TSTP Solution File: GEO189+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO189+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Sat Jul 16 02:52:28 EDT 2022

% Result   : Theorem 1.40s 1.78s
% Output   : Refutation 1.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : GEO189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : bliksem %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % DateTime : Sat Jun 18 05:00:43 EDT 2022
% 0.20/0.35  % CPUTime  : 
% 1.40/1.78  *** allocated 10000 integers for termspace/termends
% 1.40/1.78  *** allocated 10000 integers for clauses
% 1.40/1.78  *** allocated 10000 integers for justifications
% 1.40/1.78  Bliksem 1.12
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  Automatic Strategy Selection
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  Clauses:
% 1.40/1.78  
% 1.40/1.78  { ! distinct_points( X, X ) }.
% 1.40/1.78  { ! distinct_lines( X, X ) }.
% 1.40/1.78  { ! convergent_lines( X, X ) }.
% 1.40/1.78  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.40/1.78     ) }.
% 1.40/1.78  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.40/1.78     }.
% 1.40/1.78  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.40/1.78    , Z ) }.
% 1.40/1.78  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.40/1.78    , Y ) ) }.
% 1.40/1.78  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.40/1.78    , Y ) ) }.
% 1.40/1.78  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.40/1.78    , Y ), X ) }.
% 1.40/1.78  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.40/1.78    , Y ), Y ) }.
% 1.40/1.78  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.40/1.78    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, T ) }.
% 1.40/1.78  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 1.40/1.78    apart_point_and_line( Z, Y ) }.
% 1.40/1.78  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 1.40/1.78    apart_point_and_line( X, Z ) }.
% 1.40/1.78  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 1.40/1.78    Z ) }.
% 1.40/1.78  { distinct_points( skol1, skol2 ) }.
% 1.40/1.78  { distinct_points( skol1, skol3 ) }.
% 1.40/1.78  { distinct_points( skol2, skol3 ) }.
% 1.40/1.78  { ! apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  { apart_point_and_line( skol2, line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  
% 1.40/1.78  percentage equality = 0.000000, percentage horn = 0.631579
% 1.40/1.78  This a non-horn, non-equality problem
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  Options Used:
% 1.40/1.78  
% 1.40/1.78  useres =            1
% 1.40/1.78  useparamod =        0
% 1.40/1.78  useeqrefl =         0
% 1.40/1.78  useeqfact =         0
% 1.40/1.78  usefactor =         1
% 1.40/1.78  usesimpsplitting =  0
% 1.40/1.78  usesimpdemod =      0
% 1.40/1.78  usesimpres =        3
% 1.40/1.78  
% 1.40/1.78  resimpinuse      =  1000
% 1.40/1.78  resimpclauses =     20000
% 1.40/1.78  substype =          standard
% 1.40/1.78  backwardsubs =      1
% 1.40/1.78  selectoldest =      5
% 1.40/1.78  
% 1.40/1.78  litorderings [0] =  split
% 1.40/1.78  litorderings [1] =  liftord
% 1.40/1.78  
% 1.40/1.78  termordering =      none
% 1.40/1.78  
% 1.40/1.78  litapriori =        1
% 1.40/1.78  termapriori =       0
% 1.40/1.78  litaposteriori =    0
% 1.40/1.78  termaposteriori =   0
% 1.40/1.78  demodaposteriori =  0
% 1.40/1.78  ordereqreflfact =   0
% 1.40/1.78  
% 1.40/1.78  litselect =         none
% 1.40/1.78  
% 1.40/1.78  maxweight =         15
% 1.40/1.78  maxdepth =          30000
% 1.40/1.78  maxlength =         115
% 1.40/1.78  maxnrvars =         195
% 1.40/1.78  excuselevel =       1
% 1.40/1.78  increasemaxweight = 1
% 1.40/1.78  
% 1.40/1.78  maxselected =       10000000
% 1.40/1.78  maxnrclauses =      10000000
% 1.40/1.78  
% 1.40/1.78  showgenerated =    0
% 1.40/1.78  showkept =         0
% 1.40/1.78  showselected =     0
% 1.40/1.78  showdeleted =      0
% 1.40/1.78  showresimp =       1
% 1.40/1.78  showstatus =       2000
% 1.40/1.78  
% 1.40/1.78  prologoutput =     0
% 1.40/1.78  nrgoals =          5000000
% 1.40/1.78  totalproof =       1
% 1.40/1.78  
% 1.40/1.78  Symbols occurring in the translation:
% 1.40/1.78  
% 1.40/1.78  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.40/1.78  .  [1, 2]      (w:1, o:19, a:1, s:1, b:0), 
% 1.40/1.78  !  [4, 1]      (w:0, o:14, a:1, s:1, b:0), 
% 1.40/1.78  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.40/1.78  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.40/1.78  distinct_points  [36, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 1.40/1.78  distinct_lines  [37, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 1.40/1.78  convergent_lines  [38, 2]      (w:1, o:43, a:1, s:1, b:0), 
% 1.40/1.78  line_connecting  [41, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 1.40/1.78  apart_point_and_line  [42, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 1.40/1.78  intersection_point  [43, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 1.40/1.78  skol1  [46, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 1.40/1.78  skol2  [47, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 1.40/1.78  skol3  [48, 0]      (w:1, o:13, a:1, s:1, b:0).
