TSTP Solution File: GEO187+3 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 02:52:27 EDT 2022
% Result : Theorem 6.65s 7.07s
% Output : Refutation 6.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 18 05:01:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.65/7.07 *** allocated 10000 integers for termspace/termends
% 6.65/7.07 *** allocated 10000 integers for clauses
% 6.65/7.07 *** allocated 10000 integers for justifications
% 6.65/7.07 Bliksem 1.12
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 Automatic Strategy Selection
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 Clauses:
% 6.65/7.07
% 6.65/7.07 { ! distinct_points( X, X ) }.
% 6.65/7.07 { ! distinct_lines( X, X ) }.
% 6.65/7.07 { ! convergent_lines( X, X ) }.
% 6.65/7.07 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 6.65/7.07 ) }.
% 6.65/7.07 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.65/7.07 }.
% 6.65/7.07 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 6.65/7.07 , Z ) }.
% 6.65/7.07 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 6.65/7.07 , Y ) ) }.
% 6.65/7.07 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 6.65/7.07 , Y ) ) }.
% 6.65/7.07 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.65/7.07 , Y ), X ) }.
% 6.65/7.07 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.65/7.07 , Y ), Y ) }.
% 6.65/7.07 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 6.65/7.07 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 6.65/7.07 apart_point_and_line( Y, T ) }.
% 6.65/7.07 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 6.65/7.07 apart_point_and_line( Z, Y ) }.
% 6.65/7.07 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 6.65/7.07 apart_point_and_line( X, Z ) }.
% 6.65/7.07 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 6.65/7.07 Z ) }.
% 6.65/7.07 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 6.65/7.07 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 6.65/7.07 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 6.65/7.07 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.65/7.07 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 6.65/7.07 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.65/7.07 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.65/7.07 , convergent_lines( Y, Z ) }.
% 6.65/7.07 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.65/7.07 , unorthogonal_lines( Y, Z ) }.
% 6.65/7.07 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 6.65/7.07 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.65/7.07 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 6.65/7.07 }.
% 6.65/7.07 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 6.65/7.07 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 6.65/7.07 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.65/7.07 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 6.65/7.07 unorthogonal_lines( Y, T ) }.
% 6.65/7.07 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.65/7.07 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ) }.
% 6.65/7.07 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ) }.
% 6.65/7.07 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 6.65/7.07 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 6.65/7.07 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 6.65/7.07 }.
% 6.65/7.07 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 6.65/7.07 line_connecting( X, Y ) ) }.
% 6.65/7.07 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 6.65/7.07 intersection_point( X, Y ) ) }.
% 6.65/7.07 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 6.65/7.07 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 6.65/7.07 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 6.65/7.07 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 6.65/7.07 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 6.65/7.07 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 6.65/7.07 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 6.65/7.07 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 6.65/7.07 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 6.65/7.07 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.65/7.07 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 6.65/7.07 { distinct_points( skol1, skol2 ) }.
% 6.65/7.07 { distinct_points( skol3, skol4 ) }.
% 6.65/7.07 { incident_point_and_line( skol1, line_connecting( skol3, skol4 ) ) }.
% 6.65/7.07 { incident_point_and_line( skol2, line_connecting( skol3, skol4 ) ) }.
% 6.65/7.07 { ! incident_point_and_line( skol3, line_connecting( skol1, skol2 ) ), !
% 6.65/7.07 incident_point_and_line( skol4, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07
% 6.65/7.07 percentage equality = 0.000000, percentage horn = 0.627451
% 6.65/7.07 This a non-horn, non-equality problem
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 Options Used:
% 6.65/7.07
% 6.65/7.07 useres = 1
% 6.65/7.07 useparamod = 0
% 6.65/7.07 useeqrefl = 0
% 6.65/7.07 useeqfact = 0
% 6.65/7.07 usefactor = 1
% 6.65/7.07 usesimpsplitting = 0
% 6.65/7.07 usesimpdemod = 0
% 6.65/7.07 usesimpres = 3
% 6.65/7.07
% 6.65/7.07 resimpinuse = 1000
% 6.65/7.07 resimpclauses = 20000
% 6.65/7.07 substype = standard
% 6.65/7.07 backwardsubs = 1
% 6.65/7.07 selectoldest = 5
% 6.65/7.07
% 6.65/7.07 litorderings [0] = split
% 6.65/7.07 litorderings [1] = liftord
% 6.65/7.07
% 6.65/7.07 termordering = none
% 6.65/7.07
% 6.65/7.07 litapriori = 1
% 6.65/7.07 termapriori = 0
% 6.65/7.07 litaposteriori = 0
% 6.65/7.07 termaposteriori = 0
% 6.65/7.07 demodaposteriori = 0
% 6.65/7.07 ordereqreflfact = 0
% 6.65/7.07
% 6.65/7.07 litselect = none
% 6.65/7.07
% 6.65/7.07 maxweight = 15
% 6.65/7.07 maxdepth = 30000
% 6.65/7.07 maxlength = 115
% 6.65/7.07 maxnrvars = 195
% 6.65/7.07 excuselevel = 1
% 6.65/7.07 increasemaxweight = 1
% 6.65/7.07
% 6.65/7.07 maxselected = 10000000
% 6.65/7.07 maxnrclauses = 10000000
% 6.65/7.07
% 6.65/7.07 showgenerated = 0
% 6.65/7.07 showkept = 0
% 6.65/7.07 showselected = 0
% 6.65/7.07 showdeleted = 0
% 6.65/7.07 showresimp = 1
% 6.65/7.07 showstatus = 2000
% 6.65/7.07
% 6.65/7.07 prologoutput = 0
% 6.65/7.07 nrgoals = 5000000
% 6.65/7.07 totalproof = 1
% 6.65/7.07
% 6.65/7.07 Symbols occurring in the translation:
% 6.65/7.07
% 6.65/7.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.65/7.07 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 6.65/7.07 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 6.65/7.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.65/7.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.65/7.07 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 6.65/7.07 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 6.65/7.07 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 6.65/7.07 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 6.65/7.07 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 6.65/7.07 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 6.65/7.07 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 6.65/7.07 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 6.65/7.07 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 6.65/7.07 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 6.65/7.07 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 6.65/7.07 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 6.65/7.07 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 6.65/7.07 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 6.65/7.07 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 6.65/7.07 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 6.65/7.07 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 6.65/7.07 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 6.65/7.07 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 6.65/7.07 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 6.65/7.07 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 6.65/7.07 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 Starting Search:
