TSTP Solution File: GEO213+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO213+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 02:52:49 EDT 2022

% Result   : Theorem 1.19s 1.56s
% Output   : Refutation 1.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO213+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : bliksem %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Fri Jun 17 23:41:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.19/1.56  *** allocated 10000 integers for termspace/termends
% 1.19/1.56  *** allocated 10000 integers for clauses
% 1.19/1.56  *** allocated 10000 integers for justifications
% 1.19/1.56  Bliksem 1.12
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  Automatic Strategy Selection
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  Clauses:
% 1.19/1.56  
% 1.19/1.56  { ! distinct_points( X, X ) }.
% 1.19/1.56  { ! distinct_lines( X, X ) }.
% 1.19/1.56  { ! convergent_lines( X, X ) }.
% 1.19/1.56  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.19/1.56     ) }.
% 1.19/1.56  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.19/1.56     }.
% 1.19/1.56  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.19/1.56    , Z ) }.
% 1.19/1.56  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.19/1.56    , Y ) ) }.
% 1.19/1.56  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.19/1.56    , Y ) ) }.
% 1.19/1.56  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.19/1.56    , Y ), X ) }.
% 1.19/1.56  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.19/1.56    , Y ), Y ) }.
% 1.19/1.56  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.19/1.56    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.19/1.56    apart_point_and_line( Y, T ) }.
% 1.19/1.56  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 1.19/1.56    apart_point_and_line( Z, Y ) }.
% 1.19/1.56  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 1.19/1.56    apart_point_and_line( X, Z ) }.
% 1.19/1.56  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 1.19/1.56    Z ) }.
% 1.19/1.56  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.19/1.56  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.19/1.56  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 1.19/1.56    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.19/1.56  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.19/1.56  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.19/1.56    , convergent_lines( Y, Z ) }.
% 1.19/1.56  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.19/1.56    , unorthogonal_lines( Y, Z ) }.
% 1.19/1.56  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.19/1.56  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.19/1.56  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.19/1.56     }.
% 1.19/1.56  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.19/1.56  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.19/1.56  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 1.19/1.56    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 1.19/1.56    unorthogonal_lines( Y, T ) }.
% 1.19/1.56  { unorthogonal_lines( skol1, skol2 ) }.
% 1.19/1.56  { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56  { ! unorthogonal_lines( skol2, skol3 ) }.
% 1.19/1.56  
% 1.19/1.56  percentage equality = 0.000000, percentage horn = 0.586207
% 1.19/1.56  This a non-horn, non-equality problem
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  Options Used:
% 1.19/1.56  
% 1.19/1.56  useres =            1
% 1.19/1.56  useparamod =        0
% 1.19/1.56  useeqrefl =         0
% 1.19/1.56  useeqfact =         0
% 1.19/1.56  usefactor =         1
% 1.19/1.56  usesimpsplitting =  0
% 1.19/1.56  usesimpdemod =      0
% 1.19/1.56  usesimpres =        3
% 1.19/1.56  
% 1.19/1.56  resimpinuse      =  1000
% 1.19/1.56  resimpclauses =     20000
% 1.19/1.56  substype =          standard
% 1.19/1.56  backwardsubs =      1
% 1.19/1.56  selectoldest =      5
% 1.19/1.56  
% 1.19/1.56  litorderings [0] =  split
% 1.19/1.56  litorderings [1] =  liftord
% 1.19/1.56  
% 1.19/1.56  termordering =      none
% 1.19/1.56  
% 1.19/1.56  litapriori =        1
% 1.19/1.56  termapriori =       0
