TSTP Solution File: GEO177+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 02:52:18 EDT 2022
% Result : Theorem 6.54s 6.89s
% Output : Refutation 6.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sat Jun 18 02:49:12 EDT 2022
% 0.14/0.34 % CPUTime :
% 6.54/6.89 *** allocated 10000 integers for termspace/termends
% 6.54/6.89 *** allocated 10000 integers for clauses
% 6.54/6.89 *** allocated 10000 integers for justifications
% 6.54/6.89 Bliksem 1.12
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 Automatic Strategy Selection
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 Clauses:
% 6.54/6.89
% 6.54/6.89 { ! distinct_points( X, X ) }.
% 6.54/6.89 { ! distinct_lines( X, X ) }.
% 6.54/6.89 { ! convergent_lines( X, X ) }.
% 6.54/6.89 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 6.54/6.89 ) }.
% 6.54/6.89 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.54/6.89 }.
% 6.54/6.89 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 6.54/6.89 , Z ) }.
% 6.54/6.89 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 6.54/6.89 , Y ) ) }.
% 6.54/6.89 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 6.54/6.89 , Y ) ) }.
% 6.54/6.89 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.54/6.89 , Y ), X ) }.
% 6.54/6.89 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.54/6.89 , Y ), Y ) }.
% 6.54/6.89 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 6.54/6.89 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 6.54/6.89 apart_point_and_line( Y, T ) }.
% 6.54/6.89 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 6.54/6.89 apart_point_and_line( Z, Y ) }.
% 6.54/6.89 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 6.54/6.89 apart_point_and_line( X, Z ) }.
% 6.54/6.89 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 6.54/6.89 Z ) }.
% 6.54/6.89 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 6.54/6.89 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 6.54/6.89 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 6.54/6.89 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.54/6.89 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 6.54/6.89 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.54/6.89 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.54/6.89 , convergent_lines( Y, Z ) }.
% 6.54/6.89 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.54/6.89 , unorthogonal_lines( Y, Z ) }.
% 6.54/6.89 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 6.54/6.89 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.54/6.89 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 6.54/6.89 }.
% 6.54/6.89 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.89 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 6.54/6.89 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.54/6.89 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 6.54/6.89 unorthogonal_lines( Y, T ) }.
% 6.54/6.89 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.54/6.89 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, Y ) }.
% 6.54/6.89 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, Y ) }.
% 6.54/6.89 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 6.54/6.89 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 6.54/6.89 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 6.54/6.89 }.
% 6.54/6.89 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 6.54/6.89 convergent_lines( X, Y ) }.
% 6.54/6.89 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 6.54/6.89 line_connecting( X, Y ) ) }.
% 6.54/6.89 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 6.54/6.89 intersection_point( X, Y ) ) }.
% 6.54/6.89 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 6.54/6.89 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 6.54/6.89 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 6.54/6.89 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 6.54/6.89 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 6.54/6.89 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 6.54/6.89 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 6.54/6.89 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 6.54/6.89 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.89 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 6.54/6.89 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.54/6.89 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 6.54/6.89 { distinct_points( skol1, skol2 ) }.
% 6.54/6.89 { distinct_points( skol3, skol4 ) }.
% 6.54/6.89 { apart_point_and_line( skol1, line_connecting( skol3, skol4 ) ),
% 6.54/6.89 apart_point_and_line( skol2, line_connecting( skol3, skol4 ) ) }.
% 6.54/6.89 { ! apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89 { ! apart_point_and_line( skol4, line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89
% 6.54/6.89 percentage equality = 0.000000, percentage horn = 0.607843
% 6.54/6.89 This a non-horn, non-equality problem
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 Options Used:
% 6.54/6.89
% 6.54/6.89 useres = 1
% 6.54/6.89 useparamod = 0
% 6.54/6.89 useeqrefl = 0
% 6.54/6.89 useeqfact = 0
% 6.54/6.89 usefactor = 1
% 6.54/6.89 usesimpsplitting = 0
% 6.54/6.89 usesimpdemod = 0
% 6.54/6.89 usesimpres = 3
% 6.54/6.89
% 6.54/6.89 resimpinuse = 1000
% 6.54/6.89 resimpclauses = 20000
% 6.54/6.89 substype = standard
% 6.54/6.89 backwardsubs = 1
% 6.54/6.89 selectoldest = 5
% 6.54/6.89
% 6.54/6.89 litorderings [0] = split
% 6.54/6.89 litorderings [1] = liftord
% 6.54/6.89
% 6.54/6.89 termordering = none
% 6.54/6.89
% 6.54/6.89 litapriori = 1
% 6.54/6.89 termapriori = 0
% 6.54/6.89 litaposteriori = 0
% 6.54/6.89 termaposteriori = 0
% 6.54/6.89 demodaposteriori = 0
% 6.54/6.89 ordereqreflfact = 0
% 6.54/6.89
% 6.54/6.89 litselect = none
% 6.54/6.89
% 6.54/6.89 maxweight = 15
% 6.54/6.89 maxdepth = 30000
% 6.54/6.89 maxlength = 115
% 6.54/6.89 maxnrvars = 195
% 6.54/6.89 excuselevel = 1
% 6.54/6.89 increasemaxweight = 1
% 6.54/6.89
% 6.54/6.89 maxselected = 10000000
% 6.54/6.89 maxnrclauses = 10000000
% 6.54/6.89
% 6.54/6.89 showgenerated = 0
% 6.54/6.89 showkept = 0
% 6.54/6.89 showselected = 0
% 6.54/6.89 showdeleted = 0
% 6.54/6.89 showresimp = 1
% 6.54/6.89 showstatus = 2000
% 6.54/6.89
% 6.54/6.89 prologoutput = 0
% 6.54/6.89 nrgoals = 5000000
% 6.54/6.89 totalproof = 1
% 6.54/6.89
% 6.54/6.89 Symbols occurring in the translation:
% 6.54/6.89
