TSTP Solution File: GEO222+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 02:52:58 EDT 2022
% Result : Theorem 100.80s 101.23s
% Output : Refutation 100.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jun 18 07:22:13 EDT 2022
% 0.17/0.33 % CPUTime :
% 100.80/101.23 *** allocated 10000 integers for termspace/termends
% 100.80/101.23 *** allocated 10000 integers for clauses
% 100.80/101.23 *** allocated 10000 integers for justifications
% 100.80/101.23 Bliksem 1.12
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Automatic Strategy Selection
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Clauses:
% 100.80/101.23
% 100.80/101.23 { ! distinct_points( X, X ) }.
% 100.80/101.23 { ! distinct_lines( X, X ) }.
% 100.80/101.23 { ! convergent_lines( X, X ) }.
% 100.80/101.23 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 100.80/101.23 ) }.
% 100.80/101.23 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 100.80/101.23 }.
% 100.80/101.23 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 100.80/101.23 , Z ) }.
% 100.80/101.23 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 100.80/101.23 , Y ) ), distinct_points( Z, X ) }.
% 100.80/101.23 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 100.80/101.23 , Y ) ), distinct_points( Z, Y ) }.
% 100.80/101.23 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ) }.
% 100.80/101.23 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ) }.
% 100.80/101.23 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 100.80/101.23 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 100.80/101.23 apart_point_and_line( Y, T ) }.
% 100.80/101.23 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 100.80/101.23 apart_point_and_line( Z, Y ) }.
% 100.80/101.23 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 100.80/101.23 apart_point_and_line( X, Z ) }.
% 100.80/101.23 { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 100.80/101.23 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 100.80/101.23 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 100.80/101.23 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 100.80/101.23 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 100.80/101.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 100.80/101.23 , convergent_lines( Y, Z ) }.
% 100.80/101.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 100.80/101.23 , unorthogonal_lines( Y, Z ) }.
% 100.80/101.23 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 100.80/101.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 100.80/101.23 }.
% 100.80/101.23 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 100.80/101.23 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 100.80/101.23 unorthogonal_lines( Y, T ) }.
% 100.80/101.23 { convergent_lines( skol2, orthogonal_through_point(
% 100.80/101.23 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 100.80/101.23
% 100.80/101.23 percentage equality = 0.000000, percentage horn = 0.592593
% 100.80/101.23 This a non-horn, non-equality problem
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Options Used:
% 100.80/101.23
% 100.80/101.23 useres = 1
% 100.80/101.23 useparamod = 0
% 100.80/101.23 useeqrefl = 0
% 100.80/101.23 useeqfact = 0
% 100.80/101.23 usefactor = 1
% 100.80/101.23 usesimpsplitting = 0
% 100.80/101.23 usesimpdemod = 0
% 100.80/101.23 usesimpres = 3
% 100.80/101.23
% 100.80/101.23 resimpinuse = 1000
% 100.80/101.23 resimpclauses = 20000
% 100.80/101.23 substype = standard
% 100.80/101.23 backwardsubs = 1
% 100.80/101.23 selectoldest = 5
% 100.80/101.23
% 100.80/101.23 litorderings [0] = split
% 100.80/101.23 litorderings [1] = liftord
% 100.80/101.23
% 100.80/101.23 termordering = none
% 100.80/101.23
% 100.80/101.23 litapriori = 1
% 100.80/101.23 termapriori = 0
% 100.80/101.23 litaposteriori = 0
% 100.80/101.23 termaposteriori = 0
% 100.80/101.23 demodaposteriori = 0
% 100.80/101.23 ordereqreflfact = 0
% 100.80/101.23
% 100.80/101.23 litselect = none
% 100.80/101.23
% 100.80/101.23 maxweight = 15
% 100.80/101.23 maxdepth = 30000
% 100.80/101.23 maxlength = 115
% 100.80/101.23 maxnrvars = 195
% 100.80/101.23 excuselevel = 1
% 100.80/101.23 increasemaxweight = 1
% 100.80/101.23
% 100.80/101.23 maxselected = 10000000
% 100.80/101.23 maxnrclauses = 10000000
% 100.80/101.23
% 100.80/101.23 showgenerated = 0
% 100.80/101.23 showkept = 0
% 100.80/101.23 showselected = 0
% 100.80/101.23 showdeleted = 0
% 100.80/101.23 showresimp = 1
% 100.80/101.23 showstatus = 2000
% 100.80/101.23
% 100.80/101.23 prologoutput = 0
% 100.80/101.23 nrgoals = 5000000
% 100.80/101.23 totalproof = 1
% 100.80/101.23
% 100.80/101.23 Symbols occurring in the translation:
% 100.80/101.23
% 100.80/101.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 100.80/101.23 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 100.80/101.23 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 100.80/101.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 100.80/101.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 100.80/101.23 distinct_points [36, 2] (w:1, o:47, a:1, s:1, b:0),
% 100.80/101.23 distinct_lines [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 100.80/101.23 convergent_lines [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 100.80/101.23 line_connecting [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 100.80/101.23 apart_point_and_line [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 100.80/101.23 intersection_point [43, 2] (w:1, o:51, a:1, s:1, b:0),
% 100.80/101.23 parallel_through_point [46, 2] (w:1, o:53, a:1, s:1, b:0),
% 100.80/101.23 unorthogonal_lines [49, 2] (w:1, o:54, a:1, s:1, b:0),
% 100.80/101.23 orthogonal_through_point [52, 2] (w:1, o:52, a:1, s:1, b:0),
% 100.80/101.23 alpha1 [53, 2] (w:1, o:55, a:1, s:1, b:0),
% 100.80/101.23 skol1 [54, 0] (w:1, o:15, a:1, s:1, b:0),
% 100.80/101.23 skol2 [55, 0] (w:1, o:16, a:1, s:1, b:0).
