TSTP Solution File: GEO219+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO219+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 02:52:55 EDT 2022
% Result : Theorem 27.54s 27.92s
% Output : Refutation 27.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GEO219+3 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sat Jun 18 09:59:08 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.63/1.99 *** allocated 10000 integers for termspace/termends
% 1.63/1.99 *** allocated 10000 integers for clauses
% 1.63/1.99 *** allocated 10000 integers for justifications
% 1.63/1.99 Bliksem 1.12
% 1.63/1.99
% 1.63/1.99
% 1.63/1.99 Automatic Strategy Selection
% 1.63/1.99
% 1.63/1.99
% 1.63/1.99 Clauses:
% 1.63/1.99
% 1.63/1.99 { ! distinct_points( X, X ) }.
% 1.63/1.99 { ! distinct_lines( X, X ) }.
% 1.63/1.99 { ! convergent_lines( X, X ) }.
% 1.63/1.99 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.63/1.99 ) }.
% 1.63/1.99 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.63/1.99 }.
% 1.63/1.99 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.63/1.99 , Z ) }.
% 1.63/1.99 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.63/1.99 , Y ) ) }.
% 1.63/1.99 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.63/1.99 , Y ) ) }.
% 1.63/1.99 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.63/1.99 , Y ), X ) }.
% 1.63/1.99 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.63/1.99 , Y ), Y ) }.
% 1.63/1.99 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.63/1.99 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.63/1.99 apart_point_and_line( Y, T ) }.
% 1.63/1.99 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.63/1.99 apart_point_and_line( Z, Y ) }.
% 1.63/1.99 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.63/1.99 apart_point_and_line( X, Z ) }.
% 1.63/1.99 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 1.63/1.99 Z ) }.
% 1.63/1.99 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 1.63/1.99 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.63/1.99 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.63/1.99 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.63/1.99 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.63/1.99 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.63/1.99 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.63/1.99 , convergent_lines( Y, Z ) }.
% 1.63/1.99 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.63/1.99 , unorthogonal_lines( Y, Z ) }.
% 1.63/1.99 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.63/1.99 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.63/1.99 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.63/1.99 }.
% 1.63/1.99 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.63/1.99 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.63/1.99 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.63/1.99 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 1.63/1.99 unorthogonal_lines( Y, T ) }.
% 1.63/1.99 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.63/1.99 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.63/1.99 unorthogonal_lines( X, Y ) }.
% 1.63/1.99 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.63/1.99 unorthogonal_lines( X, Y ) }.
% 1.63/1.99 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 1.63/1.99 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.63/1.99 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 1.63/1.99 }.
% 1.63/1.99 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 1.63/1.99 convergent_lines( X, Y ) }.
% 1.63/1.99 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 1.63/1.99 line_connecting( X, Y ) ) }.
% 1.63/1.99 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 1.63/1.99 intersection_point( X, Y ) ) }.
% 1.63/1.99 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 1.63/1.99 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 1.63/1.99 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 1.63/1.99 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 1.63/1.99 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 1.63/1.99 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 1.63/1.99 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 1.63/1.99 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 1.63/1.99 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 1.63/1.99 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 1.63/1.99 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.63/1.99 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 1.63/1.99 { orthogonal_lines( skol3, skol1 ) }.
% 1.63/1.99 { parallel_lines( skol3, skol2 ) }.
% 1.63/1.99 { ! orthogonal_lines( skol1, skol2 ) }.
% 1.63/1.99
% 1.63/1.99 percentage equality = 0.000000, percentage horn = 0.612245
% 1.63/1.99 This a non-horn, non-equality problem
% 1.63/1.99
% 1.63/1.99
% 1.63/1.99 Options Used:
% 1.63/1.99
% 1.63/1.99 useres = 1
% 27.54/27.92 useparamod = 0
% 27.54/27.92 useeqrefl = 0
% 27.54/27.92 useeqfact = 0
% 27.54/27.92 usefactor = 1
% 27.54/27.92 usesimpsplitting = 0
% 27.54/27.92 usesimpdemod = 0
% 27.54/27.92 usesimpres = 3
% 27.54/27.92
% 27.54/27.92 resimpinuse = 1000
% 27.54/27.92 resimpclauses = 20000
% 27.54/27.92 substype = standard
% 27.54/27.92 backwardsubs = 1
% 27.54/27.92 selectoldest = 5
% 27.54/27.92
% 27.54/27.92 litorderings [0] = split
% 27.54/27.92 litorderings [1] = liftord
% 27.54/27.92
% 27.54/27.92 termordering = none
% 27.54/27.92
% 27.54/27.92 litapriori = 1
% 27.54/27.92 termapriori = 0
% 27.54/27.92 litaposteriori = 0
% 27.54/27.92 termaposteriori = 0
% 27.54/27.92 demodaposteriori = 0
% 27.54/27.92 ordereqreflfact = 0
% 27.54/27.92
% 27.54/27.92 litselect = none
% 27.54/27.92
% 27.54/27.92 maxweight = 15
% 27.54/27.92 maxdepth = 30000
% 27.54/27.92 maxlength = 115
% 27.54/27.92 maxnrvars = 195
% 27.54/27.92 excuselevel = 1
% 27.54/27.92 increasemaxweight = 1
% 27.54/27.92
% 27.54/27.92 maxselected = 10000000
% 27.54/27.92 maxnrclauses = 10000000
% 27.54/27.92
% 27.54/27.92 showgenerated = 0
% 27.54/27.92 showkept = 0
% 27.54/27.92 showselected = 0
% 27.54/27.92 showdeleted = 0
% 27.54/27.92 showresimp = 1
% 27.54/27.92 showstatus = 2000
% 27.54/27.92
% 27.54/27.92 prologoutput = 0
% 27.54/27.92 nrgoals = 5000000
% 27.54/27.92 totalproof = 1
% 27.54/27.92
% 27.54/27.92 Symbols occurring in the translation:
% 27.54/27.92
