TSTP Solution File: GEO200+2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO200+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n026.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 02:52:39 EDT 2022

% Result   : Theorem 3.25s 3.59s
% Output   : Refutation 3.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO200+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : bliksem %s
% 0.12/0.34  % Computer : n026.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 : Sat Jun 18 09:02:09 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 3.25/3.59  *** allocated 10000 integers for termspace/termends
% 3.25/3.59  *** allocated 10000 integers for clauses
% 3.25/3.59  *** allocated 10000 integers for justifications
% 3.25/3.59  Bliksem 1.12
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  Automatic Strategy Selection
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  Clauses:
% 3.25/3.59  
% 3.25/3.59  { ! distinct_points( X, X ) }.
% 3.25/3.59  { ! distinct_lines( X, X ) }.
% 3.25/3.59  { ! convergent_lines( X, X ) }.
% 3.25/3.59  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 3.25/3.59     ) }.
% 3.25/3.59  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 3.25/3.59     }.
% 3.25/3.59  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 3.25/3.59    , Z ) }.
% 3.25/3.59  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 3.25/3.59    , Y ) ), distinct_points( Z, X ) }.
% 3.25/3.59  { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 3.25/3.59    , Y ) ), distinct_points( Z, Y ) }.
% 3.25/3.59  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ), 
% 3.25/3.59    distinct_points( Z, intersection_point( X, Y ) ) }.
% 3.25/3.59  { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ), 
% 3.25/3.59    distinct_points( Z, intersection_point( X, Y ) ) }.
% 3.25/3.59  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 3.25/3.59    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 3.25/3.59    apart_point_and_line( Y, T ) }.
% 3.25/3.59  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 3.25/3.59    apart_point_and_line( Z, Y ) }.
% 3.25/3.59  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 3.25/3.59    apart_point_and_line( X, Z ) }.
% 3.25/3.59  { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 3.25/3.59  { distinct_points( skol1, skol2 ) }.
% 3.25/3.59  { distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol2, 
% 3.25/3.59    skol1 ) ) }.
% 3.25/3.59  
% 3.25/3.59  percentage equality = 0.000000, percentage horn = 0.625000
% 3.25/3.59  This a non-horn, non-equality problem
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  Options Used:
% 3.25/3.59  
% 3.25/3.59  useres =            1
% 3.25/3.59  useparamod =        0
% 3.25/3.59  useeqrefl =         0
% 3.25/3.59  useeqfact =         0
% 3.25/3.59  usefactor =         1
% 3.25/3.59  usesimpsplitting =  0
% 3.25/3.59  usesimpdemod =      0
% 3.25/3.59  usesimpres =        3
% 3.25/3.59  
% 3.25/3.59  resimpinuse      =  1000
% 3.25/3.59  resimpclauses =     20000
% 3.25/3.59  substype =          standard
% 3.25/3.59  backwardsubs =      1
% 3.25/3.59  selectoldest =      5
% 3.25/3.59  
% 3.25/3.59  litorderings [0] =  split
% 3.25/3.59  litorderings [1] =  liftord
% 3.25/3.59  
% 3.25/3.59  termordering =      none
% 3.25/3.59  
% 3.25/3.59  litapriori =        1
% 3.25/3.59  termapriori =       0
% 3.25/3.59  litaposteriori =    0
% 3.25/3.59  termaposteriori =   0
% 3.25/3.59  demodaposteriori =  0
% 3.25/3.59  ordereqreflfact =   0
% 3.25/3.59  
% 3.25/3.59  litselect =         none
% 3.25/3.59  
% 3.25/3.59  maxweight =         15
% 3.25/3.59  maxdepth =          30000
% 3.25/3.59  maxlength =         115
% 3.25/3.59  maxnrvars =         195
% 3.25/3.59  excuselevel =       1
% 3.25/3.59  increasemaxweight = 1
% 3.25/3.59  
% 3.25/3.59  maxselected =       10000000
% 3.25/3.59  maxnrclauses =      10000000
% 3.25/3.59  
% 3.25/3.59  showgenerated =    0
% 3.25/3.59  showkept =         0
% 3.25/3.59  showselected =     0
% 3.25/3.59  showdeleted =      0
% 3.25/3.59  showresimp =       1
% 3.25/3.59  showstatus =       2000
% 3.25/3.59  
% 3.25/3.59  prologoutput =     0
% 3.25/3.59  nrgoals =          5000000
% 3.25/3.59  totalproof =       1
% 3.25/3.59  
% 3.25/3.59  Symbols occurring in the translation:
% 3.25/3.59  
% 3.25/3.59  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 3.25/3.59  .  [1, 2]      (w:1, o:18, a:1, s:1, b:0), 
% 3.25/3.59  !  [4, 1]      (w:0, o:13, a:1, s:1, b:0), 
% 3.25/3.59  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 3.25/3.59  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 3.25/3.59  distinct_points  [36, 2]      (w:1, o:43, a:1, s:1, b:0), 
% 3.25/3.59  distinct_lines  [37, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 3.25/3.59  convergent_lines  [38, 2]      (w:1, o:42, a:1, s:1, b:0), 
% 3.25/3.59  line_connecting  [41, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 3.25/3.59  apart_point_and_line  [42, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 3.25/3.59  intersection_point  [43, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 3.25/3.59  skol1  [46, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 3.25/3.59  skol2  [47, 0]      (w:1, o:12, a:1, s:1, b:0).