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  Starting Search:
% 1.40/1.78  
% 1.40/1.78  *** allocated 15000 integers for clauses
% 1.40/1.78  *** allocated 22500 integers for clauses
% 1.40/1.78  *** allocated 33750 integers for clauses
% 1.40/1.78  *** allocated 15000 integers for termspace/termends
% 1.40/1.78  
% 1.40/1.78  Bliksems!, er is een bewijs:
% 1.40/1.78  % SZS status Theorem
% 1.40/1.78  % SZS output start Refutation
% 1.40/1.78  
% 1.40/1.78  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.40/1.78  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.40/1.78    , ! distinct_lines( X, Y ) }.
% 1.40/1.78  (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.40/1.78  (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines( 
% 1.40/1.78    Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 1.40/1.78  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 1.40/1.78    X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.40/1.78  (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 1.40/1.78  (15) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol3 ) }.
% 1.40/1.78  (16) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol2, skol3 ) }.
% 1.40/1.78  (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol3, line_connecting
% 1.40/1.78    ( skol1, skol2 ) ) }.
% 1.40/1.78  (18) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol2, line_connecting( 
% 1.40/1.78    skol1, skol3 ) ) }.
% 1.40/1.78  (32) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 1.40/1.78    ( X, Y ) }.
% 1.40/1.78  (33) {G2,W9,D2,L3,V3,M3} R(32,4) { distinct_lines( Z, X ), ! distinct_lines
% 1.40/1.78    ( Y, Z ), distinct_lines( X, Y ) }.
% 1.40/1.78  (76) {G1,W22,D3,L6,V4,M3} R(10,7) { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, line_connecting( T, X ) ), ! distinct_points( T, X ), 
% 1.40/1.78    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( T, X ) ) }.
% 1.40/1.78  (80) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T ), 
% 1.40/1.78    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.40/1.78  (89) {G2,W14,D3,L4,V3,M2} F(80);r(7) { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 1.40/1.78     ), apart_point_and_line( X, Z ) }.
% 1.40/1.78  (144) {G1,W8,D3,L2,V1,M1} R(12,18) { distinct_lines( line_connecting( skol1
% 1.40/1.78    , skol3 ), X ), apart_point_and_line( skol2, X ) }.
% 1.40/1.78  (148) {G2,W10,D3,L2,V1,M1} R(144,6) { ! distinct_points( skol2, X ), 
% 1.40/1.78    distinct_lines( line_connecting( skol1, skol3 ), line_connecting( skol2, 
% 1.40/1.78    X ) ) }.
% 1.40/1.78  (307) {G3,W13,D3,L3,V2,M2} R(148,33) { ! distinct_points( skol2, X ), 
% 1.40/1.78    distinct_lines( Y, line_connecting( skol1, skol3 ) ), distinct_lines( 
% 1.40/1.78    line_connecting( skol2, X ), Y ) }.
% 1.40/1.78  (548) {G2,W14,D3,L4,V1,M1} R(76,17);r(16) { ! distinct_points( skol1, skol2
% 1.40/1.78     ), ! distinct_lines( X, line_connecting( skol1, skol2 ) ), 
% 1.40/1.78    apart_point_and_line( skol2, X ), apart_point_and_line( skol3, X ) }.
% 1.40/1.78  (581) {G3,W15,D3,L3,V1,M1} R(89,17) { ! distinct_points( X, skol3 ), ! 
% 1.40/1.78    distinct_lines( line_connecting( skol1, skol2 ), line_connecting( X, 
% 1.40/1.78    skol3 ) ), apart_point_and_line( X, line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  (604) {G3,W11,D3,L3,V1,M1} S(548);r(14) { ! distinct_lines( X, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ), apart_point_and_line( skol2, X ), 
% 1.40/1.78    apart_point_and_line( skol3, X ) }.
