TSTP Solution File: GEO210+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Sat Jul 16 02:52:47 EDT 2022

% Result   : Theorem 14.77s 15.20s
% Output   : Refutation 14.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : bliksem %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Sat Jun 18 05:14:57 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 14.77/15.20  *** allocated 10000 integers for termspace/termends
% 14.77/15.20  *** allocated 10000 integers for clauses
% 14.77/15.20  *** allocated 10000 integers for justifications
% 14.77/15.20  Bliksem 1.12
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  Automatic Strategy Selection
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  Clauses:
% 14.77/15.20  
% 14.77/15.20  { ! distinct_points( X, X ) }.
% 14.77/15.20  { ! distinct_lines( X, X ) }.
% 14.77/15.20  { ! convergent_lines( X, X ) }.
% 14.77/15.20  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 14.77/15.20     ) }.
% 14.77/15.20  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 14.77/15.20     }.
% 14.77/15.20  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 14.77/15.20    , Z ) }.
% 14.77/15.20  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 14.77/15.20    , Y ) ) }.
% 14.77/15.20  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 14.77/15.20    , Y ) ) }.
% 14.77/15.20  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 14.77/15.20    , Y ), X ) }.
% 14.77/15.20  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 14.77/15.20    , Y ), Y ) }.
% 14.77/15.20  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 14.77/15.20    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 14.77/15.20    apart_point_and_line( Y, T ) }.
% 14.77/15.20  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 14.77/15.20    apart_point_and_line( Z, Y ) }.
% 14.77/15.20  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 14.77/15.20    apart_point_and_line( X, Z ) }.
% 14.77/15.20  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 14.77/15.20    Z ) }.
% 14.77/15.20  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 14.77/15.20  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 14.77/15.20  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 14.77/15.20    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 14.77/15.20  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 14.77/15.20  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 14.77/15.20    , convergent_lines( Y, Z ) }.
% 14.77/15.20  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 14.77/15.20    , unorthogonal_lines( Y, Z ) }.
% 14.77/15.20  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 14.77/15.20  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 14.77/15.20  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 14.77/15.20     }.
% 14.77/15.20  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 14.77/15.20  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 14.77/15.20  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 14.77/15.20    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 14.77/15.20    unorthogonal_lines( Y, T ) }.
% 14.77/15.20  { ! apart_point_and_line( skol1, skol2 ) }.
% 14.77/15.20  { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.77/15.20  { distinct_lines( skol2, orthogonal_through_point( skol3, skol1 ) ) }.
% 14.77/15.20  
% 14.77/15.20  percentage equality = 0.000000, percentage horn = 0.586207
% 14.77/15.20  This a non-horn, non-equality problem
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  Options Used:
% 14.77/15.20  
% 14.77/15.20  useres =            1
% 14.77/15.20  useparamod =        0
% 14.77/15.20  useeqrefl =         0
% 14.77/15.20  useeqfact =         0
% 14.77/15.20  usefactor =         1
% 14.77/15.20  usesimpsplitting =  0
% 14.77/15.20  usesimpdemod =      0
% 14.77/15.20  usesimpres =        3
% 14.77/15.20  
% 14.77/15.20  resimpinuse      =  1000
% 14.77/15.20  resimpclauses =     20000
% 14.77/15.20  substype =          standard
% 14.77/15.20  backwardsubs =      1
% 14.77/15.20  selectoldest =      5
% 14.77/15.20  
% 14.77/15.20  litorderings [0] =  split
% 14.77/15.20  litorderings [1] =  liftord
% 14.77/15.20  
% 14.77/15.20  termordering =      none
% 14.77/15.20  
% 14.77/15.20  litapriori =        1
% 14.77/15.20  termapriori =       0
% 14.77/15.20  litaposteriori =    0
% 14.77/15.20  termaposteriori =   0
% 14.77/15.20  demodaposteriori =  0
% 14.77/15.20  ordereqreflfact =   0
% 14.77/15.20  
% 14.77/15.20  litselect =         none
% 14.77/15.20  
% 14.77/15.20  maxweight =         15
% 14.77/15.20  maxdepth =          30000
% 14.77/15.20  maxlength =         115
% 14.77/15.20  maxnrvars =         195
% 14.77/15.20  excuselevel =       1
% 14.77/15.20  increasemaxweight = 1
% 14.77/15.20  
% 14.77/15.20  maxselected =       10000000
