T := T
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := U
% 100.80/101.23     Z := T
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (2023) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 100.80/101.23    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23  parent0: (10194) {G1,W14,D3,L4,V5,M4}  { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 100.80/101.23    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23     T := T
% 100.80/101.23     U := U
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 2
% 100.80/101.23     3 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  factor: (10200) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  parent0[0, 2]: (2023) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), 
% 100.80/101.23    distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23     T := orthogonal_through_point( Y, Z )
% 100.80/101.23     U := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10206) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 100.80/101.23    distinct_lines( X, Y ) }.
% 100.80/101.23  parent1[0]: (10200) {G3,W13,D3,L3,V3,M3}  { distinct_lines( X, 
% 100.80/101.23    orthogonal_through_point( Y, Z ) ), distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := orthogonal_through_point( Y, Z )
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  factor: (10208) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 100.80/101.23  parent0[0, 1]: (10206) {G2,W13,D3,L3,V3,M3}  { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := X
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23  parent0: (10208) {G2,W8,D3,L2,V3,M2}  { distinct_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10210) {G1,W13,D3,L3,V3,M3}  { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), ! 
% 100.80/101.23    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 100.80/101.23    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23  parent1[2]: (241) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 100.80/101.23     ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), ! 
% 100.80/101.23    unorthogonal_lines( X, Y ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := orthogonal_through_point( X, Y )
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10212) {G2,W11,D3,L3,V3,M3}  { convergent_lines( Z, X ), ! 
% 100.80/101.23    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ), 
% 100.80/101.23    convergent_lines( Z, X ) }.
% 100.80/101.23  parent0[0]: (10210) {G1,W13,D3,L3,V3,M3}  { ! convergent_lines( 
% 100.80/101.23    orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), ! 
% 100.80/101.23    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  parent1[1]: (99) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ), 
% 100.80/101.23    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := Z
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  factor: (10213) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 100.80/101.23  parent0[0, 2]: (10212) {G2,W11,D3,L3,V3,M3}  { convergent_lines( Z, X ), ! 
% 100.80/101.23    unorthogonal_lines( orthogonal_through_point( X, Y ), Z ), 
% 100.80/101.23    convergent_lines( Z, X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (3187) {G4,W8,D3,L2,V3,M1} R(241,23);r(99) { convergent_lines
% 100.80/101.23    ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  parent0: (10213) {G2,W8,D3,L2,V3,M2}  { convergent_lines( X, Y ), ! 
% 100.80/101.23    unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Z
% 100.80/101.23     Y := X
% 100.80/101.23     Z := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10214) {G2,W16,D3,L4,V4,M4}  { convergent_lines( X, Y ), ! 
% 100.80/101.23    convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 100.80/101.23    ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.23  parent0[1]: (3187) {G4,W8,D3,L2,V3,M1} R(241,23);r(99) { convergent_lines( 
% 100.80/101.23    Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23  parent1[3]: (249) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 100.80/101.23     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 100.80/101.23    unorthogonal_lines( Y, Z ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := Y
% 100.80/101.23     Y := Z
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := T
% 100.80/101.23     Y := orthogonal_through_point( Y, Z )
% 100.80/101.23     Z := X
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (3191) {G5,W16,D3,L4,V4,M1} R(3187,249) { convergent_lines( X
% 100.80/101.23    , Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ), 
% 100.80/101.23    convergent_lines( Z, X ), ! unorthogonal_lines( Z, 
% 100.80/101.23    orthogonal_through_point( Y, T ) ) }.
% 100.80/101.23  parent0: (10214) {G2,W16,D3,L4,V4,M4}  { convergent_lines( X, Y ), ! 
% 100.80/101.23    convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 100.80/101.23    ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23     Z := T
% 100.80/101.23     T := Z
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23     2 ==> 2
% 100.80/101.23     3 ==> 3
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  factor: (10216) {G5,W13,D3,L3,V2,M3}  { convergent_lines( X, X ), ! 
% 100.80/101.23    convergent_lines( X, orthogonal_through_point( X, Y ) ), ! 
