TSTP Solution File: GEO195+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Sat Jul 16 02:52:34 EDT 2022

% Result   : Theorem 0.74s 1.08s
% Output   : Refutation 0.74s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % DateTime : Sat Jun 18 04:12:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.74/1.08  *** allocated 10000 integers for termspace/termends
% 0.74/1.08  *** allocated 10000 integers for clauses
% 0.74/1.08  *** allocated 10000 integers for justifications
% 0.74/1.08  Bliksem 1.12
% 0.74/1.08  
% 0.74/1.08  
% 0.74/1.08  Automatic Strategy Selection
% 0.74/1.08  
% 0.74/1.08  
% 0.74/1.08  Clauses:
% 0.74/1.08  
% 0.74/1.08  { ! distinct_points( X, X ) }.
% 0.74/1.08  { ! distinct_lines( X, X ) }.
% 0.74/1.08  { ! convergent_lines( X, X ) }.
% 0.74/1.08  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.74/1.08     ) }.
% 0.74/1.08  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.74/1.08     }.
% 0.74/1.08  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.74/1.08    , Z ) }.
% 0.74/1.08  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.74/1.08    , Y ) ) }.
% 0.74/1.08  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.74/1.08    , Y ) ) }.
% 0.74/1.08  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.74/1.08    , Y ), X ) }.
% 0.74/1.08  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.74/1.08    , Y ), Y ) }.
% 0.74/1.08  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.74/1.08    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 0.74/1.08    apart_point_and_line( Y, T ) }.
% 0.74/1.08  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 0.74/1.08    apart_point_and_line( Z, Y ) }.
% 0.74/1.08  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 0.74/1.08    apart_point_and_line( X, Z ) }.
% 0.74/1.08  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 0.74/1.08    Z ) }.
% 0.74/1.08  { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.74/1.08  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.74/1.08  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.74/1.08  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 0.74/1.08    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.74/1.08  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.74/1.08  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.74/1.08    , convergent_lines( Y, Z ) }.
% 0.74/1.08  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.74/1.08    , unorthogonal_lines( Y, Z ) }.
% 0.74/1.08  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.74/1.08  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.74/1.08  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.74/1.08     }.
% 0.74/1.08  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.74/1.08  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.74/1.08  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 0.74/1.08    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 0.74/1.08    unorthogonal_lines( Y, T ) }.
% 0.74/1.08  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.74/1.08  { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), ! 
% 0.74/1.08    unorthogonal_lines( X, Y ) }.
% 0.74/1.08  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.74/1.08     unorthogonal_lines( X, Y ) }.
% 0.74/1.08  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.74/1.08  { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.74/1.08  { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.74/1.08     }.
% 0.74/1.08  { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), ! 
% 0.74/1.08    convergent_lines( X, Y ) }.
% 0.74/1.08  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.74/1.08    line_connecting( X, Y ) ) }.
% 0.74/1.08  { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point( 
% 0.74/1.08    intersection_point( X, Y ) ) }.
% 0.74/1.08  { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.74/1.08  { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.74/1.08  { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.74/1.08  { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.74/1.08  { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.74/1.08  { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.74/1.08  { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.74/1.08  { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.74/1.08  { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.74/1.08  { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.74/1.08  { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.74/1.08  { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.74/1.08  { convergent_lines( skol1, skol2 ) }.
% 0.74/1.08  { convergent_lines( skol3, skol2 ) }.
% 0.74/1.08  { convergent_lines( skol1, skol3 ) }.
% 0.74/1.08  { apart_point_and_line( intersection_point( skol1, skol2 ), skol3 ) }.
% 0.74/1.08  { ! apart_point_and_line( intersection_point( skol2, skol1 ), skol3 ) }.