% 14.77/15.20  maxnrclauses =      10000000
% 14.77/15.20  
% 14.77/15.20  showgenerated =    0
% 14.77/15.20  showkept =         0
% 14.77/15.20  showselected =     0
% 14.77/15.20  showdeleted =      0
% 14.77/15.20  showresimp =       1
% 14.77/15.20  showstatus =       2000
% 14.77/15.20  
% 14.77/15.20  prologoutput =     0
% 14.77/15.20  nrgoals =          5000000
% 14.77/15.20  totalproof =       1
% 14.77/15.20  
% 14.77/15.20  Symbols occurring in the translation:
% 14.77/15.20  
% 14.77/15.20  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 14.77/15.20  .  [1, 2]      (w:1, o:23, a:1, s:1, b:0), 
% 14.77/15.20  !  [4, 1]      (w:0, o:18, a:1, s:1, b:0), 
% 14.77/15.20  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 14.77/15.20  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 14.77/15.20  distinct_points  [36, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 14.77/15.20  distinct_lines  [37, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 14.77/15.20  convergent_lines  [38, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 14.77/15.20  line_connecting  [41, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 14.77/15.20  apart_point_and_line  [42, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 14.77/15.20  intersection_point  [43, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 14.77/15.20  parallel_through_point  [46, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 14.77/15.20  unorthogonal_lines  [49, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 14.77/15.20  orthogonal_through_point  [52, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 14.77/15.20  alpha1  [53, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 14.77/15.20  skol1  [54, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 14.77/15.20  skol2  [55, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 14.77/15.20  skol3  [56, 0]      (w:1, o:17, a:1, s:1, b:0).
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  Starting Search:
% 14.77/15.20  
% 14.77/15.20  *** allocated 15000 integers for clauses
% 14.77/15.20  *** allocated 22500 integers for clauses
% 14.77/15.20  *** allocated 33750 integers for clauses
% 14.77/15.20  *** allocated 15000 integers for termspace/termends
% 14.77/15.20  *** allocated 50625 integers for clauses
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 22500 integers for termspace/termends
% 14.77/15.20  *** allocated 75937 integers for clauses
% 14.77/15.20  *** allocated 33750 integers for termspace/termends
% 14.77/15.20  *** allocated 113905 integers for clauses
% 14.77/15.20  
% 14.77/15.20  Intermediate Status:
% 14.77/15.20  Generated:    14795
% 14.77/15.20  Kept:         2009
% 14.77/15.20  Inuse:        304
% 14.77/15.20  Deleted:      0
% 14.77/15.20  Deletedinuse: 0
% 14.77/15.20  
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 50625 integers for termspace/termends
% 14.77/15.20  *** allocated 170857 integers for clauses
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 75937 integers for termspace/termends
% 14.77/15.20  
% 14.77/15.20  Intermediate Status:
% 14.77/15.20  Generated:    63167
% 14.77/15.20  Kept:         4009
% 14.77/15.20  Inuse:        656
% 14.77/15.20  Deleted:      7
% 14.77/15.20  Deletedinuse: 0
% 14.77/15.20  
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 256285 integers for clauses
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 113905 integers for termspace/termends
% 14.77/15.20  
% 14.77/15.20  Intermediate Status:
% 14.77/15.20  Generated:    534872
% 14.77/15.20  Kept:         6114
% 14.77/15.20  Inuse:        1663
% 14.77/15.20  Deleted:      80
% 14.77/15.20  Deletedinuse: 13
% 14.77/15.20  
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 384427 integers for clauses
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 170857 integers for termspace/termends
% 14.77/15.20  
% 14.77/15.20  Intermediate Status:
% 14.77/15.20  Generated:    592732
% 14.77/15.20  Kept:         8119
% 14.77/15.20  Inuse:        1724
% 14.77/15.20  Deleted:      82
% 14.77/15.20  Deletedinuse: 13
% 14.77/15.20  
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  *** allocated 576640 integers for clauses
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  Intermediate Status:
% 14.77/15.20  Generated:    1001237
% 14.77/15.20  Kept:         10135
% 14.77/15.20  Inuse:        2214
% 14.77/15.20  Deleted:      122
% 14.77/15.20  Deletedinuse: 13
% 14.77/15.20  
% 14.77/15.20  Resimplifying inuse:
% 14.77/15.20  Done
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  Bliksems!, er is een bewijs:
% 14.77/15.20  % SZS status Theorem
% 14.77/15.20  % SZS output start Refutation
% 14.77/15.20  
% 14.77/15.20  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.77/15.20  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 14.77/15.20    , ! distinct_lines( X, Y ) }.