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Starting Search:
% 100.80/101.23
% 100.80/101.23 *** allocated 15000 integers for clauses
% 100.80/101.23 *** allocated 22500 integers for clauses
% 100.80/101.23 *** allocated 33750 integers for clauses
% 100.80/101.23 *** allocated 15000 integers for termspace/termends
% 100.80/101.23 *** allocated 50625 integers for clauses
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 *** allocated 22500 integers for termspace/termends
% 100.80/101.23 *** allocated 75937 integers for clauses
% 100.80/101.23 *** allocated 33750 integers for termspace/termends
% 100.80/101.23 *** allocated 113905 integers for clauses
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 Failed to find proof!
% 100.80/101.23 maxweight = 15
% 100.80/101.23 maxnrclauses = 10000000
% 100.80/101.23 Generated: 1577221
% 100.80/101.23 Kept: 1915
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 The strategy used was not complete!
% 100.80/101.23
% 100.80/101.23 Increased maxweight to 16
% 100.80/101.23
% 100.80/101.23 Starting Search:
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Intermediate Status:
% 100.80/101.23 Generated: 16625
% 100.80/101.23 Kept: 2008
% 100.80/101.23 Inuse: 207
% 100.80/101.23 Deleted: 0
% 100.80/101.23 Deletedinuse: 0
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 *** allocated 50625 integers for termspace/termends
% 100.80/101.23 *** allocated 170857 integers for clauses
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 *** allocated 75937 integers for termspace/termends
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 Failed to find proof!
% 100.80/101.23 maxweight = 16
% 100.80/101.23 maxnrclauses = 10000000
% 100.80/101.23 Generated: 4885100
% 100.80/101.23 Kept: 3388
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 The strategy used was not complete!
% 100.80/101.23
% 100.80/101.23 Increased maxweight to 17
% 100.80/101.23
% 100.80/101.23 Starting Search:
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Intermediate Status:
% 100.80/101.23 Generated: 13805
% 100.80/101.23 Kept: 2016
% 100.80/101.23 Inuse: 169
% 100.80/101.23 Deleted: 0
% 100.80/101.23 Deletedinuse: 0
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Intermediate Status:
% 100.80/101.23 Generated: 40532
% 100.80/101.23 Kept: 4073
% 100.80/101.23 Inuse: 371
% 100.80/101.23 Deleted: 1
% 100.80/101.23 Deletedinuse: 0
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 *** allocated 256285 integers for clauses
% 100.80/101.23 *** allocated 113905 integers for termspace/termends
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Intermediate Status:
% 100.80/101.23 Generated: 7002702
% 100.80/101.23 Kept: 6073
% 100.80/101.23 Inuse: 3788
% 100.80/101.23 Deleted: 59
% 100.80/101.23 Deletedinuse: 4
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 *** allocated 384427 integers for clauses
% 100.80/101.23 *** allocated 170857 integers for termspace/termends
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Intermediate Status:
% 100.80/101.23 Generated: 14440928
% 100.80/101.23 Kept: 8419
% 100.80/101.23 Inuse: 6289
% 100.80/101.23 Deleted: 196
% 100.80/101.23 Deletedinuse: 5
% 100.80/101.23
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23 *** allocated 576640 integers for clauses
% 100.80/101.23 Resimplifying inuse:
% 100.80/101.23 Done
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Bliksems!, er is een bewijs:
% 100.80/101.23 % SZS status Theorem
% 100.80/101.23 % SZS output start Refutation
% 100.80/101.23
% 100.80/101.23 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 100.80/101.23 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 100.80/101.23 , ! distinct_lines( X, Y ) }.
% 100.80/101.23 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 100.80/101.23 Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23 (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 100.80/101.23 , intersection_point( X, Y ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ), distinct_points( Z
% 100.80/101.23 , intersection_point( X, Y ) ), ! apart_point_and_line( Z, Y ) }.
% 100.80/101.23 (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 100.80/101.23 ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 100.80/101.23 X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), distinct_lines( X
% 100.80/101.23 , Y ) }.
