TSTP Solution File: GEO179+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n014.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 02:52:20 EDT 2022

% Result   : Theorem 0.50s 1.15s
% Output   : Refutation 0.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14  % Command  : bliksem %s
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % DateTime : Fri Jun 17 19:23:19 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.50/1.15  *** allocated 10000 integers for termspace/termends
% 0.50/1.15  *** allocated 10000 integers for clauses
% 0.50/1.15  *** allocated 10000 integers for justifications
% 0.50/1.15  Bliksem 1.12
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Automatic Strategy Selection
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Clauses:
% 0.50/1.15  
% 0.50/1.15  { ! distinct_points( X, X ) }.
% 0.50/1.15  { ! distinct_lines( X, X ) }.
% 0.50/1.15  { ! convergent_lines( X, X ) }.
% 0.50/1.15  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.50/1.15     ) }.
% 0.50/1.15  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.50/1.15     }.
% 0.50/1.15  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.50/1.15    , Z ) }.
% 0.50/1.15  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.50/1.15    , Y ) ) }.
% 0.50/1.15  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.50/1.15    , Y ) ) }.
% 0.50/1.15  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.50/1.15    , Y ), X ) }.
% 0.50/1.15  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.50/1.15    , Y ), Y ) }.
% 0.50/1.15  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.50/1.15    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 0.50/1.15    apart_point_and_line( Y, T ) }.
% 0.50/1.15  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 0.50/1.15    apart_point_and_line( Z, Y ) }.
% 0.50/1.15  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 0.50/1.15    apart_point_and_line( X, Z ) }.
% 0.50/1.15  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 0.50/1.15    Z ) }.
% 0.50/1.15  { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.50/1.15  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.50/1.15  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.50/1.15  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 0.50/1.15    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.50/1.15  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.50/1.15  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.50/1.15    , convergent_lines( Y, Z ) }.
% 0.50/1.15  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.50/1.15    , unorthogonal_lines( Y, Z ) }.
% 0.50/1.15  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.50/1.15  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.50/1.15  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.50/1.15     }.
% 0.50/1.15  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.50/1.15  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.50/1.15  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 0.50/1.15    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 0.50/1.15    unorthogonal_lines( Y, T ) }.
% 0.50/1.15  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.50/1.15  { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), ! 
% 0.50/1.15    unorthogonal_lines( X, Y ) }.
% 0.50/1.15  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.50/1.15     unorthogonal_lines( X, Y ) }.
% 0.50/1.15  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.50/1.15  { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.50/1.15  { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.50/1.15     }.
% 0.50/1.15  { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), ! 
% 0.50/1.15    convergent_lines( X, Y ) }.
% 0.50/1.15  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.50/1.15    line_connecting( X, Y ) ) }.
% 0.50/1.15  { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point( 
% 0.50/1.15    intersection_point( X, Y ) ) }.
% 0.50/1.15  { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.50/1.15  { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.50/1.15  { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.50/1.15  { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.50/1.15  { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.50/1.15  { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.50/1.15  { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.50/1.15  { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.50/1.15  { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.50/1.15  { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.50/1.15  { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.50/1.15  { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.50/1.15  { distinct_points( skol1, skol2 ) }.
% 0.50/1.15  { apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  { ! distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol3
% 0.50/1.15    , skol1 ) ), ! distinct_lines( line_connecting( skol1, skol2 ), 
% 0.50/1.15    line_connecting( skol3, skol2 ) ) }.