% 6.54/6.89 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.54/6.89 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 6.54/6.89 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 6.54/6.89 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.54/6.89 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.54/6.89 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 6.54/6.89 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 6.54/6.89 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 6.54/6.89 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 6.54/6.89 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 6.54/6.89 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 6.54/6.89 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 6.54/6.89 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 6.54/6.89 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 6.54/6.89 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 6.54/6.89 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 6.54/6.89 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 6.54/6.89 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 6.54/6.89 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 6.54/6.89 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 6.54/6.89 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 6.54/6.89 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 6.54/6.89 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 6.54/6.89 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 6.54/6.89 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 6.54/6.89 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 6.54/6.89 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 Starting Search:
% 6.54/6.89
% 6.54/6.89 *** allocated 15000 integers for clauses
% 6.54/6.89 *** allocated 22500 integers for clauses
% 6.54/6.89 *** allocated 33750 integers for clauses
% 6.54/6.89 *** allocated 15000 integers for termspace/termends
% 6.54/6.89 *** allocated 50625 integers for clauses
% 6.54/6.89 Resimplifying inuse:
% 6.54/6.89 Done
% 6.54/6.89
% 6.54/6.89 *** allocated 22500 integers for termspace/termends
% 6.54/6.89 *** allocated 75937 integers for clauses
% 6.54/6.89 *** allocated 33750 integers for termspace/termends
% 6.54/6.89 *** allocated 113905 integers for clauses
% 6.54/6.89
% 6.54/6.89 Intermediate Status:
% 6.54/6.89 Generated: 18654
% 6.54/6.89 Kept: 2001
% 6.54/6.89 Inuse: 314
% 6.54/6.89 Deleted: 2
% 6.54/6.89 Deletedinuse: 2
% 6.54/6.89
% 6.54/6.89 Resimplifying inuse:
% 6.54/6.89 Done
% 6.54/6.89
% 6.54/6.89 *** allocated 50625 integers for termspace/termends
% 6.54/6.89 *** allocated 170857 integers for clauses
% 6.54/6.89 Resimplifying inuse:
% 6.54/6.89 Done
% 6.54/6.89
% 6.54/6.89 *** allocated 75937 integers for termspace/termends
% 6.54/6.89
% 6.54/6.89 Intermediate Status:
% 6.54/6.89 Generated: 32063
% 6.54/6.89 Kept: 4032
% 6.54/6.89 Inuse: 475
% 6.54/6.89 Deleted: 5
% 6.54/6.89 Deletedinuse: 2
% 6.54/6.89
% 6.54/6.89 Resimplifying inuse:
% 6.54/6.89 Done
% 6.54/6.89
% 6.54/6.89 *** allocated 256285 integers for clauses
% 6.54/6.89 Resimplifying inuse:
% 6.54/6.89 Done
% 6.54/6.89
% 6.54/6.89 *** allocated 113905 integers for termspace/termends
% 6.54/6.89 *** allocated 384427 integers for clauses
% 6.54/6.89
% 6.54/6.89 Intermediate Status:
% 6.54/6.89 Generated: 64813
% 6.54/6.89 Kept: 6032
% 6.54/6.89 Inuse: 820
% 6.54/6.89 Deleted: 9
% 6.54/6.89 Deletedinuse: 3
% 6.54/6.89
% 6.54/6.89 Resimplifying inuse:
% 6.54/6.89 Done
% 6.54/6.89
% 6.54/6.89 Resimplifying inuse:
% 6.54/6.89 Done
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 Bliksems!, er is een bewijs:
% 6.54/6.89 % SZS status Theorem
% 6.54/6.89 % SZS output start Refutation
% 6.54/6.89
% 6.54/6.89 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.54/6.89 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.89 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.54/6.89 , ! distinct_lines( X, Y ) }.
% 6.54/6.89 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 6.54/6.89 Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.89 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 6.54/6.89 X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.89 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 6.54/6.89 , Y ) }.
% 6.54/6.89 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 6.54/6.89 , X ), Y ) }.
% 6.54/6.89 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.54/6.89 parallel_through_point( Y, X ) ) }.
% 6.54/6.89 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 6.54/6.89 X, Y ) }.
% 6.54/6.89 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.54/6.89 }.
% 6.54/6.89 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 6.54/6.89 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 6.54/6.89 ( Y, X ), Y ) }.
% 6.54/6.89 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.54/6.89 orthogonal_through_point( Y, X ) ) }.
% 6.54/6.89 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 6.54/6.89 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.54/6.89 (48) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line( skol1, line_connecting
% 6.54/6.89 ( skol3, skol4 ) ), apart_point_and_line( skol2, line_connecting( skol3,
% 6.54/6.89 skol4 ) ) }.
% 6.54/6.89 (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 6.54/6.89 ( X, Y ) }.
% 6.54/6.89 (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.54/6.89 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.89 (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.54/6.89 convergent_lines( X, Y ) }.
% 6.54/6.89 (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.54/6.89 parallel_through_point( X, Y ) ) }.
% 6.54/6.89 (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ),
% 6.54/6.89 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.89 (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y ),
% 6.54/6.89 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.89 (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 6.54/6.89 orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.89 (113) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ),
% 6.54/6.89 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.89 (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ), !
% 6.54/6.89 distinct_lines( Y, X ) }.
% 6.54/6.89 (138) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 6.54/6.89 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 6.54/6.89 apart_point_and_line( Z, X ) }.
% 6.54/6.89 (150) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 6.54/6.89 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89 (151) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 6.54/6.89 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89 (162) {G2,W11,D3,L3,V4,M1} R(150,12) { distinct_lines( X,
% 6.54/6.89 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.89 apart_point_and_line( Z, T ) }.
% 6.54/6.89 (164) {G2,W11,D3,L3,V4,M1} R(151,12) { distinct_lines( X,
% 6.54/6.89 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.89 apart_point_and_line( Z, T ) }.
% 6.54/6.89 (171) {G3,W8,D3,L2,V3,M2} R(113,69) { convergent_lines( Z, X ),
% 6.54/6.89 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.89 (178) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 6.54/6.89 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 6.54/6.89 unorthogonal_lines( Y, Z ) }.
% 6.54/6.89 (184) {G4,W8,D3,L2,V3,M2} R(171,69) { convergent_lines( X,
% 6.54/6.89 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.89 (206) {G4,W7,D4,L1,V3,M1} R(73,15) { ! convergent_lines( X,
% 6.54/6.89 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.89 (216) {G5,W10,D4,L2,V4,M2} R(206,5) { ! convergent_lines( Y, X ),
% 6.54/6.89 convergent_lines( X, parallel_through_point( parallel_through_point( Y, Z
% 6.54/6.89 ), T ) ) }.
% 6.54/6.89 (246) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X,
% 6.54/6.89 parallel_through_point( Z, T ) ), convergent_lines(
% 6.54/6.89 parallel_through_point( X, Y ), Z ) }.
% 6.54/6.89 (250) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z ), !
