TSTP Solution File: GEO216+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : GEO216+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n010.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 02:52:52 EDT 2022

% Result   : Theorem 0.46s 1.10s
% Output   : Refutation 0.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO216+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % DateTime : Fri Jun 17 20:37:53 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.46/1.10  *** allocated 10000 integers for termspace/termends
% 0.46/1.10  *** allocated 10000 integers for clauses
% 0.46/1.10  *** allocated 10000 integers for justifications
% 0.46/1.10  Bliksem 1.12
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Automatic Strategy Selection
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Clauses:
% 0.46/1.10  
% 0.46/1.10  { ! distinct_points( X, X ) }.
% 0.46/1.10  { ! distinct_lines( X, X ) }.
% 0.46/1.10  { ! convergent_lines( X, X ) }.
% 0.46/1.10  { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.46/1.10     ) }.
% 0.46/1.10  { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.46/1.10     }.
% 0.46/1.10  { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.46/1.10    , Z ) }.
% 0.46/1.10  { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.46/1.10    , Y ) ) }.
% 0.46/1.10  { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.46/1.10    , Y ) ) }.
% 0.46/1.10  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.46/1.10    , Y ), X ) }.
% 0.46/1.10  { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.46/1.10    , Y ), Y ) }.
% 0.46/1.10  { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.46/1.10    ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ), 
% 0.46/1.10    apart_point_and_line( Y, T ) }.
% 0.46/1.10  { ! apart_point_and_line( X, Y ), distinct_points( X, Z ), 
% 0.46/1.10    apart_point_and_line( Z, Y ) }.
% 0.46/1.10  { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ), 
% 0.46/1.10    apart_point_and_line( X, Z ) }.
% 0.46/1.10  { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X, 
% 0.46/1.10    Z ) }.
% 0.46/1.10  { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.46/1.10  { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.46/1.10  { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.46/1.10  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 0.46/1.10    apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.46/1.10  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.46/1.10  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.46/1.10    , convergent_lines( Y, Z ) }.
% 0.46/1.10  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.46/1.10    , unorthogonal_lines( Y, Z ) }.
% 0.46/1.10  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.46/1.10  { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.46/1.10  { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.46/1.10     }.
% 0.46/1.10  { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.46/1.10  { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.46/1.10  { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ), 
% 0.46/1.10    apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ), 
% 0.46/1.10    unorthogonal_lines( Y, T ) }.
% 0.46/1.10  { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.46/1.10  { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.46/1.10     unorthogonal_lines( X, Y ) }.
% 0.46/1.10  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.46/1.10  { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.46/1.10  { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.46/1.10     }.
% 0.46/1.10  { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), ! 
% 0.46/1.10    convergent_lines( X, Y ) }.
% 0.46/1.10  { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line( 
% 0.46/1.10    line_connecting( X, Y ) ) }.
% 0.46/1.10  { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point( 
% 0.46/1.10    intersection_point( X, Y ) ) }.
% 0.46/1.10  { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.46/1.10  { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.46/1.10  { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.46/1.10  { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.46/1.10  { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.46/1.10  { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.46/1.10  { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.46/1.10  { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.46/1.10  { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.46/1.10  { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.46/1.10  { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.46/1.10  { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.46/1.10  { orthogonal_lines( skol1, skol1 ) }.