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  Starting Search:
% 3.25/3.59  
% 3.25/3.59  *** allocated 15000 integers for clauses
% 3.25/3.59  Resimplifying inuse:
% 3.25/3.59  Done
% 3.25/3.59  
% 3.25/3.59  Failed to find proof!
% 3.25/3.59  maxweight =   15
% 3.25/3.59  maxnrclauses = 10000000
% 3.25/3.59  Generated: 36635
% 3.25/3.59  Kept: 337
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  The strategy used was not complete!
% 3.25/3.59  
% 3.25/3.59  Increased maxweight to 16
% 3.25/3.59  
% 3.25/3.59  Starting Search:
% 3.25/3.59  
% 3.25/3.59  Resimplifying inuse:
% 3.25/3.59  Done
% 3.25/3.59  
% 3.25/3.59  Failed to find proof!
% 3.25/3.59  maxweight =   16
% 3.25/3.59  maxnrclauses = 10000000
% 3.25/3.59  Generated: 38523
% 3.25/3.59  Kept: 353
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  The strategy used was not complete!
% 3.25/3.59  
% 3.25/3.59  Increased maxweight to 17
% 3.25/3.59  
% 3.25/3.59  Starting Search:
% 3.25/3.59  
% 3.25/3.59  *** allocated 22500 integers for clauses
% 3.25/3.59  Resimplifying inuse:
% 3.25/3.59  Done
% 3.25/3.59  
% 3.25/3.59  Failed to find proof!
% 3.25/3.59  maxweight =   17
% 3.25/3.59  maxnrclauses = 10000000
% 3.25/3.59  Generated: 55675
% 3.25/3.59  Kept: 481
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  The strategy used was not complete!
% 3.25/3.59  
% 3.25/3.59  Increased maxweight to 18
% 3.25/3.59  
% 3.25/3.59  Starting Search:
% 3.25/3.59  
% 3.25/3.59  *** allocated 15000 integers for termspace/termends
% 3.25/3.59  *** allocated 33750 integers for clauses
% 3.25/3.59  Resimplifying inuse:
% 3.25/3.59  Done
% 3.25/3.59  
% 3.25/3.59  Failed to find proof!
% 3.25/3.59  maxweight =   18
% 3.25/3.59  maxnrclauses = 10000000
% 3.25/3.59  Generated: 180811
% 3.25/3.59  Kept: 753
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  The strategy used was not complete!
% 3.25/3.59  
% 3.25/3.59  Increased maxweight to 19
% 3.25/3.59  
% 3.25/3.59  Starting Search:
% 3.25/3.59  
% 3.25/3.59  *** allocated 22500 integers for termspace/termends
% 3.25/3.59  *** allocated 50625 integers for clauses
% 3.25/3.59  
% 3.25/3.59  Bliksems!, er is een bewijs:
% 3.25/3.59  % SZS status Theorem
% 3.25/3.59  % SZS output start Refutation
% 3.25/3.59  
% 3.25/3.59  (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 3.25/3.59  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 3.25/3.59  (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 3.25/3.59     ), ! distinct_points( X, Y ) }.
% 3.25/3.59  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 3.25/3.59    , ! distinct_lines( X, Y ) }.