% 14.77/15.20  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 14.77/15.20    X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.77/15.20  (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 14.77/15.20    ( Y, X ), Y ) }.
% 14.77/15.20  (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 14.77/15.20    orthogonal_through_point( Y, X ) ) }.
% 14.77/15.20  (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 14.77/15.20    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 14.77/15.20    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.77/15.20  (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, skol2 ) }.
% 14.77/15.20  (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.77/15.20  (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2, 
% 14.77/15.20    orthogonal_through_point( skol3, skol1 ) ) }.
% 14.77/15.20  (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 14.77/15.20    ( X, Y ) }.
% 14.77/15.20  (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines( 
% 14.77/15.20    orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.77/15.20  (130) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 14.77/15.20    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 14.77/15.20    apart_point_and_line( Z, X ) }.
% 14.77/15.20  (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2 ), ! 
% 14.77/15.20    apart_point_and_line( skol1, X ) }.
% 14.77/15.20  (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2 ), 
% 14.77/15.20    distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.77/15.20  (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 14.77/15.20    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 14.77/15.20    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 14.77/15.20    unorthogonal_lines( Z, X ) }.
% 14.77/15.20  (3086) {G3,W15,D2,L5,V4,M1} R(130,146) { distinct_lines( X, Y ), 
% 14.77/15.20    distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines( Z, T
% 14.77/15.20     ), ! apart_point_and_line( skol1, X ) }.
% 14.77/15.20  (3100) {G4,W9,D2,L3,V2,M1} F(3086);r(34) { distinct_lines( Y, X ), 
% 14.77/15.20    distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.77/15.20  (3735) {G2,W13,D3,L3,V2,M1} R(302,27) { ! distinct_lines( 
% 14.77/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y, 
% 14.77/15.20    skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.77/15.20     }.
% 14.77/15.20  (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines( 
% 14.77/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X, 
% 14.77/15.20    skol2 ) }.
% 14.77/15.20  (10917) {G5,W3,D2,L1,V1,M1} R(10866,3100);f;r(36) { distinct_lines( X, 
% 14.77/15.20    skol2 ) }.
% 14.77/15.20  (10935) {G6,W0,D0,L0,V0,M0} R(10866,26);r(10917) {  }.
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  % SZS output end Refutation
% 14.77/15.20  found a proof!
% 14.77/15.20  
% 14.77/15.20  
% 14.77/15.20  Unprocessed initial clauses:
% 14.77/15.20  
% 14.77/15.20  (10937) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 14.77/15.20  (10938) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 14.77/15.20  (10939) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 14.77/15.20  (10940) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( 
% 14.77/15.20    X, Z ), distinct_points( Y, Z ) }.
% 14.77/15.20  (10941) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X
% 14.86/15.20    , Z ), distinct_lines( Y, Z ) }.
% 14.86/15.20  (10942) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 14.86/15.20    ( X, Z ), convergent_lines( Y, Z ) }.