% 0.46/1.10  
% 0.46/1.10  percentage equality = 0.000000, percentage horn = 0.595745
% 0.46/1.10  This a non-horn, non-equality problem
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Options Used:
% 0.46/1.10  
% 0.46/1.10  useres =            1
% 0.46/1.10  useparamod =        0
% 0.46/1.10  useeqrefl =         0
% 0.46/1.10  useeqfact =         0
% 0.46/1.10  usefactor =         1
% 0.46/1.10  usesimpsplitting =  0
% 0.46/1.10  usesimpdemod =      0
% 0.46/1.10  usesimpres =        3
% 0.46/1.10  
% 0.46/1.10  resimpinuse      =  1000
% 0.46/1.10  resimpclauses =     20000
% 0.46/1.10  substype =          standard
% 0.46/1.10  backwardsubs =      1
% 0.46/1.10  selectoldest =      5
% 0.46/1.10  
% 0.46/1.10  litorderings [0] =  split
% 0.46/1.10  litorderings [1] =  liftord
% 0.46/1.10  
% 0.46/1.10  termordering =      none
% 0.46/1.10  
% 0.46/1.10  litapriori =        1
% 0.46/1.10  termapriori =       0
% 0.46/1.10  litaposteriori =    0
% 0.46/1.10  termaposteriori =   0
% 0.46/1.10  demodaposteriori =  0
% 0.46/1.10  ordereqreflfact =   0
% 0.46/1.10  
% 0.46/1.10  litselect =         none
% 0.46/1.10  
% 0.46/1.10  maxweight =         15
% 0.46/1.10  maxdepth =          30000
% 0.46/1.10  maxlength =         115
% 0.46/1.10  maxnrvars =         195
% 0.46/1.10  excuselevel =       1
% 0.46/1.10  increasemaxweight = 1
% 0.46/1.10  
% 0.46/1.10  maxselected =       10000000
% 0.46/1.10  maxnrclauses =      10000000
% 0.46/1.10  
% 0.46/1.10  showgenerated =    0
% 0.46/1.10  showkept =         0
% 0.46/1.10  showselected =     0
% 0.46/1.10  showdeleted =      0
% 0.46/1.10  showresimp =       1
% 0.46/1.10  showstatus =       2000
% 0.46/1.10  
% 0.46/1.10  prologoutput =     0
% 0.46/1.10  nrgoals =          5000000
% 0.46/1.10  totalproof =       1
% 0.46/1.10  
% 0.46/1.10  Symbols occurring in the translation:
% 0.46/1.10  
% 0.46/1.10  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.46/1.10  .  [1, 2]      (w:1, o:24, a:1, s:1, b:0), 
% 0.46/1.10  !  [4, 1]      (w:0, o:17, a:1, s:1, b:0), 
% 0.46/1.10  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.46/1.10  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.46/1.10  distinct_points  [36, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.46/1.10  distinct_lines  [37, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.46/1.10  convergent_lines  [38, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.46/1.10  line_connecting  [41, 2]      (w:1, o:51, a:1, s:1, b:0), 
% 0.46/1.10  apart_point_and_line  [42, 2]      (w:1, o:52, a:1, s:1, b:0), 
% 0.46/1.10  intersection_point  [43, 2]      (w:1, o:53, a:1, s:1, b:0), 
% 0.46/1.10  parallel_through_point  [46, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.46/1.10  unorthogonal_lines  [49, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.46/1.10  orthogonal_through_point  [52, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.46/1.10  point  [54, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.46/1.10  line  [55, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.46/1.10  equal_points  [56, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.46/1.10  equal_lines  [57, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.46/1.10  parallel_lines  [58, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.46/1.10  incident_point_and_line  [59, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 0.46/1.10  orthogonal_lines  [60, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.46/1.10  alpha1  [61, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 0.46/1.10  alpha2  [62, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 0.46/1.10  skol1  [63, 0]      (w:1, o:16, a:1, s:1, b:0).
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Starting Search:
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Bliksems!, er is een bewijs:
% 0.46/1.10  % SZS status Theorem
% 0.46/1.10  % SZS output start Refutation
% 0.46/1.10  
% 0.46/1.10  (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.46/1.10  (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines( 
% 0.46/1.10    X, Y ) }.
% 0.46/1.10  (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol1, skol1 ) }.
% 0.46/1.10  (68) {G1,W6,D2,L2,V2,M1} R(17,44) { convergent_lines( X, Y ), ! 
% 0.46/1.10    orthogonal_lines( X, Y ) }.