% 3.25/3.59  (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), distinct_points( Z
% 3.25/3.59    , X ), ! apart_point_and_line( Z, line_connecting( X, Y ) ) }.
% 3.25/3.59  (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), distinct_points( Z
% 3.25/3.59    , Y ), ! apart_point_and_line( Z, line_connecting( X, Y ) ) }.
% 3.25/3.59  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 3.25/3.59    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 3.25/3.59    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 3.25/3.59  (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 3.25/3.59    ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 3.25/3.59  (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 3.25/3.59  (15) {G0,W7,D3,L1,V0,M1} I { distinct_lines( line_connecting( skol1, skol2
% 3.25/3.59     ), line_connecting( skol2, skol1 ) ) }.
% 3.25/3.59  (19) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  (22) {G2,W3,D2,L1,V0,M1} R(19,14) { distinct_points( skol2, skol1 ) }.
% 3.25/3.59  (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 3.25/3.59    ( X, Y ) }.
% 3.25/3.59  (42) {G2,W7,D3,L1,V0,M1} R(15,30) { distinct_lines( line_connecting( skol2
% 3.25/3.59    , skol1 ), line_connecting( skol1, skol2 ) ) }.
% 3.25/3.59  (92) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( Z, T ), distinct_points( Y, T ), ! apart_point_and_line
% 3.25/3.59    ( X, line_connecting( Z, T ) ) }.
% 3.25/3.59  (93) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( Z, T ), distinct_points( Y, Z ), ! apart_point_and_line
% 3.25/3.59    ( X, line_connecting( Z, T ) ) }.
% 3.25/3.59  (94) {G2,W8,D3,L2,V2,M1} F(93);r(0) { ! distinct_points( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 3.25/3.59  (95) {G2,W8,D3,L2,V2,M1} F(92);r(0) { ! distinct_points( Y, X ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 3.25/3.59  (120) {G1,W25,D3,L7,V5,M3} R(10,6) { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( T, U ) ), ! distinct_points( T, U ), 
% 3.25/3.59    distinct_points( X, T ), apart_point_and_line( Y, Z ), 
% 3.25/3.59    apart_point_and_line( Y, line_connecting( T, U ) ), apart_point_and_line
% 3.25/3.59    ( X, Z ) }.
% 3.25/3.59  (125) {G2,W19,D3,L5,V3,M3} F(120);r(0) { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, 
% 3.25/3.59    line_connecting( X, Y ) ), apart_point_and_line( X, Z ), 
% 3.25/3.59    apart_point_and_line( Y, Z ) }.
% 3.25/3.59  (822) {G3,W14,D3,L4,V3,M2} S(125);r(95) { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 3.25/3.59     ), apart_point_and_line( X, Z ) }.
% 3.25/3.59  (839) {G4,W18,D3,L4,V3,M1} R(822,94) { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( line_connecting( Y, Z ), line_connecting( X, Y ) ), ! 
% 3.25/3.59    distinct_points( Y, Z ), apart_point_and_line( X, line_connecting( Y, Z )
% 3.25/3.59     ) }.
% 3.25/3.59  (860) {G5,W10,D3,L2,V2,M1} R(839,95);f;r(19) { ! distinct_points( Y, X ), !
% 3.25/3.59     distinct_lines( line_connecting( Y, X ), line_connecting( X, Y ) ) }.
% 3.25/3.59  (1067) {G6,W0,D0,L0,V0,M0} R(860,42);r(22) {  }.
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  % SZS output end Refutation
% 3.25/3.59  found a proof!
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  Unprocessed initial clauses:
% 3.25/3.59  
% 3.25/3.59  (1069) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 3.25/3.59  (1070) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 3.25/3.59  (1071) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 3.25/3.59  (1072) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 3.25/3.59    , Z ), distinct_points( Y, Z ) }.
% 3.25/3.59  (1073) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, 
% 3.25/3.59    Z ), distinct_lines( Y, Z ) }.
% 3.25/3.59  (1074) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines
% 3.25/3.59    ( X, Z ), convergent_lines( Y, Z ) }.
% 3.25/3.59  (1075) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 3.25/3.59     ) }.
% 3.25/3.59  (1076) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 3.25/3.59     ) }.
% 3.25/3.59  (1077) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X, 
% 3.25/3.59    Y ) ) }.
% 3.25/3.59  (1078) {G0,W11,D3,L3,V3,M3}  { ! convergent_lines( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X, 
% 3.25/3.59    Y ) ) }.