% 100.80/101.23 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 100.80/101.23 X, Y ) }.
% 100.80/101.23 (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 100.80/101.23 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 100.80/101.23 }.
% 100.80/101.23 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 100.80/101.23 (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! alpha1( X, Y )
% 100.80/101.23 }.
% 100.80/101.23 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 100.80/101.23 ( Y, X ), Y ) }.
% 100.80/101.23 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 100.80/101.23 orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23 (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 100.80/101.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 100.80/101.23 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23 (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2,
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ) ) }.
% 100.80/101.23 (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 100.80/101.23 ( X, Y ) }.
% 100.80/101.23 (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23 (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.23 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 100.80/101.23 (45) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.23 convergent_lines( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23 (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 (99) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 (165) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ), !
% 100.80/101.23 convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z )
% 100.80/101.23 ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 (166) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ), !
% 100.80/101.23 convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T )
% 100.80/101.23 ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 (173) {G2,W8,D3,L2,V2,M1} F(166);r(0) { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23 (174) {G2,W8,D3,L2,V2,M1} F(165);r(0) { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23 (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 100.80/101.23 apart_point_and_line( Z, T ) }.
% 100.80/101.23 (241) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y ),
% 100.80/101.23 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 (249) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 100.80/101.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 100.80/101.23 unorthogonal_lines( Y, Z ) }.
% 100.80/101.23 (265) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X, skol2 ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( orthogonal_through_point(
% 100.80/101.23 skol2, skol1 ), skol1 ), X ) }.
% 100.80/101.23 (293) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ),
% 100.80/101.23 apart_point_and_line( T, orthogonal_through_point( Y, Z ) ),
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 (294) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 100.80/101.23 unorthogonal_lines( Z, X ) }.
% 100.80/101.23 (2023) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 100.80/101.23 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23 (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 (3187) {G4,W8,D3,L2,V3,M1} R(241,23);r(99) { convergent_lines( Z, X ), !
% 100.80/101.23 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 (3191) {G5,W16,D3,L4,V4,M1} R(3187,249) { convergent_lines( X, Y ), !
% 100.80/101.23 convergent_lines( Z, orthogonal_through_point( Y, T ) ), convergent_lines
% 100.80/101.23 ( Z, X ), ! unorthogonal_lines( Z, orthogonal_through_point( Y, T ) ) }.
% 100.80/101.23 (3192) {G6,W10,D3,L2,V2,M1} F(3191);r(2) { ! convergent_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 (3193) {G7,W5,D3,L1,V2,M1} S(3192);r(46) { ! unorthogonal_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 (4903) {G2,W17,D3,L3,V4,M2} R(293,23) { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.23 apart_point_and_line( T, orthogonal_through_point( X, Z ) ),
% 100.80/101.23 apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 (4904) {G8,W17,D4,L3,V4,M2} R(294,3193) { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.23 apart_point_and_line( T, X ), apart_point_and_line( T,
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 100.80/101.23 (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.23 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.23 (6026) {G5,W14,D3,L2,V4,M2} R(5820,2025) { distinct_lines(
% 100.80/101.23 orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), !
% 100.80/101.23 distinct_lines( orthogonal_through_point( X, Y ),
% 100.80/101.23 orthogonal_through_point( X, Z ) ) }.
% 100.80/101.23 (6029) {G4,W16,D5,L2,V3,M1} R(5820,174) { ! convergent_lines( Y,
% 100.80/101.23 orthogonal_through_point( X, Z ) ), ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, intersection_point( Y,
% 100.80/101.23 orthogonal_through_point( X, Z ) ) ), orthogonal_through_point( X, Z ) )
% 100.80/101.23 }.
% 100.80/101.23 (6122) {G6,W14,D3,L2,V4,M1} R(6026,13) { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ),
% 100.80/101.23 distinct_lines( orthogonal_through_point( X, Y ),
% 100.80/101.23 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.23 (6167) {G7,W14,D3,L2,V4,M1} R(6122,34) { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.23 distinct_lines( orthogonal_through_point( X, Z ),
% 100.80/101.23 orthogonal_through_point( T, Y ) ) }.
% 100.80/101.23 (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), orthogonal_through_point( Y,
% 100.80/101.23 intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), !
% 100.80/101.23 convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.23 (6725) {G9,W11,D5,L1,V2,M1} R(6706,46) { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.23 intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.23 (6726) {G9,W16,D5,L2,V3,M2} R(6706,43) { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.23 intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.23 (6852) {G10,W15,D6,L1,V0,M1} R(6725,265) { convergent_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.23 intersection_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ) ) ), skol2 ) }.
% 100.80/101.23 (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.23 apart_point_and_line( Z, X ) }.
% 100.80/101.23 (7325) {G10,W12,D4,L2,V4,M2} R(7277,2025) { distinct_lines(
% 100.80/101.23 orthogonal_through_point( T, Z ), X ), ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.23 (7329) {G10,W12,D4,L2,V3,M1} R(7277,173) { ! convergent_lines( X, Z ), !