% 0.46/1.10  (72) {G2,W0,D0,L0,V0,M0} R(68,46);r(2) {  }.
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  % SZS output end Refutation
% 0.46/1.10  found a proof!
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Unprocessed initial clauses:
% 0.46/1.10  
% 0.46/1.10  (74) {G0,W3,D2,L1,V1,M1}  { ! distinct_points( X, X ) }.
% 0.46/1.10  (75) {G0,W3,D2,L1,V1,M1}  { ! distinct_lines( X, X ) }.
% 0.46/1.10  (76) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 0.46/1.10  (77) {G0,W9,D2,L3,V3,M3}  { ! distinct_points( X, Y ), distinct_points( X, 
% 0.46/1.10    Z ), distinct_points( Y, Z ) }.
% 0.46/1.10  (78) {G0,W9,D2,L3,V3,M3}  { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.46/1.10     ), distinct_lines( Y, Z ) }.
% 0.46/1.10  (79) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), convergent_lines( X
% 0.46/1.10    , Z ), convergent_lines( Y, Z ) }.
% 0.46/1.10  (80) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.46/1.10    apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.46/1.10  (81) {G0,W8,D3,L2,V2,M2}  { ! distinct_points( X, Y ), ! 
% 0.46/1.10    apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.46/1.10  (82) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.46/1.10    apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.46/1.10  (83) {G0,W8,D3,L2,V2,M2}  { ! convergent_lines( X, Y ), ! 
% 0.46/1.10    apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.46/1.10  (84) {G0,W18,D2,L6,V4,M6}  { ! distinct_points( X, Y ), ! distinct_lines( Z
% 0.46/1.10    , T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ), 
% 0.46/1.10    apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.46/1.10  (85) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), distinct_points
% 0.46/1.10    ( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.46/1.10  (86) {G0,W9,D2,L3,V3,M3}  { ! apart_point_and_line( X, Y ), distinct_lines
% 0.46/1.10    ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.46/1.10  (87) {G0,W9,D2,L3,V3,M3}  { ! convergent_lines( X, Y ), distinct_lines( Y, 
% 0.46/1.10    Z ), convergent_lines( X, Z ) }.
% 0.46/1.10  (88) {G0,W6,D2,L2,V2,M2}  { ! distinct_lines( X, Y ), convergent_lines( X, 
% 0.46/1.10    Y ) }.
% 0.46/1.10  (89) {G0,W5,D3,L1,V2,M1}  { ! convergent_lines( parallel_through_point( Y, 
% 0.46/1.10    X ), Y ) }.
% 0.46/1.10  (90) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.46/1.10    parallel_through_point( Y, X ) ) }.
% 0.46/1.10  (91) {G0,W12,D2,L4,V3,M4}  { ! distinct_lines( X, Y ), apart_point_and_line
% 0.46/1.10    ( Z, X ), apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.46/1.10  (92) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines( X
% 0.46/1.10    , Y ) }.
% 0.46/1.10  (93) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.46/1.10  (94) {G0,W12,D2,L4,V3,M4}  { ! convergent_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.46/1.10     }.
% 0.46/1.10  (95) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.46/1.10  (96) {G0,W6,D2,L2,V2,M2}  { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.46/1.10     }.
% 0.46/1.10  (97) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.46/1.10  (98) {G0,W5,D3,L1,V2,M1}  { ! unorthogonal_lines( orthogonal_through_point
% 0.46/1.10    ( Y, X ), Y ) }.
% 0.46/1.10  (99) {G0,W5,D3,L1,V2,M1}  { ! apart_point_and_line( X, 
% 0.46/1.10    orthogonal_through_point( Y, X ) ) }.
% 0.46/1.10  (100) {G0,W15,D2,L5,V4,M5}  { ! distinct_lines( X, Y ), 
% 0.46/1.10    apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), 
% 0.46/1.10    unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.46/1.10  (101) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), unorthogonal_lines( 
% 0.46/1.10    X, Y ) }.