% 100.80/101.23    unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  parent0[0, 2]: (3191) {G5,W16,D3,L4,V4,M1} R(3187,249) { convergent_lines( 
% 100.80/101.23    X, Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ), 
% 100.80/101.23    convergent_lines( Z, X ), ! unorthogonal_lines( Z, 
% 100.80/101.23    orthogonal_through_point( Y, T ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := X
% 100.80/101.23     Z := X
% 100.80/101.23     T := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10217) {G1,W10,D3,L2,V2,M2}  { ! convergent_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23  parent1[0]: (10216) {G5,W13,D3,L3,V2,M3}  { convergent_lines( X, X ), ! 
% 100.80/101.23    convergent_lines( X, orthogonal_through_point( X, Y ) ), ! 
% 100.80/101.23    unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23  end
% 100.80/101.23  substitution1:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  subsumption: (3192) {G6,W10,D3,L2,V2,M1} F(3191);r(2) { ! convergent_lines
% 100.80/101.23    ( X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  parent0: (10217) {G1,W10,D3,L2,V2,M2}  { ! convergent_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  substitution0:
% 100.80/101.23     X := X
% 100.80/101.23     Y := Y
% 100.80/101.23  end
% 100.80/101.23  permutation0:
% 100.80/101.23     0 ==> 0
% 100.80/101.23     1 ==> 1
% 100.80/101.23  end
% 100.80/101.23  
% 100.80/101.23  resolution: (10218) {G3,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( X, 
% 100.80/101.23    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23  parent0[0]: (3192) {G6,W10,D3,L2,V2,M1} F(3191);r(2) { ! convergent_lines( 
% 100.80/101.23    X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X, 
% 100.80/101.24    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  parent1[0]: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (3193) {G7,W5,D3,L1,V2,M1} S(3192);r(46) { ! 
% 100.80/101.24    unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  parent0: (10218) {G3,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( X, 
% 100.80/101.24    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10219) {G1,W17,D3,L3,V4,M3}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 100.80/101.24    orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.24  parent1[3]: (293) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X, 
% 100.80/101.24    orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( Y, Z ) ), 
% 100.80/101.24    unorthogonal_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := X
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( X, Y )
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Z
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (4903) {G2,W17,D3,L3,V4,M2} R(293,23) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  parent0: (10219) {G1,W17,D3,L3,V4,M3}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Y ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 2
% 100.80/101.24     2 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10221) {G2,W17,D4,L3,V4,M3}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 100.80/101.24  parent0[0]: (3193) {G7,W5,D3,L1,V2,M1} S(3192);r(46) { ! unorthogonal_lines
% 100.80/101.24    ( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  parent1[3]: (294) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 100.80/101.24    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 100.80/101.24    unorthogonal_lines( Z, X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( X, Y )
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := X
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (4904) {G8,W17,D4,L3,V4,M2} R(294,3193) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.24    apart_point_and_line( T, X ), apart_point_and_line( T, 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 100.80/101.24  parent0: (10221) {G2,W17,D4,L3,V4,M3}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 2
% 100.80/101.24     2 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10223) {G1,W12,D3,L2,V3,M2}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ), 
% 100.80/101.24    apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 100.80/101.24    orthogonal_through_point( Y, X ) ) }.
% 100.80/101.24  parent1[2]: (4903) {G2,W17,D3,L3,V4,M2} R(293,23) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Z
% 100.80/101.24     T := X
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24  parent0: (10223) {G1,W12,D3,L2,V3,M2}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ), 
% 100.80/101.24    apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10225) {G4,W14,D3,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 100.80/101.24    distinct_lines( orthogonal_through_point( Z, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  parent0[1]: (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.24  parent1[1]: (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := orthogonal_through_point( Z, T )
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := T
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6026) {G5,W14,D3,L2,V4,M2} R(5820,2025) { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), ! 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Y ), 
% 100.80/101.24    orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24  parent0: (10225) {G4,W14,D3,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 100.80/101.24    distinct_lines( orthogonal_through_point( Z, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := T
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := X
% 100.80/101.24     T := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10226) {G3,W16,D5,L2,V3,M2}  { ! convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( Y, Z ) ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Y, intersection_point( X, 
% 100.80/101.24    orthogonal_through_point( Y, Z ) ) ), orthogonal_through_point( Y, Z ) )
% 100.80/101.24     }.