% 1.19/1.56  litaposteriori =    0
% 1.19/1.56  termaposteriori =   0
% 1.19/1.56  demodaposteriori =  0
% 1.19/1.56  ordereqreflfact =   0
% 1.19/1.56  
% 1.19/1.56  litselect =         none
% 1.19/1.56  
% 1.19/1.56  maxweight =         15
% 1.19/1.56  maxdepth =          30000
% 1.19/1.56  maxlength =         115
% 1.19/1.56  maxnrvars =         195
% 1.19/1.56  excuselevel =       1
% 1.19/1.56  increasemaxweight = 1
% 1.19/1.56  
% 1.19/1.56  maxselected =       10000000
% 1.19/1.56  maxnrclauses =      10000000
% 1.19/1.56  
% 1.19/1.56  showgenerated =    0
% 1.19/1.56  showkept =         0
% 1.19/1.56  showselected =     0
% 1.19/1.56  showdeleted =      0
% 1.19/1.56  showresimp =       1
% 1.19/1.56  showstatus =       2000
% 1.19/1.56  
% 1.19/1.56  prologoutput =     0
% 1.19/1.56  nrgoals =          5000000
% 1.19/1.56  totalproof =       1
% 1.19/1.56  
% 1.19/1.56  Symbols occurring in the translation:
% 1.19/1.56  
% 1.19/1.56  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.19/1.56  .  [1, 2]      (w:1, o:23, a:1, s:1, b:0), 
% 1.19/1.56  !  [4, 1]      (w:0, o:18, a:1, s:1, b:0), 
% 1.19/1.56  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.19/1.56  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.19/1.56  distinct_points  [36, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 1.19/1.56  distinct_lines  [37, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 1.19/1.56  convergent_lines  [38, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 1.19/1.56  line_connecting  [41, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 1.19/1.56  apart_point_and_line  [42, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 1.19/1.56  intersection_point  [43, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 1.19/1.56  parallel_through_point  [46, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 1.19/1.56  unorthogonal_lines  [49, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 1.19/1.56  orthogonal_through_point  [52, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 1.19/1.56  alpha1  [53, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 1.19/1.56  skol1  [54, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 1.19/1.56  skol2  [55, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 1.19/1.56  skol3  [56, 0]      (w:1, o:17, a:1, s:1, b:0).
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  Starting Search:
% 1.19/1.56  
% 1.19/1.56  *** allocated 15000 integers for clauses
% 1.19/1.56  *** allocated 22500 integers for clauses
% 1.19/1.56  *** allocated 33750 integers for clauses
% 1.19/1.56  *** allocated 50625 integers for clauses
% 1.19/1.56  *** allocated 15000 integers for termspace/termends
% 1.19/1.56  Resimplifying inuse:
% 1.19/1.56  Done
% 1.19/1.56  
% 1.19/1.56  *** allocated 22500 integers for termspace/termends
% 1.19/1.56  *** allocated 75937 integers for clauses
% 1.19/1.56  *** allocated 33750 integers for termspace/termends
% 1.19/1.56  *** allocated 113905 integers for clauses
% 1.19/1.56  
% 1.19/1.56  Intermediate Status:
% 1.19/1.56  Generated:    22658
% 1.19/1.56  Kept:         2000
% 1.19/1.56  Inuse:        340
% 1.19/1.56  Deleted:      0
% 1.19/1.56  Deletedinuse: 0
% 1.19/1.56  
% 1.19/1.56  Resimplifying inuse:
% 1.19/1.56  Done
% 1.19/1.56  
% 1.19/1.56  *** allocated 50625 integers for termspace/termends
% 1.19/1.56  *** allocated 170857 integers for clauses
% 1.19/1.56  Resimplifying inuse:
% 1.19/1.56  Done
% 1.19/1.56  
% 1.19/1.56  *** allocated 75937 integers for termspace/termends
% 1.19/1.56  
% 1.19/1.56  Intermediate Status:
% 1.19/1.56  Generated:    35661
% 1.19/1.56  Kept:         4010
% 1.19/1.56  Inuse:        468
% 1.19/1.56  Deleted:      0
% 1.19/1.56  Deletedinuse: 0
% 1.19/1.56  
% 1.19/1.56  Resimplifying inuse:
% 1.19/1.56  Done
% 1.19/1.56  
% 1.19/1.56  *** allocated 256285 integers for clauses
% 1.19/1.56  
% 1.19/1.56  Bliksems!, er is een bewijs:
% 1.19/1.56  % SZS status Theorem
% 1.19/1.56  % SZS output start Refutation
% 1.19/1.56  
% 1.19/1.56  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.19/1.56  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.19/1.56    , ! distinct_lines( X, Y ) }.