% 27.54/27.92 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 27.54/27.92 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 27.54/27.92 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 27.54/27.92 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 27.54/27.92 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 27.54/27.92 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 27.54/27.92 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 27.54/27.92 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 27.54/27.92 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 27.54/27.92 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 27.54/27.92 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 27.54/27.92 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 27.54/27.92 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 27.54/27.92 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 27.54/27.92 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 27.54/27.92 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 27.54/27.92 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 27.54/27.92 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 27.54/27.92 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 27.54/27.92 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 27.54/27.92 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 27.54/27.92 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 27.54/27.92 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 27.54/27.92 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 27.54/27.92 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 27.54/27.92 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Starting Search:
% 27.54/27.92
% 27.54/27.92 *** allocated 15000 integers for clauses
% 27.54/27.92 *** allocated 22500 integers for clauses
% 27.54/27.92 *** allocated 33750 integers for clauses
% 27.54/27.92 *** allocated 50625 integers for clauses
% 27.54/27.92 *** allocated 15000 integers for termspace/termends
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 22500 integers for termspace/termends
% 27.54/27.92 *** allocated 75937 integers for clauses
% 27.54/27.92 *** allocated 33750 integers for termspace/termends
% 27.54/27.92 *** allocated 113905 integers for clauses
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 13873
% 27.54/27.92 Kept: 2001
% 27.54/27.92 Inuse: 327
% 27.54/27.92 Deleted: 1
% 27.54/27.92 Deletedinuse: 0
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 50625 integers for termspace/termends
% 27.54/27.92 *** allocated 170857 integers for clauses
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 75937 integers for termspace/termends
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 33888
% 27.54/27.92 Kept: 4027
% 27.54/27.92 Inuse: 514
% 27.54/27.92 Deleted: 9
% 27.54/27.92 Deletedinuse: 2
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 256285 integers for clauses
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 113905 integers for termspace/termends
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 48945
% 27.54/27.92 Kept: 6046
% 27.54/27.92 Inuse: 692
% 27.54/27.92 Deleted: 20
% 27.54/27.92 Deletedinuse: 4
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 384427 integers for clauses
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 61711
% 27.54/27.92 Kept: 8047
% 27.54/27.92 Inuse: 836
% 27.54/27.92 Deleted: 20
% 27.54/27.92 Deletedinuse: 4
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 170857 integers for termspace/termends
% 27.54/27.92 *** allocated 576640 integers for clauses
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 71999
% 27.54/27.92 Kept: 10104
% 27.54/27.92 Inuse: 874
% 27.54/27.92 Deleted: 59
% 27.54/27.92 Deletedinuse: 43
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 84981
% 27.54/27.92 Kept: 12376
% 27.54/27.92 Inuse: 905
% 27.54/27.92 Deleted: 62
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 256285 integers for termspace/termends
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 864960 integers for clauses
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 96363
% 27.54/27.92 Kept: 14438
% 27.54/27.92 Inuse: 949
% 27.54/27.92 Deleted: 64
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 111981
% 27.54/27.92 Kept: 16439
% 27.54/27.92 Inuse: 1020
% 27.54/27.92 Deleted: 67
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 127190
% 27.54/27.92 Kept: 18459
% 27.54/27.92 Inuse: 1077
% 27.54/27.92 Deleted: 71
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 384427 integers for termspace/termends
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying clauses:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 155703
% 27.54/27.92 Kept: 20643
% 27.54/27.92 Inuse: 1201
% 27.54/27.92 Deleted: 859
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 1297440 integers for clauses
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 173735
% 27.54/27.92 Kept: 22956
% 27.54/27.92 Inuse: 1236
% 27.54/27.92 Deleted: 859
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 198844
% 27.54/27.92 Kept: 25584
% 27.54/27.92 Inuse: 1296
% 27.54/27.92 Deleted: 859
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 576640 integers for termspace/termends
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 227915
% 27.54/27.92 Kept: 27653
% 27.54/27.92 Inuse: 1366
% 27.54/27.92 Deleted: 859
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 294143
% 27.54/27.92 Kept: 29661
% 27.54/27.92 Inuse: 1454
% 27.54/27.92 Deleted: 859
% 27.54/27.92 Deletedinuse: 46
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 317282
% 27.54/27.92 Kept: 31694
% 27.54/27.92 Inuse: 1480
% 27.54/27.92 Deleted: 871
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 1946160 integers for clauses
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 360006
% 27.54/27.92 Kept: 33801
% 27.54/27.92 Inuse: 1551
% 27.54/27.92 Deleted: 871
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 436809
% 27.54/27.92 Kept: 35824
% 27.54/27.92 Inuse: 1637
% 27.54/27.92 Deleted: 871
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 535736
% 27.54/27.92 Kept: 37833
% 27.54/27.92 Inuse: 1770
% 27.54/27.92 Deleted: 871
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 *** allocated 864960 integers for termspace/termends
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 606877
% 27.54/27.92 Kept: 39971
% 27.54/27.92 Inuse: 1858
% 27.54/27.92 Deleted: 871
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying clauses:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 635047
% 27.54/27.92 Kept: 42041
% 27.54/27.92 Inuse: 1868
% 27.54/27.92 Deleted: 1434
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 697502
% 27.54/27.92 Kept: 44053
% 27.54/27.92 Inuse: 1899
% 27.54/27.92 Deleted: 1434
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 813286
% 27.54/27.92 Kept: 46055
% 27.54/27.92 Inuse: 1970
% 27.54/27.92 Deleted: 1434
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Intermediate Status:
% 27.54/27.92 Generated: 974735
% 27.54/27.92 Kept: 48067
% 27.54/27.92 Inuse: 2052
% 27.54/27.92 Deleted: 1434
% 27.54/27.92 Deletedinuse: 58
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92 Resimplifying inuse:
% 27.54/27.92 Done
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Bliksems!, er is een bewijs:
% 27.54/27.92 % SZS status Theorem
% 27.54/27.92 % SZS output start Refutation
% 27.54/27.92
% 27.54/27.92 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 27.54/27.92 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 27.54/27.92 Z ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 27.54/27.92 , X ), Y ) }.