% 100.80/101.24  parent0[1]: (174) {G2,W8,D3,L2,V2,M1} F(165);r(0) { ! convergent_lines( X, 
% 100.80/101.24    Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.24  parent1[1]: (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := orthogonal_through_point( Y, Z )
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := intersection_point( X, orthogonal_through_point( Y, Z ) )
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6029) {G4,W16,D5,L2,V3,M1} R(5820,174) { ! convergent_lines( 
% 100.80/101.24    Y, orthogonal_through_point( X, Z ) ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, intersection_point( Y, 
% 100.80/101.24    orthogonal_through_point( X, Z ) ) ), orthogonal_through_point( X, Z ) )
% 100.80/101.24     }.
% 100.80/101.24  parent0: (10226) {G3,W16,D5,L2,V3,M2}  { ! convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( Y, Z ) ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Y, intersection_point( X, 
% 100.80/101.24    orthogonal_through_point( Y, Z ) ) ), orthogonal_through_point( Y, Z ) )
% 100.80/101.24     }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10227) {G1,W14,D3,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( Z, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  parent0[1]: (6026) {G5,W14,D3,L2,V4,M2} R(5820,2025) { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), ! 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Y ), 
% 100.80/101.24    orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24  parent1[1]: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 100.80/101.24    distinct_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := T
% 100.80/101.24     T := X
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( Z, Y )
% 100.80/101.24     Y := orthogonal_through_point( Z, T )
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6122) {G6,W14,D3,L2,V4,M1} R(6026,13) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ), 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  parent0: (10227) {G1,W14,D3,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( Z, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10228) {G2,W14,D3,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( Z, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 100.80/101.24    distinct_lines( X, Y ) }.
% 100.80/101.24  parent1[1]: (6122) {G6,W14,D3,L2,V4,M1} R(6026,13) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ), 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := orthogonal_through_point( Z, T )
% 100.80/101.24     Y := orthogonal_through_point( X, Y )
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6167) {G7,W14,D3,L2,V4,M1} R(6122,34) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Z ), 
% 100.80/101.24    orthogonal_through_point( T, Y ) ) }.
% 100.80/101.24  parent0: (10228) {G2,W14,D3,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( Z, Y ), 
% 100.80/101.24    orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := T
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := X
% 100.80/101.24     T := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10229) {G5,W16,D5,L2,V3,M2}  { ! convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( Y, Z ) ), ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), orthogonal_through_point( Y, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ) }.
% 100.80/101.24  parent0[1]: (6029) {G4,W16,D5,L2,V3,M1} R(5820,174) { ! convergent_lines( Y
% 100.80/101.24    , orthogonal_through_point( X, Z ) ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, intersection_point( Y, 
% 100.80/101.24    orthogonal_through_point( X, Z ) ) ), orthogonal_through_point( X, Z ) )
% 100.80/101.24     }.
% 100.80/101.24  parent1[1]: (6167) {G7,W14,D3,L2,V4,M1} R(6122,34) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ), 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Z ), 
% 100.80/101.24    orthogonal_through_point( T, Y ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := intersection_point( X, orthogonal_through_point( Y, Z ) )
% 100.80/101.24     T := Y
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines
% 100.80/101.24    ( orthogonal_through_point( Y, Z ), orthogonal_through_point( Y, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), ! 
% 100.80/101.24    convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24  parent0: (10229) {G5,W16,D5,L2,V3,M2}  { ! convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( Y, Z ) ), ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), orthogonal_through_point( Y, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10230) {G3,W11,D5,L1,V2,M1}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24  parent0[1]: (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), orthogonal_through_point( Y, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), ! 
% 100.80/101.24    convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24  parent1[0]: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6725) {G9,W11,D5,L1,V2,M1} R(6706,46) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24  parent0: (10230) {G3,W11,D5,L1,V2,M1}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10232) {G2,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24  parent0[1]: (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), orthogonal_through_point( Y, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), ! 