% 0.50/1.15  
% 0.50/1.15  percentage equality = 0.000000, percentage horn = 0.612245
% 0.50/1.15  This a non-horn, non-equality problem
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Options Used:
% 0.50/1.15  
% 0.50/1.15  useres =            1
% 0.50/1.15  useparamod =        0
% 0.50/1.15  useeqrefl =         0
% 0.50/1.15  useeqfact =         0
% 0.50/1.15  usefactor =         1
% 0.50/1.15  usesimpsplitting =  0
% 0.50/1.15  usesimpdemod =      0
% 0.50/1.15  usesimpres =        3
% 0.50/1.15  
% 0.50/1.15  resimpinuse      =  1000
% 0.50/1.15  resimpclauses =     20000
% 0.50/1.15  substype =          standard
% 0.50/1.15  backwardsubs =      1
% 0.50/1.15  selectoldest =      5
% 0.50/1.15  
% 0.50/1.15  litorderings [0] =  split
% 0.50/1.15  litorderings [1] =  liftord
% 0.50/1.15  
% 0.50/1.15  termordering =      none
% 0.50/1.15  
% 0.50/1.15  litapriori =        1
% 0.50/1.15  termapriori =       0
% 0.50/1.15  litaposteriori =    0
% 0.50/1.15  termaposteriori =   0
% 0.50/1.15  demodaposteriori =  0
% 0.50/1.15  ordereqreflfact =   0
% 0.50/1.15  
% 0.50/1.15  litselect =         none
% 0.50/1.15  
% 0.50/1.15  maxweight =         15
% 0.50/1.15  maxdepth =          30000
% 0.50/1.15  maxlength =         115
% 0.50/1.15  maxnrvars =         195
% 0.50/1.15  excuselevel =       1
% 0.50/1.15  increasemaxweight = 1
% 0.50/1.15  
% 0.50/1.15  maxselected =       10000000
% 0.50/1.15  maxnrclauses =      10000000
% 0.50/1.15  
% 0.50/1.15  showgenerated =    0
% 0.50/1.15  showkept =         0
% 0.50/1.15  showselected =     0
% 0.50/1.15  showdeleted =      0
% 0.50/1.15  showresimp =       1
% 0.50/1.15  showstatus =       2000
% 0.50/1.15  
% 0.50/1.15  prologoutput =     0
% 0.50/1.15  nrgoals =          5000000
% 0.50/1.15  totalproof =       1
% 0.50/1.15  
% 0.50/1.15  Symbols occurring in the translation:
% 0.50/1.15  
% 0.50/1.15  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.50/1.15  .  [1, 2]      (w:1, o:26, a:1, s:1, b:0), 
% 0.50/1.15  !  [4, 1]      (w:0, o:19, a:1, s:1, b:0), 
% 0.50/1.15  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.50/1.15  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.50/1.15  distinct_points  [36, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 0.50/1.15  distinct_lines  [37, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.50/1.15  convergent_lines  [38, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.50/1.15  line_connecting  [41, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.50/1.15  apart_point_and_line  [42, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.50/1.15  intersection_point  [43, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.50/1.15  parallel_through_point  [46, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.50/1.15  unorthogonal_lines  [49, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.50/1.15  orthogonal_through_point  [52, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.50/1.15  point  [54, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 0.50/1.15  line  [55, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 0.50/1.15  equal_points  [56, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.50/1.15  equal_lines  [57, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 0.50/1.15  parallel_lines  [58, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 0.50/1.15  incident_point_and_line  [59, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 0.50/1.15  orthogonal_lines  [60, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.50/1.15  alpha1  [61, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 0.50/1.15  alpha2  [62, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.50/1.15  skol1  [63, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 0.50/1.15  skol2  [64, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 0.50/1.15  skol3  [65, 0]      (w:1, o:18, a:1, s:1, b:0).
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Starting Search:
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Bliksems!, er is een bewijs:
% 0.50/1.15  % SZS status Theorem
% 0.50/1.15  % SZS output start Refutation
% 0.50/1.15  
% 0.50/1.15  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.50/1.15  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.50/1.15    , ! distinct_lines( X, Y ) }.
% 0.50/1.15  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 0.50/1.15    X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.50/1.15  (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.50/1.15    , Y ) }.
% 0.50/1.15  (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.50/1.15    , X ), Y ) }.
% 0.50/1.15  (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 0.50/1.15    parallel_through_point( Y, X ) ) }.
% 0.50/1.15  (47) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3, line_connecting( 
% 0.50/1.15    skol1, skol2 ) ) }.
% 0.50/1.15  (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.50/1.15    ( X, Y ) }.