% 27.54/27.92 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 27.54/27.92 X, Y ) }.
% 27.54/27.92 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 27.54/27.92 }.
% 27.54/27.92 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 27.54/27.92 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 27.54/27.92 ( Y, X ), Y ) }.
% 27.54/27.92 (27) {G0,W12,D2,L4,V3,M1} I { unorthogonal_lines( Z, Y ), !
% 27.54/27.92 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha2( X, Z )
% 27.54/27.92 }.
% 27.54/27.92 (28) {G0,W6,D2,L2,V2,M1} I { convergent_lines( Y, X ), ! alpha2( X, Y ) }.
% 27.54/27.92 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 27.54/27.92 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), ! parallel_lines(
% 27.54/27.92 X, Y ) }.
% 27.54/27.92 (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 (45) {G0,W6,D2,L2,V2,M1} I { orthogonal_lines( X, Y ), unorthogonal_lines(
% 27.54/27.92 X, Y ) }.
% 27.54/27.92 (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol1 ) }.
% 27.54/27.92 (47) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol3, skol2 ) }.
% 27.54/27.92 (48) {G0,W3,D2,L1,V0,M1} I { ! orthogonal_lines( skol1, skol2 ) }.
% 27.54/27.92 (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 (67) {G2,W5,D3,L1,V2,M1} R(64,15) { ! convergent_lines( X,
% 27.54/27.92 parallel_through_point( X, Y ) ) }.
% 27.54/27.92 (68) {G3,W8,D3,L2,V3,M2} R(67,5) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 27.54/27.92 (70) {G1,W3,D2,L1,V0,M1} R(40,47) { ! convergent_lines( skol3, skol2 ) }.
% 27.54/27.92 (71) {G2,W3,D2,L1,V0,M1} R(70,64) { ! convergent_lines( skol2, skol3 ) }.
% 27.54/27.92 (75) {G3,W6,D2,L2,V1,M1} R(71,5) { ! convergent_lines( X, skol2 ),
% 27.54/27.92 convergent_lines( X, skol3 ) }.
% 27.54/27.92 (76) {G1,W6,D2,L2,V2,M1} R(17,44) { convergent_lines( X, Y ), !
% 27.54/27.92 orthogonal_lines( X, Y ) }.
% 27.54/27.92 (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 27.54/27.92 orthogonal_through_point( X, Y ), X ) }.
% 27.54/27.92 (79) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 27.54/27.92 (106) {G2,W3,D2,L1,V0,M1} R(76,46) { convergent_lines( skol3, skol1 ) }.
% 27.54/27.92 (108) {G3,W6,D2,L2,V1,M1} R(106,5) { convergent_lines( skol1, X ),
% 27.54/27.92 convergent_lines( skol3, X ) }.
% 27.54/27.92 (125) {G4,W3,D2,L1,V0,M1} R(108,70) { convergent_lines( skol1, skol2 ) }.
% 27.54/27.92 (164) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 27.54/27.92 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( Y, Z ) }.
% 27.54/27.92 (188) {G4,W6,D2,L2,V1,M2} R(75,64) { convergent_lines( skol3, X ), !
% 27.54/27.92 convergent_lines( X, skol2 ) }.
% 27.54/27.92 (205) {G1,W12,D2,L4,V3,M2} R(27,28) { ! convergent_lines( Z, Y ),
% 27.54/27.92 convergent_lines( X, Z ), unorthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 (220) {G1,W9,D2,L3,V3,M1} R(31,44) { ! convergent_lines( X, Y ), !
% 27.54/27.92 orthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 (243) {G3,W8,D3,L2,V3,M2} R(79,64) { convergent_lines( Z, X ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 27.54/27.92 (327) {G4,W8,D3,L2,V3,M2} R(243,64) { convergent_lines( X,
% 27.54/27.92 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 27.54/27.92 (394) {G4,W8,D3,L2,V3,M2} R(68,64) { convergent_lines(
% 27.54/27.92 parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 (519) {G5,W8,D3,L2,V2,M2} R(394,188) { ! convergent_lines( Y, skol2 ),
% 27.54/27.92 convergent_lines( parallel_through_point( skol3, X ), Y ) }.
% 27.54/27.92 (1846) {G2,W9,D2,L3,V3,M2} R(220,44) { ! convergent_lines( X, Y ), !
% 27.54/27.92 orthogonal_lines( Z, Y ), ! orthogonal_lines( Z, X ) }.
% 27.54/27.92 (1848) {G3,W6,D2,L2,V1,M1} R(1846,46) { ! convergent_lines( skol1, X ), !
% 27.54/27.92 orthogonal_lines( skol3, X ) }.
% 27.54/27.92 (2715) {G5,W8,D3,L2,V3,M1} R(164,23);r(327) { convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 (2726) {G6,W8,D3,L2,V3,M1} R(2715,45) { convergent_lines( X, Y ),
% 27.54/27.92 orthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 (2727) {G7,W8,D3,L2,V2,M2} R(2726,1848) { ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( X, Y ) ), convergent_lines( skol3, X ) }.
% 27.54/27.92 (2749) {G8,W5,D3,L1,V1,M1} R(2727,519);r(15) { ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( skol2, X ) ) }.