% 100.80/101.24    convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24  parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.24    convergent_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := orthogonal_through_point( X, Y )
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6726) {G9,W16,D5,L2,V3,M2} R(6706,43) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24  parent0: (10232) {G2,W16,D5,L2,V3,M2}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10233) {G4,W15,D6,L1,V0,M1}  { convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    intersection_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24     ) ) ), skol2 ) }.
% 100.80/101.24  parent0[0]: (6725) {G9,W11,D5,L1,V2,M1} R(6706,46) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24  parent1[1]: (265) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X, 
% 100.80/101.24    skol2 ), convergent_lines( orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := orthogonal_through_point( skol2, skol1 )
% 100.80/101.24     Y := skol1
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 100.80/101.24    , intersection_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24     ) ) )
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (6852) {G10,W15,D6,L1,V0,M1} R(6725,265) { convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    intersection_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24     ) ) ), skol2 ) }.
% 100.80/101.24  parent0: (10233) {G4,W15,D6,L1,V0,M1}  { convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    intersection_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24     ) ) ), skol2 ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10235) {G1,W10,D4,L2,V3,M2}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ), 
% 100.80/101.24    apart_point_and_line( X, Y ) }.
% 100.80/101.24  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 100.80/101.24    orthogonal_through_point( Y, X ) ) }.
% 100.80/101.24  parent1[2]: (4904) {G8,W17,D4,L3,V4,M2} R(294,3193) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.24    apart_point_and_line( T, X ), apart_point_and_line( T, 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := orthogonal_through_point( Y, Z )
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := X
% 100.80/101.24     T := X
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.24    apart_point_and_line( Z, X ) }.
% 100.80/101.24  parent0: (10235) {G1,W10,D4,L2,V3,M2}  { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ), 
% 100.80/101.24    apart_point_and_line( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10237) {G5,W12,D4,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24  parent0[1]: (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.24  parent1[1]: (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.24    apart_point_and_line( Z, X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := T
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (7325) {G10,W12,D4,L2,V4,M2} R(7277,2025) { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( T, Z ), X ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24  parent0: (10237) {G5,W12,D4,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := T
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := X
% 100.80/101.24     T := Y
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10238) {G3,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.24    distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Z
% 100.80/101.24     ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24  parent0[1]: (173) {G2,W8,D3,L2,V2,M1} F(166);r(0) { ! convergent_lines( X, 
% 100.80/101.24    Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.24  parent1[1]: (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), 
% 100.80/101.24    apart_point_and_line( Z, X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := intersection_point( X, Y )
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (7329) {G10,W12,D4,L2,V3,M1} R(7277,173) { ! convergent_lines
% 100.80/101.24    ( X, Z ), ! distinct_lines( orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24  parent0: (10238) {G3,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.24    distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Z
% 100.80/101.24     ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24     1 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10239) {G1,W12,D4,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24  parent0[1]: (7325) {G10,W12,D4,L2,V4,M2} R(7277,2025) { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( T, Z ), X ), ! distinct_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24  parent1[1]: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), 
% 100.80/101.24    distinct_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Z
% 100.80/101.24     Y := T
% 100.80/101.24     Z := Y
% 100.80/101.24     T := X
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( orthogonal_through_point( Z, T ), Y )
% 100.80/101.24     Y := Z
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (9130) {G11,W12,D4,L2,V4,M1} R(7325,13) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ), 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24  parent0: (10239) {G1,W12,D4,L2,V4,M2}  { distinct_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10240) {G11,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 100.80/101.24    T ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24  parent0[1]: (7329) {G10,W12,D4,L2,V3,M1} R(7277,173) { ! convergent_lines( 
% 100.80/101.24    X, Z ), ! distinct_lines( orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24  parent1[1]: (9130) {G11,W12,D4,L2,V4,M1} R(7325,13) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ), 
% 100.80/101.24    distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( X, Z )
% 100.80/101.24     Y := intersection_point( X, Y )
% 100.80/101.24     Z := X
% 100.80/101.24     T := T
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (9294) {G12,W12,D4,L2,V3,M2} R(7329,9130) { ! convergent_lines
% 100.80/101.24    ( orthogonal_through_point( orthogonal_through_point( X, Z ), 
% 100.80/101.24    intersection_point( X, Y ) ), X ), ! convergent_lines( X, Y ) }.