% 3.25/3.59  (1079) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines
% 3.25/3.59    ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 3.25/3.59    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 3.25/3.59  (1080) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 3.25/3.59    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 3.25/3.59  (1081) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 3.25/3.59    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 3.25/3.59  (1082) {G0,W6,D2,L2,V2,M2}  { ! convergent_lines( X, Y ), distinct_lines( X
% 3.25/3.59    , Y ) }.
% 3.25/3.59  (1083) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 3.25/3.59  (1084) {G0,W7,D3,L1,V0,M1}  { distinct_lines( line_connecting( skol1, skol2
% 3.25/3.59     ), line_connecting( skol2, skol1 ) ) }.
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  Total Proof:
% 3.25/3.59  
% 3.25/3.59  subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 3.25/3.59  parent0: (1069) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 3.25/3.59  parent0: (1070) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 3.25/3.59    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 3.25/3.59  parent0: (1072) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 2
% 3.25/3.59     1 ==> 0
% 3.25/3.59     2 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 3.25/3.59    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 3.25/3.59  parent0: (1073) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 3.25/3.59    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 2
% 3.25/3.59     1 ==> 0
% 3.25/3.59     2 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent0: (1075) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 3.25/3.59     ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 2
% 3.25/3.59     2 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, Y ), ! apart_point_and_line( Z, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent0: (1076) {G0,W11,D3,L3,V3,M3}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 3.25/3.59     ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 2
% 3.25/3.59     2 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 3.25/3.59    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 3.25/3.59    apart_point_and_line( X, Z ) }.
% 3.25/3.59  parent0: (1079) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 3.25/3.59    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 3.25/3.59    apart_point_and_line( Y, T ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59     T := T
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 1
% 3.25/3.59     2 ==> 5
% 3.25/3.59     3 ==> 2
% 3.25/3.59     4 ==> 3
% 3.25/3.59     5 ==> 4
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 3.25/3.59    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 3.25/3.59  parent0: (1080) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 3.25/3.59    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 2
% 3.25/3.59     1 ==> 0
% 3.25/3.59     2 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 3.25/3.59     }.
% 3.25/3.59  parent0: (1083) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (15) {G0,W7,D3,L1,V0,M1} I { distinct_lines( line_connecting( 
% 3.25/3.59    skol1, skol2 ), line_connecting( skol2, skol1 ) ) }.
% 3.25/3.59  parent0: (1084) {G0,W7,D3,L1,V0,M1}  { distinct_lines( line_connecting( 
% 3.25/3.59    skol1, skol2 ), line_connecting( skol2, skol1 ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1130) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 3.25/3.59  parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), 
% 3.25/3.59    distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := X
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (19) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  parent0: (1130) {G1,W6,D2,L2,V2,M2}  { distinct_points( Y, X ), ! 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 1
% 3.25/3.59     1 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1132) {G1,W3,D2,L1,V0,M1}  { distinct_points( skol2, skol1 )
% 3.25/3.59     }.
% 3.25/3.59  parent0[0]: (19) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 3.25/3.59     }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := skol2
% 3.25/3.59     Y := skol1
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (22) {G2,W3,D2,L1,V0,M1} R(19,14) { distinct_points( skol2, 
% 3.25/3.59    skol1 ) }.
% 3.25/3.59  parent0: (1132) {G1,W3,D2,L1,V0,M1}  { distinct_points( skol2, skol1 ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1133) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 3.25/3.59    distinct_lines( X, Y ) }.
% 3.25/3.59  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 3.25/3.59  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 3.25/3.59    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := X
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 3.25/3.59    distinct_lines( X, Y ) }.
% 3.25/3.59  parent0: (1133) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 3.25/3.59    distinct_lines( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 1
% 3.25/3.59     1 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1135) {G1,W7,D3,L1,V0,M1}  { distinct_lines( line_connecting( 
% 3.25/3.59    skol2, skol1 ), line_connecting( skol1, skol2 ) ) }.
% 3.25/3.59  parent0[0]: (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 3.25/3.59    distinct_lines( X, Y ) }.