% 6.65/7.07
% 6.65/7.07 *** allocated 15000 integers for clauses
% 6.65/7.07 *** allocated 22500 integers for clauses
% 6.65/7.07 *** allocated 33750 integers for clauses
% 6.65/7.07 *** allocated 15000 integers for termspace/termends
% 6.65/7.07 *** allocated 50625 integers for clauses
% 6.65/7.07 Resimplifying inuse:
% 6.65/7.07 Done
% 6.65/7.07
% 6.65/7.07 *** allocated 22500 integers for termspace/termends
% 6.65/7.07 *** allocated 75937 integers for clauses
% 6.65/7.07 *** allocated 33750 integers for termspace/termends
% 6.65/7.07 *** allocated 113905 integers for clauses
% 6.65/7.07
% 6.65/7.07 Intermediate Status:
% 6.65/7.07 Generated: 15119
% 6.65/7.07 Kept: 2001
% 6.65/7.07 Inuse: 297
% 6.65/7.07 Deleted: 2
% 6.65/7.07 Deletedinuse: 2
% 6.65/7.07
% 6.65/7.07 Resimplifying inuse:
% 6.65/7.07 Done
% 6.65/7.07
% 6.65/7.07 *** allocated 50625 integers for termspace/termends
% 6.65/7.07 *** allocated 170857 integers for clauses
% 6.65/7.07 Resimplifying inuse:
% 6.65/7.07 Done
% 6.65/7.07
% 6.65/7.07 *** allocated 75937 integers for termspace/termends
% 6.65/7.07
% 6.65/7.07 Intermediate Status:
% 6.65/7.07 Generated: 30105
% 6.65/7.07 Kept: 4050
% 6.65/7.07 Inuse: 472
% 6.65/7.07 Deleted: 6
% 6.65/7.07 Deletedinuse: 3
% 6.65/7.07
% 6.65/7.07 Resimplifying inuse:
% 6.65/7.07 Done
% 6.65/7.07
% 6.65/7.07 *** allocated 256285 integers for clauses
% 6.65/7.07 Resimplifying inuse:
% 6.65/7.07 Done
% 6.65/7.07
% 6.65/7.07 *** allocated 113905 integers for termspace/termends
% 6.65/7.07 *** allocated 384427 integers for clauses
% 6.65/7.07
% 6.65/7.07 Intermediate Status:
% 6.65/7.07 Generated: 134785
% 6.65/7.07 Kept: 6062
% 6.65/7.07 Inuse: 1117
% 6.65/7.07 Deleted: 19
% 6.65/7.07 Deletedinuse: 3
% 6.65/7.07
% 6.65/7.07 Resimplifying inuse:
% 6.65/7.07 Done
% 6.65/7.07
% 6.65/7.07 Resimplifying inuse:
% 6.65/7.07 Done
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 Bliksems!, er is een bewijs:
% 6.65/7.07 % SZS status Theorem
% 6.65/7.07 % SZS output start Refutation
% 6.65/7.07
% 6.65/7.07 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.65/7.07 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.65/7.07 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.65/7.07 , ! distinct_lines( X, Y ) }.
% 6.65/7.07 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 6.65/7.07 Z ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 6.65/7.07 X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.65/7.07 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 6.65/7.07 , Y ) }.
% 6.65/7.07 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 6.65/7.07 , X ), Y ) }.
% 6.65/7.07 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.65/7.07 parallel_through_point( Y, X ) ) }.
% 6.65/7.07 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 6.65/7.07 X, Y ) }.
% 6.65/7.07 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.65/7.07 }.
% 6.65/7.07 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 6.65/7.07 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 6.65/7.07 ( Y, X ), Y ) }.
% 6.65/7.07 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 6.65/7.07 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.65/7.07 (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 6.65/7.07 incident_point_and_line( X, Y ) }.
% 6.65/7.07 (50) {G0,W10,D3,L2,V0,M1} I { ! incident_point_and_line( skol3,
% 6.65/7.07 line_connecting( skol1, skol2 ) ), ! incident_point_and_line( skol4,
% 6.65/7.07 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07 (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 6.65/7.07 ( X, Y ) }.
% 6.65/7.07 (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.65/7.07 (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.65/7.07 (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y ),
% 6.65/7.07 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.65/7.07 (105) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), X ) }.
% 6.65/7.07 (107) {G2,W8,D3,L2,V3,M2} R(105,5) { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.07 (121) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ), !
% 6.65/7.07 distinct_lines( Y, X ) }.
% 6.65/7.07 (128) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 6.65/7.07 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 6.65/7.07 apart_point_and_line( Z, X ) }.
% 6.65/7.07 (140) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 6.65/7.07 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.07 (165) {G3,W8,D3,L2,V3,M2} R(107,69) { convergent_lines( Z, X ),
% 6.65/7.07 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.07 (170) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 6.65/7.07 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 6.65/7.07 unorthogonal_lines( Y, Z ) }.
% 6.65/7.07 (178) {G4,W8,D3,L2,V3,M2} R(165,69) { convergent_lines( X,
% 6.65/7.07 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.65/7.07 (236) {G4,W10,D3,L2,V4,M2} R(67,74) { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Z, T ), X ), convergent_lines(
% 6.65/7.07 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 (240) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( Z, T ) ), convergent_lines(
% 6.65/7.07 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 (244) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z ), !
% 6.65/7.07 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 (256) {G3,W8,D3,L2,V3,M2} R(244,69) { ! convergent_lines( Y,
% 6.65/7.07 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.65/7.07 (271) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 6.65/7.07 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.65/7.07 (347) {G1,W10,D3,L2,V0,M1} R(50,43) { apart_point_and_line( skol4,
% 6.65/7.07 line_connecting( skol1, skol2 ) ), ! incident_point_and_line( skol3,
% 6.65/7.07 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07 (1222) {G2,W10,D3,L2,V0,M1} R(347,43) { apart_point_and_line( skol3,
% 6.65/7.07 line_connecting( skol1, skol2 ) ), apart_point_and_line( skol4,
% 6.65/7.07 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07 (1225) {G3,W13,D3,L3,V1,M2} R(1222,12) { distinct_lines( line_connecting(
% 6.65/7.07 skol1, skol2 ), X ), apart_point_and_line( skol4, X ),
% 6.65/7.07 apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07 (2159) {G2,W14,D3,L4,V5,M1} R(128,140) { distinct_lines( X, Y ),
% 6.65/7.07 distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U, T )
% 6.65/7.07 ), ! apart_point_and_line( T, X ) }.
% 6.65/7.07 (2167) {G3,W8,D3,L2,V3,M1} F(2159);r(58) { distinct_lines(
% 6.65/7.07 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.07 (2657) {G5,W8,D3,L2,V3,M1} R(170,23);r(178) { convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.65/7.07 (2664) {G6,W10,D3,L2,V4,M2} R(2657,271) { ! convergent_lines(
% 6.65/7.07 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.07 (2833) {G7,W7,D4,L1,V3,M1} R(2664,2) { ! convergent_lines(
% 6.65/7.07 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.65/7.07 (2931) {G8,W9,D5,L1,V4,M1} R(2833,256) { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( orthogonal_through_point(
% 6.65/7.07 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.65/7.07 (3323) {G9,W13,D7,L1,V6,M1} R(2931,240) { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.07 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.07 , W ) ) }.