% 100.80/101.24  parent0: (10240) {G11,W12,D4,L2,V3,M2}  { ! convergent_lines( X, Y ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 100.80/101.24    T ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := T
% 100.80/101.24     T := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10242) {G2,W12,D4,L2,V3,M2}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), 
% 100.80/101.24    intersection_point( X, Z ) ), X ), ! convergent_lines( Z, X ) }.
% 100.80/101.24  parent0[1]: (9294) {G12,W12,D4,L2,V3,M2} R(7329,9130) { ! convergent_lines
% 100.80/101.24    ( orthogonal_through_point( orthogonal_through_point( X, Z ), 
% 100.80/101.24    intersection_point( X, Y ) ), X ), ! convergent_lines( X, Y ) }.
% 100.80/101.24  parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 100.80/101.24    convergent_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Z
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (9544) {G13,W12,D4,L2,V3,M2} R(9294,43) { ! convergent_lines( 
% 100.80/101.24    Z, X ), ! convergent_lines( orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24  parent0: (10242) {G2,W12,D4,L2,V3,M2}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), 
% 100.80/101.24    intersection_point( X, Z ) ), X ), ! convergent_lines( Z, X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10246) {G3,W15,D4,L3,V4,M3}  { ! convergent_lines( X, Y ), 
% 100.80/101.24    convergent_lines( T, orthogonal_through_point( orthogonal_through_point( 
% 100.80/101.24    Y, Z ), intersection_point( Y, X ) ) ), ! convergent_lines( T, Y ) }.
% 100.80/101.24  parent0[1]: (9544) {G13,W12,D4,L2,V3,M2} R(9294,43) { ! convergent_lines( Z
% 100.80/101.24    , X ), ! convergent_lines( orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24  parent1[2]: (45) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), ! 
% 100.80/101.24    convergent_lines( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := Y
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := X
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( orthogonal_through_point( Y, Z ), 
% 100.80/101.24    intersection_point( Y, X ) )
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := T
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (9775) {G14,W15,D4,L3,V4,M3} R(9544,45) { convergent_lines( Z
% 100.80/101.24    , orthogonal_through_point( orthogonal_through_point( Y, T ), 
% 100.80/101.24    intersection_point( Y, X ) ) ), ! convergent_lines( Z, Y ), ! 
% 100.80/101.24    convergent_lines( X, Y ) }.
% 100.80/101.24  parent0: (10246) {G3,W15,D4,L3,V4,M3}  { ! convergent_lines( X, Y ), 
% 100.80/101.24    convergent_lines( T, orthogonal_through_point( orthogonal_through_point( 
% 100.80/101.24    Y, Z ), intersection_point( Y, X ) ) ), ! convergent_lines( T, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := T
% 100.80/101.24     T := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 2
% 100.80/101.24     1 ==> 0
% 100.80/101.24     2 ==> 1
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  factor: (10249) {G14,W12,D4,L2,V3,M2}  { convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Y, Z ), 
% 100.80/101.24    intersection_point( Y, X ) ) ), ! convergent_lines( X, Y ) }.
% 100.80/101.24  parent0[1, 2]: (9775) {G14,W15,D4,L3,V4,M3} R(9544,45) { convergent_lines( 
% 100.80/101.24    Z, orthogonal_through_point( orthogonal_through_point( Y, T ), 
% 100.80/101.24    intersection_point( Y, X ) ) ), ! convergent_lines( Z, Y ), ! 
% 100.80/101.24    convergent_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := X
% 100.80/101.24     T := Z
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (9792) {G15,W12,D4,L2,V3,M2} F(9775) { ! convergent_lines( X, 
% 100.80/101.24    Y ), convergent_lines( X, orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), intersection_point( Y, X ) ) ) }.