% 0.74/1.08  
% 0.74/1.08  percentage equality = 0.000000, percentage horn = 0.627451
% 0.74/1.08  This a non-horn, non-equality problem
% 0.74/1.08  
% 0.74/1.08  
% 0.74/1.08  Options Used:
% 0.74/1.08  
% 0.74/1.08  useres =            1
% 0.74/1.08  useparamod =        0
% 0.74/1.08  useeqrefl =         0
% 0.74/1.08  useeqfact =         0
% 0.74/1.08  usefactor =         1
% 0.74/1.08  usesimpsplitting =  0
% 0.74/1.08  usesimpdemod =      0
% 0.74/1.08  usesimpres =        3
% 0.74/1.08  
% 0.74/1.08  resimpinuse      =  1000
% 0.74/1.08  resimpclauses =     20000
% 0.74/1.08  substype =          standard
% 0.74/1.08  backwardsubs =      1
% 0.74/1.08  selectoldest =      5
% 0.74/1.08  
% 0.74/1.08  litorderings [0] =  split
% 0.74/1.08  litorderings [1] =  liftord
% 0.74/1.08  
% 0.74/1.08  termordering =      none
% 0.74/1.08  
% 0.74/1.08  litapriori =        1
% 0.74/1.08  termapriori =       0
% 0.74/1.08  litaposteriori =    0
% 0.74/1.08  termaposteriori =   0
% 0.74/1.08  demodaposteriori =  0
% 0.74/1.08  ordereqreflfact =   0
% 0.74/1.08  
% 0.74/1.08  litselect =         none
% 0.74/1.08  
% 0.74/1.08  maxweight =         15
% 0.74/1.08  maxdepth =          30000
% 0.74/1.08  maxlength =         115
% 0.74/1.08  maxnrvars =         195
% 0.74/1.08  excuselevel =       1
% 0.74/1.08  increasemaxweight = 1
% 0.74/1.08  
% 0.74/1.08  maxselected =       10000000
% 0.74/1.08  maxnrclauses =      10000000
% 0.74/1.08  
% 0.74/1.08  showgenerated =    0
% 0.74/1.08  showkept =         0
% 0.74/1.08  showselected =     0
% 0.74/1.08  showdeleted =      0
% 0.74/1.08  showresimp =       1
% 0.74/1.08  showstatus =       2000
% 0.74/1.08  
% 0.74/1.08  prologoutput =     0
% 0.74/1.08  nrgoals =          5000000
% 0.74/1.08  totalproof =       1
% 0.74/1.08  
% 0.74/1.08  Symbols occurring in the translation:
% 0.74/1.08  
% 0.74/1.08  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.74/1.08  .  [1, 2]      (w:1, o:26, a:1, s:1, b:0), 
% 0.74/1.08  !  [4, 1]      (w:0, o:19, a:1, s:1, b:0), 
% 0.74/1.08  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.74/1.08  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.74/1.08  distinct_points  [36, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 0.74/1.08  distinct_lines  [37, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.74/1.08  convergent_lines  [38, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.74/1.08  line_connecting  [41, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.74/1.08  apart_point_and_line  [42, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.74/1.08  intersection_point  [43, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.74/1.08  parallel_through_point  [46, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.74/1.08  unorthogonal_lines  [49, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.74/1.08  orthogonal_through_point  [52, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.74/1.08  point  [54, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 0.74/1.08  line  [55, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 0.74/1.08  equal_points  [56, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.74/1.08  equal_lines  [57, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 0.74/1.08  parallel_lines  [58, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 0.74/1.08  incident_point_and_line  [59, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 0.74/1.08  orthogonal_lines  [60, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.74/1.08  alpha1  [61, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 0.74/1.08  alpha2  [62, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.74/1.08  skol1  [63, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 0.74/1.08  skol2  [64, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 0.74/1.08  skol3  [65, 0]      (w:1, o:18, a:1, s:1, b:0).
% 0.74/1.08  
% 0.74/1.08  
% 0.74/1.08  Starting Search:
% 0.74/1.08  
% 0.74/1.08  
% 0.74/1.08  Bliksems!, er is een bewijs:
% 0.74/1.08  % SZS status Theorem
% 0.74/1.08  % SZS output start Refutation
% 0.74/1.08  
% 0.74/1.08  (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.74/1.08  (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.74/1.08    , ! distinct_lines( X, Y ) }.
% 0.74/1.08  (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line( 
% 0.74/1.08    X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.74/1.08  (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.74/1.08    , Y ) }.
% 0.74/1.08  (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.74/1.08    , X ), Y ) }.
% 0.74/1.08  (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 0.74/1.08    parallel_through_point( Y, X ) ) }.
% 0.74/1.08  (49) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( intersection_point( 
% 0.74/1.08    skol1, skol2 ), skol3 ) }.
% 0.74/1.08  (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.74/1.08    ( X, Y ) }.
% 0.74/1.08  (125) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ), ! 