% 1.19/1.56  (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y, 
% 1.19/1.56    Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56  (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines( 
% 1.19/1.56    X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56  (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines( 
% 1.19/1.56    X, Y ) }.
% 1.19/1.56  (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.19/1.56     }.
% 1.19/1.56  (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 1.19/1.56  (26) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 ) }.
% 1.19/1.56  (27) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56  (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3 ) }.
% 1.19/1.56  (36) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 1.19/1.56    ( X, Y ) }.
% 1.19/1.56  (39) {G2,W3,D2,L1,V0,M1} R(36,27) { ! distinct_lines( skol3, skol1 ) }.
% 1.19/1.56  (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  (55) {G1,W3,D2,L1,V0,M1} R(17,28) { convergent_lines( skol2, skol3 ) }.
% 1.19/1.56  (57) {G2,W6,D2,L2,V1,M1} R(55,5) { convergent_lines( skol2, X ), 
% 1.19/1.56    convergent_lines( skol3, X ) }.
% 1.19/1.56  (61) {G3,W6,D2,L2,V1,M2} R(57,48) { convergent_lines( X, skol3 ), 
% 1.19/1.56    convergent_lines( skol2, X ) }.
% 1.19/1.56  (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X, skol1 ), ! 
% 1.19/1.56    convergent_lines( X, skol3 ) }.
% 1.19/1.56  (171) {G4,W3,D2,L1,V0,M1} R(161,61);r(2) { convergent_lines( skol2, skol1 )
% 1.19/1.56     }.
% 1.19/1.56  (173) {G4,W6,D2,L2,V1,M2} R(161,48) { ! convergent_lines( skol3, X ), 
% 1.19/1.56    convergent_lines( X, skol1 ) }.
% 1.19/1.56  (176) {G5,W3,D2,L1,V0,M1} R(171,48) { convergent_lines( skol1, skol2 ) }.
% 1.19/1.56  (206) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ), 
% 1.19/1.56    convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 1.19/1.56    unorthogonal_lines( Y, Z ) }.
% 1.19/1.56  (212) {G5,W9,D2,L3,V2,M2} R(173,5) { convergent_lines( X, skol1 ), ! 
% 1.19/1.56    convergent_lines( Y, skol3 ), convergent_lines( Y, X ) }.
% 1.19/1.56  (216) {G6,W3,D2,L1,V0,M1} F(212);r(2) { ! convergent_lines( skol1, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  (4678) {G6,W6,D2,L2,V1,M1} R(206,26);r(176) { convergent_lines( skol1, X )
% 1.19/1.56    , unorthogonal_lines( skol2, X ) }.
% 1.19/1.56  (4683) {G7,W0,D0,L0,V0,M0} R(4678,28);r(216) {  }.
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  % SZS output end Refutation
% 1.19/1.56  found a proof!
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  Unprocessed initial clauses:
% 1.19/1.56  
% 1.19/1.56  (4685) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 1.19/1.56  (4686) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 1.19/1.56  (4687) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 1.19/1.56  (4688) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 1.19/1.56    , Z ), distinct_points( Y, Z ) }.
% 1.19/1.56  (4689) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 1.19/1.56    Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56  (4690) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 1.19/1.56    ( X, Z ), convergent_lines( Y, Z ) }.
% 1.19/1.56  (4691) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.19/1.56    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.19/1.56  (4692) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.19/1.56    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.19/1.56  (4693) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.19/1.56  (4694) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.19/1.56  (4695) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 1.19/1.56    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 1.19/1.56    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.19/1.56  (4696) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.19/1.56    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.19/1.56  (4697) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.19/1.56    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.19/1.56  (4698) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.19/1.56    , Z ), convergent_lines( X, Z ) }.
% 1.19/1.56  (4699) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( Y
% 1.19/1.56    , X ), Y ) }.