% 27.54/27.92 (2852) {G9,W5,D3,L1,V1,M1} R(2749,64) { ! convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 (3100) {G2,W11,D3,L3,V3,M1} R(205,23) { ! convergent_lines( X, Y ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( Y, Z ), X ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 (50048) {G3,W11,D3,L3,V3,M1} R(3100,45) { ! convergent_lines( X, Y ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( Y, Z ), X ), orthogonal_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 (50049) {G5,W5,D3,L1,V1,M1} R(50048,48);r(125) { convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 (50050) {G10,W0,D0,L0,V0,M0} S(50049);r(2852) { }.
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 % SZS output end Refutation
% 27.54/27.92 found a proof!
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Unprocessed initial clauses:
% 27.54/27.92
% 27.54/27.92 (50052) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 27.54/27.92 (50053) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 27.54/27.92 (50054) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 27.54/27.92 (50055) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 27.54/27.92 X, Z ), distinct_points( Y, Z ) }.
% 27.54/27.92 (50056) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 27.54/27.92 , Z ), distinct_lines( Y, Z ) }.
% 27.54/27.92 (50057) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 27.54/27.92 ( X, Z ), convergent_lines( Y, Z ) }.
% 27.54/27.92 (50058) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 27.54/27.92 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 27.54/27.92 (50059) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 27.54/27.92 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 27.54/27.92 (50060) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 27.54/27.92 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 27.54/27.92 (50061) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 27.54/27.92 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 27.54/27.92 (50062) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 27.54/27.92 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 27.54/27.92 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 27.54/27.92 (50063) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 27.54/27.92 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 27.54/27.92 (50064) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 27.54/27.92 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 27.54/27.92 (50065) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines(
% 27.54/27.92 Y, Z ), convergent_lines( X, Z ) }.
% 27.54/27.92 (50066) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines(
% 27.54/27.92 X, Y ) }.
% 27.54/27.92 (50067) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point(
% 27.54/27.92 Y, X ), Y ) }.
% 27.54/27.92 (50068) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 27.54/27.92 parallel_through_point( Y, X ) ) }.
% 27.54/27.92 (50069) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 27.54/27.92 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 (50070) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 (50071) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 27.54/27.92 (50072) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 27.54/27.92 }.
% 27.54/27.92 (50073) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 27.54/27.92 }.
% 27.54/27.92 (50074) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 27.54/27.92 }.
% 27.54/27.92 (50075) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 27.54/27.92 (50076) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 27.54/27.92 orthogonal_through_point( Y, X ), Y ) }.
% 27.54/27.92 (50077) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 27.54/27.92 orthogonal_through_point( Y, X ) ) }.
% 27.54/27.92 (50078) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 27.54/27.92 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 27.54/27.92 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 27.54/27.92 (50079) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 (50080) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 27.54/27.92 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 27.54/27.92 (50081) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y )
% 27.54/27.92 , ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 27.54/27.92 (50082) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 27.54/27.92 }.
% 27.54/27.92 (50083) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 27.54/27.92 }.
% 27.54/27.92 (50084) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 27.54/27.92 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 27.54/27.92 (50085) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 27.54/27.92 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 (50086) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 27.54/27.92 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 27.54/27.92 (50087) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), !
% 27.54/27.92 convergent_lines( X, Y ), point( intersection_point( X, Y ) ) }.
% 27.54/27.92 (50088) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 27.54/27.92 parallel_through_point( X, Y ) ) }.
% 27.54/27.92 (50089) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 27.54/27.92 orthogonal_through_point( X, Y ) ) }.
% 27.54/27.92 (50090) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 27.54/27.92 , Y ) }.
% 27.54/27.92 (50091) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y
% 27.54/27.92 ) }.
% 27.54/27.92 (50092) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X,
% 27.54/27.92 Y ) }.
% 27.54/27.92 (50093) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 27.54/27.92 }.
% 27.54/27.92 (50094) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 (50095) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X
% 27.54/27.92 , Y ) }.
% 27.54/27.92 (50096) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 27.54/27.92 apart_point_and_line( X, Y ) }.
% 27.54/27.92 (50097) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 27.54/27.92 incident_point_and_line( X, Y ) }.
% 27.54/27.92 (50098) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 (50099) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 (50100) {G0,W3,D2,L1,V0,M1} { orthogonal_lines( skol3, skol1 ) }.
% 27.54/27.92 (50101) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol3, skol2 ) }.
% 27.54/27.92 (50102) {G0,W3,D2,L1,V0,M1} { ! orthogonal_lines( skol1, skol2 ) }.
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Total Proof:
% 27.54/27.92
% 27.54/27.92 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 27.54/27.92 parent0: (50054) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 parent0: (50057) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 27.54/27.92 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 2
% 27.54/27.92 1 ==> 0
% 27.54/27.92 2 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 27.54/27.92 parallel_through_point( Y, X ), Y ) }.
% 27.54/27.92 parent0: (50067) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 27.54/27.92 parallel_through_point( Y, X ), Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent0: (50070) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 27.54/27.92 }.
% 27.54/27.92 parent0: (50072) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 2 ==> 3
% 27.54/27.92 3 ==> 2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 27.54/27.92 alpha1( X, Y ) }.
% 27.54/27.92 parent0: (50073) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 27.54/27.92 orthogonal_through_point( Y, X ), Y ) }.
% 27.54/27.92 parent0: (50076) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 27.54/27.92 orthogonal_through_point( Y, X ), Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (27) {G0,W12,D2,L4,V3,M1} I { unorthogonal_lines( Z, Y ), !
% 27.54/27.92 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha2( X, Z )
% 27.54/27.92 }.
% 27.54/27.92 parent0: (50081) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines
% 27.54/27.92 ( Z, Y ), ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 3
% 27.54/27.92 1 ==> 0
% 27.54/27.92 2 ==> 1
% 27.54/27.92 3 ==> 2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (28) {G0,W6,D2,L2,V2,M1} I { convergent_lines( Y, X ), !
% 27.54/27.92 alpha2( X, Y ) }.