% 0.50/1.15  (102) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), ! 
% 0.50/1.15    distinct_lines( Y, X ) }.
% 0.50/1.15  (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 0.50/1.15    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.50/1.15  (144) {G2,W7,D3,L1,V1,M1} R(141,47) { distinct_lines( line_connecting( 
% 0.50/1.15    skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.50/1.15  (145) {G3,W7,D3,L1,V1,M1} R(144,102) { convergent_lines( 
% 0.50/1.15    parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  (150) {G4,W0,D0,L0,V0,M0} R(145,15) {  }.
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  % SZS output end Refutation
% 0.50/1.15  found a proof!
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Unprocessed initial clauses:
% 0.50/1.15  
% 0.50/1.15  (152) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.50/1.15  (153) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.50/1.15  (154) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 0.50/1.15  (155) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 0.50/1.15    , Z ), distinct_points( Y, Z ) }.
% 0.50/1.15  (156) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.50/1.15     ), distinct_lines( Y, Z ) }.
% 0.50/1.15  (157) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines( 
% 0.50/1.15    X, Z ), convergent_lines( Y, Z ) }.
% 0.50/1.15  (158) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.50/1.15    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.50/1.15  (159) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.50/1.15    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.50/1.15  (160) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.50/1.15    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.50/1.15  (161) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.50/1.15    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.50/1.15  (162) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines( 
% 0.50/1.15    Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 0.50/1.15    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.50/1.15  (163) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 0.50/1.15    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.50/1.15  (164) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), distinct_lines
% 0.50/1.15    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.50/1.15  (165) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.50/1.15    , Z ), convergent_lines( X, Z ) }.
% 0.50/1.15  (166) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), convergent_lines( X
% 0.50/1.15    , Y ) }.
% 0.50/1.15  (167) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( Y
% 0.50/1.15    , X ), Y ) }.
% 0.50/1.15  (168) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.50/1.15    parallel_through_point( Y, X ) ) }.
% 0.50/1.15  (169) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 0.50/1.15    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 0.50/1.15    convergent_lines( X, Y ) }.
% 0.50/1.15  (170) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines( 
% 0.50/1.15    X, Y ) }.
% 0.50/1.15  (171) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 0.50/1.15    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.50/1.15  (172) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 0.50/1.15    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.50/1.15     }.
% 0.50/1.15  (173) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.50/1.15  (174) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.50/1.15     }.
% 0.50/1.15  (175) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 0.50/1.15    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.50/1.15  (176) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( orthogonal_through_point
% 0.50/1.15    ( Y, X ), Y ) }.
% 0.50/1.15  (177) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.50/1.15    orthogonal_through_point( Y, X ) ) }.
% 0.50/1.15  (178) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 0.50/1.15    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 0.50/1.15    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.50/1.15  (179) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines( 
% 0.50/1.15    X, Y ) }.
% 0.50/1.15  (180) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), convergent_lines( Z, Y ), ! 
% 0.50/1.15    convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.50/1.15  (181) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.50/1.15     convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.50/1.15  (182) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.50/1.15  (183) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.50/1.15     }.
% 0.50/1.15  (184) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 0.50/1.15    unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.50/1.15  (185) {G0,W9,D2,L3,V3,M3}  { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.50/1.15    ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.50/1.15  (186) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.50/1.15    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.50/1.15  (187) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), ! convergent_lines
% 0.50/1.15    ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.50/1.15  (188) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.50/1.15    parallel_through_point( X, Y ) ) }.
% 0.50/1.15  (189) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.50/1.15    orthogonal_through_point( X, Y ) ) }.
% 0.50/1.15  (190) {G0,W6,D2,L2,V2,M2}  { ! equal_points( X, Y ), ! distinct_points( X, 
% 0.50/1.15    Y ) }.
% 0.50/1.15  (191) {G0,W6,D2,L2,V2,M2}  { distinct_points( X, Y ), equal_points( X, Y )
% 0.50/1.15     }.
% 0.50/1.15  (192) {G0,W6,D2,L2,V2,M2}  { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.50/1.15     ) }.