% 6.54/6.89 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.89 (261) {G3,W8,D3,L2,V3,M2} R(250,69) { ! convergent_lines( Y,
% 6.54/6.89 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.89 (285) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 6.54/6.89 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.54/6.89 (2003) {G3,W14,D3,L4,V5,M1} R(164,12) { distinct_lines( X,
% 6.54/6.89 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 6.54/6.89 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.89 (2005) {G4,W8,D3,L2,V3,M1} F(2003);r(58) { distinct_lines(
% 6.54/6.89 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89 (2024) {G3,W14,D3,L4,V5,M1} R(162,12) { distinct_lines( X,
% 6.54/6.89 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.89 ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.89 (2026) {G4,W8,D3,L2,V3,M1} F(2024);r(58) { distinct_lines(
% 6.54/6.89 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.89 (2352) {G2,W15,D2,L5,V5,M2} R(138,12) { distinct_lines( X, Y ),
% 6.54/6.89 distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line( T,
% 6.54/6.89 U ), ! apart_point_and_line( T, X ) }.
% 6.54/6.89 (2356) {G3,W9,D2,L3,V3,M2} F(2352);r(58) { distinct_lines( Y, X ), !
% 6.54/6.89 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 6.54/6.89 (2411) {G4,W13,D3,L3,V1,M2} R(2356,48) { distinct_lines( X, line_connecting
% 6.54/6.89 ( skol3, skol4 ) ), apart_point_and_line( skol1, line_connecting( skol3,
% 6.54/6.89 skol4 ) ), apart_point_and_line( skol2, X ) }.
% 6.54/6.89 (2738) {G5,W8,D3,L2,V3,M1} R(178,23);r(184) { convergent_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.89 (2745) {G6,W10,D3,L2,V4,M2} R(2738,285) { ! convergent_lines(
% 6.54/6.89 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 6.54/6.89 orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.89 (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines(
% 6.54/6.89 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.89 (3012) {G8,W9,D5,L1,V4,M1} R(2914,261) { ! convergent_lines( X,
% 6.54/6.89 parallel_through_point( orthogonal_through_point(
% 6.54/6.89 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.89 (3015) {G8,W9,D5,L1,V4,M1} R(2914,74) { ! convergent_lines(
% 6.54/6.89 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.89 parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.89 (3404) {G9,W13,D7,L1,V6,M1} R(3012,246) { ! convergent_lines( X,
% 6.54/6.89 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.54/6.89 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.89 , W ) ) }.
% 6.54/6.89 (3478) {G9,W13,D7,L1,V6,M1} R(3015,216) { ! convergent_lines( X,
% 6.54/6.89 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.89 parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.89 , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.89 (7272) {G5,W15,D3,L3,V2,M1} R(2411,2005) { distinct_lines( X,
% 6.54/6.89 line_connecting( skol3, skol4 ) ), distinct_lines(
% 6.54/6.89 orthogonal_through_point( Y, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.89 apart_point_and_line( skol2, X ) }.
% 6.54/6.89 (7273) {G6,W12,D3,L2,V1,M1} F(7272) { distinct_lines(
% 6.54/6.89 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.89 apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.89 (7287) {G7,W14,D3,L2,V2,M1} R(7273,2026) { distinct_lines(
% 6.54/6.89 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.89 distinct_lines( parallel_through_point( Y, skol2 ),
% 6.54/6.89 orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.89 (7343) {G8,W14,D3,L2,V2,M1} R(7287,114) { convergent_lines(
% 6.54/6.89 orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.89 ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.89 ( skol3, skol4 ) ) }.
% 6.54/6.89 (7345) {G9,W14,D3,L2,V2,M1} R(7343,114) { convergent_lines( line_connecting
% 6.54/6.89 ( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ),
% 6.54/6.89 convergent_lines( orthogonal_through_point( X, skol1 ),
% 6.54/6.89 parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.89 (7354) {G10,W7,D3,L1,V1,M1} R(7345,3404) { convergent_lines(
% 6.54/6.89 line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.89 }.
% 6.54/6.89 (7355) {G11,W0,D0,L0,V0,M0} R(7354,3478) { }.
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 % SZS output end Refutation
% 6.54/6.89 found a proof!
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 Unprocessed initial clauses:
% 6.54/6.89
% 6.54/6.89 (7357) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 6.54/6.89 (7358) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 6.54/6.89 (7359) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 6.54/6.89 (7360) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 6.54/6.89 , Z ), distinct_points( Y, Z ) }.
% 6.54/6.89 (7361) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 6.54/6.89 Z ), distinct_lines( Y, Z ) }.
% 6.54/6.89 (7362) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 6.54/6.89 ( X, Z ), convergent_lines( Y, Z ) }.
% 6.54/6.89 (7363) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 6.54/6.89 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 6.54/6.89 (7364) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 6.54/6.89 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 6.54/6.89 (7365) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.54/6.89 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.54/6.89 (7366) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.54/6.89 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.54/6.89 (7367) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 6.54/6.89 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 6.54/6.89 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 6.54/6.89 (7368) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.54/6.89 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 6.54/6.89 (7369) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.54/6.89 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 6.54/6.89 (7370) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 6.54/6.89 , Z ), convergent_lines( X, Z ) }.
% 6.54/6.89 (7371) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 6.54/6.89 , Y ) }.
% 6.54/6.89 (7372) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 6.54/6.89 , X ), Y ) }.
% 6.54/6.89 (7373) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.54/6.89 parallel_through_point( Y, X ) ) }.
% 6.54/6.89 (7374) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 6.54/6.89 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 6.54/6.89 convergent_lines( X, Y ) }.
% 6.54/6.89 (7375) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 6.54/6.89 ( X, Y ) }.
% 6.54/6.89 (7376) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 6.54/6.89 (7377) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 6.54/6.89 }.
% 6.54/6.89 (7378) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 6.54/6.89 }.
% 6.54/6.89 (7379) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 6.54/6.89 }.
% 6.54/6.89 (7380) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 6.54/6.89 (7381) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 6.54/6.89 orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.89 (7382) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.54/6.89 orthogonal_through_point( Y, X ) ) }.
% 6.54/6.89 (7383) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 6.54/6.89 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 6.54/6.89 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 6.54/6.89 (7384) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 6.54/6.89 ( X, Y ) }.
% 6.54/6.89 (7385) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 6.54/6.89 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.54/6.89 (7386) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 6.54/6.89 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.54/6.89 (7387) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 6.54/6.89 }.
% 6.54/6.89 (7388) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 6.54/6.89 }.
% 6.54/6.89 (7389) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 6.54/6.89 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 6.54/6.89 (7390) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 6.54/6.89 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.54/6.89 (7391) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 6.54/6.89 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 6.54/6.89 (7392) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 6.54/6.89 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 6.54/6.89 (7393) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 6.54/6.89 parallel_through_point( X, Y ) ) }.