% 100.80/101.23 distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Y
% 100.80/101.23 ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.23 (9130) {G11,W12,D4,L2,V4,M1} R(7325,13) { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ),
% 100.80/101.23 distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 (9294) {G12,W12,D4,L2,V3,M2} R(7329,9130) { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( X, Z ),
% 100.80/101.23 intersection_point( X, Y ) ), X ), ! convergent_lines( X, Y ) }.
% 100.80/101.23 (9544) {G13,W12,D4,L2,V3,M2} R(9294,43) { ! convergent_lines( Z, X ), !
% 100.80/101.23 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 100.80/101.23 Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.23 (9775) {G14,W15,D4,L3,V4,M3} R(9544,45) { convergent_lines( Z,
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( Y, T ),
% 100.80/101.23 intersection_point( Y, X ) ) ), ! convergent_lines( Z, Y ), !
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 (9792) {G15,W12,D4,L2,V3,M2} F(9775) { ! convergent_lines( X, Y ),
% 100.80/101.23 convergent_lines( X, orthogonal_through_point( orthogonal_through_point(
% 100.80/101.23 Y, Z ), intersection_point( Y, X ) ) ) }.
% 100.80/101.23 (9799) {G16,W7,D4,L1,V3,M1} R(9792,6726);f { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.23 (9996) {G17,W0,D0,L0,V0,M0} R(9799,6852) { }.
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 % SZS output end Refutation
% 100.80/101.23 found a proof!
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Unprocessed initial clauses:
% 100.80/101.23
% 100.80/101.23 (9998) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 100.80/101.23 (9999) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 100.80/101.23 (10000) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 100.80/101.23 (10001) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 100.80/101.23 X, Z ), distinct_points( Y, Z ) }.
% 100.80/101.23 (10002) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 100.80/101.23 , Z ), distinct_lines( Y, Z ) }.
% 100.80/101.23 (10003) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 100.80/101.23 ( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23 (10004) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 100.80/101.23 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 100.80/101.23 ) }.
% 100.80/101.23 (10005) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 100.80/101.23 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 100.80/101.23 ) }.
% 100.80/101.23 (10006) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 100.80/101.23 Y ) ) }.
% 100.80/101.23 (10007) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 100.80/101.23 Y ) ) }.
% 100.80/101.23 (10008) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 100.80/101.23 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 100.80/101.23 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 100.80/101.23 (10009) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 100.80/101.23 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 100.80/101.23 (10010) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 100.80/101.23 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 100.80/101.23 (10011) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ), distinct_lines(
% 100.80/101.23 X, Y ) }.
% 100.80/101.23 (10012) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point(
% 100.80/101.23 Y, X ), Y ) }.
% 100.80/101.23 (10013) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 100.80/101.23 parallel_through_point( Y, X ) ) }.
% 100.80/101.23 (10014) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 100.80/101.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 (10015) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 100.80/101.23 ( X, Y ) }.
% 100.80/101.23 (10016) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23 (10017) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 100.80/101.23 }.
% 100.80/101.23 (10018) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 100.80/101.23 }.
% 100.80/101.23 (10019) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 100.80/101.23 }.
% 100.80/101.23 (10020) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 100.80/101.23 (10021) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 100.80/101.23 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 (10022) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 100.80/101.23 orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23 (10023) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 100.80/101.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 100.80/101.23 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 100.80/101.23 (10024) {G0,W7,D4,L1,V0,M1} { convergent_lines( skol2,
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ) ) }.
% 100.80/101.23
% 100.80/101.23
% 100.80/101.23 Total Proof:
% 100.80/101.23
% 100.80/101.23 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23 parent0: (9998) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 100.80/101.23 parent0: (9999) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23 parent0: (10000) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 100.80/101.23 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 100.80/101.23 parent0: (10002) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 100.80/101.23 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 2
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23 parent0: (10003) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 100.80/101.23 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 2
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23 ( Z, X ) }.
% 100.80/101.23 parent0: (10006) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 100.80/101.23 Y ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 2
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23 ( Z, Y ) }.
% 100.80/101.23 parent0: (10007) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 100.80/101.23 Y ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 2
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 100.80/101.23 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 parent0: (10009) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 100.80/101.23 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 2
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 100.80/101.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 parent0: (10010) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 100.80/101.23 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 2
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_lines( X, Y ) }.
% 100.80/101.23 parent0: (10011) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 parent0: (10015) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 100.80/101.23 parent0: (10016) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 3
% 100.80/101.23 3 ==> 2
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 100.80/101.23 }.
% 100.80/101.23 parent0: (10017) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 100.80/101.23 }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 3
% 100.80/101.23 3 ==> 2
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 100.80/101.23 alpha1( X, Y ) }.
% 100.80/101.23 parent0: (10018) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines
% 100.80/101.23 ( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 100.80/101.23 alpha1( X, Y ) }.