% 0.74/1.08    distinct_lines( Y, X ) }.
% 0.74/1.08  (145) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 0.74/1.08    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.74/1.08  (194) {G2,W7,D4,L1,V1,M1} R(145,49) { distinct_lines( skol3, 
% 0.74/1.08    parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.74/1.08  (197) {G3,W7,D4,L1,V1,M1} R(194,125) { convergent_lines( 
% 0.74/1.08    parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.74/1.08     }.
% 0.74/1.08  (202) {G4,W0,D0,L0,V0,M0} R(197,15) {  }.
% 0.74/1.08  
% 0.74/1.08  
% 0.74/1.08  % SZS output end Refutation
% 0.74/1.08  found a proof!
% 0.74/1.08  
% 0.74/1.08  *** allocated 15000 integers for clauses
% 0.74/1.08  
% 0.74/1.08  Unprocessed initial clauses:
% 0.74/1.08  
% 0.74/1.08  (204) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.74/1.08  (205) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.74/1.08  (206) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 0.74/1.08  (207) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X
% 0.74/1.08    , Z ), distinct_points( Y, Z ) }.
% 0.74/1.08  (208) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.74/1.08     ), distinct_lines( Y, Z ) }.
% 0.74/1.08  (209) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines( 
% 0.74/1.08    X, Z ), convergent_lines( Y, Z ) }.
% 0.74/1.08  (210) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.74/1.08    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.74/1.08  (211) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.74/1.08    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.74/1.08  (212) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.74/1.08    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.74/1.08  (213) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.74/1.08    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.74/1.08  (214) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines( 
% 0.74/1.08    Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 0.74/1.08    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.74/1.08  (215) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 0.74/1.08    distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.74/1.08  (216) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), distinct_lines
% 0.74/1.08    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.74/1.08  (217) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.74/1.08    , Z ), convergent_lines( X, Z ) }.
% 0.74/1.08  (218) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), convergent_lines( X
% 0.74/1.08    , Y ) }.
% 0.74/1.08  (219) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( Y
% 0.74/1.08    , X ), Y ) }.
% 0.74/1.08  (220) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.74/1.08    parallel_through_point( Y, X ) ) }.
% 0.74/1.08  (221) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), 
% 0.74/1.08    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 0.74/1.08    convergent_lines( X, Y ) }.
% 0.74/1.08  (222) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines( 
% 0.74/1.08    X, Y ) }.
% 0.74/1.08  (223) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 0.74/1.08    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.74/1.08  (224) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 0.74/1.08    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.74/1.08     }.
% 0.74/1.08  (225) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.74/1.08  (226) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.74/1.08     }.
% 0.74/1.08  (227) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 0.74/1.08    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.74/1.08  (228) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( orthogonal_through_point
% 0.74/1.08    ( Y, X ), Y ) }.
% 0.74/1.08  (229) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.74/1.08    orthogonal_through_point( Y, X ) ) }.
% 0.74/1.08  (230) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 0.74/1.08    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 0.74/1.08    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.74/1.08  (231) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines( 
% 0.74/1.08    X, Y ) }.
% 0.74/1.08  (232) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), convergent_lines( Z, Y ), ! 
% 0.74/1.08    convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.74/1.08  (233) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.74/1.08     convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.74/1.08  (234) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.74/1.08  (235) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.74/1.08     }.
% 0.74/1.08  (236) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 0.74/1.08    unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.74/1.08  (237) {G0,W9,D2,L3,V3,M3}  { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.74/1.08    ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.74/1.08  (238) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.74/1.08    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.74/1.08  (239) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), ! convergent_lines
% 0.74/1.08    ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.74/1.08  (240) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.74/1.08    parallel_through_point( X, Y ) ) }.
% 0.74/1.08  (241) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.74/1.08    orthogonal_through_point( X, Y ) ) }.
% 0.74/1.08  (242) {G0,W6,D2,L2,V2,M2}  { ! equal_points( X, Y ), ! distinct_points( X, 
% 0.74/1.08    Y ) }.
% 0.74/1.08  (243) {G0,W6,D2,L2,V2,M2}  { distinct_points( X, Y ), equal_points( X, Y )
% 0.74/1.08     }.
% 0.74/1.08  (244) {G0,W6,D2,L2,V2,M2}  { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.74/1.08     ) }.