% 14.86/15.20  (10943) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 14.86/15.20    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 14.86/15.20  (10944) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 14.86/15.20    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 14.86/15.20  (10945) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 14.86/15.20    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 14.86/15.20  (10946) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 14.86/15.20    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 14.86/15.20  (10947) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 14.86/15.20    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 14.86/15.20    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 14.86/15.20  (10948) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 14.86/15.20    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 14.86/15.20  (10949) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 14.86/15.20    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 14.86/15.20  (10950) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( 
% 14.86/15.20    Y, Z ), convergent_lines( X, Z ) }.
% 14.86/15.20  (10951) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( 
% 14.86/15.20    Y, X ), Y ) }.
% 14.86/15.20  (10952) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 14.86/15.20    parallel_through_point( Y, X ) ) }.
% 14.86/15.20  (10953) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 14.86/15.20    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 14.86/15.20    convergent_lines( X, Y ) }.
% 14.86/15.20  (10954) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 14.86/15.20    ( X, Y ) }.
% 14.86/15.20  (10955) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 14.86/15.20    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 14.86/15.20  (10956) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 14.86/15.20    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 14.86/15.20     }.
% 14.86/15.20  (10957) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y )
% 14.86/15.20     }.
% 14.86/15.20  (10958) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 14.86/15.20     }.
% 14.86/15.20  (10959) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 14.86/15.20    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 14.86/15.20  (10960) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 14.86/15.20    orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20  (10961) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 14.86/15.20    orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20  (10962) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 14.86/15.20    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 14.86/15.20    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 14.86/15.20  (10963) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, skol2 ) }.
% 14.86/15.20  (10964) {G0,W3,D2,L1,V0,M1}  { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.86/15.20  (10965) {G0,W5,D3,L1,V0,M1}  { distinct_lines( skol2, 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20  
% 14.86/15.20  
% 14.86/15.20  Total Proof:
% 14.86/15.20  
% 14.86/15.20  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.86/15.20  parent0: (10938) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 14.86/15.20    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 14.86/15.20  parent0: (10941) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 14.86/15.20    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20     Z := Z
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 2
% 14.86/15.20     1 ==> 0
% 14.86/15.20     2 ==> 1
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 14.86/15.20    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20  parent0: (10949) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 14.86/15.20    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20     Z := Z
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 2
% 14.86/15.20     1 ==> 0
% 14.86/15.20     2 ==> 1
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 14.86/15.20    orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20  parent0: (10960) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 14.86/15.20    orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 14.86/15.20    orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20  parent0: (10961) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 14.86/15.20    orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 14.86/15.20    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 14.86/15.20    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.86/15.20  parent0: (10962) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 14.86/15.20    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 14.86/15.20    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20     Z := Z
% 14.86/15.20     T := T
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20     1 ==> 1
% 14.86/15.20     2 ==> 2
% 14.86/15.20     3 ==> 4
% 14.86/15.20     4 ==> 3
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  parent0: (10963) {G0,W3,D2,L1,V0,M1}  { ! apart_point_and_line( skol1, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, 
% 14.86/15.20    skol3 ) }.
% 14.86/15.20  parent0: (10964) {G0,W3,D2,L1,V0,M1}  { ! unorthogonal_lines( skol2, skol3
% 14.86/15.20     ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2, 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20  parent0: (10965) {G0,W5,D3,L1,V0,M1}  { distinct_lines( skol2, 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11045) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 14.86/15.20    distinct_lines( X, Y ) }.
% 14.86/15.20  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.86/15.20  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 14.86/15.20    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20     Z := X
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 14.86/15.20    distinct_lines( X, Y ) }.
% 14.86/15.20  parent0: (11045) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 14.86/15.20    distinct_lines( X, Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := Y
% 14.86/15.20     Y := X
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 1
% 14.86/15.20     1 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11047) {G1,W5,D3,L1,V0,M1}  { distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 14.86/15.20    distinct_lines( X, Y ) }.