% 0.50/1.15  (193) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.50/1.15     }.
% 0.50/1.15  (194) {G0,W6,D2,L2,V2,M2}  { ! parallel_lines( X, Y ), ! convergent_lines( 
% 0.50/1.15    X, Y ) }.
% 0.50/1.15  (195) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.50/1.15     ) }.
% 0.50/1.15  (196) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), ! 
% 0.50/1.15    apart_point_and_line( X, Y ) }.
% 0.50/1.15  (197) {G0,W6,D2,L2,V2,M2}  { apart_point_and_line( X, Y ), 
% 0.50/1.15    incident_point_and_line( X, Y ) }.
% 0.50/1.15  (198) {G0,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), ! 
% 0.50/1.15    unorthogonal_lines( X, Y ) }.
% 0.50/1.15  (199) {G0,W6,D2,L2,V2,M2}  { unorthogonal_lines( X, Y ), orthogonal_lines( 
% 0.50/1.15    X, Y ) }.
% 0.50/1.15  (200) {G0,W3,D2,L1,V0,M1}  { distinct_points( skol1, skol2 ) }.
% 0.50/1.15  (201) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( skol3, line_connecting( 
% 0.50/1.15    skol1, skol2 ) ) }.
% 0.50/1.15  (202) {G0,W14,D3,L2,V0,M2}  { ! distinct_lines( line_connecting( skol1, 
% 0.50/1.15    skol2 ), line_connecting( skol3, skol1 ) ), ! distinct_lines( 
% 0.50/1.15    line_connecting( skol1, skol2 ), line_connecting( skol3, skol2 ) ) }.
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Total Proof:
% 0.50/1.15  
% 0.50/1.15  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.50/1.15  parent0: (153) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 0.50/1.15    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.50/1.15  parent0: (156) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 0.50/1.15    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15     Z := Z
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 2
% 0.50/1.15     1 ==> 0
% 0.50/1.15     2 ==> 1
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 0.50/1.15    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.50/1.15  parent0: (164) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 0.50/1.15    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15     Z := Z
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 2
% 0.50/1.15     1 ==> 0
% 0.50/1.15     2 ==> 1
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 0.50/1.15    distinct_lines( X, Y ) }.
% 0.50/1.15  parent0: (166) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), 
% 0.50/1.15    convergent_lines( X, Y ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 1
% 0.50/1.15     1 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 0.50/1.15    parallel_through_point( Y, X ), Y ) }.
% 0.50/1.15  parent0: (167) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( 
% 0.50/1.15    parallel_through_point( Y, X ), Y ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 0.50/1.15    parallel_through_point( Y, X ) ) }.
% 0.50/1.15  parent0: (168) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.50/1.15    parallel_through_point( Y, X ) ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (47) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3, 
% 0.50/1.15    line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  parent0: (201) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( skol3, 
% 0.50/1.15    line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  resolution: (256) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 0.50/1.15    distinct_lines( X, Y ) }.
% 0.50/1.15  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.50/1.15  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 0.50/1.15    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15  end
% 0.50/1.15  substitution1:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15     Z := X
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 0.50/1.15    distinct_lines( X, Y ) }.
% 0.50/1.15  parent0: (256) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 0.50/1.15    distinct_lines( X, Y ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := Y
% 0.50/1.15     Y := X
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 1
% 0.50/1.15     1 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  resolution: (258) {G1,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), ! 
% 0.50/1.15    distinct_lines( Y, X ) }.
% 0.50/1.15  parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 0.50/1.15    distinct_lines( X, Y ) }.
% 0.50/1.15  parent1[1]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 0.50/1.15    distinct_lines( X, Y ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15  end
% 0.50/1.15  substitution1:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (102) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y )
% 0.50/1.15    , ! distinct_lines( Y, X ) }.
% 0.50/1.15  parent0: (258) {G1,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), ! 
% 0.50/1.15    distinct_lines( Y, X ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15     1 ==> 1
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  resolution: (259) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 0.50/1.15    parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.50/1.15  parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 0.50/1.15    parallel_through_point( Y, X ) ) }.