% 6.65/7.07 (3325) {G9,W13,D7,L1,V6,M1} R(2931,236) { ! convergent_lines(
% 6.65/7.07 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.07 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.07 , W ), X ) }.
% 6.65/7.07 (7298) {G4,W15,D3,L3,V2,M1} R(1225,140) { distinct_lines( line_connecting(
% 6.65/7.07 skol1, skol2 ), X ), distinct_lines( line_connecting( skol1, skol2 ),
% 6.65/7.07 parallel_through_point( Y, skol3 ) ), apart_point_and_line( skol4, X )
% 6.65/7.07 }.
% 6.65/7.07 (7299) {G5,W12,D3,L2,V1,M1} F(7298) { distinct_lines( line_connecting(
% 6.65/7.07 skol1, skol2 ), parallel_through_point( X, skol3 ) ),
% 6.65/7.07 apart_point_and_line( skol4, parallel_through_point( X, skol3 ) ) }.
% 6.65/7.07 (7312) {G6,W14,D3,L2,V2,M1} R(7299,2167) { distinct_lines( line_connecting
% 6.65/7.07 ( skol1, skol2 ), parallel_through_point( X, skol3 ) ), distinct_lines(
% 6.65/7.07 parallel_through_point( Y, skol4 ), parallel_through_point( X, skol3 ) )
% 6.65/7.07 }.
% 6.65/7.07 (7369) {G7,W14,D3,L2,V2,M1} R(7312,121) { convergent_lines(
% 6.65/7.07 parallel_through_point( X, skol3 ), parallel_through_point( Y, skol4 ) )
% 6.65/7.07 , distinct_lines( line_connecting( skol1, skol2 ), parallel_through_point
% 6.65/7.07 ( X, skol3 ) ) }.
% 6.65/7.07 (7371) {G8,W14,D3,L2,V2,M1} R(7369,121) { convergent_lines(
% 6.65/7.07 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ),
% 6.65/7.07 convergent_lines( parallel_through_point( X, skol3 ),
% 6.65/7.07 parallel_through_point( Y, skol4 ) ) }.
% 6.65/7.07 (7376) {G10,W7,D3,L1,V1,M1} R(7371,3323) { convergent_lines(
% 6.65/7.07 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07 (7377) {G11,W0,D0,L0,V0,M0} R(7376,3325) { }.
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 % SZS output end Refutation
% 6.65/7.07 found a proof!
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 Unprocessed initial clauses:
% 6.65/7.07
% 6.65/7.07 (7379) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 6.65/7.07 (7380) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 6.65/7.07 (7381) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 6.65/7.07 (7382) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 6.65/7.07 , Z ), distinct_points( Y, Z ) }.
% 6.65/7.07 (7383) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 6.65/7.07 Z ), distinct_lines( Y, Z ) }.
% 6.65/7.07 (7384) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 6.65/7.07 ( X, Z ), convergent_lines( Y, Z ) }.
% 6.65/7.07 (7385) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 6.65/7.07 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 6.65/7.07 (7386) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 6.65/7.07 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 6.65/7.07 (7387) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.65/7.07 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.65/7.07 (7388) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.65/7.07 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.65/7.07 (7389) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 6.65/7.07 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 6.65/7.07 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 6.65/7.07 (7390) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.65/7.07 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 6.65/7.07 (7391) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.65/7.07 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 6.65/7.07 (7392) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 6.65/7.07 , Z ), convergent_lines( X, Z ) }.
% 6.65/7.07 (7393) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 6.65/7.07 , Y ) }.
% 6.65/7.07 (7394) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 6.65/7.07 , X ), Y ) }.
% 6.65/7.07 (7395) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.65/7.07 parallel_through_point( Y, X ) ) }.
% 6.65/7.07 (7396) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 6.65/7.07 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 (7397) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 6.65/7.07 ( X, Y ) }.
% 6.65/7.07 (7398) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 6.65/7.07 (7399) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 6.65/7.07 }.
% 6.65/7.07 (7400) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 6.65/7.07 }.
% 6.65/7.07 (7401) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 6.65/7.07 }.
% 6.65/7.07 (7402) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 6.65/7.07 (7403) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 6.65/7.07 orthogonal_through_point( Y, X ), Y ) }.
% 6.65/7.07 (7404) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.65/7.07 orthogonal_through_point( Y, X ) ) }.
% 6.65/7.07 (7405) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 6.65/7.07 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 6.65/7.07 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 6.65/7.07 (7406) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 6.65/7.07 ( X, Y ) }.
% 6.65/7.07 (7407) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 6.65/7.07 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.65/7.07 (7408) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 6.65/7.07 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.65/7.07 (7409) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 6.65/7.07 }.
% 6.65/7.07 (7410) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 6.65/7.07 }.
% 6.65/7.07 (7411) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 6.65/7.07 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 6.65/7.07 (7412) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 6.65/7.07 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 (7413) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 6.65/7.07 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 6.65/7.07 (7414) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 6.65/7.07 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 6.65/7.07 (7415) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 (7416) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 6.65/7.07 orthogonal_through_point( X, Y ) ) }.
% 6.65/7.07 (7417) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 6.65/7.07 , Y ) }.
% 6.65/7.07 (7418) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 6.65/7.07 }.
% 6.65/7.07 (7419) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 6.65/7.07 ) }.
% 6.65/7.07 (7420) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 6.65/7.07 }.
% 6.65/7.07 (7421) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 6.65/7.07 ( X, Y ) }.
% 6.65/7.07 (7422) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 6.65/7.07 Y ) }.
% 6.65/7.07 (7423) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 6.65/7.07 apart_point_and_line( X, Y ) }.
% 6.65/7.07 (7424) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 6.65/7.07 incident_point_and_line( X, Y ) }.
% 6.65/7.07 (7425) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ) }.
% 6.65/7.07 (7426) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 6.65/7.07 ( X, Y ) }.
% 6.65/7.07 (7427) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 6.65/7.07 (7428) {G0,W3,D2,L1,V0,M1} { distinct_points( skol3, skol4 ) }.
% 6.65/7.07 (7429) {G0,W5,D3,L1,V0,M1} { incident_point_and_line( skol1,
% 6.65/7.07 line_connecting( skol3, skol4 ) ) }.
% 6.65/7.07 (7430) {G0,W5,D3,L1,V0,M1} { incident_point_and_line( skol2,
% 6.65/7.07 line_connecting( skol3, skol4 ) ) }.