% 27.54/27.92 parent0: (50082) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines
% 27.54/27.92 ( Y, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 parent0: (50085) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 27.54/27.92 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 2
% 27.54/27.92 2 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 27.54/27.92 parallel_lines( X, Y ) }.
% 27.54/27.92 parent0: (50094) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), !
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent0: (50098) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (45) {G0,W6,D2,L2,V2,M1} I { orthogonal_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent0: (50099) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ),
% 27.54/27.92 orthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol1 )
% 27.54/27.92 }.
% 27.54/27.92 parent0: (50100) {G0,W3,D2,L1,V0,M1} { orthogonal_lines( skol3, skol1 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (47) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol3, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 parent0: (50101) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol3, skol2 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { ! orthogonal_lines( skol1, skol2
% 27.54/27.92 ) }.
% 27.54/27.92 parent0: (50102) {G0,W3,D2,L1,V0,M1} { ! orthogonal_lines( skol1, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50282) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 27.54/27.92 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent0: (50282) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50284) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 27.54/27.92 parallel_through_point( X, Y ) ) }.
% 27.54/27.92 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 27.54/27.92 parallel_through_point( Y, X ), Y ) }.
% 27.54/27.92 parent1[1]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := parallel_through_point( X, Y )
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (67) {G2,W5,D3,L1,V2,M1} R(64,15) { ! convergent_lines( X,
% 27.54/27.92 parallel_through_point( X, Y ) ) }.
% 27.54/27.92 parent0: (50284) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 27.54/27.92 parallel_through_point( X, Y ) ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50285) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 27.54/27.92 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 27.54/27.92 parent0[0]: (67) {G2,W5,D3,L1,V2,M1} R(64,15) { ! convergent_lines( X,
% 27.54/27.92 parallel_through_point( X, Y ) ) }.
% 27.54/27.92 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := parallel_through_point( X, Y )
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (68) {G3,W8,D3,L2,V3,M2} R(67,5) { ! convergent_lines( Y, X )
% 27.54/27.92 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 27.54/27.92 parent0: (50285) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 27.54/27.92 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50287) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol3, skol2
% 27.54/27.92 ) }.
% 27.54/27.92 parent0[1]: (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 27.54/27.92 parallel_lines( X, Y ) }.
% 27.54/27.92 parent1[0]: (47) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol3, skol2 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := skol3
% 27.54/27.92 Y := skol2
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (70) {G1,W3,D2,L1,V0,M1} R(40,47) { ! convergent_lines( skol3
% 27.54/27.92 , skol2 ) }.
% 27.54/27.92 parent0: (50287) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol3, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50288) {G2,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol3
% 27.54/27.92 ) }.
% 27.54/27.92 parent0[0]: (70) {G1,W3,D2,L1,V0,M1} R(40,47) { ! convergent_lines( skol3,
% 27.54/27.92 skol2 ) }.
% 27.54/27.92 parent1[1]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := skol3
% 27.54/27.92 Y := skol2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (71) {G2,W3,D2,L1,V0,M1} R(70,64) { ! convergent_lines( skol2
% 27.54/27.92 , skol3 ) }.
% 27.54/27.92 parent0: (50288) {G2,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol3 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50290) {G1,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ), !
% 27.54/27.92 convergent_lines( X, skol2 ) }.
% 27.54/27.92 parent0[0]: (71) {G2,W3,D2,L1,V0,M1} R(70,64) { ! convergent_lines( skol2,
% 27.54/27.92 skol3 ) }.
% 27.54/27.92 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := skol2
% 27.54/27.92 Z := skol3
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (75) {G3,W6,D2,L2,V1,M1} R(71,5) { ! convergent_lines( X,
% 27.54/27.92 skol2 ), convergent_lines( X, skol3 ) }.
% 27.54/27.92 parent0: (50290) {G1,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ), !
% 27.54/27.92 convergent_lines( X, skol2 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50291) {G1,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent0[1]: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (76) {G1,W6,D2,L2,V2,M1} R(17,44) { convergent_lines( X, Y ),
% 27.54/27.92 ! orthogonal_lines( X, Y ) }.
% 27.54/27.92 parent0: (50291) {G1,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50292) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 27.54/27.92 orthogonal_through_point( X, Y ), X ) }.
% 27.54/27.92 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 27.54/27.92 orthogonal_through_point( Y, X ), Y ) }.
% 27.54/27.92 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := orthogonal_through_point( X, Y )
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 27.54/27.92 orthogonal_through_point( X, Y ), X ) }.
% 27.54/27.92 parent0: (50292) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 27.54/27.92 orthogonal_through_point( X, Y ), X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50293) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 27.54/27.92 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 27.54/27.92 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 parent1[0]: (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 27.54/27.92 orthogonal_through_point( X, Y ), X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := orthogonal_through_point( X, Y )
% 27.54/27.92 Y := X
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (79) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 27.54/27.92 parent0: (50293) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 27.54/27.92 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50294) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol1 )
% 27.54/27.92 }.
% 27.54/27.92 parent0[1]: (76) {G1,W6,D2,L2,V2,M1} R(17,44) { convergent_lines( X, Y ), !
% 27.54/27.92 orthogonal_lines( X, Y ) }.
% 27.54/27.92 parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol1 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := skol3
% 27.54/27.92 Y := skol1
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (106) {G2,W3,D2,L1,V0,M1} R(76,46) { convergent_lines( skol3,
% 27.54/27.92 skol1 ) }.
% 27.54/27.92 parent0: (50294) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol1 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50295) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 27.54/27.92 convergent_lines( skol1, X ) }.
% 27.54/27.92 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 parent1[0]: (106) {G2,W3,D2,L1,V0,M1} R(76,46) { convergent_lines( skol3,
% 27.54/27.92 skol1 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := skol3
% 27.54/27.92 Y := skol1
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (108) {G3,W6,D2,L2,V1,M1} R(106,5) { convergent_lines( skol1,
% 27.54/27.92 X ), convergent_lines( skol3, X ) }.