% 14.86/15.20  parent1[0]: (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2, 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := orthogonal_through_point( skol3, skol1 )
% 14.86/15.20     Y := skol2
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20  parent0: (11047) {G1,W5,D3,L1,V0,M1}  { distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11048) {G1,W12,D2,L4,V4,M4}  { distinct_lines( X, Y ), 
% 14.86/15.20    apart_point_and_line( Z, Y ), distinct_lines( T, X ), ! 
% 14.86/15.20    apart_point_and_line( Z, T ) }.
% 14.86/15.20  parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 14.86/15.20    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 14.86/15.20    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := Z
% 14.86/15.20     Y := X
% 14.86/15.20     Z := Y
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := Z
% 14.86/15.20     Y := T
% 14.86/15.20     Z := X
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (130) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 14.86/15.20    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 14.86/15.20    apart_point_and_line( Z, X ) }.
% 14.86/15.20  parent0: (11048) {G1,W12,D2,L4,V4,M4}  { distinct_lines( X, Y ), 
% 14.86/15.20    apart_point_and_line( Z, Y ), distinct_lines( T, X ), ! 
% 14.86/15.20    apart_point_and_line( Z, T ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := Y
% 14.86/15.20     Y := T
% 14.86/15.20     Z := Z
% 14.86/15.20     T := X
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 1
% 14.86/15.20     1 ==> 2
% 14.86/15.20     2 ==> 0
% 14.86/15.20     3 ==> 3
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11050) {G1,W6,D2,L2,V1,M2}  { distinct_lines( X, skol2 ), ! 
% 14.86/15.20    apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent0[0]: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 14.86/15.20    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := skol1
% 14.86/15.20     Y := X
% 14.86/15.20     Z := skol2
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2
% 14.86/15.20     ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent0: (11050) {G1,W6,D2,L2,V1,M2}  { distinct_lines( X, skol2 ), ! 
% 14.86/15.20    apart_point_and_line( skol1, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20     1 ==> 1
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11051) {G1,W9,D2,L3,V2,M3}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20  parent0[1]: (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2 )
% 14.86/15.20    , ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 14.86/15.20    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := skol1
% 14.86/15.20     Y := Y
% 14.86/15.20     Z := X
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2
% 14.86/15.20     ), distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20  parent0: (11051) {G1,W9,D2,L3,V2,M3}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20     1 ==> 1
% 14.86/15.20     2 ==> 2
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11054) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 14.86/15.20    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 14.86/15.20    unorthogonal_lines( Z, X ) }.
% 14.86/15.20  parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( 
% 14.86/15.20    orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20  parent1[4]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ), 
% 14.86/15.20    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 14.86/15.20    unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := Y
% 14.86/15.20     Y := X
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := orthogonal_through_point( X, Y )
% 14.86/15.20     Y := Z
% 14.86/15.20     Z := T
% 14.86/15.20     T := X
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 14.86/15.20    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 14.86/15.20    unorthogonal_lines( Z, X ) }.
% 14.86/15.20  parent0: (11054) {G1,W16,D3,L4,V4,M4}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 14.86/15.20    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 14.86/15.20    unorthogonal_lines( Z, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20     Z := Z
% 14.86/15.20     T := T
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20     1 ==> 1
% 14.86/15.20     2 ==> 2
% 14.86/15.20     3 ==> 3
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11056) {G2,W15,D2,L5,V4,M5}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( Y, X ), distinct_lines( Z, T ), distinct_lines( T, Y ), !
% 14.86/15.20     apart_point_and_line( skol1, Z ) }.
% 14.86/15.20  parent0[2]: (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2
% 14.86/15.20     ), distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20  parent1[2]: (130) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ), 
% 14.86/15.20    distinct_lines( Y, T ), apart_point_and_line( Z, T ), ! 
% 14.86/15.20    apart_point_and_line( Z, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := Z
% 14.86/15.20     Y := T
% 14.86/15.20     Z := skol1
% 14.86/15.20     T := Y
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (3086) {G3,W15,D2,L5,V4,M1} R(130,146) { distinct_lines( X, Y
% 14.86/15.20     ), distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines( Z
% 14.86/15.20    , T ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent0: (11056) {G2,W15,D2,L5,V4,M5}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( Y, X ), distinct_lines( Z, T ), distinct_lines( T, Y ), !