% 3.25/3.59  parent1[0]: (15) {G0,W7,D3,L1,V0,M1} I { distinct_lines( line_connecting( 
% 3.25/3.59    skol1, skol2 ), line_connecting( skol2, skol1 ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := line_connecting( skol2, skol1 )
% 3.25/3.59     Y := line_connecting( skol1, skol2 )
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (42) {G2,W7,D3,L1,V0,M1} R(15,30) { distinct_lines( 
% 3.25/3.59    line_connecting( skol2, skol1 ), line_connecting( skol1, skol2 ) ) }.
% 3.25/3.59  parent0: (1135) {G1,W7,D3,L1,V0,M1}  { distinct_lines( line_connecting( 
% 3.25/3.59    skol2, skol1 ), line_connecting( skol1, skol2 ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1137) {G1,W14,D3,L4,V4,M4}  { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, Y ), distinct_points( T, Z ), ! apart_point_and_line
% 3.25/3.59    ( T, line_connecting( X, Y ) ) }.
% 3.25/3.59  parent0[2]: (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, Y ), ! apart_point_and_line( Z, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 3.25/3.59    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := T
% 3.25/3.59     Y := line_connecting( X, Y )
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (92) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y ), !
% 3.25/3.59     distinct_points( Z, T ), distinct_points( Y, T ), ! apart_point_and_line
% 3.25/3.59    ( X, line_connecting( Z, T ) ) }.
% 3.25/3.59  parent0: (1137) {G1,W14,D3,L4,V4,M4}  { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, Y ), distinct_points( T, Z ), ! apart_point_and_line
% 3.25/3.59    ( T, line_connecting( X, Y ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Z
% 3.25/3.59     Y := T
% 3.25/3.59     Z := Y
% 3.25/3.59     T := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 1
% 3.25/3.59     1 ==> 2
% 3.25/3.59     2 ==> 0
% 3.25/3.59     3 ==> 3
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1141) {G1,W14,D3,L4,V4,M4}  { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, X ), distinct_points( T, Z ), ! apart_point_and_line
% 3.25/3.59    ( T, line_connecting( X, Y ) ) }.
% 3.25/3.59  parent0[2]: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), 
% 3.25/3.59    apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := T
% 3.25/3.59     Y := line_connecting( X, Y )
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (93) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y ), !
% 3.25/3.59     distinct_points( Z, T ), distinct_points( Y, Z ), ! apart_point_and_line
% 3.25/3.59    ( X, line_connecting( Z, T ) ) }.
% 3.25/3.59  parent0: (1141) {G1,W14,D3,L4,V4,M4}  { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, X ), distinct_points( T, Z ), ! apart_point_and_line
% 3.25/3.59    ( T, line_connecting( X, Y ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Z
% 3.25/3.59     Y := T
% 3.25/3.59     Z := Y
% 3.25/3.59     T := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 1
% 3.25/3.59     1 ==> 2
% 3.25/3.59     2 ==> 0
% 3.25/3.59     3 ==> 3
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  factor: (1144) {G1,W11,D3,L3,V2,M3}  { distinct_points( X, X ), ! 
% 3.25/3.59    distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent0[0, 2]: (93) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y )
% 3.25/3.59    , ! distinct_points( Z, T ), distinct_points( Y, Z ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := X
% 3.25/3.59     Z := X
% 3.25/3.59     T := Y
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1145) {G1,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 3.25/3.59  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 3.25/3.59  parent1[0]: (1144) {G1,W11,D3,L3,V2,M3}  { distinct_points( X, X ), ! 
% 3.25/3.59    distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (94) {G2,W8,D3,L2,V2,M1} F(93);r(0) { ! distinct_points( X, Y
% 3.25/3.59     ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 3.25/3.59  parent0: (1145) {G1,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  factor: (1146) {G1,W11,D3,L3,V2,M3}  { distinct_points( X, X ), ! 
% 3.25/3.59    distinct_points( Y, X ), ! apart_point_and_line( X, line_connecting( Y, X
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent0[0, 2]: (92) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y )
% 3.25/3.59    , ! distinct_points( Z, T ), distinct_points( Y, T ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := X
% 3.25/3.59     Z := Y
% 3.25/3.59     T := X
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1147) {G1,W8,D3,L2,V2,M2}  { ! distinct_points( Y, X ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 3.25/3.59  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 3.25/3.59  parent1[0]: (1146) {G1,W11,D3,L3,V2,M3}  { distinct_points( X, X ), ! 