% 0.50/1.15  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 0.50/1.15    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Y
% 0.50/1.15  end
% 0.50/1.15  substitution1:
% 0.50/1.15     X := X
% 0.50/1.15     Y := Z
% 0.50/1.15     Z := parallel_through_point( Y, X )
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 0.50/1.15    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.50/1.15  parent0: (259) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 0.50/1.15    parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := Z
% 0.50/1.15     Y := Y
% 0.50/1.15     Z := X
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15     1 ==> 1
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  resolution: (260) {G1,W7,D3,L1,V1,M1}  { distinct_lines( line_connecting( 
% 0.50/1.15    skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.50/1.15  parent0[1]: (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 0.50/1.15    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.50/1.15  parent1[0]: (47) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3, 
% 0.50/1.15    line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := line_connecting( skol1, skol2 )
% 0.50/1.15     Y := X
% 0.50/1.15     Z := skol3
% 0.50/1.15  end
% 0.50/1.15  substitution1:
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (144) {G2,W7,D3,L1,V1,M1} R(141,47) { distinct_lines( 
% 0.50/1.15    line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.50/1.15  parent0: (260) {G1,W7,D3,L1,V1,M1}  { distinct_lines( line_connecting( 
% 0.50/1.15    skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  resolution: (261) {G3,W7,D3,L1,V1,M1}  { convergent_lines( 
% 0.50/1.15    parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  parent0[1]: (102) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), 
% 0.50/1.15    ! distinct_lines( Y, X ) }.
% 0.50/1.15  parent1[0]: (144) {G2,W7,D3,L1,V1,M1} R(141,47) { distinct_lines( 
% 0.50/1.15    line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := parallel_through_point( X, skol3 )
% 0.50/1.15     Y := line_connecting( skol1, skol2 )
% 0.50/1.15  end
% 0.50/1.15  substitution1:
% 0.50/1.15     X := X
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (145) {G3,W7,D3,L1,V1,M1} R(144,102) { convergent_lines( 
% 0.50/1.15    parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  parent0: (261) {G3,W7,D3,L1,V1,M1}  { convergent_lines( 
% 0.50/1.15    parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := X
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15     0 ==> 0
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  resolution: (262) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.50/1.15  parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 0.50/1.15    parallel_through_point( Y, X ), Y ) }.
% 0.50/1.15  parent1[0]: (145) {G3,W7,D3,L1,V1,M1} R(144,102) { convergent_lines( 
% 0.50/1.15    parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.50/1.15  substitution0:
% 0.50/1.15     X := skol3
% 0.50/1.15     Y := line_connecting( skol1, skol2 )
% 0.50/1.15  end
% 0.50/1.15  substitution1:
% 0.50/1.15     X := line_connecting( skol1, skol2 )
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  subsumption: (150) {G4,W0,D0,L0,V0,M0} R(145,15) {  }.
% 0.50/1.15  parent0: (262) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.50/1.15  substitution0:
% 0.50/1.15  end
% 0.50/1.15  permutation0:
% 0.50/1.15  end
% 0.50/1.15  
% 0.50/1.15  Proof check complete!
% 0.50/1.15  
% 0.50/1.15  Memory use:
% 0.50/1.15  
% 0.50/1.15  space for terms:        3081
% 0.50/1.15  space for clauses:      7105
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  clauses generated:      395
% 0.50/1.15  clauses kept:           151
% 0.50/1.15  clauses selected:       54
% 0.50/1.15  clauses deleted:        0
% 0.50/1.15  clauses inuse deleted:  0
% 0.50/1.15  
% 0.50/1.15  subsentry:          593
% 0.50/1.15  literals s-matched: 471
% 0.50/1.15  literals matched:   446
% 0.50/1.15  full subsumption:   146
% 0.50/1.15  
% 0.50/1.15  checksum:           -1472815898
% 0.50/1.15  
% 0.50/1.15  
% 0.50/1.15  Bliksem ended
%------------------------------------------------------------------------------