% 14.86/15.20     apart_point_and_line( skol1, Z ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := T
% 14.86/15.20     Y := Z
% 14.86/15.20     Z := X
% 14.86/15.20     T := Y
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 2
% 14.86/15.20     1 ==> 3
% 14.86/15.20     2 ==> 0
% 14.86/15.20     3 ==> 1
% 14.86/15.20     4 ==> 4
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  factor: (11070) {G3,W12,D2,L4,V2,M4}  { distinct_lines( X, Y ), 
% 14.86/15.20    distinct_lines( Y, X ), distinct_lines( Y, skol2 ), ! 
% 14.86/15.20    apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent0[0, 3]: (3086) {G3,W15,D2,L5,V4,M1} R(130,146) { distinct_lines( X, 
% 14.86/15.20    Y ), distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines( 
% 14.86/15.20    Z, T ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20     Z := X
% 14.86/15.20     T := Y
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11094) {G2,W12,D2,L4,V2,M4}  { distinct_lines( Y, X ), 
% 14.86/15.20    distinct_lines( Y, X ), distinct_lines( Y, skol2 ), ! 
% 14.86/15.20    apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 14.86/15.20    distinct_lines( X, Y ) }.
% 14.86/15.20  parent1[0]: (11070) {G3,W12,D2,L4,V2,M4}  { distinct_lines( X, Y ), 
% 14.86/15.20    distinct_lines( Y, X ), distinct_lines( Y, skol2 ), ! 
% 14.86/15.20    apart_point_and_line( skol1, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := Y
% 14.86/15.20     Y := X
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  factor: (11097) {G2,W9,D2,L3,V2,M3}  { distinct_lines( X, Y ), 
% 14.86/15.20    distinct_lines( X, skol2 ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20  parent0[0, 1]: (11094) {G2,W12,D2,L4,V2,M4}  { distinct_lines( Y, X ), 
% 14.86/15.20    distinct_lines( Y, X ), distinct_lines( Y, skol2 ), ! 
% 14.86/15.20    apart_point_and_line( skol1, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := Y
% 14.86/15.20     Y := X
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (3100) {G4,W9,D2,L3,V2,M1} F(3086);r(34) { distinct_lines( Y, 
% 14.86/15.20    X ), distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent0: (11097) {G2,W9,D2,L3,V2,M3}  { distinct_lines( X, Y ), 
% 14.86/15.20    distinct_lines( X, skol2 ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := Y
% 14.86/15.20     Y := X
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20     1 ==> 1
% 14.86/15.20     2 ==> 2
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11101) {G1,W13,D3,L3,V2,M3}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y, 
% 14.86/15.20    orthogonal_through_point( skol3, X ) ), apart_point_and_line( Y, skol2 )
% 14.86/15.20     }.
% 14.86/15.20  parent0[0]: (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3
% 14.86/15.20     ) }.
% 14.86/15.20  parent1[3]: (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T, 
% 14.86/15.20    orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ), 
% 14.86/15.20    unorthogonal_lines( Z, X ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := skol3
% 14.86/15.20     Y := X
% 14.86/15.20     Z := skol2
% 14.86/15.20     T := Y
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (3735) {G2,W13,D3,L3,V2,M1} R(302,27) { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y, 
% 14.86/15.20    skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.86/15.20     }.