% 3.25/3.59    distinct_points( Y, X ), ! apart_point_and_line( X, line_connecting( Y, X
% 3.25/3.59     ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (95) {G2,W8,D3,L2,V2,M1} F(92);r(0) { ! distinct_points( Y, X
% 3.25/3.59     ), ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 3.25/3.59  parent0: (1147) {G1,W8,D3,L2,V2,M2}  { ! distinct_points( Y, X ), ! 
% 3.25/3.59    apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1156) {G1,W25,D3,L7,V5,M7}  { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, X ), ! distinct_points( Z, T ), ! distinct_lines( U, 
% 3.25/3.59    line_connecting( X, Y ) ), apart_point_and_line( T, U ), 
% 3.25/3.59    apart_point_and_line( T, line_connecting( X, Y ) ), apart_point_and_line
% 3.25/3.59    ( Z, U ) }.
% 3.25/3.59  parent0[2]: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 3.25/3.59    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 3.25/3.59    apart_point_and_line( X, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := Z
% 3.25/3.59     Y := T
% 3.25/3.59     Z := U
% 3.25/3.59     T := line_connecting( X, Y )
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (120) {G1,W25,D3,L7,V5,M3} R(10,6) { ! distinct_points( X, Y )
% 3.25/3.59    , ! distinct_lines( Z, line_connecting( T, U ) ), ! distinct_points( T, U
% 3.25/3.59     ), distinct_points( X, T ), apart_point_and_line( Y, Z ), 
% 3.25/3.59    apart_point_and_line( Y, line_connecting( T, U ) ), apart_point_and_line
% 3.25/3.59    ( X, Z ) }.
% 3.25/3.59  parent0: (1156) {G1,W25,D3,L7,V5,M7}  { ! distinct_points( X, Y ), 
% 3.25/3.59    distinct_points( Z, X ), ! distinct_points( Z, T ), ! distinct_lines( U, 
% 3.25/3.59    line_connecting( X, Y ) ), apart_point_and_line( T, U ), 
% 3.25/3.59    apart_point_and_line( T, line_connecting( X, Y ) ), apart_point_and_line
% 3.25/3.59    ( Z, U ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := T
% 3.25/3.59     Y := U
% 3.25/3.59     Z := X
% 3.25/3.59     T := Y
% 3.25/3.59     U := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 2
% 3.25/3.59     1 ==> 3
% 3.25/3.59     2 ==> 0
% 3.25/3.59     3 ==> 1
% 3.25/3.59     4 ==> 4
% 3.25/3.59     5 ==> 5
% 3.25/3.59     6 ==> 6
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  factor: (1174) {G1,W22,D3,L6,V3,M6}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), distinct_points( X, X ), 
% 3.25/3.59    apart_point_and_line( Y, Z ), apart_point_and_line( Y, line_connecting( X
% 3.25/3.59    , Y ) ), apart_point_and_line( X, Z ) }.
% 3.25/3.59  parent0[0, 2]: (120) {G1,W25,D3,L7,V5,M3} R(10,6) { ! distinct_points( X, Y
% 3.25/3.59     ), ! distinct_lines( Z, line_connecting( T, U ) ), ! distinct_points( T
% 3.25/3.59    , U ), distinct_points( X, T ), apart_point_and_line( Y, Z ), 
% 3.25/3.59    apart_point_and_line( Y, line_connecting( T, U ) ), apart_point_and_line
% 3.25/3.59    ( X, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59     T := X
% 3.25/3.59     U := Y
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1181) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 3.25/3.59     ), apart_point_and_line( Y, line_connecting( X, Y ) ), 
% 3.25/3.59    apart_point_and_line( X, Z ) }.
% 3.25/3.59  parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 3.25/3.59  parent1[2]: (1174) {G1,W22,D3,L6,V3,M6}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), distinct_points( X, X ), 
% 3.25/3.59    apart_point_and_line( Y, Z ), apart_point_and_line( Y, line_connecting( X
% 3.25/3.59    , Y ) ), apart_point_and_line( X, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (125) {G2,W19,D3,L5,V3,M3} F(120);r(0) { ! distinct_points( X
% 3.25/3.59    , Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 3.25/3.59    apart_point_and_line( Y, line_connecting( X, Y ) ), apart_point_and_line
% 3.25/3.59    ( X, Z ), apart_point_and_line( Y, Z ) }.