% 1.40/1.78  (609) {G4,W15,D3,L3,V1,M1} R(604,7) { ! distinct_lines( line_connecting( X
% 1.40/1.78    , skol3 ), line_connecting( skol1, skol2 ) ), ! distinct_points( X, skol3
% 1.40/1.78     ), apart_point_and_line( skol2, line_connecting( X, skol3 ) ) }.
% 1.40/1.78  (613) {G5,W7,D3,L1,V0,M1} R(609,6);f;r(16) { ! distinct_lines( 
% 1.40/1.78    line_connecting( skol2, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  (616) {G6,W7,D3,L1,V0,M1} R(613,307);r(16) { distinct_lines( 
% 1.40/1.78    line_connecting( skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  (786) {G4,W10,D3,L2,V0,M1} R(581,6);r(15) { ! distinct_points( skol1, skol2
% 1.40/1.78     ), ! distinct_lines( line_connecting( skol1, skol2 ), line_connecting( 
% 1.40/1.78    skol1, skol3 ) ) }.
% 1.40/1.78  (787) {G7,W0,D0,L0,V0,M0} S(786);r(14);r(616) {  }.
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  % SZS output end Refutation
% 1.40/1.78  found a proof!
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  Unprocessed initial clauses:
% 1.40/1.78  
% 1.40/1.78  (789) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 1.40/1.78  (790) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 1.40/1.78  (791) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 1.40/1.78  (792) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 1.40/1.78    , Z ), distinct_points( Y, Z ) }.
% 1.40/1.78  (793) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 1.40/1.78     ), distinct_lines( Y, Z ) }.
% 1.40/1.78  (794) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines( 
% 1.40/1.78    X, Z ), convergent_lines( Y, Z ) }.
% 1.40/1.78  (795) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  (796) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.40/1.78  (797) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.40/1.78  (798) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.40/1.78  (799) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines( 
% 1.40/1.78    Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 1.40/1.78    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.40/1.78  (800) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.40/1.78    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.40/1.78  (801) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), distinct_lines
% 1.40/1.78    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.40/1.78  (802) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.40/1.78    , Z ), convergent_lines( X, Z ) }.
% 1.40/1.78  (803) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 1.40/1.78  (804) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol3 ) }.
% 1.40/1.78  (805) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol2, skol3 ) }.
% 1.40/1.78  (806) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( skol3, line_connecting
% 1.40/1.78    ( skol1, skol2 ) ) }.
% 1.40/1.78  (807) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( skol2, line_connecting( 
% 1.40/1.78    skol1, skol3 ) ) }.
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  Total Proof:
% 1.40/1.78  
% 1.40/1.78  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.40/1.78  parent0: (790) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 1.40/1.78    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.40/1.78  parent0: (793) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 1.40/1.78    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := Z
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 2
% 1.40/1.78     1 ==> 0
% 1.40/1.78     2 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent0: (795) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent0: (796) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 1.40/1.78    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 1.40/1.78    apart_point_and_line( X, Z ) }.
% 1.40/1.78  parent0: (799) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, T ), apart_point_and_line( X, Z ), 
% 1.40/1.78    apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, T ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := Z
% 1.40/1.78     T := T
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78     2 ==> 5
% 1.40/1.78     3 ==> 2
% 1.40/1.78     4 ==> 3
% 1.40/1.78     5 ==> 4
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 1.40/1.78    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.40/1.78  parent0: (801) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 1.40/1.78    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := Z
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 2
% 1.40/1.78     1 ==> 0
% 1.40/1.78     2 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.40/1.78     }.
% 1.40/1.78  parent0: (803) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (15) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol3 )
% 1.40/1.78     }.
% 1.40/1.78  parent0: (804) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol3 ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (16) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol2, skol3 )
% 1.40/1.78     }.
% 1.40/1.78  parent0: (805) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol2, skol3 ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol3, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  parent0: (806) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( skol3, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (18) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol2, 
% 1.40/1.78    line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent0: (807) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( skol2, 
% 1.40/1.78    line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (879) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 1.40/1.78    distinct_lines( X, Y ) }.
% 1.40/1.78  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.40/1.78  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 1.40/1.78    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := X
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (32) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 1.40/1.78    distinct_lines( X, Y ) }.
% 1.40/1.78  parent0: (879) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 1.40/1.78    distinct_lines( X, Y ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := Y
% 1.40/1.78     Y := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 1
% 1.40/1.78     1 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (881) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), 
% 1.40/1.78    distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 1.40/1.78  parent0[0]: (32) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 1.40/1.78    distinct_lines( X, Y ) }.