% 0.46/1.10  (102) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), convergent_lines( Z, Y ), ! 
% 0.46/1.10    convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.46/1.10  (103) {G0,W12,D2,L4,V3,M4}  { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.46/1.10     convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.46/1.10  (104) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.46/1.10  (105) {G0,W6,D2,L2,V2,M2}  { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.46/1.10     }.
% 0.46/1.10  (106) {G0,W9,D2,L3,V2,M3}  { ! convergent_lines( Y, X ), ! 
% 0.46/1.10    unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.46/1.10  (107) {G0,W9,D2,L3,V3,M3}  { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.46/1.10    ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.46/1.10  (108) {G0,W11,D3,L4,V2,M4}  { ! point( X ), ! point( Y ), ! distinct_points
% 0.46/1.10    ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.46/1.10  (109) {G0,W11,D3,L4,V2,M4}  { ! line( X ), ! line( Y ), ! convergent_lines
% 0.46/1.10    ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.46/1.10  (110) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.46/1.10    parallel_through_point( X, Y ) ) }.
% 0.46/1.10  (111) {G0,W8,D3,L3,V2,M3}  { ! line( X ), ! point( Y ), line( 
% 0.46/1.10    orthogonal_through_point( X, Y ) ) }.
% 0.46/1.10  (112) {G0,W6,D2,L2,V2,M2}  { ! equal_points( X, Y ), ! distinct_points( X, 
% 0.46/1.10    Y ) }.
% 0.46/1.10  (113) {G0,W6,D2,L2,V2,M2}  { distinct_points( X, Y ), equal_points( X, Y )
% 0.46/1.10     }.
% 0.46/1.10  (114) {G0,W6,D2,L2,V2,M2}  { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.46/1.10     ) }.
% 0.46/1.10  (115) {G0,W6,D2,L2,V2,M2}  { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.46/1.10     }.
% 0.46/1.10  (116) {G0,W6,D2,L2,V2,M2}  { ! parallel_lines( X, Y ), ! convergent_lines( 
% 0.46/1.10    X, Y ) }.
% 0.46/1.10  (117) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.46/1.10     ) }.
% 0.46/1.10  (118) {G0,W6,D2,L2,V2,M2}  { ! incident_point_and_line( X, Y ), ! 
% 0.46/1.10    apart_point_and_line( X, Y ) }.
% 0.46/1.10  (119) {G0,W6,D2,L2,V2,M2}  { apart_point_and_line( X, Y ), 
% 0.46/1.10    incident_point_and_line( X, Y ) }.
% 0.46/1.10  (120) {G0,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  (121) {G0,W6,D2,L2,V2,M2}  { unorthogonal_lines( X, Y ), orthogonal_lines( 
% 0.46/1.10    X, Y ) }.
% 0.46/1.10  (122) {G0,W3,D2,L1,V0,M1}  { orthogonal_lines( skol1, skol1 ) }.
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Total Proof:
% 0.46/1.10  
% 0.46/1.10  subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.46/1.10  parent0: (76) {G0,W3,D2,L1,V1,M1}  { ! convergent_lines( X, X ) }.
% 0.46/1.10  substitution0:
% 0.46/1.10     X := X
% 0.46/1.10  end
% 0.46/1.10  permutation0:
% 0.46/1.10     0 ==> 0
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  parent0: (92) {G0,W6,D2,L2,V2,M2}  { convergent_lines( X, Y ), 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  substitution0:
% 0.46/1.10     X := X
% 0.46/1.10     Y := Y
% 0.46/1.10  end
% 0.46/1.10  permutation0:
% 0.46/1.10     0 ==> 0
% 0.46/1.10     1 ==> 1
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  subsumption: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  parent0: (120) {G0,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  substitution0:
% 0.46/1.10     X := X
% 0.46/1.10     Y := Y
% 0.46/1.10  end
% 0.46/1.10  permutation0:
% 0.46/1.10     0 ==> 0
% 0.46/1.10     1 ==> 1
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  subsumption: (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol1, skol1 )
% 0.46/1.10     }.