% 3.25/3.59  parent0: (1181) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 3.25/3.59     ), apart_point_and_line( Y, line_connecting( X, Y ) ), 
% 3.25/3.59    apart_point_and_line( X, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 1
% 3.25/3.59     2 ==> 4
% 3.25/3.59     3 ==> 2
% 3.25/3.59     4 ==> 3
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1197) {G3,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 3.25/3.59    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 3.25/3.59  parent0[1]: (95) {G2,W8,D3,L2,V2,M1} F(92);r(0) { ! distinct_points( Y, X )
% 3.25/3.59    , ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 3.25/3.59  parent1[2]: (125) {G2,W19,D3,L5,V3,M3} F(120);r(0) { ! distinct_points( X, 
% 3.25/3.59    Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 3.25/3.59    ( Y, line_connecting( X, Y ) ), apart_point_and_line( X, Z ), 
% 3.25/3.59    apart_point_and_line( Y, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := X
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  factor: (1198) {G3,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 3.25/3.59     ), apart_point_and_line( Y, Z ) }.
% 3.25/3.59  parent0[0, 1]: (1197) {G3,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 3.25/3.59    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (822) {G3,W14,D3,L4,V3,M2} S(125);r(95) { ! distinct_points( X
% 3.25/3.59    , Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 3.25/3.59    apart_point_and_line( Y, Z ), apart_point_and_line( X, Z ) }.
% 3.25/3.59  parent0: (1198) {G3,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 3.25/3.59     ), apart_point_and_line( Y, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59     Z := Z
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 1
% 3.25/3.59     2 ==> 3
% 3.25/3.59     3 ==> 2
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1200) {G3,W18,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( Z, X ), ! distinct_lines( line_connecting( X, Y ), 
% 3.25/3.59    line_connecting( Z, X ) ), apart_point_and_line( Z, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  parent0[1]: (94) {G2,W8,D3,L2,V2,M1} F(93);r(0) { ! distinct_points( X, Y )
% 3.25/3.59    , ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 3.25/3.59  parent1[2]: (822) {G3,W14,D3,L4,V3,M2} S(125);r(95) { ! distinct_points( X
% 3.25/3.59    , Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 3.25/3.59    apart_point_and_line( Y, Z ), apart_point_and_line( X, Z ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := Z
% 3.25/3.59     Y := X
% 3.25/3.59     Z := line_connecting( X, Y )
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (839) {G4,W18,D3,L4,V3,M1} R(822,94) { ! distinct_points( X, Y
% 3.25/3.59     ), ! distinct_lines( line_connecting( Y, Z ), line_connecting( X, Y ) )
% 3.25/3.59    , ! distinct_points( Y, Z ), apart_point_and_line( X, line_connecting( Y
% 3.25/3.59    , Z ) ) }.
% 3.25/3.59  parent0: (1200) {G3,W18,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( Z, X ), ! distinct_lines( line_connecting( X, Y ), 
% 3.25/3.59    line_connecting( Z, X ) ), apart_point_and_line( Z, line_connecting( X, Y
% 3.25/3.59     ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := Z
% 3.25/3.59     Z := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 2
% 3.25/3.59     1 ==> 0
% 3.25/3.59     2 ==> 1
% 3.25/3.59     3 ==> 3
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1204) {G3,W16,D3,L4,V2,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( Y, X ), ! distinct_lines( line_connecting( X, Y ), 
% 3.25/3.59    line_connecting( Y, X ) ), ! distinct_points( X, Y ) }.
% 3.25/3.59  parent0[1]: (95) {G2,W8,D3,L2,V2,M1} F(92);r(0) { ! distinct_points( Y, X )
% 3.25/3.59    , ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 3.25/3.59  parent1[3]: (839) {G4,W18,D3,L4,V3,M1} R(822,94) { ! distinct_points( X, Y
% 3.25/3.59     ), ! distinct_lines( line_connecting( Y, Z ), line_connecting( X, Y ) )
% 3.25/3.59    , ! distinct_points( Y, Z ), apart_point_and_line( X, line_connecting( Y
% 3.25/3.59    , Z ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := X
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := X
% 3.25/3.59     Z := Y
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1209) {G2,W16,D3,L4,V2,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( line_connecting( X, Y ), line_connecting( Y, X ) ), ! 
% 3.25/3.59    distinct_points( X, Y ), ! distinct_points( X, Y ) }.