% 6.65/7.07 (7431) {G0,W10,D3,L2,V0,M2} { ! incident_point_and_line( skol3,
% 6.65/7.07 line_connecting( skol1, skol2 ) ), ! incident_point_and_line( skol4,
% 6.65/7.07 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07
% 6.65/7.07
% 6.65/7.07 Total Proof:
% 6.65/7.07
% 6.65/7.07 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.65/7.07 parent0: (7380) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.65/7.07 parent0: (7381) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 6.65/7.07 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.65/7.07 parent0: (7383) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 6.65/7.07 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 2
% 6.65/7.07 1 ==> 0
% 6.65/7.07 2 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 parent0: (7384) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 6.65/7.07 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 2
% 6.65/7.07 1 ==> 0
% 6.65/7.07 2 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.65/7.07 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.65/7.07 parent0: (7391) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.65/7.07 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 2
% 6.65/7.07 1 ==> 0
% 6.65/7.07 2 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.65/7.07 distinct_lines( X, Y ) }.
% 6.65/7.07 parent0: (7393) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Y, X ), Y ) }.
% 6.65/7.07 parent0: (7394) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Y, X ), Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.65/7.07 parallel_through_point( Y, X ) ) }.
% 6.65/7.07 parent0: (7395) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.65/7.07 parallel_through_point( Y, X ) ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 6.65/7.07 unorthogonal_lines( X, Y ) }.
% 6.65/7.07 parent0: (7397) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 6.65/7.07 unorthogonal_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.65/7.07 }.
% 6.65/7.07 parent0: (7399) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 6.65/7.07 }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 2 ==> 3
% 6.65/7.07 3 ==> 2
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.65/7.07 alpha1( X, Y ) }.
% 6.65/7.07 parent0: (7400) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 6.65/7.07 X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.65/7.07 orthogonal_through_point( Y, X ), Y ) }.
% 6.65/7.07 parent0: (7403) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 6.65/7.07 orthogonal_through_point( Y, X ), Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 6.65/7.07 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.65/7.07 parent0: (7412) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 6.65/7.07 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 2
% 6.65/7.07 2 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 6.65/7.07 incident_point_and_line( X, Y ) }.
% 6.65/7.07 parent0: (7424) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 6.65/7.07 incident_point_and_line( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (50) {G0,W10,D3,L2,V0,M1} I { ! incident_point_and_line( skol3
% 6.65/7.07 , line_connecting( skol1, skol2 ) ), ! incident_point_and_line( skol4,
% 6.65/7.07 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07 parent0: (7431) {G0,W10,D3,L2,V0,M2} { ! incident_point_and_line( skol3,
% 6.65/7.07 line_connecting( skol1, skol2 ) ), ! incident_point_and_line( skol4,
% 6.65/7.07 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7556) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 6.65/7.07 distinct_lines( X, Y ) }.
% 6.65/7.07 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.65/7.07 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 6.65/7.07 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.65/7.07 distinct_lines( X, Y ) }.
% 6.65/7.07 parent0: (7556) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 6.65/7.07 distinct_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7558) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 6.65/7.07 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Y, X ), Y ) }.
% 6.65/7.07 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := parallel_through_point( X, Y )
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.65/7.07 parent0: (7558) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 6.65/7.07 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7560) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.65/7.07 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 parent0: (7560) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7562) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Y, X ), Y ) }.
% 6.65/7.07 parent1[1]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := parallel_through_point( X, Y )
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 parent0: (7562) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7563) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.65/7.07 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 6.65/7.07 parent0[0]: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := parallel_through_point( X, Y )
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X )
% 6.65/7.07 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.65/7.07 parent0: (7563) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.65/7.07 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7566) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.65/7.07 parallel_through_point( X, Y ) ), ! convergent_lines( Z, X ) }.
% 6.65/7.07 parent0[0]: (72) {G2,W5,D3,L1,V2,M1} R(69,15) { ! convergent_lines( X,
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := Z
% 6.65/7.07 Y := X
% 6.65/7.07 Z := parallel_through_point( X, Y )
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y )
% 6.65/7.07 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.65/7.07 parent0: (7566) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.65/7.07 parallel_through_point( X, Y ) ), ! convergent_lines( Z, X ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7567) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), X ) }.
% 6.65/7.07 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.65/7.07 orthogonal_through_point( Y, X ), Y ) }.
% 6.65/7.07 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 6.65/7.07 unorthogonal_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := orthogonal_through_point( X, Y )
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (105) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), X ) }.
% 6.65/7.07 parent0: (7567) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), X ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7568) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 6.65/7.07 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 6.65/7.07 parent1[0]: (105) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), X ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := orthogonal_through_point( X, Y )
% 6.65/7.07 Y := X
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (107) {G2,W8,D3,L2,V3,M2} R(105,5) { convergent_lines( X, Z )
% 6.65/7.07 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.07 parent0: (7568) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 6.65/7.07 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7569) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 6.65/7.07 distinct_lines( Y, X ) }.
% 6.65/7.07 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.65/7.07 distinct_lines( X, Y ) }.
% 6.65/7.07 parent1[1]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.65/7.07 distinct_lines( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (121) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y )
% 6.65/7.07 , ! distinct_lines( Y, X ) }.
% 6.65/7.07 parent0: (7569) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 6.65/7.07 distinct_lines( Y, X ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7570) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 6.65/7.07 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 6.65/7.07 apart_point_and_line( Z, T ) }.
% 6.65/7.07 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.65/7.07 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.65/7.07 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.65/7.07 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Z
% 6.65/7.07 Y := X
% 6.65/7.07 Z := Y
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := Z
% 6.65/7.07 Y := T
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (128) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 6.65/7.07 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 6.65/7.07 apart_point_and_line( Z, X ) }.
% 6.65/7.07 parent0: (7570) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 6.65/7.07 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 6.65/7.07 apart_point_and_line( Z, T ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := T
% 6.65/7.07 Z := Z
% 6.65/7.07 T := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 2
% 6.65/7.07 2 ==> 0
% 6.65/7.07 3 ==> 3
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7572) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 6.65/7.07 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.65/7.07 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 6.65/7.07 parallel_through_point( Y, X ) ) }.
% 6.65/7.07 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.65/7.07 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := parallel_through_point( Y, X )
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (140) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 6.65/7.07 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.07 parent0: (7572) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 6.65/7.07 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Z
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7573) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 6.65/7.07 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 parent1[0]: (107) {G2,W8,D3,L2,V3,M2} R(105,5) { convergent_lines( X, Z ),
% 6.65/7.07 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := X
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := Y
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (165) {G3,W8,D3,L2,V3,M2} R(107,69) { convergent_lines( Z, X )
% 6.65/7.07 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.07 parent0: (7573) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7576) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 6.65/7.07 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 6.65/7.07 unorthogonal_lines( Z, Y ) }.