% 1.40/1.78  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 1.40/1.78    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := Y
% 1.40/1.78     Y := X
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Z
% 1.40/1.78     Z := Y
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (33) {G2,W9,D2,L3,V3,M3} R(32,4) { distinct_lines( Z, X ), ! 
% 1.40/1.78    distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 1.40/1.78  parent0: (881) {G1,W9,D2,L3,V3,M3}  { distinct_lines( Y, X ), 
% 1.40/1.78    distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := Y
% 1.40/1.78     Y := X
% 1.40/1.78     Z := Z
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 2
% 1.40/1.78     1 ==> 0
% 1.40/1.78     2 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (884) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_points( Y, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.40/1.78    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.40/1.78    , Y ) ), apart_point_and_line( Y, T ) }.
% 1.40/1.78  parent0[1]: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 1.40/1.78    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 1.40/1.78    apart_point_and_line( X, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := Y
% 1.40/1.78     Y := Z
% 1.40/1.78     Z := T
% 1.40/1.78     T := line_connecting( X, Y )
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (76) {G1,W22,D3,L6,V4,M3} R(10,7) { ! distinct_points( X, Y )
% 1.40/1.78    , ! distinct_lines( Z, line_connecting( T, X ) ), ! distinct_points( T, X
% 1.40/1.78     ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( T, X ) ) }.
% 1.40/1.78  parent0: (884) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_points( Y, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.40/1.78    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.40/1.78    , Y ) ), apart_point_and_line( Y, T ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := T
% 1.40/1.78     Y := X
% 1.40/1.78     Z := Y
% 1.40/1.78     T := Z
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 2
% 1.40/1.78     1 ==> 0
% 1.40/1.78     2 ==> 1
% 1.40/1.78     3 ==> 4
% 1.40/1.78     4 ==> 5
% 1.40/1.78     5 ==> 3
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (900) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.40/1.78    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.40/1.78    , Y ) ), apart_point_and_line( X, T ) }.
% 1.40/1.78  parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, T ), apart_point_and_line( X, T ), 
% 1.40/1.78    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ), 
% 1.40/1.78    apart_point_and_line( X, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Z
% 1.40/1.78     Z := T
% 1.40/1.78     T := line_connecting( X, Y )
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (80) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y )
% 1.40/1.78    , ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T
% 1.40/1.78     ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.40/1.78  parent0: (900) {G1,W22,D3,L6,V4,M6}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ), 
% 1.40/1.78    apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.40/1.78    , Y ) ), apart_point_and_line( X, T ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := T
% 1.40/1.78     Z := Y
% 1.40/1.78     T := Z
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 2
% 1.40/1.78     1 ==> 0
% 1.40/1.78     2 ==> 1
% 1.40/1.78     3 ==> 4
% 1.40/1.78     4 ==> 5
% 1.40/1.78     5 ==> 3
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  factor: (916) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.40/1.78     ), apart_point_and_line( Y, Z ), apart_point_and_line( Y, 
% 1.40/1.78    line_connecting( X, Y ) ) }.
% 1.40/1.78  parent0[0, 2]: (80) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y
% 1.40/1.78     ), ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X
% 1.40/1.78    , T ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := Z
% 1.40/1.78     T := Y
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (923) {G1,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 1.40/1.78    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.40/1.78  parent0[1]: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent1[4]: (916) {G1,W19,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.40/1.78     ), apart_point_and_line( Y, Z ), apart_point_and_line( Y, 
% 1.40/1.78    line_connecting( X, Y ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := Z
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  factor: (924) {G1,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.40/1.78     ), apart_point_and_line( Y, Z ) }.
% 1.40/1.78  parent0[0, 1]: (923) {G1,W17,D3,L5,V3,M5}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), 
% 1.40/1.78    apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := Z
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (89) {G2,W14,D3,L4,V3,M2} F(80);r(7) { ! distinct_points( X, Y
% 1.40/1.78     ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.40/1.78    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.40/1.78  parent0: (924) {G1,W14,D3,L4,V3,M4}  { ! distinct_points( X, Y ), ! 
% 1.40/1.78    distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.40/1.78     ), apart_point_and_line( Y, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78     Z := Z
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78     2 ==> 3
% 1.40/1.78     3 ==> 2
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (926) {G1,W8,D3,L2,V1,M2}  { distinct_lines( line_connecting( 
% 1.40/1.78    skol1, skol3 ), X ), apart_point_and_line( skol2, X ) }.