% 3.25/3.59  parent0[1]: (1204) {G3,W16,D3,L4,V2,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_points( Y, X ), ! distinct_lines( line_connecting( X, Y ), 
% 3.25/3.59    line_connecting( Y, X ) ), ! distinct_points( X, Y ) }.
% 3.25/3.59  parent1[1]: (19) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ), 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := X
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  factor: (1213) {G2,W13,D3,L3,V2,M3}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( line_connecting( X, Y ), line_connecting( Y, X ) ), ! 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  parent0[0, 2]: (1209) {G2,W16,D3,L4,V2,M4}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( line_connecting( X, Y ), line_connecting( Y, X ) ), ! 
% 3.25/3.59    distinct_points( X, Y ), ! distinct_points( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  factor: (1214) {G2,W10,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( line_connecting( X, Y ), line_connecting( Y, X ) ) }.
% 3.25/3.59  parent0[0, 2]: (1213) {G2,W13,D3,L3,V2,M3}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( line_connecting( X, Y ), line_connecting( Y, X ) ), ! 
% 3.25/3.59    distinct_points( X, Y ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := X
% 3.25/3.59     Y := Y
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (860) {G5,W10,D3,L2,V2,M1} R(839,95);f;r(19) { ! 
% 3.25/3.59    distinct_points( Y, X ), ! distinct_lines( line_connecting( Y, X ), 
% 3.25/3.59    line_connecting( X, Y ) ) }.
% 3.25/3.59  parent0: (1214) {G2,W10,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 3.25/3.59    distinct_lines( line_connecting( X, Y ), line_connecting( Y, X ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := Y
% 3.25/3.59     Y := X
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59     0 ==> 0
% 3.25/3.59     1 ==> 1
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1215) {G3,W3,D2,L1,V0,M1}  { ! distinct_points( skol2, skol1 )
% 3.25/3.59     }.
% 3.25/3.59  parent0[1]: (860) {G5,W10,D3,L2,V2,M1} R(839,95);f;r(19) { ! 
% 3.25/3.59    distinct_points( Y, X ), ! distinct_lines( line_connecting( Y, X ), 
% 3.25/3.59    line_connecting( X, Y ) ) }.
% 3.25/3.59  parent1[0]: (42) {G2,W7,D3,L1,V0,M1} R(15,30) { distinct_lines( 
% 3.25/3.59    line_connecting( skol2, skol1 ), line_connecting( skol1, skol2 ) ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59     X := skol1
% 3.25/3.59     Y := skol2
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  resolution: (1216) {G3,W0,D0,L0,V0,M0}  {  }.
% 3.25/3.59  parent0[0]: (1215) {G3,W3,D2,L1,V0,M1}  { ! distinct_points( skol2, skol1 )
% 3.25/3.59     }.
% 3.25/3.59  parent1[0]: (22) {G2,W3,D2,L1,V0,M1} R(19,14) { distinct_points( skol2, 
% 3.25/3.59    skol1 ) }.
% 3.25/3.59  substitution0:
% 3.25/3.59  end
% 3.25/3.59  substitution1:
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  subsumption: (1067) {G6,W0,D0,L0,V0,M0} R(860,42);r(22) {  }.
% 3.25/3.59  parent0: (1216) {G3,W0,D0,L0,V0,M0}  {  }.
% 3.25/3.59  substitution0:
% 3.25/3.59  end
% 3.25/3.59  permutation0:
% 3.25/3.59  end
% 3.25/3.59  
% 3.25/3.59  Proof check complete!
% 3.25/3.59  
% 3.25/3.59  Memory use:
% 3.25/3.59  
% 3.25/3.59  space for terms:        19289
% 3.25/3.59  space for clauses:      38176
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  clauses generated:      194083
% 3.25/3.59  clauses kept:           1068
% 3.25/3.59  clauses selected:       774
% 3.25/3.59  clauses deleted:        4
% 3.25/3.59  clauses inuse deleted:  0
% 3.25/3.59  
% 3.25/3.59  subsentry:          407125
% 3.25/3.59  literals s-matched: 345973
% 3.25/3.59  literals matched:   345872
% 3.25/3.59  full subsumption:   317430
% 3.25/3.59  
% 3.25/3.59  checksum:           -700602
% 3.25/3.59  
% 3.25/3.59  
% 3.25/3.59  Bliksem ended
%------------------------------------------------------------------------------