% 6.65/7.07 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 6.65/7.07 ( X, Y ) }.
% 6.65/7.07 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 6.65/7.07 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 6.65/7.07 }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := Y
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (170) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 6.65/7.07 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 6.65/7.07 unorthogonal_lines( Y, Z ) }.
% 6.65/7.07 parent0: (7576) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 6.65/7.07 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 6.65/7.07 unorthogonal_lines( Z, Y ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 2 ==> 2
% 6.65/7.07 3 ==> 3
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7578) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.65/7.07 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 6.65/7.07 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.65/7.07 convergent_lines( X, Y ) }.
% 6.65/7.07 parent1[1]: (165) {G3,W8,D3,L2,V3,M2} R(107,69) { convergent_lines( Z, X )
% 6.65/7.07 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Z
% 6.65/7.07 Y := orthogonal_through_point( X, Y )
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := X
% 6.65/7.07 Y := Y
% 6.65/7.07 Z := Z
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (178) {G4,W8,D3,L2,V3,M2} R(165,69) { convergent_lines( X,
% 6.65/7.07 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.65/7.07 parent0: (7578) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 6.65/7.07 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Y
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := X
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 0
% 6.65/7.07 1 ==> 1
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7579) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.65/7.07 parallel_through_point( Z, T ), X ), ! convergent_lines(
% 6.65/7.07 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 parent0[0]: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.65/7.07 parent1[1]: (74) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( X, Y ),
% 6.65/7.07 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := parallel_through_point( Z, T )
% 6.65/7.07 Y := X
% 6.65/7.07 Z := Y
% 6.65/7.07 end
% 6.65/7.07 substitution1:
% 6.65/7.07 X := parallel_through_point( X, Y )
% 6.65/7.07 Y := Z
% 6.65/7.07 Z := T
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 subsumption: (236) {G4,W10,D3,L2,V4,M2} R(67,74) { ! convergent_lines(
% 6.65/7.07 parallel_through_point( Z, T ), X ), convergent_lines(
% 6.65/7.07 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 parent0: (7579) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.65/7.07 parallel_through_point( Z, T ), X ), ! convergent_lines(
% 6.65/7.07 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.07 substitution0:
% 6.65/7.07 X := Z
% 6.65/7.07 Y := T
% 6.65/7.07 Z := X
% 6.65/7.07 T := Y
% 6.65/7.07 end
% 6.65/7.07 permutation0:
% 6.65/7.07 0 ==> 1
% 6.65/7.07 1 ==> 0
% 6.65/7.07 end
% 6.65/7.07
% 6.65/7.07 resolution: (7580) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.65/7.07 parallel_through_point( Z, T ), X ), ! convergent_lines( Z,
% 6.65/7.07 parallel_through_point( X, Y ) ) }.
% 6.65/7.07 parent0[0]: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.65/7.08 parent1[1]: (73) {G3,W8,D3,L2,V3,M2} R(72,5) { ! convergent_lines( Y, X ),
% 6.65/7.08 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( Z, T )
% 6.65/7.08 Y := X
% 6.65/7.08 Z := Y
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := parallel_through_point( X, Y )
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := T
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (240) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X,
% 6.65/7.08 parallel_through_point( Z, T ) ), convergent_lines(
% 6.65/7.08 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.08 parent0: (7580) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.65/7.08 parallel_through_point( Z, T ), X ), ! convergent_lines( Z,
% 6.65/7.08 parallel_through_point( X, Y ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Z
% 6.65/7.08 Y := T
% 6.65/7.08 Z := X
% 6.65/7.08 T := Y
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 1
% 6.65/7.08 1 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7582) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 6.65/7.08 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 6.65/7.08 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.65/7.08 convergent_lines( X, Y ) }.
% 6.65/7.08 parent1[1]: (67) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := X
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (244) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z )
% 6.65/7.08 , ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.65/7.08 parent0: (7582) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 6.65/7.08 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Z
% 6.65/7.08 Y := X
% 6.65/7.08 Z := Y
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7583) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.65/7.08 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 6.65/7.08 parent0[1]: (244) {G2,W8,D3,L2,V3,M2} R(67,69) { convergent_lines( X, Z ),
% 6.65/7.08 ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 6.65/7.08 parent1[1]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 6.65/7.08 convergent_lines( X, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := Y
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := parallel_through_point( X, Z )
% 6.65/7.08 Y := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (256) {G3,W8,D3,L2,V3,M2} R(244,69) { ! convergent_lines( Y,
% 6.65/7.08 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.65/7.08 parent0: (7583) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.65/7.08 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 1
% 6.65/7.08 1 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7585) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 6.65/7.08 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.08 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.65/7.08 orthogonal_through_point( Y, X ), Y ) }.