% 1.40/1.78  parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 1.40/1.78    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.40/1.78  parent1[0]: (18) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol2, 
% 1.40/1.78    line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := skol2
% 1.40/1.78     Y := line_connecting( skol1, skol3 )
% 1.40/1.78     Z := X
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (144) {G1,W8,D3,L2,V1,M1} R(12,18) { distinct_lines( 
% 1.40/1.78    line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol2, X )
% 1.40/1.78     }.
% 1.40/1.78  parent0: (926) {G1,W8,D3,L2,V1,M2}  { distinct_lines( line_connecting( 
% 1.40/1.78    skol1, skol3 ), X ), apart_point_and_line( skol2, X ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (927) {G1,W10,D3,L2,V1,M2}  { ! distinct_points( skol2, X ), 
% 1.40/1.78    distinct_lines( line_connecting( skol1, skol3 ), line_connecting( skol2, 
% 1.40/1.78    X ) ) }.
% 1.40/1.78  parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent1[1]: (144) {G1,W8,D3,L2,V1,M1} R(12,18) { distinct_lines( 
% 1.40/1.78    line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol2, X )
% 1.40/1.78     }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := skol2
% 1.40/1.78     Y := X
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := line_connecting( skol2, X )
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (148) {G2,W10,D3,L2,V1,M1} R(144,6) { ! distinct_points( skol2
% 1.40/1.78    , X ), distinct_lines( line_connecting( skol1, skol3 ), line_connecting( 
% 1.40/1.78    skol2, X ) ) }.
% 1.40/1.78  parent0: (927) {G1,W10,D3,L2,V1,M2}  { ! distinct_points( skol2, X ), 
% 1.40/1.78    distinct_lines( line_connecting( skol1, skol3 ), line_connecting( skol2, 
% 1.40/1.78    X ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (928) {G3,W13,D3,L3,V2,M3}  { distinct_lines( line_connecting( 
% 1.40/1.78    skol2, X ), Y ), distinct_lines( Y, line_connecting( skol1, skol3 ) ), ! 
% 1.40/1.78    distinct_points( skol2, X ) }.
% 1.40/1.78  parent0[1]: (33) {G2,W9,D2,L3,V3,M3} R(32,4) { distinct_lines( Z, X ), ! 
% 1.40/1.78    distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 1.40/1.78  parent1[1]: (148) {G2,W10,D3,L2,V1,M1} R(144,6) { ! distinct_points( skol2
% 1.40/1.78    , X ), distinct_lines( line_connecting( skol1, skol3 ), line_connecting( 
% 1.40/1.78    skol2, X ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := Y
% 1.40/1.78     Y := line_connecting( skol1, skol3 )
% 1.40/1.78     Z := line_connecting( skol2, X )
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (307) {G3,W13,D3,L3,V2,M2} R(148,33) { ! distinct_points( 
% 1.40/1.78    skol2, X ), distinct_lines( Y, line_connecting( skol1, skol3 ) ), 
% 1.40/1.78    distinct_lines( line_connecting( skol2, X ), Y ) }.
% 1.40/1.78  parent0: (928) {G3,W13,D3,L3,V2,M3}  { distinct_lines( line_connecting( 
% 1.40/1.78    skol2, X ), Y ), distinct_lines( Y, line_connecting( skol1, skol3 ) ), ! 
% 1.40/1.78    distinct_points( skol2, X ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := Y
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 2
% 1.40/1.78     1 ==> 1
% 1.40/1.78     2 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (931) {G1,W17,D3,L5,V1,M5}  { ! distinct_points( skol2, skol3 )
% 1.40/1.78    , ! distinct_lines( X, line_connecting( skol1, skol2 ) ), ! 
% 1.40/1.78    distinct_points( skol1, skol2 ), apart_point_and_line( skol2, X ), 
% 1.40/1.78    apart_point_and_line( skol3, X ) }.
% 1.40/1.78  parent0[0]: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol3, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  parent1[5]: (76) {G1,W22,D3,L6,V4,M3} R(10,7) { ! distinct_points( X, Y ), 
% 1.40/1.78    ! distinct_lines( Z, line_connecting( T, X ) ), ! distinct_points( T, X )
% 1.40/1.78    , apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ), 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( T, X ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := skol2
% 1.40/1.78     Y := skol3
% 1.40/1.78     Z := X
% 1.40/1.78     T := skol1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (933) {G1,W14,D3,L4,V1,M4}  { ! distinct_lines( X, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ), ! distinct_points( skol1, skol2 ), 
% 1.40/1.78    apart_point_and_line( skol2, X ), apart_point_and_line( skol3, X ) }.