% 27.54/27.92 parent0: (50295) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 27.54/27.92 convergent_lines( skol1, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50296) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 parent0[0]: (70) {G1,W3,D2,L1,V0,M1} R(40,47) { ! convergent_lines( skol3,
% 27.54/27.92 skol2 ) }.
% 27.54/27.92 parent1[1]: (108) {G3,W6,D2,L2,V1,M1} R(106,5) { convergent_lines( skol1, X
% 27.54/27.92 ), convergent_lines( skol3, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := skol2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (125) {G4,W3,D2,L1,V0,M1} R(108,70) { convergent_lines( skol1
% 27.54/27.92 , skol2 ) }.
% 27.54/27.92 parent0: (50296) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50298) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 27.54/27.92 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 27.54/27.92 unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (164) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 27.54/27.92 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( Y, Z ) }.
% 27.54/27.92 parent0: (50298) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 27.54/27.92 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 27.54/27.92 unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 2 ==> 2
% 27.54/27.92 3 ==> 3
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50300) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 27.54/27.92 convergent_lines( X, skol2 ) }.
% 27.54/27.92 parent0[0]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent1[1]: (75) {G3,W6,D2,L2,V1,M1} R(71,5) { ! convergent_lines( X, skol2
% 27.54/27.92 ), convergent_lines( X, skol3 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := skol3
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (188) {G4,W6,D2,L2,V1,M2} R(75,64) { convergent_lines( skol3,
% 27.54/27.92 X ), ! convergent_lines( X, skol2 ) }.
% 27.54/27.92 parent0: (50300) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 27.54/27.92 convergent_lines( X, skol2 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50302) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Z ), ! convergent_lines( Y, Z ), !
% 27.54/27.92 unorthogonal_lines( Y, Z ) }.
% 27.54/27.92 parent0[1]: (28) {G0,W6,D2,L2,V2,M1} I { convergent_lines( Y, X ), ! alpha2
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 parent1[3]: (27) {G0,W12,D2,L4,V3,M1} I { unorthogonal_lines( Z, Y ), !
% 27.54/27.92 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha2( X, Z )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (205) {G1,W12,D2,L4,V3,M2} R(27,28) { ! convergent_lines( Z, Y
% 27.54/27.92 ), convergent_lines( X, Z ), unorthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 parent0: (50302) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Z ), ! convergent_lines( Y, Z ), !
% 27.54/27.92 unorthogonal_lines( Y, Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 2
% 27.54/27.92 2 ==> 0
% 27.54/27.92 3 ==> 3
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50303) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 27.54/27.92 parent0[1]: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent1[1]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (220) {G1,W9,D2,L3,V3,M1} R(31,44) { ! convergent_lines( X, Y
% 27.54/27.92 ), ! orthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 parent0: (50303) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Z
% 27.54/27.92 Y := X
% 27.54/27.92 Z := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 2 ==> 2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50305) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 27.54/27.92 parent0[0]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent1[0]: (79) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (243) {G3,W8,D3,L2,V3,M2} R(79,64) { convergent_lines( Z, X )
% 27.54/27.92 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 27.54/27.92 parent0: (50305) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50308) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 27.54/27.92 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 27.54/27.92 parent0[0]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent1[1]: (243) {G3,W8,D3,L2,V3,M2} R(79,64) { convergent_lines( Z, X ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Z
% 27.54/27.92 Y := orthogonal_through_point( X, Y )
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (327) {G4,W8,D3,L2,V3,M2} R(243,64) { convergent_lines( X,
% 27.54/27.92 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 27.54/27.92 parent0: (50308) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 27.54/27.92 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50310) {G2,W8,D3,L2,V3,M2} { convergent_lines(
% 27.54/27.92 parallel_through_point( Y, Z ), X ), ! convergent_lines( Y, X ) }.
% 27.54/27.92 parent0[0]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent1[1]: (68) {G3,W8,D3,L2,V3,M2} R(67,5) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := parallel_through_point( Y, Z )
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (394) {G4,W8,D3,L2,V3,M2} R(68,64) { convergent_lines(
% 27.54/27.92 parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 parent0: (50310) {G2,W8,D3,L2,V3,M2} { convergent_lines(
% 27.54/27.92 parallel_through_point( Y, Z ), X ), ! convergent_lines( Y, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50311) {G5,W8,D3,L2,V2,M2} { convergent_lines(
% 27.54/27.92 parallel_through_point( skol3, X ), Y ), ! convergent_lines( Y, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 parent0[1]: (394) {G4,W8,D3,L2,V3,M2} R(68,64) { convergent_lines(
% 27.54/27.92 parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 27.54/27.92 parent1[0]: (188) {G4,W6,D2,L2,V1,M2} R(75,64) { convergent_lines( skol3, X
% 27.54/27.92 ), ! convergent_lines( X, skol2 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := skol3
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (519) {G5,W8,D3,L2,V2,M2} R(394,188) { ! convergent_lines( Y,
% 27.54/27.92 skol2 ), convergent_lines( parallel_through_point( skol3, X ), Y ) }.
% 27.54/27.92 parent0: (50311) {G5,W8,D3,L2,V2,M2} { convergent_lines(
% 27.54/27.92 parallel_through_point( skol3, X ), Y ), ! convergent_lines( Y, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50312) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 convergent_lines( Z, Y ), ! orthogonal_lines( X, Z ) }.
% 27.54/27.92 parent0[1]: (44) {G0,W6,D2,L2,V2,M1} I { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent1[2]: (220) {G1,W9,D2,L3,V3,M1} R(31,44) { ! convergent_lines( X, Y )
% 27.54/27.92 , ! orthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := Z
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (1846) {G2,W9,D2,L3,V3,M2} R(220,44) { ! convergent_lines( X,
% 27.54/27.92 Y ), ! orthogonal_lines( Z, Y ), ! orthogonal_lines( Z, X ) }.