% 1.19/1.56  (4700) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 1.19/1.56    parallel_through_point( Y, X ) ) }.
% 1.19/1.56  (4701) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 1.19/1.56    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  (4702) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines
% 1.19/1.56    ( X, Y ) }.
% 1.19/1.56  (4703) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.19/1.56  (4704) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.19/1.56     }.
% 1.19/1.56  (4705) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y )
% 1.19/1.56     }.
% 1.19/1.56  (4706) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 1.19/1.56     }.
% 1.19/1.56  (4707) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 1.19/1.56  (4708) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( 
% 1.19/1.56    orthogonal_through_point( Y, X ), Y ) }.
% 1.19/1.56  (4709) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 1.19/1.56    orthogonal_through_point( Y, X ) ) }.
% 1.19/1.56  (4710) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 1.19/1.56    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 1.19/1.56    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 1.19/1.56  (4711) {G0,W3,D2,L1,V0,M1}  { unorthogonal_lines( skol1, skol2 ) }.
% 1.19/1.56  (4712) {G0,W3,D2,L1,V0,M1}  { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56  (4713) {G0,W3,D2,L1,V0,M1}  { ! unorthogonal_lines( skol2, skol3 ) }.
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  Total Proof:
% 1.19/1.56  
% 1.19/1.56  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.19/1.56  parent0: (4686) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56  parent0: (4687) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 1.19/1.56    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.19/1.56  parent0: (4689) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 1.19/1.56    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56     Z := Z
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 2
% 1.19/1.56     1 ==> 0
% 1.19/1.56     2 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 1.19/1.56    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56  parent0: (4690) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 1.19/1.56    convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56     Z := Z
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 2
% 1.19/1.56     1 ==> 0
% 1.19/1.56     2 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 1.19/1.56    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56  parent0: (4698) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), 
% 1.19/1.56    distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56     Z := Z
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56     1 ==> 2
% 1.19/1.56     2 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 1.19/1.56    unorthogonal_lines( X, Y ) }.
% 1.19/1.56  parent0: (4702) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), 
% 1.19/1.56    unorthogonal_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56     1 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.19/1.56     }.
% 1.19/1.56  parent0: (4704) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.19/1.56     }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56     Z := Z
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56     1 ==> 1
% 1.19/1.56     2 ==> 3
% 1.19/1.56     3 ==> 2
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 1.19/1.56    alpha1( X, Y ) }.
% 1.19/1.56  parent0: (4705) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( 
% 1.19/1.56    X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 1
% 1.19/1.56     1 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (26) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2
% 1.19/1.56     ) }.
% 1.19/1.56  parent0: (4711) {G0,W3,D2,L1,V0,M1}  { unorthogonal_lines( skol1, skol2 )
% 1.19/1.56     }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (27) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  parent0: (4712) {G0,W3,D2,L1,V0,M1}  { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, 
% 1.19/1.56    skol3 ) }.
% 1.19/1.56  parent0: (4713) {G0,W3,D2,L1,V0,M1}  { ! unorthogonal_lines( skol2, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4794) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 1.19/1.56    distinct_lines( X, Y ) }.
% 1.19/1.56  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.19/1.56  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 1.19/1.56    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56     Z := X
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (36) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 1.19/1.56    distinct_lines( X, Y ) }.
% 1.19/1.56  parent0: (4794) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 1.19/1.56    distinct_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := Y
% 1.19/1.56     Y := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 1
% 1.19/1.56     1 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4796) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol3, skol1 )
% 1.19/1.56     }.
% 1.19/1.56  parent0[0]: (27) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  parent1[1]: (36) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 1.19/1.56    distinct_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := skol1
% 1.19/1.56     Y := skol3
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (39) {G2,W3,D2,L1,V0,M1} R(36,27) { ! distinct_lines( skol3, 
% 1.19/1.56    skol1 ) }.