% 6.65/7.08 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 6.65/7.08 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := X
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := Z
% 6.65/7.08 Y := X
% 6.65/7.08 Z := orthogonal_through_point( X, Y )
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (271) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 6.65/7.08 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.65/7.08 parent0: (7585) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 6.65/7.08 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := X
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7587) {G1,W10,D3,L2,V0,M2} { ! incident_point_and_line( skol3
% 6.65/7.08 , line_connecting( skol1, skol2 ) ), apart_point_and_line( skol4,
% 6.65/7.08 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0[1]: (50) {G0,W10,D3,L2,V0,M1} I { ! incident_point_and_line( skol3
% 6.65/7.08 , line_connecting( skol1, skol2 ) ), ! incident_point_and_line( skol4,
% 6.65/7.08 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 6.65/7.08 incident_point_and_line( X, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := skol4
% 6.65/7.08 Y := line_connecting( skol1, skol2 )
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (347) {G1,W10,D3,L2,V0,M1} R(50,43) { apart_point_and_line(
% 6.65/7.08 skol4, line_connecting( skol1, skol2 ) ), ! incident_point_and_line(
% 6.65/7.08 skol3, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0: (7587) {G1,W10,D3,L2,V0,M2} { ! incident_point_and_line( skol3,
% 6.65/7.08 line_connecting( skol1, skol2 ) ), apart_point_and_line( skol4,
% 6.65/7.08 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 1
% 6.65/7.08 1 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7588) {G1,W10,D3,L2,V0,M2} { apart_point_and_line( skol4,
% 6.65/7.08 line_connecting( skol1, skol2 ) ), apart_point_and_line( skol3,
% 6.65/7.08 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0[1]: (347) {G1,W10,D3,L2,V0,M1} R(50,43) { apart_point_and_line(
% 6.65/7.08 skol4, line_connecting( skol1, skol2 ) ), ! incident_point_and_line(
% 6.65/7.08 skol3, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 6.65/7.08 incident_point_and_line( X, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := skol3
% 6.65/7.08 Y := line_connecting( skol1, skol2 )
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (1222) {G2,W10,D3,L2,V0,M1} R(347,43) { apart_point_and_line(
% 6.65/7.08 skol3, line_connecting( skol1, skol2 ) ), apart_point_and_line( skol4,
% 6.65/7.08 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0: (7588) {G1,W10,D3,L2,V0,M2} { apart_point_and_line( skol4,
% 6.65/7.08 line_connecting( skol1, skol2 ) ), apart_point_and_line( skol3,
% 6.65/7.08 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 1
% 6.65/7.08 1 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7590) {G1,W13,D3,L3,V1,M3} { distinct_lines( line_connecting
% 6.65/7.08 ( skol1, skol2 ), X ), apart_point_and_line( skol4, X ),
% 6.65/7.08 apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 6.65/7.08 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 6.65/7.08 parent1[1]: (1222) {G2,W10,D3,L2,V0,M1} R(347,43) { apart_point_and_line(
% 6.65/7.08 skol3, line_connecting( skol1, skol2 ) ), apart_point_and_line( skol4,
% 6.65/7.08 line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := skol4
% 6.65/7.08 Y := line_connecting( skol1, skol2 )
% 6.65/7.08 Z := X
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (1225) {G3,W13,D3,L3,V1,M2} R(1222,12) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), X ), apart_point_and_line( skol4, X ),
% 6.65/7.08 apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0: (7590) {G1,W13,D3,L3,V1,M3} { distinct_lines( line_connecting(
% 6.65/7.08 skol1, skol2 ), X ), apart_point_and_line( skol4, X ),
% 6.65/7.08 apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 2 ==> 2
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7591) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 6.65/7.08 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 6.65/7.08 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 6.65/7.08 parent0[1]: (140) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 6.65/7.08 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 parent1[2]: (128) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 6.65/7.08 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 6.65/7.08 apart_point_and_line( Z, X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := T
% 6.65/7.08 Y := U
% 6.65/7.08 Z := Z
% 6.65/7.08 T := X
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (2159) {G2,W14,D3,L4,V5,M1} R(128,140) { distinct_lines( X, Y
% 6.65/7.08 ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 6.65/7.08 , T ) ), ! apart_point_and_line( T, X ) }.
% 6.65/7.08 parent0: (7591) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 6.65/7.08 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 6.65/7.08 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Z
% 6.65/7.08 Y := U
% 6.65/7.08 Z := T
% 6.65/7.08 T := X
% 6.65/7.08 U := Y
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 2
% 6.65/7.08 1 ==> 0
% 6.65/7.08 2 ==> 1
% 6.65/7.08 3 ==> 3
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 factor: (7597) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 6.65/7.08 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 6.65/7.08 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 parent0[0, 2]: (2159) {G2,W14,D3,L4,V5,M1} R(128,140) { distinct_lines( X,
% 6.65/7.08 Y ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 6.65/7.08 , T ) ), ! apart_point_and_line( T, X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := parallel_through_point( Y, Z )
% 6.65/7.08 Z := X
% 6.65/7.08 T := Z
% 6.65/7.08 U := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7603) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), distinct_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 parent0[0]: (58) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.65/7.08 distinct_lines( X, Y ) }.
% 6.65/7.08 parent1[0]: (7597) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 6.65/7.08 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 6.65/7.08 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( Y, Z )
% 6.65/7.08 Y := X
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 factor: (7605) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 6.65/7.08 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.65/7.08 parent0[0, 1]: (7603) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), distinct_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Z
% 6.65/7.08 Y := X
% 6.65/7.08 Z := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (2167) {G3,W8,D3,L2,V3,M1} F(2159);r(58) { distinct_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 parent0: (7605) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 6.65/7.08 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := X
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7607) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 6.65/7.08 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 6.65/7.08 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 6.65/7.08 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 6.65/7.08 orthogonal_through_point( Y, X ), Y ) }.
% 6.65/7.08 parent1[3]: (170) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 6.65/7.08 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 6.65/7.08 unorthogonal_lines( Y, Z ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := X
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := Z
% 6.65/7.08 Y := orthogonal_through_point( X, Y )
% 6.65/7.08 Z := X
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7608) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.65/7.08 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 6.65/7.08 convergent_lines( X, Y ) }.
% 6.65/7.08 parent0[0]: (7607) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 6.65/7.08 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 6.65/7.08 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 6.65/7.08 parent1[0]: (178) {G4,W8,D3,L2,V3,M2} R(165,69) { convergent_lines( X,
% 6.65/7.08 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := X
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 factor: (7609) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.65/7.08 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.65/7.08 parent0[0, 2]: (7608) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.65/7.08 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 6.65/7.08 convergent_lines( X, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (2657) {G5,W8,D3,L2,V3,M1} R(170,23);r(178) { convergent_lines
% 6.65/7.08 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.65/7.08 parent0: (7609) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 6.65/7.08 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7610) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( Z, T ), X ) }.
% 6.65/7.08 parent0[1]: (2657) {G5,W8,D3,L2,V3,M1} R(170,23);r(178) { convergent_lines
% 6.65/7.08 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 6.65/7.08 parent1[1]: (271) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 6.65/7.08 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := orthogonal_through_point( X, Y )
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := T
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := orthogonal_through_point( Z, T )
% 6.65/7.08 Y := X
% 6.65/7.08 Z := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (2664) {G6,W10,D3,L2,V4,M2} R(2657,271) { ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.08 parent0: (7610) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( Z, T ), X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 T := T
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 1
% 6.65/7.08 1 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7611) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.65/7.08 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.65/7.08 parent1[1]: (2664) {G6,W10,D3,L2,V4,M2} R(2657,271) { ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := orthogonal_through_point( X, Y )
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := orthogonal_through_point( X, Y )
% 6.65/7.08 T := Z
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (2833) {G7,W7,D4,L1,V3,M1} R(2664,2) { ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.65/7.08 parent0: (7611) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7612) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 6.65/7.08 parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.65/7.08 parent0[0]: (2833) {G7,W7,D4,L1,V3,M1} R(2664,2) { ! convergent_lines(
% 6.65/7.08 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 6.65/7.08 parent1[1]: (256) {G3,W8,D3,L2,V3,M2} R(244,69) { ! convergent_lines( Y,
% 6.65/7.08 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 6.65/7.08 Y := X
% 6.65/7.08 Z := T
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (2931) {G8,W9,D5,L1,V4,M1} R(2833,256) { ! convergent_lines( X
% 6.65/7.08 , parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.65/7.08 parent0: (7612) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 6.65/7.08 parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 T := T
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7613) {G5,W13,D7,L1,V6,M1} { ! convergent_lines( X,
% 6.65/7.08 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.08 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 , W ) ) }.