% 27.54/27.92 parent0: (50312) {G1,W9,D2,L3,V3,M3} { ! orthogonal_lines( X, Y ), !
% 27.54/27.92 convergent_lines( Z, Y ), ! orthogonal_lines( X, Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Z
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 1
% 27.54/27.92 1 ==> 0
% 27.54/27.92 2 ==> 2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50315) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( skol1, X ),
% 27.54/27.92 ! orthogonal_lines( skol3, X ) }.
% 27.54/27.92 parent0[2]: (1846) {G2,W9,D2,L3,V3,M2} R(220,44) { ! convergent_lines( X, Y
% 27.54/27.92 ), ! orthogonal_lines( Z, Y ), ! orthogonal_lines( Z, X ) }.
% 27.54/27.92 parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { orthogonal_lines( skol3, skol1 )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := skol1
% 27.54/27.92 Y := X
% 27.54/27.92 Z := skol3
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (1848) {G3,W6,D2,L2,V1,M1} R(1846,46) { ! convergent_lines(
% 27.54/27.92 skol1, X ), ! orthogonal_lines( skol3, X ) }.
% 27.54/27.92 parent0: (50315) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( skol1, X ), !
% 27.54/27.92 orthogonal_lines( skol3, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50316) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 27.54/27.92 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 27.54/27.92 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 27.54/27.92 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 27.54/27.92 orthogonal_through_point( Y, X ), Y ) }.
% 27.54/27.92 parent1[3]: (164) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 27.54/27.92 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( Y, Z ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := Z
% 27.54/27.92 Y := orthogonal_through_point( X, Y )
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50317) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 parent0[0]: (50316) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 27.54/27.92 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 27.54/27.92 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 27.54/27.92 parent1[0]: (327) {G4,W8,D3,L2,V3,M2} R(243,64) { convergent_lines( X,
% 27.54/27.92 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 factor: (50318) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 parent0[0, 2]: (50317) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (2715) {G5,W8,D3,L2,V3,M1} R(164,23);r(327) { convergent_lines
% 27.54/27.92 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 parent0: (50318) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50319) {G1,W8,D3,L2,V3,M2} { convergent_lines( X, Y ),
% 27.54/27.92 orthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 parent0[1]: (2715) {G5,W8,D3,L2,V3,M1} R(164,23);r(327) { convergent_lines
% 27.54/27.92 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 parent1[1]: (45) {G0,W6,D2,L2,V2,M1} I { orthogonal_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := orthogonal_through_point( Y, Z )
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (2726) {G6,W8,D3,L2,V3,M1} R(2715,45) { convergent_lines( X, Y
% 27.54/27.92 ), orthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 parent0: (50319) {G1,W8,D3,L2,V3,M2} { convergent_lines( X, Y ),
% 27.54/27.92 orthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50321) {G4,W8,D3,L2,V2,M2} { ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( X, Y ) ), convergent_lines( skol3, X ) }.
% 27.54/27.92 parent0[1]: (1848) {G3,W6,D2,L2,V1,M1} R(1846,46) { ! convergent_lines(
% 27.54/27.92 skol1, X ), ! orthogonal_lines( skol3, X ) }.
% 27.54/27.92 parent1[1]: (2726) {G6,W8,D3,L2,V3,M1} R(2715,45) { convergent_lines( X, Y
% 27.54/27.92 ), orthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := orthogonal_through_point( X, Y )
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := skol3
% 27.54/27.92 Y := X
% 27.54/27.92 Z := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (2727) {G7,W8,D3,L2,V2,M2} R(2726,1848) { ! convergent_lines(
% 27.54/27.92 skol1, orthogonal_through_point( X, Y ) ), convergent_lines( skol3, X )
% 27.54/27.92 }.
% 27.54/27.92 parent0: (50321) {G4,W8,D3,L2,V2,M2} { ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( X, Y ) ), convergent_lines( skol3, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50322) {G6,W10,D3,L2,V2,M2} { convergent_lines(
% 27.54/27.92 parallel_through_point( skol3, X ), skol3 ), ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( skol2, Y ) ) }.
% 27.54/27.92 parent0[0]: (519) {G5,W8,D3,L2,V2,M2} R(394,188) { ! convergent_lines( Y,
% 27.54/27.92 skol2 ), convergent_lines( parallel_through_point( skol3, X ), Y ) }.
% 27.54/27.92 parent1[1]: (2727) {G7,W8,D3,L2,V2,M2} R(2726,1848) { ! convergent_lines(
% 27.54/27.92 skol1, orthogonal_through_point( X, Y ) ), convergent_lines( skol3, X )
% 27.54/27.92 }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := skol3
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := skol2
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50323) {G1,W5,D3,L1,V1,M1} { ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( skol2, Y ) ) }.
% 27.54/27.92 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 27.54/27.92 parallel_through_point( Y, X ), Y ) }.
% 27.54/27.92 parent1[0]: (50322) {G6,W10,D3,L2,V2,M2} { convergent_lines(
% 27.54/27.92 parallel_through_point( skol3, X ), skol3 ), ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( skol2, Y ) ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := skol3
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (2749) {G8,W5,D3,L1,V1,M1} R(2727,519);r(15) { !
% 27.54/27.92 convergent_lines( skol1, orthogonal_through_point( skol2, X ) ) }.
% 27.54/27.92 parent0: (50323) {G1,W5,D3,L1,V1,M1} { ! convergent_lines( skol1,
% 27.54/27.92 orthogonal_through_point( skol2, Y ) ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50324) {G2,W5,D3,L1,V1,M1} { ! convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 parent0[0]: (2749) {G8,W5,D3,L1,V1,M1} R(2727,519);r(15) { !