% 1.19/1.56  parent0: (4796) {G1,W3,D2,L1,V0,M1}  { ! distinct_lines( skol3, skol1 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4797) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56  parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 1.19/1.56    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56     Z := X
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  parent0: (4797) {G1,W6,D2,L2,V2,M2}  { convergent_lines( Y, X ), ! 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := Y
% 1.19/1.56     Y := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 1
% 1.19/1.56     1 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4799) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  parent0[0]: (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3
% 1.19/1.56     ) }.
% 1.19/1.56  parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 1.19/1.56    unorthogonal_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := skol2
% 1.19/1.56     Y := skol3
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (55) {G1,W3,D2,L1,V0,M1} R(17,28) { convergent_lines( skol2, 
% 1.19/1.56    skol3 ) }.
% 1.19/1.56  parent0: (4799) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol3 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4800) {G1,W6,D2,L2,V1,M2}  { convergent_lines( skol2, X ), 
% 1.19/1.56    convergent_lines( skol3, X ) }.
% 1.19/1.56  parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 1.19/1.56    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56  parent1[0]: (55) {G1,W3,D2,L1,V0,M1} R(17,28) { convergent_lines( skol2, 
% 1.19/1.56    skol3 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := skol2
% 1.19/1.56     Y := skol3
% 1.19/1.56     Z := X
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (57) {G2,W6,D2,L2,V1,M1} R(55,5) { convergent_lines( skol2, X
% 1.19/1.56     ), convergent_lines( skol3, X ) }.
% 1.19/1.56  parent0: (4800) {G1,W6,D2,L2,V1,M2}  { convergent_lines( skol2, X ), 
% 1.19/1.56    convergent_lines( skol3, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56     1 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4802) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol3 ), 
% 1.19/1.56    convergent_lines( skol2, X ) }.
% 1.19/1.56  parent0[0]: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  parent1[1]: (57) {G2,W6,D2,L2,V1,M1} R(55,5) { convergent_lines( skol2, X )
% 1.19/1.56    , convergent_lines( skol3, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := skol3
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (61) {G3,W6,D2,L2,V1,M2} R(57,48) { convergent_lines( X, skol3
% 1.19/1.56     ), convergent_lines( skol2, X ) }.
% 1.19/1.56  parent0: (4802) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol3 ), 
% 1.19/1.56    convergent_lines( skol2, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56     1 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4803) {G1,W6,D2,L2,V1,M2}  { ! convergent_lines( X, skol3 ), 
% 1.19/1.56    convergent_lines( X, skol1 ) }.
% 1.19/1.56  parent0[0]: (39) {G2,W3,D2,L1,V0,M1} R(36,27) { ! distinct_lines( skol3, 
% 1.19/1.56    skol1 ) }.
% 1.19/1.56  parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), 
% 1.19/1.56    convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := X
% 1.19/1.56     Y := skol3
% 1.19/1.56     Z := skol1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X, 
% 1.19/1.56    skol1 ), ! convergent_lines( X, skol3 ) }.
% 1.19/1.56  parent0: (4803) {G1,W6,D2,L2,V1,M2}  { ! convergent_lines( X, skol3 ), 
% 1.19/1.56    convergent_lines( X, skol1 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 1
% 1.19/1.56     1 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4805) {G4,W6,D2,L2,V0,M2}  { convergent_lines( skol2, skol1 )
% 1.19/1.56    , convergent_lines( skol3, skol3 ) }.
% 1.19/1.56  parent0[1]: (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X, skol1
% 1.19/1.56     ), ! convergent_lines( X, skol3 ) }.
% 1.19/1.56  parent1[1]: (61) {G3,W6,D2,L2,V1,M2} R(57,48) { convergent_lines( X, skol3
% 1.19/1.56     ), convergent_lines( skol2, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := skol2
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := skol3
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4806) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol1 )
% 1.19/1.56     }.
% 1.19/1.56  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56  parent1[1]: (4805) {G4,W6,D2,L2,V0,M2}  { convergent_lines( skol2, skol1 )
% 1.19/1.56    , convergent_lines( skol3, skol3 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := skol3
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (171) {G4,W3,D2,L1,V0,M1} R(161,61);r(2) { convergent_lines( 
% 1.19/1.56    skol2, skol1 ) }.