% 6.65/7.08 parent0[0]: (2931) {G8,W9,D5,L1,V4,M1} R(2833,256) { ! convergent_lines( X
% 6.65/7.08 , parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.65/7.08 parent1[1]: (240) {G4,W10,D3,L2,V4,M2} R(67,73) { ! convergent_lines( X,
% 6.65/7.08 parallel_through_point( Z, T ) ), convergent_lines(
% 6.65/7.08 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( X, Y )
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := T
% 6.65/7.08 T := U
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 T := W
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (3323) {G9,W13,D7,L1,V6,M1} R(2931,240) { ! convergent_lines(
% 6.65/7.08 X, parallel_through_point( parallel_through_point(
% 6.65/7.08 orthogonal_through_point( orthogonal_through_point(
% 6.65/7.08 parallel_through_point( X, Y ), Z ), T ), U ), W ) ) }.
% 6.65/7.08 parent0: (7613) {G5,W13,D7,L1,V6,M1} { ! convergent_lines( X,
% 6.65/7.08 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.08 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 , W ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 T := T
% 6.65/7.08 U := U
% 6.65/7.08 W := W
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7614) {G5,W13,D7,L1,V6,M1} { ! convergent_lines(
% 6.65/7.08 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.08 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 , W ), X ) }.
% 6.65/7.08 parent0[0]: (2931) {G8,W9,D5,L1,V4,M1} R(2833,256) { ! convergent_lines( X
% 6.65/7.08 , parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( X, Y ), Z ), T ) ) }.
% 6.65/7.08 parent1[1]: (236) {G4,W10,D3,L2,V4,M2} R(67,74) { ! convergent_lines(
% 6.65/7.08 parallel_through_point( Z, T ), X ), convergent_lines(
% 6.65/7.08 parallel_through_point( X, Y ), Z ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( X, Y )
% 6.65/7.08 Y := Z
% 6.65/7.08 Z := T
% 6.65/7.08 T := U
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 T := W
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (3325) {G9,W13,D7,L1,V6,M1} R(2931,236) { ! convergent_lines(
% 6.65/7.08 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.08 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 , W ), X ) }.
% 6.65/7.08 parent0: (7614) {G5,W13,D7,L1,V6,M1} { ! convergent_lines(
% 6.65/7.08 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.08 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 , W ), X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 T := T
% 6.65/7.08 U := U
% 6.65/7.08 W := W
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7616) {G2,W15,D3,L3,V2,M3} { distinct_lines( line_connecting
% 6.65/7.08 ( skol1, skol2 ), parallel_through_point( X, skol3 ) ), distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), Y ), apart_point_and_line( skol4, Y )
% 6.65/7.08 }.
% 6.65/7.08 parent0[1]: (140) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 6.65/7.08 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 parent1[2]: (1225) {G3,W13,D3,L3,V1,M2} R(1222,12) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), X ), apart_point_and_line( skol4, X ),
% 6.65/7.08 apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := line_connecting( skol1, skol2 )
% 6.65/7.08 Y := X
% 6.65/7.08 Z := skol3
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (7298) {G4,W15,D3,L3,V2,M1} R(1225,140) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), X ), distinct_lines( line_connecting(
% 6.65/7.08 skol1, skol2 ), parallel_through_point( Y, skol3 ) ),
% 6.65/7.08 apart_point_and_line( skol4, X ) }.
% 6.65/7.08 parent0: (7616) {G2,W15,D3,L3,V2,M3} { distinct_lines( line_connecting(
% 6.65/7.08 skol1, skol2 ), parallel_through_point( X, skol3 ) ), distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), Y ), apart_point_and_line( skol4, Y )
% 6.65/7.08 }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := X
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 1
% 6.65/7.08 1 ==> 0
% 6.65/7.08 2 ==> 2
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 factor: (7618) {G4,W12,D3,L2,V1,M2} { distinct_lines( line_connecting(
% 6.65/7.08 skol1, skol2 ), parallel_through_point( X, skol3 ) ),
% 6.65/7.08 apart_point_and_line( skol4, parallel_through_point( X, skol3 ) ) }.
% 6.65/7.08 parent0[0, 1]: (7298) {G4,W15,D3,L3,V2,M1} R(1225,140) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), X ), distinct_lines( line_connecting(
% 6.65/7.08 skol1, skol2 ), parallel_through_point( Y, skol3 ) ),
% 6.65/7.08 apart_point_and_line( skol4, X ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( X, skol3 )
% 6.65/7.08 Y := X
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (7299) {G5,W12,D3,L2,V1,M1} F(7298) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ),
% 6.65/7.08 apart_point_and_line( skol4, parallel_through_point( X, skol3 ) ) }.
% 6.65/7.08 parent0: (7618) {G4,W12,D3,L2,V1,M2} { distinct_lines( line_connecting(
% 6.65/7.08 skol1, skol2 ), parallel_through_point( X, skol3 ) ),
% 6.65/7.08 apart_point_and_line( skol4, parallel_through_point( X, skol3 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7619) {G4,W14,D3,L2,V2,M2} { distinct_lines(
% 6.65/7.08 parallel_through_point( X, skol4 ), parallel_through_point( Y, skol3 ) )
% 6.65/7.08 , distinct_lines( line_connecting( skol1, skol2 ), parallel_through_point
% 6.65/7.08 ( Y, skol3 ) ) }.
% 6.65/7.08 parent0[1]: (2167) {G3,W8,D3,L2,V3,M1} F(2159);r(58) { distinct_lines(
% 6.65/7.08 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 6.65/7.08 parent1[1]: (7299) {G5,W12,D3,L2,V1,M1} F(7298) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ),
% 6.65/7.08 apart_point_and_line( skol4, parallel_through_point( X, skol3 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( Y, skol3 )
% 6.65/7.08 Y := X
% 6.65/7.08 Z := skol4
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (7312) {G6,W14,D3,L2,V2,M1} R(7299,2167) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ),
% 6.65/7.08 distinct_lines( parallel_through_point( Y, skol4 ),
% 6.65/7.08 parallel_through_point( X, skol3 ) ) }.
% 6.65/7.08 parent0: (7619) {G4,W14,D3,L2,V2,M2} { distinct_lines(
% 6.65/7.08 parallel_through_point( X, skol4 ), parallel_through_point( Y, skol3 ) )
% 6.65/7.08 , distinct_lines( line_connecting( skol1, skol2 ), parallel_through_point
% 6.65/7.08 ( Y, skol3 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := Y
% 6.65/7.08 Y := X
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 1
% 6.65/7.08 1 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7621) {G3,W14,D3,L2,V2,M2} { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), parallel_through_point( Y, skol4 ) )
% 6.65/7.08 , distinct_lines( line_connecting( skol1, skol2 ), parallel_through_point
% 6.65/7.08 ( X, skol3 ) ) }.