% 1.40/1.78  parent0[0]: (931) {G1,W17,D3,L5,V1,M5}  { ! distinct_points( skol2, skol3 )
% 1.40/1.78    , ! distinct_lines( X, line_connecting( skol1, skol2 ) ), ! 
% 1.40/1.78    distinct_points( skol1, skol2 ), apart_point_and_line( skol2, X ), 
% 1.40/1.78    apart_point_and_line( skol3, X ) }.
% 1.40/1.78  parent1[0]: (16) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol2, skol3 )
% 1.40/1.78     }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (548) {G2,W14,D3,L4,V1,M1} R(76,17);r(16) { ! distinct_points
% 1.40/1.78    ( skol1, skol2 ), ! distinct_lines( X, line_connecting( skol1, skol2 ) )
% 1.40/1.78    , apart_point_and_line( skol2, X ), apart_point_and_line( skol3, X ) }.
% 1.40/1.78  parent0: (933) {G1,W14,D3,L4,V1,M4}  { ! distinct_lines( X, line_connecting
% 1.40/1.78    ( skol1, skol2 ) ), ! distinct_points( skol1, skol2 ), 
% 1.40/1.78    apart_point_and_line( skol2, X ), apart_point_and_line( skol3, X ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 1
% 1.40/1.78     1 ==> 0
% 1.40/1.78     2 ==> 2
% 1.40/1.78     3 ==> 3
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  *** allocated 50625 integers for clauses
% 1.40/1.78  resolution: (934) {G1,W15,D3,L3,V1,M3}  { ! distinct_points( X, skol3 ), ! 
% 1.40/1.78    distinct_lines( line_connecting( skol1, skol2 ), line_connecting( X, 
% 1.40/1.78    skol3 ) ), apart_point_and_line( X, line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  parent0[0]: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol3, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  parent1[2]: (89) {G2,W14,D3,L4,V3,M2} F(80);r(7) { ! distinct_points( X, Y
% 1.40/1.78     ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.40/1.78    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := X
% 1.40/1.78     Y := skol3
% 1.40/1.78     Z := line_connecting( skol1, skol2 )
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (581) {G3,W15,D3,L3,V1,M1} R(89,17) { ! distinct_points( X, 
% 1.40/1.78    skol3 ), ! distinct_lines( line_connecting( skol1, skol2 ), 
% 1.40/1.78    line_connecting( X, skol3 ) ), apart_point_and_line( X, line_connecting( 
% 1.40/1.78    skol1, skol2 ) ) }.
% 1.40/1.78  parent0: (934) {G1,W15,D3,L3,V1,M3}  { ! distinct_points( X, skol3 ), ! 
% 1.40/1.78    distinct_lines( line_connecting( skol1, skol2 ), line_connecting( X, 
% 1.40/1.78    skol3 ) ), apart_point_and_line( X, line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78     2 ==> 2
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (936) {G1,W11,D3,L3,V1,M3}  { ! distinct_lines( X, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ), apart_point_and_line( skol2, X ), 
% 1.40/1.78    apart_point_and_line( skol3, X ) }.
% 1.40/1.78  parent0[0]: (548) {G2,W14,D3,L4,V1,M1} R(76,17);r(16) { ! distinct_points( 
% 1.40/1.78    skol1, skol2 ), ! distinct_lines( X, line_connecting( skol1, skol2 ) ), 
% 1.40/1.78    apart_point_and_line( skol2, X ), apart_point_and_line( skol3, X ) }.
% 1.40/1.78  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.40/1.78     }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (604) {G3,W11,D3,L3,V1,M1} S(548);r(14) { ! distinct_lines( X
% 1.40/1.78    , line_connecting( skol1, skol2 ) ), apart_point_and_line( skol2, X ), 
% 1.40/1.78    apart_point_and_line( skol3, X ) }.
% 1.40/1.78  parent0: (936) {G1,W11,D3,L3,V1,M3}  { ! distinct_lines( X, line_connecting
% 1.40/1.78    ( skol1, skol2 ) ), apart_point_and_line( skol2, X ), 
% 1.40/1.78    apart_point_and_line( skol3, X ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78     2 ==> 2
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (938) {G1,W15,D3,L3,V1,M3}  { ! distinct_points( X, skol3 ), ! 
% 1.40/1.78    distinct_lines( line_connecting( X, skol3 ), line_connecting( skol1, 
% 1.40/1.78    skol2 ) ), apart_point_and_line( skol2, line_connecting( X, skol3 ) ) }.