% 0.74/1.08  (245) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.74/1.08     }.
% 0.74/1.08  (246) {G0,W6,D2,L2,V2,M2}  { ! parallel_lines( X, Y ), ! convergent_lines( 
% 0.74/1.08    X, Y ) }.
% 0.74/1.08  (247) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.74/1.08     ) }.
% 0.74/1.08  (248) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), ! 
% 0.74/1.08    apart_point_and_line( X, Y ) }.
% 0.74/1.08  (249) {G0,W6,D2,L2,V2,M2}  { apart_point_and_line( X, Y ), 
% 0.74/1.08    incident_point_and_line( X, Y ) }.
% 0.74/1.08  (250) {G0,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), ! 
% 0.74/1.08    unorthogonal_lines( X, Y ) }.
% 0.74/1.08  (251) {G0,W6,D2,L2,V2,M2}  { unorthogonal_lines( X, Y ), orthogonal_lines( 
% 0.74/1.08    X, Y ) }.
% 0.74/1.08  (252) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol2 ) }.
% 0.74/1.08  (253) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol3, skol2 ) }.
% 0.74/1.08  (254) {G0,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol3 ) }.
% 0.74/1.09  (255) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( intersection_point( 
% 0.74/1.09    skol1, skol2 ), skol3 ) }.
% 0.74/1.09  (256) {G0,W5,D3,L1,V0,M1}  { ! apart_point_and_line( intersection_point( 
% 0.74/1.09    skol2, skol1 ), skol3 ) }.
% 0.74/1.09  
% 0.74/1.09  
% 0.74/1.09  Total Proof:
% 0.74/1.09  
% 0.74/1.09  subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.74/1.09  parent0: (205) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 0.74/1.09    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.74/1.09  parent0: (208) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), 
% 0.74/1.09    distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09     Z := Z
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 2
% 0.74/1.09     1 ==> 0
% 0.74/1.09     2 ==> 1
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 0.74/1.09    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.74/1.09  parent0: (216) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), 
% 0.74/1.09    distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09     Z := Z
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 2
% 0.74/1.09     1 ==> 0
% 0.74/1.09     2 ==> 1
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 0.74/1.09    distinct_lines( X, Y ) }.
% 0.74/1.09  parent0: (218) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), 
% 0.74/1.09    convergent_lines( X, Y ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 1
% 0.74/1.09     1 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 0.74/1.09    parallel_through_point( Y, X ), Y ) }.
% 0.74/1.09  parent0: (219) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( 
% 0.74/1.09    parallel_through_point( Y, X ), Y ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 0.74/1.09    parallel_through_point( Y, X ) ) }.
% 0.74/1.09  parent0: (220) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.74/1.09    parallel_through_point( Y, X ) ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (49) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 0.74/1.09    intersection_point( skol1, skol2 ), skol3 ) }.
% 0.74/1.09  parent0: (255) {G0,W5,D3,L1,V0,M1}  { apart_point_and_line( 
% 0.74/1.09    intersection_point( skol1, skol2 ), skol3 ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  resolution: (310) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 0.74/1.09    distinct_lines( X, Y ) }.
% 0.74/1.09  parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.74/1.09  parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), 
% 0.74/1.09    distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09  end
% 0.74/1.09  substitution1:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09     Z := X
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 0.74/1.09    distinct_lines( X, Y ) }.
% 0.74/1.09  parent0: (310) {G1,W6,D2,L2,V2,M2}  { distinct_lines( Y, X ), ! 
% 0.74/1.09    distinct_lines( X, Y ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := Y
% 0.74/1.09     Y := X
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 1
% 0.74/1.09     1 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  resolution: (312) {G1,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), ! 
% 0.74/1.09    distinct_lines( Y, X ) }.
% 0.74/1.09  parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! 
% 0.74/1.09    distinct_lines( X, Y ) }.
% 0.74/1.09  parent1[1]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), 
% 0.74/1.09    distinct_lines( X, Y ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09  end
% 0.74/1.09  substitution1:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (125) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y )
% 0.74/1.09    , ! distinct_lines( Y, X ) }.
% 0.74/1.09  parent0: (312) {G1,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), ! 
% 0.74/1.09    distinct_lines( Y, X ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09     1 ==> 1
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  resolution: (313) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 0.74/1.09    parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.74/1.09  parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X, 
% 0.74/1.09    parallel_through_point( Y, X ) ) }.