% 100.80/101.24  parent0: (10249) {G14,W12,D4,L2,V3,M2}  { convergent_lines( X, 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( Y, Z ), 
% 100.80/101.24    intersection_point( Y, X ) ) ), ! convergent_lines( X, Y ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 1
% 100.80/101.24     1 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10251) {G10,W14,D4,L2,V3,M2}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 100.80/101.24    Y ), Z ), X ) }.
% 100.80/101.24  parent0[1]: (6726) {G9,W16,D5,L2,V3,M2} R(6706,43) { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), Z ), ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( X, Y ), orthogonal_through_point( X, 
% 100.80/101.24    intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24  parent1[1]: (9792) {G15,W12,D4,L2,V3,M2} F(9775) { ! convergent_lines( X, Y
% 100.80/101.24     ), convergent_lines( X, orthogonal_through_point( 
% 100.80/101.24    orthogonal_through_point( Y, Z ), intersection_point( Y, X ) ) ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := orthogonal_through_point( X, Y )
% 100.80/101.24     Y := Z
% 100.80/101.24     Z := X
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24     X := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 100.80/101.24     Y := X
% 100.80/101.24     Z := Y
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  factor: (10252) {G10,W7,D4,L1,V3,M1}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24  parent0[0, 1]: (10251) {G10,W14,D4,L2,V3,M2}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 100.80/101.24    Y ), Z ), X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (9799) {G16,W7,D4,L1,V3,M1} R(9792,6726);f { ! 
% 100.80/101.24    convergent_lines( orthogonal_through_point( orthogonal_through_point( X, 
% 100.80/101.24    Y ), Z ), X ) }.
% 100.80/101.24  parent0: (10252) {G10,W7,D4,L1,V3,M1}  { ! convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := X
% 100.80/101.24     Y := Y
% 100.80/101.24     Z := Z
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24     0 ==> 0
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  resolution: (10253) {G11,W0,D0,L0,V0,M0}  {  }.
% 100.80/101.24  parent0[0]: (9799) {G16,W7,D4,L1,V3,M1} R(9792,6726);f { ! convergent_lines
% 100.80/101.24    ( orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X )
% 100.80/101.24     }.
% 100.80/101.24  parent1[0]: (6852) {G10,W15,D6,L1,V0,M1} R(6725,265) { convergent_lines( 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    intersection_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24     ) ) ), skol2 ) }.
% 100.80/101.24  substitution0:
% 100.80/101.24     X := skol2
% 100.80/101.24     Y := skol1
% 100.80/101.24     Z := intersection_point( orthogonal_through_point( skol2, skol1 ), 
% 100.80/101.24    orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24     ) )
% 100.80/101.24  end
% 100.80/101.24  substitution1:
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  subsumption: (9996) {G17,W0,D0,L0,V0,M0} R(9799,6852) {  }.
% 100.80/101.24  parent0: (10253) {G11,W0,D0,L0,V0,M0}  {  }.
% 100.80/101.24  substitution0:
% 100.80/101.24  end
% 100.80/101.24  permutation0:
% 100.80/101.24  end
% 100.80/101.24  
% 100.80/101.24  Proof check complete!
% 100.80/101.24  
% 100.80/101.24  Memory use:
% 100.80/101.24  
% 100.80/101.24  space for terms:        166328
% 100.80/101.24  space for clauses:      450138
% 100.80/101.24  
% 100.80/101.24  
% 100.80/101.24  clauses generated:      14625628
% 100.80/101.24  clauses kept:           9997
% 100.80/101.24  clauses selected:       6356
% 100.80/101.24  clauses deleted:        198
% 100.80/101.24  clauses inuse deleted:  6
% 100.80/101.24  
% 100.80/101.24  subsentry:          72246578
% 100.80/101.24  literals s-matched: 21522204
% 100.80/101.24  literals matched:   21520218
% 100.80/101.24  full subsumption:   14184190
% 100.80/101.24  
% 100.80/101.24  checksum:           -769214163
% 100.80/101.24  
% 100.80/101.24  
% 100.80/101.24  Bliksem ended
%------------------------------------------------------------------------------