% 1.19/1.56  parent0: (4806) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol2, skol1 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4807) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol1 ), ! 
% 1.19/1.56    convergent_lines( skol3, X ) }.
% 1.19/1.56  parent0[1]: (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X, skol1
% 1.19/1.56     ), ! convergent_lines( X, skol3 ) }.
% 1.19/1.56  parent1[1]: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := X
% 1.19/1.56     Y := skol3
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (173) {G4,W6,D2,L2,V1,M2} R(161,48) { ! convergent_lines( 
% 1.19/1.56    skol3, X ), convergent_lines( X, skol1 ) }.
% 1.19/1.56  parent0: (4807) {G2,W6,D2,L2,V1,M2}  { convergent_lines( X, skol1 ), ! 
% 1.19/1.56    convergent_lines( skol3, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 1
% 1.19/1.56     1 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4808) {G2,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 )
% 1.19/1.56     }.
% 1.19/1.56  parent0[0]: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ), 
% 1.19/1.56    convergent_lines( X, Y ) }.
% 1.19/1.56  parent1[0]: (171) {G4,W3,D2,L1,V0,M1} R(161,61);r(2) { convergent_lines( 
% 1.19/1.56    skol2, skol1 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := skol1
% 1.19/1.56     Y := skol2
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (176) {G5,W3,D2,L1,V0,M1} R(171,48) { convergent_lines( skol1
% 1.19/1.56    , skol2 ) }.
% 1.19/1.56  parent0: (4808) {G2,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4810) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 1.19/1.56    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 1.19/1.56    unorthogonal_lines( Z, Y ) }.
% 1.19/1.56  parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 1.19/1.56    ( X, Y ) }.
% 1.19/1.56  parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), ! 
% 1.19/1.56    unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.19/1.56     }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Z
% 1.19/1.56     Z := Y
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (206) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 1.19/1.56     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 1.19/1.56    unorthogonal_lines( Y, Z ) }.
% 1.19/1.56  parent0: (4810) {G1,W12,D2,L4,V3,M4}  { convergent_lines( X, Y ), ! 
% 1.19/1.56    convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), 
% 1.19/1.56    unorthogonal_lines( Z, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Z
% 1.19/1.56     Z := Y
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 1
% 1.19/1.56     1 ==> 0
% 1.19/1.56     2 ==> 2
% 1.19/1.56     3 ==> 3
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4812) {G1,W9,D2,L3,V2,M3}  { convergent_lines( X, skol1 ), 
% 1.19/1.56    convergent_lines( Y, X ), ! convergent_lines( Y, skol3 ) }.
% 1.19/1.56  parent0[0]: (173) {G4,W6,D2,L2,V1,M2} R(161,48) { ! convergent_lines( skol3
% 1.19/1.56    , X ), convergent_lines( X, skol1 ) }.
% 1.19/1.56  parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), 
% 1.19/1.56    convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := Y
% 1.19/1.56     Y := skol3
% 1.19/1.56     Z := X
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (212) {G5,W9,D2,L3,V2,M2} R(173,5) { convergent_lines( X, 
% 1.19/1.56    skol1 ), ! convergent_lines( Y, skol3 ), convergent_lines( Y, X ) }.
% 1.19/1.56  parent0: (4812) {G1,W9,D2,L3,V2,M3}  { convergent_lines( X, skol1 ), 
% 1.19/1.56    convergent_lines( Y, X ), ! convergent_lines( Y, skol3 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56     Y := Y
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56     1 ==> 2
% 1.19/1.56     2 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  factor: (4815) {G5,W6,D2,L2,V0,M2}  { convergent_lines( skol1, skol1 ), ! 
% 1.19/1.56    convergent_lines( skol1, skol3 ) }.
% 1.19/1.56  parent0[0, 2]: (212) {G5,W9,D2,L3,V2,M2} R(173,5) { convergent_lines( X, 
% 1.19/1.56    skol1 ), ! convergent_lines( Y, skol3 ), convergent_lines( Y, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := skol1
% 1.19/1.56     Y := skol1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4816) {G1,W3,D2,L1,V0,M1}  { ! convergent_lines( skol1, skol3
% 1.19/1.56     ) }.