% 1.40/1.78  parent0[1]: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent1[2]: (604) {G3,W11,D3,L3,V1,M1} S(548);r(14) { ! distinct_lines( X, 
% 1.40/1.78    line_connecting( skol1, skol2 ) ), apart_point_and_line( skol2, X ), 
% 1.40/1.78    apart_point_and_line( skol3, X ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78     Y := skol3
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := line_connecting( X, skol3 )
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (609) {G4,W15,D3,L3,V1,M1} R(604,7) { ! distinct_lines( 
% 1.40/1.78    line_connecting( X, skol3 ), line_connecting( skol1, skol2 ) ), ! 
% 1.40/1.78    distinct_points( X, skol3 ), apart_point_and_line( skol2, line_connecting
% 1.40/1.78    ( X, skol3 ) ) }.
% 1.40/1.78  parent0: (938) {G1,W15,D3,L3,V1,M3}  { ! distinct_points( X, skol3 ), ! 
% 1.40/1.78    distinct_lines( line_connecting( X, skol3 ), line_connecting( skol1, 
% 1.40/1.78    skol2 ) ), apart_point_and_line( skol2, line_connecting( X, skol3 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := X
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 1
% 1.40/1.78     1 ==> 0
% 1.40/1.78     2 ==> 2
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (939) {G1,W13,D3,L3,V0,M3}  { ! distinct_points( skol2, skol3 )
% 1.40/1.78    , ! distinct_lines( line_connecting( skol2, skol3 ), line_connecting( 
% 1.40/1.78    skol1, skol2 ) ), ! distinct_points( skol2, skol3 ) }.
% 1.40/1.78  parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent1[2]: (609) {G4,W15,D3,L3,V1,M1} R(604,7) { ! distinct_lines( 
% 1.40/1.78    line_connecting( X, skol3 ), line_connecting( skol1, skol2 ) ), ! 
% 1.40/1.78    distinct_points( X, skol3 ), apart_point_and_line( skol2, line_connecting
% 1.40/1.78    ( X, skol3 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := skol2
% 1.40/1.78     Y := skol3
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := skol2
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  factor: (940) {G1,W10,D3,L2,V0,M2}  { ! distinct_points( skol2, skol3 ), ! 
% 1.40/1.78    distinct_lines( line_connecting( skol2, skol3 ), line_connecting( skol1, 
% 1.40/1.78    skol2 ) ) }.
% 1.40/1.78  parent0[0, 2]: (939) {G1,W13,D3,L3,V0,M3}  { ! distinct_points( skol2, 
% 1.40/1.78    skol3 ), ! distinct_lines( line_connecting( skol2, skol3 ), 
% 1.40/1.78    line_connecting( skol1, skol2 ) ), ! distinct_points( skol2, skol3 ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (942) {G1,W7,D3,L1,V0,M1}  { ! distinct_lines( line_connecting
% 1.40/1.78    ( skol2, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  parent0[0]: (940) {G1,W10,D3,L2,V0,M2}  { ! distinct_points( skol2, skol3 )
% 1.40/1.78    , ! distinct_lines( line_connecting( skol2, skol3 ), line_connecting( 
% 1.40/1.78    skol1, skol2 ) ) }.
% 1.40/1.78  parent1[0]: (16) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol2, skol3 )
% 1.40/1.78     }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (613) {G5,W7,D3,L1,V0,M1} R(609,6);f;r(16) { ! distinct_lines
% 1.40/1.78    ( line_connecting( skol2, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  parent0: (942) {G1,W7,D3,L1,V0,M1}  { ! distinct_lines( line_connecting( 
% 1.40/1.78    skol2, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (943) {G4,W10,D3,L2,V0,M2}  { ! distinct_points( skol2, skol3 )
% 1.40/1.78    , distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol1
% 1.40/1.78    , skol3 ) ) }.
% 1.40/1.78  parent0[0]: (613) {G5,W7,D3,L1,V0,M1} R(609,6);f;r(16) { ! distinct_lines( 
% 1.40/1.78    line_connecting( skol2, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.40/1.78  parent1[2]: (307) {G3,W13,D3,L3,V2,M2} R(148,33) { ! distinct_points( skol2
% 1.40/1.78    , X ), distinct_lines( Y, line_connecting( skol1, skol3 ) ), 
% 1.40/1.78    distinct_lines( line_connecting( skol2, X ), Y ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := skol3
% 1.40/1.78     Y := line_connecting( skol1, skol2 )
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (944) {G1,W7,D3,L1,V0,M1}  { distinct_lines( line_connecting( 
% 1.40/1.78    skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent0[0]: (943) {G4,W10,D3,L2,V0,M2}  { ! distinct_points( skol2, skol3 )
% 1.40/1.78    , distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol1
% 1.40/1.78    , skol3 ) ) }.