% 6.54/6.89 (7394) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 6.54/6.89 orthogonal_through_point( X, Y ) ) }.
% 6.54/6.89 (7395) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 6.54/6.89 , Y ) }.
% 6.54/6.89 (7396) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 6.54/6.89 }.
% 6.54/6.89 (7397) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 6.54/6.89 ) }.
% 6.54/6.89 (7398) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 6.54/6.89 }.
% 6.54/6.89 (7399) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 6.54/6.89 ( X, Y ) }.
% 6.54/6.89 (7400) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 6.54/6.89 Y ) }.
% 6.54/6.89 (7401) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 6.54/6.89 apart_point_and_line( X, Y ) }.
% 6.54/6.89 (7402) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 6.54/6.89 incident_point_and_line( X, Y ) }.
% 6.54/6.89 (7403) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 6.54/6.89 unorthogonal_lines( X, Y ) }.
% 6.54/6.89 (7404) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 6.54/6.89 ( X, Y ) }.
% 6.54/6.89 (7405) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 6.54/6.89 (7406) {G0,W3,D2,L1,V0,M1} { distinct_points( skol3, skol4 ) }.
% 6.54/6.89 (7407) {G0,W10,D3,L2,V0,M2} { apart_point_and_line( skol1, line_connecting
% 6.54/6.89 ( skol3, skol4 ) ), apart_point_and_line( skol2, line_connecting( skol3,
% 6.54/6.89 skol4 ) ) }.
% 6.54/6.89 (7408) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( skol3,
% 6.54/6.89 line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89 (7409) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( skol4,
% 6.54/6.89 line_connecting( skol1, skol2 ) ) }.
% 6.54/6.89
% 6.54/6.89
% 6.54/6.89 Total Proof:
% 6.54/6.89
% 6.54/6.89 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.54/6.89 parent0: (7358) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 6.54/6.89 substitution0:
% 6.54/6.89 X := X
% 6.54/6.89 end
% 6.54/6.89 permutation0:
% 6.54/6.89 0 ==> 0
% 6.54/6.89 end
% 6.54/6.89
% 6.54/6.89 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.89 parent0: (7359) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 6.54/6.89 substitution0:
% 6.54/6.89 X := X
% 6.54/6.89 end
% 6.54/6.89 permutation0:
% 6.54/6.89 0 ==> 0
% 6.54/6.89 end
% 6.54/6.89
% 6.54/6.89 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 6.54/6.89 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.54/6.89 parent0: (7361) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 6.54/6.89 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 6.54/6.89 substitution0:
% 6.54/6.89 X := X
% 6.54/6.89 Y := Y
% 6.54/6.89 Z := Z
% 6.54/6.89 end
% 6.54/6.89 permutation0:
% 6.54/6.89 0 ==> 2
% 6.54/6.89 1 ==> 0
% 6.54/6.89 2 ==> 1
% 6.54/6.89 end
% 6.54/6.89
% 6.54/6.89 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.54/6.89 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.89 parent0: (7362) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 6.54/6.89 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 6.54/6.89 substitution0:
% 6.54/6.89 X := X
% 6.54/6.89 Y := Y
% 6.54/6.89 Z := Z
% 6.54/6.89 end
% 6.54/6.89 permutation0:
% 6.54/6.89 0 ==> 2
% 6.54/6.89 1 ==> 0
% 6.54/6.89 2 ==> 1
% 6.54/6.89 end
% 6.54/6.89
% 6.54/6.89 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.89 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.89 parent0: (7369) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.54/6.89 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 6.54/6.89 substitution0:
% 6.54/6.89 X := X
% 6.54/6.89 Y := Y
% 6.54/6.89 Z := Z
% 6.54/6.89 end
% 6.54/6.89 permutation0:
% 6.54/6.89 0 ==> 2
% 6.54/6.89 1 ==> 0
% 6.54/6.89 2 ==> 1
% 6.54/6.89 end
% 6.54/6.89
% 6.54/6.89 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.54/6.89 distinct_lines( X, Y ) }.
% 6.54/6.89 parent0: (7371) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 6.54/6.89 convergent_lines( X, Y ) }.
% 6.54/6.89 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent0: (7372) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.54/6.90 parallel_through_point( Y, X ) ) }.
% 6.54/6.90 parent0: (7373) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.54/6.90 parallel_through_point( Y, X ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 6.54/6.90 unorthogonal_lines( X, Y ) }.
% 6.54/6.90 parent0: (7375) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 6.54/6.90 unorthogonal_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 6.54/6.90 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.54/6.90 }.
% 6.54/6.90 parent0: (7377) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.54/6.90 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 6.54/6.90 }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 2 ==> 3
% 6.54/6.90 3 ==> 2
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.54/6.90 alpha1( X, Y ) }.
% 6.54/6.90 parent0: (7378) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 6.54/6.90 X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.54/6.90 orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent0: (7381) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 6.54/6.90 orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.54/6.90 orthogonal_through_point( Y, X ) ) }.
% 6.54/6.90 parent0: (7382) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.54/6.90 orthogonal_through_point( Y, X ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 6.54/6.90 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.54/6.90 parent0: (7390) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 6.54/6.90 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 2
% 6.54/6.90 2 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (48) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line( skol1,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2,
% 6.54/6.90 line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90 parent0: (7407) {G0,W10,D3,L2,V0,M2} { apart_point_and_line( skol1,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2,
% 6.54/6.90 line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7529) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.54/6.90 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 6.54/6.90 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 parent0: (7529) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7531) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 6.54/6.90 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := parallel_through_point( X, Y )
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.90 parent0: (7531) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 6.54/6.90 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7533) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.90 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 parent0: (7533) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7535) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( X, Y ) ) }.
% 6.54/6.90 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent1[1]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := parallel_through_point( X, Y )
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( X, Y ) ) }.
% 6.54/6.90 parent0: (7535) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( X, Y ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7536) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.54/6.90 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 6.54/6.90 parent0[0]: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( X, Y ) ) }.
% 6.54/6.90 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := parallel_through_point( X, Y )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X )
% 6.54/6.90 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90 parent0: (7536) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.54/6.90 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7539) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.54/6.90 parallel_through_point( X, Y ) ), ! convergent_lines( Z, X ) }.
% 6.54/6.90 parent0[0]: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( X, Y ) ) }.