% 14.86/15.20  parent0: (11101) {G1,W13,D3,L3,V2,M3}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y, 
% 14.86/15.20    orthogonal_through_point( skol3, X ) ), apart_point_and_line( Y, skol2 )
% 14.86/15.20     }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := Y
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20     1 ==> 2
% 14.86/15.20     2 ==> 1
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11102) {G1,W8,D3,L2,V1,M2}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 14.86/15.20    orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20  parent1[2]: (3735) {G2,W13,D3,L3,V2,M1} R(302,27) { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y, 
% 14.86/15.20    skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.86/15.20     }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20     Y := skol3
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := X
% 14.86/15.20     Y := X
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  parent0: (11102) {G1,W8,D3,L2,V1,M2}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20     1 ==> 1
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11105) {G4,W11,D3,L3,V1,M3}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( X, skol2 ), ! distinct_lines( orthogonal_through_point( 
% 14.86/15.20    skol3, skol1 ), skol2 ) }.
% 14.86/15.20  parent0[2]: (3100) {G4,W9,D2,L3,V2,M1} F(3086);r(34) { distinct_lines( Y, X
% 14.86/15.20     ), distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20  parent1[1]: (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := skol2
% 14.86/15.20     Y := X
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := skol1
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11107) {G3,W6,D2,L2,V1,M2}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( X, skol2 ) }.
% 14.86/15.20  parent0[2]: (11105) {G4,W11,D3,L3,V1,M3}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( X, skol2 ), ! distinct_lines( orthogonal_through_point( 
% 14.86/15.20    skol3, skol1 ), skol2 ) }.
% 14.86/15.20  parent1[0]: (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  factor: (11108) {G3,W3,D2,L1,V1,M1}  { distinct_lines( X, skol2 ) }.
% 14.86/15.20  parent0[0, 1]: (11107) {G3,W6,D2,L2,V1,M2}  { distinct_lines( X, skol2 ), 
% 14.86/15.20    distinct_lines( X, skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (10917) {G5,W3,D2,L1,V1,M1} R(10866,3100);f;r(36) { 
% 14.86/15.20    distinct_lines( X, skol2 ) }.
% 14.86/15.20  parent0: (11108) {G3,W3,D2,L1,V1,M1}  { distinct_lines( X, skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20     X := X
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20     0 ==> 0
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11109) {G1,W5,D3,L1,V0,M1}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20  parent0[0]: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  parent1[1]: (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X, 
% 14.86/15.20    skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := skol1
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  resolution: (11110) {G2,W0,D0,L0,V0,M0}  {  }.
% 14.86/15.20  parent0[0]: (11109) {G1,W5,D3,L1,V0,M1}  { ! distinct_lines( 
% 14.86/15.20    orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20  parent1[0]: (10917) {G5,W3,D2,L1,V1,M1} R(10866,3100);f;r(36) { 
% 14.86/15.20    distinct_lines( X, skol2 ) }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  substitution1:
% 14.86/15.20     X := orthogonal_through_point( skol3, skol1 )
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  subsumption: (10935) {G6,W0,D0,L0,V0,M0} R(10866,26);r(10917) {  }.
% 14.86/15.20  parent0: (11110) {G2,W0,D0,L0,V0,M0}  {  }.
% 14.86/15.20  substitution0:
% 14.86/15.20  end
% 14.86/15.20  permutation0:
% 14.86/15.20  end
% 14.86/15.20  
% 14.86/15.20  Proof check complete!
% 14.86/15.20  
% 14.86/15.20  Memory use:
% 14.86/15.20  
% 14.86/15.20  space for terms:        159640
% 14.86/15.20  space for clauses:      461406
% 14.86/15.20  
% 14.86/15.20  
% 14.86/15.20  clauses generated:      1260822
% 14.86/15.20  clauses kept:           10936
% 14.86/15.20  clauses selected:       2754
% 14.86/15.20  clauses deleted:        126
% 14.86/15.20  clauses inuse deleted:  13
% 14.86/15.20  
% 14.86/15.20  subsentry:          8901560
% 14.86/15.20  literals s-matched: 2700027
% 14.86/15.20  literals matched:   2699970
% 14.86/15.20  full subsumption:   1515057
% 14.86/15.20  
% 14.86/15.20  checksum:           -1019671627
% 14.86/15.20  
% 14.86/15.20  
% 14.86/15.20  Bliksem ended
%------------------------------------------------------------------------------