% 1.40/1.78  parent1[0]: (16) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol2, skol3 )
% 1.40/1.78     }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (616) {G6,W7,D3,L1,V0,M1} R(613,307);r(16) { distinct_lines( 
% 1.40/1.78    line_connecting( skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent0: (944) {G1,W7,D3,L1,V0,M1}  { distinct_lines( line_connecting( 
% 1.40/1.78    skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (945) {G1,W13,D3,L3,V0,M3}  { ! distinct_points( skol1, skol2 )
% 1.40/1.78    , ! distinct_points( skol1, skol3 ), ! distinct_lines( line_connecting( 
% 1.40/1.78    skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), ! 
% 1.40/1.78    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.40/1.78  parent1[2]: (581) {G3,W15,D3,L3,V1,M1} R(89,17) { ! distinct_points( X, 
% 1.40/1.78    skol3 ), ! distinct_lines( line_connecting( skol1, skol2 ), 
% 1.40/1.78    line_connecting( X, skol3 ) ), apart_point_and_line( X, line_connecting( 
% 1.40/1.78    skol1, skol2 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78     X := skol1
% 1.40/1.78     Y := skol2
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78     X := skol1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (946) {G1,W10,D3,L2,V0,M2}  { ! distinct_points( skol1, skol2 )
% 1.40/1.78    , ! distinct_lines( line_connecting( skol1, skol2 ), line_connecting( 
% 1.40/1.78    skol1, skol3 ) ) }.
% 1.40/1.78  parent0[1]: (945) {G1,W13,D3,L3,V0,M3}  { ! distinct_points( skol1, skol2 )
% 1.40/1.78    , ! distinct_points( skol1, skol3 ), ! distinct_lines( line_connecting( 
% 1.40/1.78    skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol3 )
% 1.40/1.78     }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (786) {G4,W10,D3,L2,V0,M1} R(581,6);r(15) { ! distinct_points
% 1.40/1.78    ( skol1, skol2 ), ! distinct_lines( line_connecting( skol1, skol2 ), 
% 1.40/1.78    line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent0: (946) {G1,W10,D3,L2,V0,M2}  { ! distinct_points( skol1, skol2 ), !
% 1.40/1.78     distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol1
% 1.40/1.78    , skol3 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78     0 ==> 0
% 1.40/1.78     1 ==> 1
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (947) {G1,W7,D3,L1,V0,M1}  { ! distinct_lines( line_connecting
% 1.40/1.78    ( skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent0[0]: (786) {G4,W10,D3,L2,V0,M1} R(581,6);r(15) { ! distinct_points( 
% 1.40/1.78    skol1, skol2 ), ! distinct_lines( line_connecting( skol1, skol2 ), 
% 1.40/1.78    line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.40/1.78     }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  resolution: (948) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.40/1.78  parent0[0]: (947) {G1,W7,D3,L1,V0,M1}  { ! distinct_lines( line_connecting
% 1.40/1.78    ( skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  parent1[0]: (616) {G6,W7,D3,L1,V0,M1} R(613,307);r(16) { distinct_lines( 
% 1.40/1.78    line_connecting( skol1, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  substitution1:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  subsumption: (787) {G7,W0,D0,L0,V0,M0} S(786);r(14);r(616) {  }.
% 1.40/1.78  parent0: (948) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.40/1.78  substitution0:
% 1.40/1.78  end
% 1.40/1.78  permutation0:
% 1.40/1.78  end
% 1.40/1.78  
% 1.40/1.78  Proof check complete!
% 1.40/1.78  
% 1.40/1.78  Memory use:
% 1.40/1.78  
% 1.40/1.78  space for terms:        11325
% 1.40/1.78  space for clauses:      30453
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  clauses generated:      77385
% 1.40/1.78  clauses kept:           788
% 1.40/1.78  clauses selected:       643
% 1.40/1.78  clauses deleted:        5
% 1.40/1.78  clauses inuse deleted:  0
% 1.40/1.78  
% 1.40/1.78  subsentry:          90244
% 1.40/1.78  literals s-matched: 67622
% 1.40/1.78  literals matched:   67521
% 1.40/1.78  full subsumption:   54170
% 1.40/1.78  
% 1.40/1.78  checksum:           -528718253
% 1.40/1.78  
% 1.40/1.78  
% 1.40/1.78  Bliksem ended
%------------------------------------------------------------------------------