% 27.54/27.92 convergent_lines( skol1, orthogonal_through_point( skol2, X ) ) }.
% 27.54/27.92 parent1[1]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 27.54/27.92 convergent_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := skol1
% 27.54/27.92 Y := orthogonal_through_point( skol2, X )
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (2852) {G9,W5,D3,L1,V1,M1} R(2749,64) { ! convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 parent0: (50324) {G2,W5,D3,L1,V1,M1} { ! convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50325) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( Z, X ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Y ), Z ), !
% 27.54/27.92 unorthogonal_lines( Z, X ) }.
% 27.54/27.92 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 27.54/27.92 orthogonal_through_point( Y, X ), Y ) }.
% 27.54/27.92 parent1[2]: (205) {G1,W12,D2,L4,V3,M2} R(27,28) { ! convergent_lines( Z, Y
% 27.54/27.92 ), convergent_lines( X, Z ), unorthogonal_lines( X, Y ), !
% 27.54/27.92 unorthogonal_lines( Z, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := orthogonal_through_point( X, Y )
% 27.54/27.92 Y := X
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (3100) {G2,W11,D3,L3,V3,M1} R(205,23) { ! convergent_lines( X
% 27.54/27.92 , Y ), convergent_lines( orthogonal_through_point( Y, Z ), X ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent0: (50325) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( Z, X ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( X, Y ), Z ), !
% 27.54/27.92 unorthogonal_lines( Z, X ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := Y
% 27.54/27.92 Y := Z
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 2 ==> 2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50326) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( Y, Z ), X ), orthogonal_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 parent0[2]: (3100) {G2,W11,D3,L3,V3,M1} R(205,23) { ! convergent_lines( X,
% 27.54/27.92 Y ), convergent_lines( orthogonal_through_point( Y, Z ), X ), !
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 parent1[1]: (45) {G0,W6,D2,L2,V2,M1} I { orthogonal_lines( X, Y ),
% 27.54/27.92 unorthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (50048) {G3,W11,D3,L3,V3,M1} R(3100,45) { ! convergent_lines(
% 27.54/27.92 X, Y ), convergent_lines( orthogonal_through_point( Y, Z ), X ),
% 27.54/27.92 orthogonal_lines( X, Y ) }.
% 27.54/27.92 parent0: (50326) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ),
% 27.54/27.92 convergent_lines( orthogonal_through_point( Y, Z ), X ), orthogonal_lines
% 27.54/27.92 ( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 Y := Y
% 27.54/27.92 Z := Z
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 1 ==> 1
% 27.54/27.92 2 ==> 2
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50327) {G1,W8,D3,L2,V1,M2} { ! convergent_lines( skol1, skol2
% 27.54/27.92 ), convergent_lines( orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 parent0[0]: (48) {G0,W3,D2,L1,V0,M1} I { ! orthogonal_lines( skol1, skol2 )
% 27.54/27.92 }.
% 27.54/27.92 parent1[2]: (50048) {G3,W11,D3,L3,V3,M1} R(3100,45) { ! convergent_lines( X
% 27.54/27.92 , Y ), convergent_lines( orthogonal_through_point( Y, Z ), X ),
% 27.54/27.92 orthogonal_lines( X, Y ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := skol1
% 27.54/27.92 Y := skol2
% 27.54/27.92 Z := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50328) {G2,W5,D3,L1,V1,M1} { convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 parent0[0]: (50327) {G1,W8,D3,L2,V1,M2} { ! convergent_lines( skol1, skol2
% 27.54/27.92 ), convergent_lines( orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 parent1[0]: (125) {G4,W3,D2,L1,V0,M1} R(108,70) { convergent_lines( skol1,
% 27.54/27.92 skol2 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (50049) {G5,W5,D3,L1,V1,M1} R(50048,48);r(125) {
% 27.54/27.92 convergent_lines( orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 parent0: (50328) {G2,W5,D3,L1,V1,M1} { convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 0 ==> 0
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 resolution: (50329) {G6,W0,D0,L0,V0,M0} { }.
% 27.54/27.92 parent0[0]: (2852) {G9,W5,D3,L1,V1,M1} R(2749,64) { ! convergent_lines(
% 27.54/27.92 orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 parent1[0]: (50049) {G5,W5,D3,L1,V1,M1} R(50048,48);r(125) {
% 27.54/27.92 convergent_lines( orthogonal_through_point( skol2, X ), skol1 ) }.
% 27.54/27.92 substitution0:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92 substitution1:
% 27.54/27.92 X := X
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 subsumption: (50050) {G10,W0,D0,L0,V0,M0} S(50049);r(2852) { }.
% 27.54/27.92 parent0: (50329) {G6,W0,D0,L0,V0,M0} { }.
% 27.54/27.92 substitution0:
% 27.54/27.92 end
% 27.54/27.92 permutation0:
% 27.54/27.92 end
% 27.54/27.92
% 27.54/27.92 Proof check complete!
% 27.54/27.92
% 27.54/27.92 Memory use:
% 27.54/27.92
% 27.54/27.92 space for terms: 738310
% 27.54/27.92 space for clauses: 1895809
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 clauses generated: 1301841
% 27.54/27.92 clauses kept: 50051
% 27.54/27.92 clauses selected: 2184
% 27.54/27.92 clauses deleted: 1435
% 27.54/27.92 clauses inuse deleted: 58
% 27.54/27.92
% 27.54/27.92 subsentry: 41244954
% 27.54/27.92 literals s-matched: 13085668
% 27.54/27.92 literals matched: 13084809
% 27.54/27.92 full subsumption: 7606603
% 27.54/27.92
% 27.54/27.92 checksum: -1708894154
% 27.54/27.92
% 27.54/27.92
% 27.54/27.92 Bliksem ended
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