% 0.74/1.09  parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), 
% 0.74/1.09    apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Y
% 0.74/1.09  end
% 0.74/1.09  substitution1:
% 0.74/1.09     X := X
% 0.74/1.09     Y := Z
% 0.74/1.09     Z := parallel_through_point( Y, X )
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (145) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 0.74/1.09    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.74/1.09  parent0: (313) {G1,W8,D3,L2,V3,M2}  { distinct_lines( Z, 
% 0.74/1.09    parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := Z
% 0.74/1.09     Y := Y
% 0.74/1.09     Z := X
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09     1 ==> 1
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  resolution: (314) {G1,W7,D4,L1,V1,M1}  { distinct_lines( skol3, 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.74/1.09  parent0[1]: (145) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X, 
% 0.74/1.09    parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.74/1.09  parent1[0]: (49) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( 
% 0.74/1.09    intersection_point( skol1, skol2 ), skol3 ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := skol3
% 0.74/1.09     Y := X
% 0.74/1.09     Z := intersection_point( skol1, skol2 )
% 0.74/1.09  end
% 0.74/1.09  substitution1:
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (194) {G2,W7,D4,L1,V1,M1} R(145,49) { distinct_lines( skol3, 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.74/1.09  parent0: (314) {G1,W7,D4,L1,V1,M1}  { distinct_lines( skol3, 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  resolution: (315) {G3,W7,D4,L1,V1,M1}  { convergent_lines( 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.74/1.09     }.
% 0.74/1.09  parent0[1]: (125) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ), 
% 0.74/1.09    ! distinct_lines( Y, X ) }.
% 0.74/1.09  parent1[0]: (194) {G2,W7,D4,L1,V1,M1} R(145,49) { distinct_lines( skol3, 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ) ) }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := parallel_through_point( X, intersection_point( skol1, skol2 ) )
% 0.74/1.09     Y := skol3
% 0.74/1.09  end
% 0.74/1.09  substitution1:
% 0.74/1.09     X := X
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (197) {G3,W7,D4,L1,V1,M1} R(194,125) { convergent_lines( 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.74/1.09     }.
% 0.74/1.09  parent0: (315) {G3,W7,D4,L1,V1,M1}  { convergent_lines( 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.74/1.09     }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := X
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09     0 ==> 0
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  resolution: (316) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.74/1.09  parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( 
% 0.74/1.09    parallel_through_point( Y, X ), Y ) }.
% 0.74/1.09  parent1[0]: (197) {G3,W7,D4,L1,V1,M1} R(194,125) { convergent_lines( 
% 0.74/1.09    parallel_through_point( X, intersection_point( skol1, skol2 ) ), skol3 )
% 0.74/1.09     }.
% 0.74/1.09  substitution0:
% 0.74/1.09     X := intersection_point( skol1, skol2 )
% 0.74/1.09     Y := skol3
% 0.74/1.09  end
% 0.74/1.09  substitution1:
% 0.74/1.09     X := skol3
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  subsumption: (202) {G4,W0,D0,L0,V0,M0} R(197,15) {  }.
% 0.74/1.09  parent0: (316) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.74/1.09  substitution0:
% 0.74/1.09  end
% 0.74/1.09  permutation0:
% 0.74/1.09  end
% 0.74/1.09  
% 0.74/1.09  Proof check complete!
% 0.74/1.09  
% 0.74/1.09  Memory use:
% 0.74/1.09  
% 0.74/1.09  space for terms:        3535
% 0.74/1.09  space for clauses:      9316
% 0.74/1.09  
% 0.74/1.09  
% 0.74/1.09  clauses generated:      531
% 0.74/1.09  clauses kept:           203
% 0.74/1.09  clauses selected:       83
% 0.74/1.09  clauses deleted:        0
% 0.74/1.09  clauses inuse deleted:  0
% 0.74/1.09  
% 0.74/1.09  subsentry:          840
% 0.74/1.09  literals s-matched: 662
% 0.74/1.09  literals matched:   637
% 0.74/1.09  full subsumption:   176
% 0.74/1.09  
% 0.74/1.09  checksum:           2084928953
% 0.74/1.09  
% 0.74/1.09  
% 0.74/1.09  Bliksem ended
%------------------------------------------------------------------------------