% 100.80/101.23 parent0: (10019) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ),
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 100.80/101.23 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 parent0: (10021) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 100.80/101.23 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 100.80/101.23 orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23 parent0: (10022) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 100.80/101.23 orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 100.80/101.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 100.80/101.23 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23 parent0: (10023) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 100.80/101.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 100.80/101.23 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 T := T
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 2
% 100.80/101.23 3 ==> 4
% 100.80/101.23 4 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2,
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ) ) }.
% 100.80/101.23 parent0: (10024) {G0,W7,D4,L1,V0,M1} { convergent_lines( skol2,
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10157) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 100.80/101.23 distinct_lines( X, Y ) }.
% 100.80/101.23 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 100.80/101.23 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 100.80/101.23 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 100.80/101.23 distinct_lines( X, Y ) }.
% 100.80/101.23 parent0: (10157) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 100.80/101.23 distinct_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10159) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 100.80/101.23 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := orthogonal_through_point( X, Y )
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23 parent0: (10159) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10160) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 100.80/101.23 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23 parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := orthogonal_through_point( X, Y )
% 100.80/101.23 Y := X
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 parent0: (10160) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10161) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 parent0: (10161) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10163) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 100.80/101.23 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.23 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 100.80/101.23 parent0: (10163) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 2
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10167) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( Z, Y ), ! convergent_lines( Z, X ) }.
% 100.80/101.23 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := X
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (45) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.23 convergent_lines( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.23 parent0: (10167) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( Z, Y ), ! convergent_lines( Z, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 2
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10169) {G2,W5,D3,L1,V2,M1} { convergent_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 parent1[0]: (37) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := orthogonal_through_point( X, Y )
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 parent0: (10169) {G2,W5,D3,L1,V2,M1} { convergent_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10170) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 100.80/101.23 parent0[0]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( X, Y ) }.
% 100.80/101.23 parent1[0]: (40) {G2,W8,D3,L2,V3,M2} R(5,37) { convergent_lines( X, Z ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (99) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 parent0: (10170) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10172) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23 , ! apart_point_and_line( T, Y ) }.
% 100.80/101.23 parent0[2]: (9) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23 ( Z, Y ) }.
% 100.80/101.23 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 100.80/101.23 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := T
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (165) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y ),
% 100.80/101.23 ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T, Z
% 100.80/101.23 ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 parent0: (10172) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23 , ! apart_point_and_line( T, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := T
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 T := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 2
% 100.80/101.23 2 ==> 0
% 100.80/101.23 3 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10174) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23 , ! apart_point_and_line( T, X ) }.
% 100.80/101.23 parent0[2]: (8) {G0,W11,D3,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 100.80/101.23 ( Z, X ) }.
% 100.80/101.23 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 100.80/101.23 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := T
% 100.80/101.23 Y := X
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (166) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y ),
% 100.80/101.23 ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z, T
% 100.80/101.23 ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 parent0: (10174) {G1,W14,D3,L4,V4,M4} { ! convergent_lines( X, Y ),
% 100.80/101.23 distinct_points( Z, intersection_point( X, Y ) ), distinct_points( T, Z )
% 100.80/101.23 , ! apart_point_and_line( T, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := T
% 100.80/101.23 Z := Y
% 100.80/101.23 T := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 2
% 100.80/101.23 2 ==> 0
% 100.80/101.23 3 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 factor: (10176) {G1,W15,D3,L3,V2,M3} { distinct_points( intersection_point
% 100.80/101.23 ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23 parent0[0, 2]: (166) {G1,W14,D3,L4,V4,M1} R(11,8) { distinct_points( X, Y )
% 100.80/101.23 , ! convergent_lines( Z, T ), distinct_points( Y, intersection_point( Z,
% 100.80/101.23 T ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := intersection_point( X, Y )
% 100.80/101.23 Y := intersection_point( X, Y )
% 100.80/101.23 Z := X
% 100.80/101.23 T := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10177) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23 parent1[0]: (10176) {G1,W15,D3,L3,V2,M3} { distinct_points(
% 100.80/101.23 intersection_point( X, Y ), intersection_point( X, Y ) ), !
% 100.80/101.23 convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X,
% 100.80/101.23 Y ), X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := intersection_point( X, Y )
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (173) {G2,W8,D3,L2,V2,M1} F(166);r(0) { ! convergent_lines( X
% 100.80/101.23 , Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23 parent0: (10177) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 factor: (10178) {G1,W15,D3,L3,V2,M3} { distinct_points( intersection_point
% 100.80/101.23 ( X, Y ), intersection_point( X, Y ) ), ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23 parent0[0, 2]: (165) {G1,W14,D3,L4,V4,M1} R(11,9) { distinct_points( X, Y )
% 100.80/101.23 , ! convergent_lines( T, Z ), distinct_points( Y, intersection_point( T,
% 100.80/101.23 Z ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := intersection_point( X, Y )
% 100.80/101.23 Y := intersection_point( X, Y )
% 100.80/101.23 Z := Y
% 100.80/101.23 T := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10179) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 100.80/101.23 parent1[0]: (10178) {G1,W15,D3,L3,V2,M3} { distinct_points(
% 100.80/101.23 intersection_point( X, Y ), intersection_point( X, Y ) ), !