% 6.54/6.90 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := X
% 6.54/6.90 Z := parallel_through_point( X, Y )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y )
% 6.54/6.90 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90 parent0: (7539) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.54/6.90 parallel_through_point( X, Y ) ), ! convergent_lines( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7540) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.54/6.90 orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 6.54/6.90 unorthogonal_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := orthogonal_through_point( X, Y )
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90 parent0: (7540) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7541) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 6.54/6.90 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90 parent1[0]: (77) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( X, Y )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (113) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent0: (7541) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7542) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 6.54/6.90 distinct_lines( Y, X ) }.
% 6.54/6.90 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 parent1[1]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y )
% 6.54/6.90 , ! distinct_lines( Y, X ) }.
% 6.54/6.90 parent0: (7542) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 6.54/6.90 distinct_lines( Y, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7543) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 6.54/6.90 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := T
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (138) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 6.54/6.90 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 6.54/6.90 apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0: (7543) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 6.54/6.90 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := T
% 6.54/6.90 Z := Z
% 6.54/6.90 T := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 2
% 6.54/6.90 2 ==> 0
% 6.54/6.90 3 ==> 3
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7545) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 6.54/6.90 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.54/6.90 parallel_through_point( Y, X ) ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := parallel_through_point( Y, X )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (150) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0: (7545) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 6.54/6.90 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7546) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 6.54/6.90 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.54/6.90 orthogonal_through_point( Y, X ) ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := orthogonal_through_point( Y, X )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (151) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0: (7546) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 6.54/6.90 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7547) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 parent0[1]: (150) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := T
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (162) {G2,W11,D3,L3,V4,M1} R(150,12) { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 parent0: (7547) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 2 ==> 2
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7549) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 parent0[1]: (151) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := T
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (164) {G2,W11,D3,L3,V4,M1} R(151,12) { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 parent0: (7549) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 2 ==> 2
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7551) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 6.54/6.90 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 parent1[0]: (113) {G2,W8,D3,L2,V3,M2} R(77,5) { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (171) {G3,W8,D3,L2,V3,M2} R(113,69) { convergent_lines( Z, X )
% 6.54/6.90 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent0: (7551) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7554) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 6.54/6.90 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 6.54/6.90 unorthogonal_lines( Z, Y ) }.
% 6.54/6.90 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 6.54/6.90 ( X, Y ) }.
% 6.54/6.90 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 6.54/6.90 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.54/6.90 }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (178) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 6.54/6.90 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 6.54/6.90 unorthogonal_lines( Y, Z ) }.
% 6.54/6.90 parent0: (7554) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 6.54/6.90 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 6.54/6.90 unorthogonal_lines( Z, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 2 ==> 2
% 6.54/6.90 3 ==> 3
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7556) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.54/6.90 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 6.54/6.90 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 parent1[1]: (171) {G3,W8,D3,L2,V3,M2} R(113,69) { convergent_lines( Z, X )
% 6.54/6.90 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := orthogonal_through_point( X, Y )
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (184) {G4,W8,D3,L2,V3,M2} R(171,69) { convergent_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90 parent0: (7556) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.54/6.90 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7557) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent1[1]: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := parallel_through_point( X, Y )
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := parallel_through_point( parallel_through_point( X, Y ), Z )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (206) {G4,W7,D4,L1,V3,M1} R(73,15) { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90 parent0: (7557) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7558) {G1,W10,D4,L2,V4,M2} { convergent_lines( T,
% 6.54/6.90 parallel_through_point( parallel_through_point( X, Y ), Z ) ), !
% 6.54/6.90 convergent_lines( X, T ) }.
% 6.54/6.90 parent0[0]: (206) {G4,W7,D4,L1,V3,M1} R(73,15) { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 6.54/6.90 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.54/6.90 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := T
% 6.54/6.90 Z := parallel_through_point( parallel_through_point( X, Y ), Z )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (216) {G5,W10,D4,L2,V4,M2} R(206,5) { ! convergent_lines( Y, X
% 6.54/6.90 ), convergent_lines( X, parallel_through_point( parallel_through_point(
% 6.54/6.90 Y, Z ), T ) ) }.
% 6.54/6.90 parent0: (7558) {G1,W10,D4,L2,V4,M2} { convergent_lines( T,
% 6.54/6.90 parallel_through_point( parallel_through_point( X, Y ), Z ) ), !
% 6.54/6.90 convergent_lines( X, T ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := T
% 6.54/6.90 T := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7560) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.54/6.90 parallel_through_point( Z, T ), X ), ! convergent_lines( Z,
% 6.54/6.90 parallel_through_point( X, Y ) ) }.
% 6.54/6.90 parent0[0]: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.90 parent1[1]: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := parallel_through_point( Z, T )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := parallel_through_point( X, Y )
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := T
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (246) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( Z, T ) ), convergent_lines(
% 6.54/6.90 parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent0: (7560) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.54/6.90 parallel_through_point( Z, T ), X ), ! convergent_lines( Z,
% 6.54/6.90 parallel_through_point( X, Y ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := T
% 6.54/6.90 Z := X
% 6.54/6.90 T := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7562) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 6.54/6.90 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 6.54/6.90 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 parent1[1]: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (250) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z )
% 6.54/6.90 , ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent0: (7562) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 6.54/6.90 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7563) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.54/6.90 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 6.54/6.90 parent0[1]: (250) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z ),
% 6.54/6.90 ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent1[1]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := parallel_through_point( X, Z )
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (261) {G3,W8,D3,L2,V3,M2} R(250,69) { ! convergent_lines( Y,
% 6.54/6.90 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90 parent0: (7563) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.54/6.90 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7565) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 6.54/6.90 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.54/6.90 orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 6.54/6.90 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := X
% 6.54/6.90 Z := orthogonal_through_point( X, Y )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (285) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 6.54/6.90 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.54/6.90 parent0: (7565) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 6.54/6.90 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7566) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 6.54/6.90 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 parent0[2]: (164) {G2,W11,D3,L3,V4,M1} R(151,12) { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := U
% 6.54/6.90 Z := T
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2003) {G3,W14,D3,L4,V5,M1} R(164,12) { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 6.54/6.90 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 parent0: (7566) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 6.54/6.90 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 U := U
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 2 ==> 2
% 6.54/6.90 3 ==> 3
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7572) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0[0, 2]: (2003) {G3,W14,D3,L4,V5,M1} R(164,12) { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 6.54/6.90 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := orthogonal_through_point( Y, Z )
% 6.54/6.90 U := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7578) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0[0]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 parent1[0]: (7572) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( Y, Z )
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7580) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90 parent0[0, 1]: (7578) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2005) {G4,W8,D3,L2,V3,M1} F(2003);r(58) { distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0: (7580) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7582) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90 ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 parent0[2]: (162) {G2,W11,D3,L3,V4,M1} R(150,12) { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 6.54/6.90 apart_point_and_line( Z, T ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := U
% 6.54/6.90 Z := T
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2024) {G3,W14,D3,L4,V5,M1} R(162,12) { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90 ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 parent0: (7582) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90 ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 U := U
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 2 ==> 2
% 6.54/6.90 3 ==> 3
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7588) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 6.54/6.90 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0[0, 2]: (2024) {G3,W14,D3,L4,V5,M1} R(162,12) { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( T, X ), distinct_lines
% 6.54/6.90 ( U, T ), ! apart_point_and_line( Z, U ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := parallel_through_point( Y, Z )
% 6.54/6.90 U := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7594) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), distinct_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0[0]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 parent1[0]: (7588) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 6.54/6.90 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 6.54/6.90 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := parallel_through_point( Y, Z )
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7596) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90 parent0[0, 1]: (7594) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), distinct_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2026) {G4,W8,D3,L2,V3,M1} F(2024);r(58) { distinct_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0: (7596) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7598) {G1,W15,D2,L5,V5,M5} { distinct_lines( X, Y ),
% 6.54/6.90 distinct_lines( Y, Z ), apart_point_and_line( T, Z ), distinct_lines( U,
% 6.54/6.90 X ), ! apart_point_and_line( T, U ) }.