% 0.46/1.10  parent0: (122) {G0,W3,D2,L1,V0,M1}  { orthogonal_lines( skol1, skol1 ) }.
% 0.46/1.10  substitution0:
% 0.46/1.10  end
% 0.46/1.10  permutation0:
% 0.46/1.10     0 ==> 0
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  resolution: (163) {G1,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), 
% 0.46/1.10    convergent_lines( X, Y ) }.
% 0.46/1.10  parent0[1]: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), ! 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), 
% 0.46/1.10    unorthogonal_lines( X, Y ) }.
% 0.46/1.10  substitution0:
% 0.46/1.10     X := X
% 0.46/1.10     Y := Y
% 0.46/1.10  end
% 0.46/1.10  substitution1:
% 0.46/1.10     X := X
% 0.46/1.10     Y := Y
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  subsumption: (68) {G1,W6,D2,L2,V2,M1} R(17,44) { convergent_lines( X, Y ), 
% 0.46/1.10    ! orthogonal_lines( X, Y ) }.
% 0.46/1.10  parent0: (163) {G1,W6,D2,L2,V2,M2}  { ! orthogonal_lines( X, Y ), 
% 0.46/1.10    convergent_lines( X, Y ) }.
% 0.46/1.10  substitution0:
% 0.46/1.10     X := X
% 0.46/1.10     Y := Y
% 0.46/1.10  end
% 0.46/1.10  permutation0:
% 0.46/1.10     0 ==> 1
% 0.46/1.10     1 ==> 0
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  resolution: (164) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol1 )
% 0.46/1.10     }.
% 0.46/1.10  parent0[1]: (68) {G1,W6,D2,L2,V2,M1} R(17,44) { convergent_lines( X, Y ), !
% 0.46/1.10     orthogonal_lines( X, Y ) }.
% 0.46/1.10  parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol1, skol1 )
% 0.46/1.10     }.
% 0.46/1.10  substitution0:
% 0.46/1.10     X := skol1
% 0.46/1.10     Y := skol1
% 0.46/1.10  end
% 0.46/1.10  substitution1:
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  resolution: (165) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.46/1.10  parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.46/1.10  parent1[0]: (164) {G1,W3,D2,L1,V0,M1}  { convergent_lines( skol1, skol1 )
% 0.46/1.10     }.
% 0.46/1.10  substitution0:
% 0.46/1.10     X := skol1
% 0.46/1.10  end
% 0.46/1.10  substitution1:
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  subsumption: (72) {G2,W0,D0,L0,V0,M0} R(68,46);r(2) {  }.
% 0.46/1.10  parent0: (165) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.46/1.10  substitution0:
% 0.46/1.10  end
% 0.46/1.10  permutation0:
% 0.46/1.10  end
% 0.46/1.10  
% 0.46/1.10  Proof check complete!
% 0.46/1.10  
% 0.46/1.10  Memory use:
% 0.46/1.10  
% 0.46/1.10  space for terms:        1812
% 0.46/1.10  space for clauses:      3633
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  clauses generated:      143
% 0.46/1.10  clauses kept:           73
% 0.46/1.10  clauses selected:       38
% 0.46/1.10  clauses deleted:        0
% 0.46/1.10  clauses inuse deleted:  0
% 0.46/1.10  
% 0.46/1.10  subsentry:          195
% 0.46/1.10  literals s-matched: 130
% 0.46/1.10  literals matched:   115
% 0.46/1.10  full subsumption:   54
% 0.46/1.10  
% 0.46/1.10  checksum:           -1882625533
% 0.46/1.10  
% 0.46/1.10  
% 0.46/1.10  Bliksem ended
%------------------------------------------------------------------------------