% 100.80/101.23 convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X,
% 100.80/101.23 Y ), Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := intersection_point( X, Y )
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (174) {G2,W8,D3,L2,V2,M1} F(165);r(0) { ! convergent_lines( X
% 100.80/101.23 , Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23 parent0: (10179) {G1,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.23 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10180) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 100.80/101.23 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 100.80/101.23 orthogonal_through_point( Y, X ) ) }.
% 100.80/101.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 100.80/101.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := orthogonal_through_point( Y, X )
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 parent0: (10180) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 100.80/101.23 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10181) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 100.80/101.23 apart_point_and_line( Z, T ) }.
% 100.80/101.23 parent0[1]: (198) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 100.80/101.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := T
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 100.80/101.23 apart_point_and_line( Z, T ) }.
% 100.80/101.23 parent0: (10181) {G1,W11,D3,L3,V4,M3} { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 100.80/101.23 apart_point_and_line( Z, T ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 T := T
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 2
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10184) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 100.80/101.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 100.80/101.23 ( Z, Y ) }.
% 100.80/101.23 parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 100.80/101.23 alpha1( X, Y ) }.
% 100.80/101.23 parent1[3]: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (241) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 100.80/101.23 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 parent0: (10184) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 100.80/101.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 100.80/101.23 ( Z, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 2
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 3
% 100.80/101.23 3 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10186) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 100.80/101.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 100.80/101.23 unorthogonal_lines( Z, Y ) }.
% 100.80/101.23 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 100.80/101.23 ( X, Y ) }.
% 100.80/101.23 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 100.80/101.23 }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (249) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 100.80/101.23 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 100.80/101.23 unorthogonal_lines( Y, Z ) }.
% 100.80/101.23 parent0: (10186) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 100.80/101.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 100.80/101.23 unorthogonal_lines( Z, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 0
% 100.80/101.23 2 ==> 2
% 100.80/101.23 3 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10187) {G1,W10,D4,L2,V1,M2} { convergent_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ), X ), convergent_lines( X, skol2 ) }.
% 100.80/101.23 parent0[1]: (44) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.23 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 100.80/101.23 parent1[0]: (26) {G0,W7,D4,L1,V0,M1} I { convergent_lines( skol2,
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := skol2
% 100.80/101.23 Z := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 100.80/101.23 , skol1 )
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (265) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X,
% 100.80/101.23 skol2 ), convergent_lines( orthogonal_through_point(
% 100.80/101.23 orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 100.80/101.23 parent0: (10187) {G1,W10,D4,L2,V1,M2} { convergent_lines(
% 100.80/101.23 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.23 ), X ), convergent_lines( X, skol2 ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 1
% 100.80/101.23 1 ==> 0
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10188) {G1,W16,D3,L4,V4,M4} { ! distinct_lines( Z,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 100.80/101.23 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 100.80/101.23 unorthogonal_lines( Z, X ) }.
% 100.80/101.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 100.80/101.23 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 parent1[3]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 100.80/101.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 100.80/101.23 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := orthogonal_through_point( X, Y )
% 100.80/101.23 Z := T
% 100.80/101.23 T := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (293) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ),
% 100.80/101.23 apart_point_and_line( T, orthogonal_through_point( Y, Z ) ),
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 parent0: (10188) {G1,W16,D3,L4,V4,M4} { ! distinct_lines( Z,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 100.80/101.23 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 100.80/101.23 unorthogonal_lines( Z, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := X
% 100.80/101.23 T := T
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 2
% 100.80/101.23 3 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10192) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 100.80/101.23 unorthogonal_lines( Z, X ) }.
% 100.80/101.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 100.80/101.23 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 parent1[4]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 100.80/101.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 100.80/101.23 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := orthogonal_through_point( X, Y )
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := T
% 100.80/101.23 T := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (294) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 100.80/101.23 unorthogonal_lines( Z, X ) }.
% 100.80/101.23 parent0: (10192) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 100.80/101.23 unorthogonal_lines( Z, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 T := T
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 2
% 100.80/101.23 3 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10194) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 100.80/101.23 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23 parent0[2]: (200) {G2,W11,D3,L3,V4,M1} R(198,12) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ), !
% 100.80/101.23 apart_point_and_line( Z, T ) }.
% 100.80/101.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 100.80/101.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 T := T
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := U
% 100.80/101.23 Z := T
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (2023) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 100.80/101.23 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23 parent0: (10194) {G1,W14,D3,L4,V5,M4} { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 100.80/101.23 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 T := T
% 100.80/101.23 U := U
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 2
% 100.80/101.23 3 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 factor: (10200) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 parent0[0, 2]: (2023) {G3,W14,D3,L4,V5,M1} R(200,12) { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, X ),
% 100.80/101.23 distinct_lines( U, T ), ! apart_point_and_line( Z, U ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 T := orthogonal_through_point( Y, Z )
% 100.80/101.23 U := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10206) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 100.80/101.23 distinct_lines( X, Y ) }.