% 6.65/7.08 parent0[1]: (121) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ),
% 6.65/7.08 ! distinct_lines( Y, X ) }.
% 6.65/7.08 parent1[1]: (7312) {G6,W14,D3,L2,V2,M1} R(7299,2167) { distinct_lines(
% 6.65/7.08 line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ),
% 6.65/7.08 distinct_lines( parallel_through_point( Y, skol4 ),
% 6.65/7.08 parallel_through_point( X, skol3 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( X, skol3 )
% 6.65/7.08 Y := parallel_through_point( Y, skol4 )
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (7369) {G7,W14,D3,L2,V2,M1} R(7312,121) { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), parallel_through_point( Y, skol4 ) )
% 6.65/7.08 , distinct_lines( line_connecting( skol1, skol2 ), parallel_through_point
% 6.65/7.08 ( X, skol3 ) ) }.
% 6.65/7.08 parent0: (7621) {G3,W14,D3,L2,V2,M2} { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), parallel_through_point( Y, skol4 ) )
% 6.65/7.08 , distinct_lines( line_connecting( skol1, skol2 ), parallel_through_point
% 6.65/7.08 ( X, skol3 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7622) {G3,W14,D3,L2,V2,M2} { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ),
% 6.65/7.08 convergent_lines( parallel_through_point( X, skol3 ),
% 6.65/7.08 parallel_through_point( Y, skol4 ) ) }.
% 6.65/7.08 parent0[1]: (121) {G2,W6,D2,L2,V2,M1} R(14,58) { convergent_lines( X, Y ),
% 6.65/7.08 ! distinct_lines( Y, X ) }.
% 6.65/7.08 parent1[1]: (7369) {G7,W14,D3,L2,V2,M1} R(7312,121) { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), parallel_through_point( Y, skol4 ) )
% 6.65/7.08 , distinct_lines( line_connecting( skol1, skol2 ), parallel_through_point
% 6.65/7.08 ( X, skol3 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( X, skol3 )
% 6.65/7.08 Y := line_connecting( skol1, skol2 )
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (7371) {G8,W14,D3,L2,V2,M1} R(7369,121) { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ),
% 6.65/7.08 convergent_lines( parallel_through_point( X, skol3 ),
% 6.65/7.08 parallel_through_point( Y, skol4 ) ) }.
% 6.65/7.08 parent0: (7622) {G3,W14,D3,L2,V2,M2} { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ),
% 6.65/7.08 convergent_lines( parallel_through_point( X, skol3 ),
% 6.65/7.08 parallel_through_point( Y, skol4 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 Y := Y
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 1 ==> 1
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7623) {G9,W7,D3,L1,V1,M1} { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0[0]: (3323) {G9,W13,D7,L1,V6,M1} R(2931,240) { ! convergent_lines( X
% 6.65/7.08 , parallel_through_point( parallel_through_point(
% 6.65/7.08 orthogonal_through_point( orthogonal_through_point(
% 6.65/7.08 parallel_through_point( X, Y ), Z ), T ), U ), W ) ) }.
% 6.65/7.08 parent1[1]: (7371) {G8,W14,D3,L2,V2,M1} R(7369,121) { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ),
% 6.65/7.08 convergent_lines( parallel_through_point( X, skol3 ),
% 6.65/7.08 parallel_through_point( Y, skol4 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := parallel_through_point( X, skol3 )
% 6.65/7.08 Y := Y
% 6.65/7.08 Z := Z
% 6.65/7.08 T := T
% 6.65/7.08 U := U
% 6.65/7.08 W := skol4
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := X
% 6.65/7.08 Y := parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( parallel_through_point( parallel_through_point
% 6.65/7.08 ( X, skol3 ), Y ), Z ), T ), U )
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (7376) {G10,W7,D3,L1,V1,M1} R(7371,3323) { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 parent0: (7623) {G9,W7,D3,L1,V1,M1} { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := X
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 0 ==> 0
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 resolution: (7624) {G10,W0,D0,L0,V0,M0} { }.
% 6.65/7.08 parent0[0]: (3325) {G9,W13,D7,L1,V6,M1} R(2931,236) { ! convergent_lines(
% 6.65/7.08 parallel_through_point( parallel_through_point( orthogonal_through_point
% 6.65/7.08 ( orthogonal_through_point( parallel_through_point( X, Y ), Z ), T ), U )
% 6.65/7.08 , W ), X ) }.
% 6.65/7.08 parent1[0]: (7376) {G10,W7,D3,L1,V1,M1} R(7371,3323) { convergent_lines(
% 6.65/7.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 6.65/7.08 substitution0:
% 6.65/7.08 X := line_connecting( skol1, skol2 )
% 6.65/7.08 Y := X
% 6.65/7.08 Z := Y
% 6.65/7.08 T := Z
% 6.65/7.08 U := T
% 6.65/7.08 W := skol3
% 6.65/7.08 end
% 6.65/7.08 substitution1:
% 6.65/7.08 X := parallel_through_point( orthogonal_through_point(
% 6.65/7.08 orthogonal_through_point( parallel_through_point( line_connecting( skol1
% 6.65/7.08 , skol2 ), X ), Y ), Z ), T )
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 subsumption: (7377) {G11,W0,D0,L0,V0,M0} R(7376,3325) { }.
% 6.65/7.08 parent0: (7624) {G10,W0,D0,L0,V0,M0} { }.
% 6.65/7.08 substitution0:
% 6.65/7.08 end
% 6.65/7.08 permutation0:
% 6.65/7.08 end
% 6.65/7.08
% 6.65/7.08 Proof check complete!
% 6.65/7.08
% 6.65/7.08 Memory use:
% 6.65/7.08
% 6.65/7.08 space for terms: 107006
% 6.65/7.08 space for clauses: 324201
% 6.65/7.08
% 6.65/7.08
% 6.65/7.08 clauses generated: 1242553
% 6.65/7.08 clauses kept: 7378
% 6.65/7.08 clauses selected: 3261
% 6.65/7.08 clauses deleted: 89
% 6.65/7.08 clauses inuse deleted: 3
% 6.65/7.08
% 6.65/7.08 subsentry: 8872538
% 6.65/7.08 literals s-matched: 3519556
% 6.65/7.08 literals matched: 3519057
% 6.65/7.08 full subsumption: 2478850
% 6.65/7.08
% 6.65/7.08 checksum: 2037774553
% 6.65/7.08
% 6.65/7.08
% 6.65/7.08 Bliksem ended
%------------------------------------------------------------------------------