% 6.54/6.90 parent0[3]: (138) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 6.54/6.90 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 6.54/6.90 apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.54/6.90 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := T
% 6.54/6.90 T := Z
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := T
% 6.54/6.90 Y := U
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2352) {G2,W15,D2,L5,V5,M2} R(138,12) { distinct_lines( X, Y )
% 6.54/6.90 , distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line( T
% 6.54/6.90 , U ), ! apart_point_and_line( T, X ) }.
% 6.54/6.90 parent0: (7598) {G1,W15,D2,L5,V5,M5} { distinct_lines( X, Y ),
% 6.54/6.90 distinct_lines( Y, Z ), apart_point_and_line( T, Z ), distinct_lines( U,
% 6.54/6.90 X ), ! apart_point_and_line( T, U ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := U
% 6.54/6.90 T := T
% 6.54/6.90 U := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 2
% 6.54/6.90 2 ==> 3
% 6.54/6.90 3 ==> 0
% 6.54/6.90 4 ==> 4
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7604) {G2,W12,D2,L4,V3,M4} { distinct_lines( X, Y ),
% 6.54/6.90 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 6.54/6.90 apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0[0, 2]: (2352) {G2,W15,D2,L5,V5,M2} R(138,12) { distinct_lines( X, Y
% 6.54/6.90 ), distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line
% 6.54/6.90 ( T, U ), ! apart_point_and_line( T, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := X
% 6.54/6.90 T := Z
% 6.54/6.90 U := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7610) {G2,W12,D2,L4,V3,M4} { distinct_lines( Y, X ),
% 6.54/6.90 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 6.54/6.90 apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent0[0]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.54/6.90 distinct_lines( X, Y ) }.
% 6.54/6.90 parent1[0]: (7604) {G2,W12,D2,L4,V3,M4} { distinct_lines( X, Y ),
% 6.54/6.90 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 6.54/6.90 apart_point_and_line( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7612) {G2,W9,D2,L3,V3,M3} { distinct_lines( X, Y ),
% 6.54/6.90 apart_point_and_line( Z, X ), ! apart_point_and_line( Z, Y ) }.
% 6.54/6.90 parent0[0, 1]: (7610) {G2,W12,D2,L4,V3,M4} { distinct_lines( Y, X ),
% 6.54/6.90 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 6.54/6.90 apart_point_and_line( Z, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2356) {G3,W9,D2,L3,V3,M2} F(2352);r(58) { distinct_lines( Y,
% 6.54/6.90 X ), ! apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 6.54/6.90 parent0: (7612) {G2,W9,D2,L3,V3,M3} { distinct_lines( X, Y ),
% 6.54/6.90 apart_point_and_line( Z, X ), ! apart_point_and_line( Z, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 2
% 6.54/6.90 2 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7615) {G1,W13,D3,L3,V1,M3} { distinct_lines( X,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, X ),
% 6.54/6.90 apart_point_and_line( skol1, line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90 parent0[1]: (2356) {G3,W9,D2,L3,V3,M2} F(2352);r(58) { distinct_lines( Y, X
% 6.54/6.90 ), ! apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 6.54/6.90 parent1[1]: (48) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line( skol1,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2,
% 6.54/6.90 line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := line_connecting( skol3, skol4 )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := skol2
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2411) {G4,W13,D3,L3,V1,M2} R(2356,48) { distinct_lines( X,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol1,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, X ) }.
% 6.54/6.90 parent0: (7615) {G1,W13,D3,L3,V1,M3} { distinct_lines( X, line_connecting
% 6.54/6.90 ( skol3, skol4 ) ), apart_point_and_line( skol2, X ),
% 6.54/6.90 apart_point_and_line( skol1, line_connecting( skol3, skol4 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 2
% 6.54/6.90 2 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7616) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 6.54/6.90 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 6.54/6.90 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 6.54/6.90 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.54/6.90 orthogonal_through_point( Y, X ), Y ) }.
% 6.54/6.90 parent1[3]: (178) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 6.54/6.90 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 6.54/6.90 unorthogonal_lines( Y, Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Z
% 6.54/6.90 Y := orthogonal_through_point( X, Y )
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7617) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.54/6.90 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 parent0[0]: (7616) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 6.54/6.90 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 6.54/6.90 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 6.54/6.90 parent1[0]: (184) {G4,W8,D3,L2,V3,M2} R(171,69) { convergent_lines( X,
% 6.54/6.90 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := X
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7618) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.54/6.90 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90 parent0[0, 2]: (7617) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.54/6.90 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 6.54/6.90 convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2738) {G5,W8,D3,L2,V3,M1} R(178,23);r(184) { convergent_lines
% 6.54/6.90 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90 parent0: (7618) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.54/6.90 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7619) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( Z, T ), X ) }.