% 100.80/101.23 parent1[0]: (10200) {G3,W13,D3,L3,V3,M3} { distinct_lines( X,
% 100.80/101.23 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := orthogonal_through_point( Y, Z )
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 factor: (10208) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 100.80/101.23 parent0[0, 1]: (10206) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := X
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines(
% 100.80/101.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.23 parent0: (10208) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10210) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 100.80/101.23 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 100.80/101.23 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.23 parent1[2]: (241) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 100.80/101.23 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 100.80/101.23 unorthogonal_lines( X, Y ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := orthogonal_through_point( X, Y )
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10212) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 100.80/101.23 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 100.80/101.23 convergent_lines( Z, X ) }.
% 100.80/101.23 parent0[0]: (10210) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 100.80/101.23 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 100.80/101.23 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 parent1[1]: (99) {G3,W8,D3,L2,V3,M2} R(40,43) { convergent_lines( Z, X ),
% 100.80/101.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := Z
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 factor: (10213) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 100.80/101.23 parent0[0, 2]: (10212) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 100.80/101.23 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 100.80/101.23 convergent_lines( Z, X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (3187) {G4,W8,D3,L2,V3,M1} R(241,23);r(99) { convergent_lines
% 100.80/101.23 ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 parent0: (10213) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 100.80/101.23 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Z
% 100.80/101.23 Y := X
% 100.80/101.23 Z := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10214) {G2,W16,D3,L4,V4,M4} { convergent_lines( X, Y ), !
% 100.80/101.23 convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 100.80/101.23 ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.23 parent0[1]: (3187) {G4,W8,D3,L2,V3,M1} R(241,23);r(99) { convergent_lines(
% 100.80/101.23 Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.23 parent1[3]: (249) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 100.80/101.23 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 100.80/101.23 unorthogonal_lines( Y, Z ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := Y
% 100.80/101.23 Y := Z
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := T
% 100.80/101.23 Y := orthogonal_through_point( Y, Z )
% 100.80/101.23 Z := X
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (3191) {G5,W16,D3,L4,V4,M1} R(3187,249) { convergent_lines( X
% 100.80/101.23 , Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ),
% 100.80/101.23 convergent_lines( Z, X ), ! unorthogonal_lines( Z,
% 100.80/101.23 orthogonal_through_point( Y, T ) ) }.
% 100.80/101.23 parent0: (10214) {G2,W16,D3,L4,V4,M4} { convergent_lines( X, Y ), !
% 100.80/101.23 convergent_lines( T, orthogonal_through_point( Y, Z ) ), convergent_lines
% 100.80/101.23 ( T, X ), ! unorthogonal_lines( T, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 Z := T
% 100.80/101.23 T := Z
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 2 ==> 2
% 100.80/101.23 3 ==> 3
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 factor: (10216) {G5,W13,D3,L3,V2,M3} { convergent_lines( X, X ), !
% 100.80/101.23 convergent_lines( X, orthogonal_through_point( X, Y ) ), !
% 100.80/101.23 unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 parent0[0, 2]: (3191) {G5,W16,D3,L4,V4,M1} R(3187,249) { convergent_lines(
% 100.80/101.23 X, Y ), ! convergent_lines( Z, orthogonal_through_point( Y, T ) ),
% 100.80/101.23 convergent_lines( Z, X ), ! unorthogonal_lines( Z,
% 100.80/101.23 orthogonal_through_point( Y, T ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := X
% 100.80/101.23 Z := X
% 100.80/101.23 T := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10217) {G1,W10,D3,L2,V2,M2} { ! convergent_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 100.80/101.23 parent1[0]: (10216) {G5,W13,D3,L3,V2,M3} { convergent_lines( X, X ), !
% 100.80/101.23 convergent_lines( X, orthogonal_through_point( X, Y ) ), !
% 100.80/101.23 unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 end
% 100.80/101.23 substitution1:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 subsumption: (3192) {G6,W10,D3,L2,V2,M1} F(3191);r(2) { ! convergent_lines
% 100.80/101.23 ( X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 parent0: (10217) {G1,W10,D3,L2,V2,M2} { ! convergent_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 substitution0:
% 100.80/101.23 X := X
% 100.80/101.23 Y := Y
% 100.80/101.23 end
% 100.80/101.23 permutation0:
% 100.80/101.23 0 ==> 0
% 100.80/101.23 1 ==> 1
% 100.80/101.23 end
% 100.80/101.23
% 100.80/101.23 resolution: (10218) {G3,W5,D3,L1,V2,M1} { ! unorthogonal_lines( X,
% 100.80/101.23 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.23 parent0[0]: (3192) {G6,W10,D3,L2,V2,M1} F(3191);r(2) { ! convergent_lines(
% 100.80/101.23 X, orthogonal_through_point( X, Y ) ), ! unorthogonal_lines( X,
% 100.80/101.24 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 parent1[0]: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (3193) {G7,W5,D3,L1,V2,M1} S(3192);r(46) { !