% 1.19/1.56  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56  parent1[0]: (4815) {G5,W6,D2,L2,V0,M2}  { convergent_lines( skol1, skol1 )
% 1.19/1.56    , ! convergent_lines( skol1, skol3 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := skol1
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (216) {G6,W3,D2,L1,V0,M1} F(212);r(2) { ! convergent_lines( 
% 1.19/1.56    skol1, skol3 ) }.
% 1.19/1.56  parent0: (4816) {G1,W3,D2,L1,V0,M1}  { ! convergent_lines( skol1, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4817) {G1,W9,D2,L3,V1,M3}  { ! convergent_lines( skol1, skol2
% 1.19/1.56     ), convergent_lines( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56  parent0[2]: (206) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 1.19/1.56     ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ), 
% 1.19/1.56    unorthogonal_lines( Y, Z ) }.
% 1.19/1.56  parent1[0]: (26) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 )
% 1.19/1.56     }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := skol1
% 1.19/1.56     Y := skol2
% 1.19/1.56     Z := X
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4818) {G2,W6,D2,L2,V1,M2}  { convergent_lines( skol1, X ), 
% 1.19/1.56    unorthogonal_lines( skol2, X ) }.
% 1.19/1.56  parent0[0]: (4817) {G1,W9,D2,L3,V1,M3}  { ! convergent_lines( skol1, skol2
% 1.19/1.56     ), convergent_lines( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56  parent1[0]: (176) {G5,W3,D2,L1,V0,M1} R(171,48) { convergent_lines( skol1, 
% 1.19/1.56    skol2 ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (4678) {G6,W6,D2,L2,V1,M1} R(206,26);r(176) { convergent_lines
% 1.19/1.56    ( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56  parent0: (4818) {G2,W6,D2,L2,V1,M2}  { convergent_lines( skol1, X ), 
% 1.19/1.56    unorthogonal_lines( skol2, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56     X := X
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56     0 ==> 0
% 1.19/1.56     1 ==> 1
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4819) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  parent0[0]: (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3
% 1.19/1.56     ) }.
% 1.19/1.56  parent1[1]: (4678) {G6,W6,D2,L2,V1,M1} R(206,26);r(176) { convergent_lines
% 1.19/1.56    ( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56     X := skol3
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  resolution: (4820) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.19/1.56  parent0[0]: (216) {G6,W3,D2,L1,V0,M1} F(212);r(2) { ! convergent_lines( 
% 1.19/1.56    skol1, skol3 ) }.
% 1.19/1.56  parent1[0]: (4819) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol3 )
% 1.19/1.56     }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  substitution1:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  subsumption: (4683) {G7,W0,D0,L0,V0,M0} R(4678,28);r(216) {  }.
% 1.19/1.56  parent0: (4820) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.19/1.56  substitution0:
% 1.19/1.56  end
% 1.19/1.56  permutation0:
% 1.19/1.56  end
% 1.19/1.56  
% 1.19/1.56  Proof check complete!
% 1.19/1.56  
% 1.19/1.56  Memory use:
% 1.19/1.56  
% 1.19/1.56  space for terms:        61642
% 1.19/1.56  space for clauses:      183681
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  clauses generated:      45185
% 1.19/1.56  clauses kept:           4684
% 1.19/1.56  clauses selected:       567
% 1.19/1.56  clauses deleted:        0
% 1.19/1.56  clauses inuse deleted:  0
% 1.19/1.56  
% 1.19/1.56  subsentry:          815582
% 1.19/1.56  literals s-matched: 252795
% 1.19/1.56  literals matched:   252760
% 1.19/1.56  full subsumption:   142278
% 1.19/1.56  
% 1.19/1.56  checksum:           1067422009
% 1.19/1.56  
% 1.19/1.56  
% 1.19/1.56  Bliksem ended
%------------------------------------------------------------------------------