% 6.54/6.90 parent0[1]: (2738) {G5,W8,D3,L2,V3,M1} R(178,23);r(184) { convergent_lines
% 6.54/6.90 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.54/6.90 parent1[1]: (285) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 6.54/6.90 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( X, Y )
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := T
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := orthogonal_through_point( Z, T )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2745) {G6,W10,D3,L2,V4,M2} R(2738,285) { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 parent0: (7619) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( Z, T ), X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7620) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.54/6.90 parent1[1]: (2745) {G6,W10,D3,L2,V4,M2} R(2738,285) { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( X, Y )
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := orthogonal_through_point( X, Y )
% 6.54/6.90 T := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90 parent0: (7620) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7621) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( orthogonal_through_point(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90 parent0[0]: (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90 parent1[1]: (261) {G3,W8,D3,L2,V3,M2} R(250,69) { ! convergent_lines( Y,
% 6.54/6.90 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := T
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (3012) {G8,W9,D5,L1,V4,M1} R(2914,261) { ! convergent_lines( X
% 6.54/6.90 , parallel_through_point( orthogonal_through_point(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90 parent0: (7621) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( orthogonal_through_point(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7622) {G4,W9,D5,L1,V4,M1} { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90 parent0[0]: (2914) {G7,W7,D4,L1,V3,M1} R(2745,2) { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.54/6.90 parent1[1]: (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y ),
% 6.54/6.90 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := parallel_through_point( X, Y )
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := T
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), T )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (3015) {G8,W9,D5,L1,V4,M1} R(2914,74) { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90 parent0: (7622) {G4,W9,D5,L1,V4,M1} { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7623) {G5,W13,D7,L1,V6,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.54/6.90 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.90 , W ) ) }.
% 6.54/6.90 parent0[0]: (3012) {G8,W9,D5,L1,V4,M1} R(2914,261) { ! convergent_lines( X
% 6.54/6.90 , parallel_through_point( orthogonal_through_point(
% 6.54/6.90 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.54/6.90 parent1[1]: (246) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( Z, T ) ), convergent_lines(
% 6.54/6.90 parallel_through_point( X, Y ), Z ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := parallel_through_point( X, Y )
% 6.54/6.90 Y := Z
% 6.54/6.90 Z := T
% 6.54/6.90 T := U
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := parallel_through_point( orthogonal_through_point(
% 6.54/6.90 orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.90 T := W
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (3404) {G9,W13,D7,L1,V6,M1} R(3012,246) { ! convergent_lines(
% 6.54/6.90 X, parallel_through_point( parallel_through_point(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90 parent0: (7623) {G5,W13,D7,L1,V6,M1} { ! convergent_lines( X,
% 6.54/6.90 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.54/6.90 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.54/6.90 , W ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 U := U
% 6.54/6.90 W := W
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7624) {G6,W13,D7,L1,V6,M1} { ! convergent_lines( X,
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90 , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90 parent0[0]: (3015) {G8,W9,D5,L1,V4,M1} R(2914,74) { ! convergent_lines(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), T ), X ) }.
% 6.54/6.90 parent1[1]: (216) {G5,W10,D4,L2,V4,M2} R(206,5) { ! convergent_lines( Y, X
% 6.54/6.90 ), convergent_lines( X, parallel_through_point( parallel_through_point(
% 6.54/6.90 Y, Z ), T ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := parallel_through_point( parallel_through_point( X, Y ), Z )
% 6.54/6.90 Y := T
% 6.54/6.90 Z := U
% 6.54/6.90 T := W
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90 , Y ), Z ), T ), U ), W )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 T := Z
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (3478) {G9,W13,D7,L1,V6,M1} R(3015,216) { ! convergent_lines(
% 6.54/6.90 X, orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90 , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90 parent0: (7624) {G6,W13,D7,L1,V6,M1} { ! convergent_lines( X,
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90 , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 U := U
% 6.54/6.90 W := W
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7625) {G5,W15,D3,L3,V2,M3} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 distinct_lines( Y, line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, Y ) }.
% 6.54/6.90 parent0[1]: (2005) {G4,W8,D3,L2,V3,M1} F(2003);r(58) { distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent1[1]: (2411) {G4,W13,D3,L3,V1,M2} R(2356,48) { distinct_lines( X,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol1,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), apart_point_and_line( skol2, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := line_connecting( skol3, skol4 )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := skol1
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (7272) {G5,W15,D3,L3,V2,M1} R(2411,2005) { distinct_lines( X,
% 6.54/6.90 line_connecting( skol3, skol4 ) ), distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, X ) }.
% 6.54/6.90 parent0: (7625) {G5,W15,D3,L3,V2,M3} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 distinct_lines( Y, line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, Y ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 2 ==> 2
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 factor: (7628) {G5,W12,D3,L2,V1,M2} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90 parent0[0, 1]: (7272) {G5,W15,D3,L3,V2,M1} R(2411,2005) { distinct_lines( X
% 6.54/6.90 , line_connecting( skol3, skol4 ) ), distinct_lines(
% 6.54/6.90 orthogonal_through_point( Y, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, X ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( X, skol1 )
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (7273) {G6,W12,D3,L2,V1,M1} F(7272) { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90 parent0: (7628) {G5,W12,D3,L2,V1,M2} { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7629) {G5,W14,D3,L2,V2,M2} { distinct_lines(
% 6.54/6.90 parallel_through_point( X, skol2 ), orthogonal_through_point( Y, skol1 )
% 6.54/6.90 ), distinct_lines( orthogonal_through_point( Y, skol1 ), line_connecting
% 6.54/6.90 ( skol3, skol4 ) ) }.
% 6.54/6.90 parent0[1]: (2026) {G4,W8,D3,L2,V3,M1} F(2024);r(58) { distinct_lines(
% 6.54/6.90 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.54/6.90 parent1[1]: (7273) {G6,W12,D3,L2,V1,M1} F(7272) { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 apart_point_and_line( skol2, orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( Y, skol1 )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := skol2
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (7287) {G7,W14,D3,L2,V2,M1} R(7273,2026) { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 distinct_lines( parallel_through_point( Y, skol2 ),
% 6.54/6.90 orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90 parent0: (7629) {G5,W14,D3,L2,V2,M2} { distinct_lines(
% 6.54/6.90 parallel_through_point( X, skol2 ), orthogonal_through_point( Y, skol1 )
% 6.54/6.90 ), distinct_lines( orthogonal_through_point( Y, skol1 ), line_connecting
% 6.54/6.90 ( skol3, skol4 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := Y
% 6.54/6.90 Y := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 1
% 6.54/6.90 1 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7631) {G3,W14,D3,L2,V2,M2} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90 ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90 ( skol3, skol4 ) ) }.
% 6.54/6.90 parent0[1]: (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ),
% 6.54/6.90 ! distinct_lines( Y, X ) }.
% 6.54/6.90 parent1[1]: (7287) {G7,W14,D3,L2,V2,M1} R(7273,2026) { distinct_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), line_connecting( skol3, skol4 ) ),
% 6.54/6.90 distinct_lines( parallel_through_point( Y, skol2 ),
% 6.54/6.90 orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( X, skol1 )
% 6.54/6.90 Y := parallel_through_point( Y, skol2 )
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (7343) {G8,W14,D3,L2,V2,M1} R(7287,114) { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90 ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90 ( skol3, skol4 ) ) }.
% 6.54/6.90 parent0: (7631) {G3,W14,D3,L2,V2,M2} { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90 ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90 ( skol3, skol4 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7632) {G3,W14,D3,L2,V2,M2} { convergent_lines(
% 6.54/6.90 line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ),
% 6.54/6.90 convergent_lines( orthogonal_through_point( X, skol1 ),
% 6.54/6.90 parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.90 parent0[1]: (114) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ),
% 6.54/6.90 ! distinct_lines( Y, X ) }.
% 6.54/6.90 parent1[1]: (7343) {G8,W14,D3,L2,V2,M1} R(7287,114) { convergent_lines(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2 )
% 6.54/6.90 ), distinct_lines( orthogonal_through_point( X, skol1 ), line_connecting
% 6.54/6.90 ( skol3, skol4 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := line_connecting( skol3, skol4 )
% 6.54/6.90 Y := orthogonal_through_point( X, skol1 )
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (7345) {G9,W14,D3,L2,V2,M1} R(7343,114) { convergent_lines(
% 6.54/6.90 line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ),
% 6.54/6.90 convergent_lines( orthogonal_through_point( X, skol1 ),
% 6.54/6.90 parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.90 parent0: (7632) {G3,W14,D3,L2,V2,M2} { convergent_lines( line_connecting(
% 6.54/6.90 skol3, skol4 ), orthogonal_through_point( X, skol1 ) ), convergent_lines
% 6.54/6.90 ( orthogonal_through_point( X, skol1 ), parallel_through_point( Y, skol2
% 6.54/6.90 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 Y := Y
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 1 ==> 1
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7633) {G10,W7,D3,L1,V1,M1} { convergent_lines(
% 6.54/6.90 line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.90 }.
% 6.54/6.90 parent0[0]: (3404) {G9,W13,D7,L1,V6,M1} R(3012,246) { ! convergent_lines( X
% 6.54/6.90 , parallel_through_point( parallel_through_point(
% 6.54/6.90 orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( X, Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90 parent1[1]: (7345) {G9,W14,D3,L2,V2,M1} R(7343,114) { convergent_lines(
% 6.54/6.90 line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) ),
% 6.54/6.90 convergent_lines( orthogonal_through_point( X, skol1 ),
% 6.54/6.90 parallel_through_point( Y, skol2 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := orthogonal_through_point( X, skol1 )
% 6.54/6.90 Y := Y
% 6.54/6.90 Z := Z
% 6.54/6.90 T := T
% 6.54/6.90 U := U
% 6.54/6.90 W := skol2
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := X
% 6.54/6.90 Y := parallel_through_point( orthogonal_through_point(
% 6.54/6.90 orthogonal_through_point( parallel_through_point(
% 6.54/6.90 orthogonal_through_point( X, skol1 ), Y ), Z ), T ), U )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (7354) {G10,W7,D3,L1,V1,M1} R(7345,3404) { convergent_lines(
% 6.54/6.90 line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.90 }.
% 6.54/6.90 parent0: (7633) {G10,W7,D3,L1,V1,M1} { convergent_lines( line_connecting(
% 6.54/6.90 skol3, skol4 ), orthogonal_through_point( X, skol1 ) ) }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := X
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 0 ==> 0
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 resolution: (7634) {G10,W0,D0,L0,V0,M0} { }.
% 6.54/6.90 parent0[0]: (3478) {G9,W13,D7,L1,V6,M1} R(3015,216) { ! convergent_lines( X
% 6.54/6.90 , orthogonal_through_point( orthogonal_through_point(
% 6.54/6.90 parallel_through_point( parallel_through_point( parallel_through_point( X
% 6.54/6.90 , Y ), Z ), T ), U ), W ) ) }.
% 6.54/6.90 parent1[0]: (7354) {G10,W7,D3,L1,V1,M1} R(7345,3404) { convergent_lines(
% 6.54/6.90 line_connecting( skol3, skol4 ), orthogonal_through_point( X, skol1 ) )
% 6.54/6.90 }.
% 6.54/6.90 substitution0:
% 6.54/6.90 X := line_connecting( skol3, skol4 )
% 6.54/6.90 Y := X
% 6.54/6.90 Z := Y
% 6.54/6.90 T := Z
% 6.54/6.90 U := T
% 6.54/6.90 W := skol1
% 6.54/6.90 end
% 6.54/6.90 substitution1:
% 6.54/6.90 X := orthogonal_through_point( parallel_through_point(
% 6.54/6.90 parallel_through_point( parallel_through_point( line_connecting( skol3,
% 6.54/6.90 skol4 ), X ), Y ), Z ), T )
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 subsumption: (7355) {G11,W0,D0,L0,V0,M0} R(7354,3478) { }.
% 6.54/6.90 parent0: (7634) {G10,W0,D0,L0,V0,M0} { }.
% 6.54/6.90 substitution0:
% 6.54/6.90 end
% 6.54/6.90 permutation0:
% 6.54/6.90 end
% 6.54/6.90
% 6.54/6.90 Proof check complete!
% 6.54/6.90
% 6.54/6.90 Memory use:
% 6.54/6.90
% 6.54/6.90 space for terms: 107037
% 6.54/6.90 space for clauses: 322898
% 6.54/6.90
% 6.54/6.90
% 6.54/6.90 clauses generated: 1159821
% 6.54/6.90 clauses kept: 7356
% 6.54/6.90 clauses selected: 3124
% 6.54/6.90 clauses deleted: 81
% 6.54/6.90 clauses inuse deleted: 3
% 6.54/6.90
% 6.54/6.90 subsentry: 8619761
% 6.54/6.90 literals s-matched: 3438184
% 6.54/6.90 literals matched: 3437674
% 6.54/6.90 full subsumption: 2423971
% 6.54/6.90
% 6.54/6.90 checksum: 1592567474
% 6.54/6.90
% 6.54/6.90
% 6.54/6.90 Bliksem ended
%------------------------------------------------------------------------------