% 100.80/101.24 unorthogonal_lines( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 parent0: (10218) {G3,W5,D3,L1,V2,M1} { ! unorthogonal_lines( X,
% 100.80/101.24 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10219) {G1,W17,D3,L3,V4,M3} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 100.80/101.24 orthogonal_through_point( Y, X ), Y ) }.
% 100.80/101.24 parent1[3]: (293) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines( X,
% 100.80/101.24 orthogonal_through_point( Y, Z ) ), apart_point_and_line( T, X ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( Y, Z ) ),
% 100.80/101.24 unorthogonal_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := X
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( X, Y )
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Z
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (4903) {G2,W17,D3,L3,V4,M2} R(293,23) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 parent0: (10219) {G1,W17,D3,L3,V4,M3} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Y ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 2
% 100.80/101.24 2 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10221) {G2,W17,D4,L3,V4,M3} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 100.80/101.24 parent0[0]: (3193) {G7,W5,D3,L1,V2,M1} S(3192);r(46) { ! unorthogonal_lines
% 100.80/101.24 ( X, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 parent1[3]: (294) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 100.80/101.24 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 100.80/101.24 unorthogonal_lines( Z, X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( X, Y )
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := X
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (4904) {G8,W17,D4,L3,V4,M2} R(294,3193) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.24 apart_point_and_line( T, X ), apart_point_and_line( T,
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 100.80/101.24 parent0: (10221) {G2,W17,D4,L3,V4,M3} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ) ), apart_point_and_line( T, X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 2
% 100.80/101.24 2 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10223) {G1,W12,D3,L2,V3,M2} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ),
% 100.80/101.24 apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 100.80/101.24 orthogonal_through_point( Y, X ) ) }.
% 100.80/101.24 parent1[2]: (4903) {G2,W17,D3,L3,V4,M2} R(293,23) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( T, orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Z
% 100.80/101.24 T := X
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24 parent0: (10223) {G1,W12,D3,L2,V3,M2} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( Y, X ), orthogonal_through_point( Y, Z ) ),
% 100.80/101.24 apart_point_and_line( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10225) {G4,W14,D3,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 100.80/101.24 distinct_lines( orthogonal_through_point( Z, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 parent0[1]: (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines(
% 100.80/101.24 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.24 parent1[1]: (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := orthogonal_through_point( Z, T )
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := T
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6026) {G5,W14,D3,L2,V4,M2} R(5820,2025) { distinct_lines(
% 100.80/101.24 orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), !
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Y ),
% 100.80/101.24 orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24 parent0: (10225) {G4,W14,D3,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 100.80/101.24 distinct_lines( orthogonal_through_point( Z, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := T
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := X
% 100.80/101.24 T := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10226) {G3,W16,D5,L2,V3,M2} { ! convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( Y, Z ) ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( Y, intersection_point( X,
% 100.80/101.24 orthogonal_through_point( Y, Z ) ) ), orthogonal_through_point( Y, Z ) )
% 100.80/101.24 }.
% 100.80/101.24 parent0[1]: (174) {G2,W8,D3,L2,V2,M1} F(165);r(0) { ! convergent_lines( X,
% 100.80/101.24 Y ), ! apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 100.80/101.24 parent1[1]: (5820) {G3,W12,D3,L2,V3,M1} R(4903,24) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 apart_point_and_line( Y, orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := orthogonal_through_point( Y, Z )
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := intersection_point( X, orthogonal_through_point( Y, Z ) )
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6029) {G4,W16,D5,L2,V3,M1} R(5820,174) { ! convergent_lines(
% 100.80/101.24 Y, orthogonal_through_point( X, Z ) ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, intersection_point( Y,
% 100.80/101.24 orthogonal_through_point( X, Z ) ) ), orthogonal_through_point( X, Z ) )
% 100.80/101.24 }.
% 100.80/101.24 parent0: (10226) {G3,W16,D5,L2,V3,M2} { ! convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( Y, Z ) ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( Y, intersection_point( X,
% 100.80/101.24 orthogonal_through_point( Y, Z ) ) ), orthogonal_through_point( Y, Z ) )
% 100.80/101.24 }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10227) {G1,W14,D3,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( Z, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 parent0[1]: (6026) {G5,W14,D3,L2,V4,M2} R(5820,2025) { distinct_lines(
% 100.80/101.24 orthogonal_through_point( T, Y ), orthogonal_through_point( X, Z ) ), !
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Y ),
% 100.80/101.24 orthogonal_through_point( X, Z ) ) }.
% 100.80/101.24 parent1[1]: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 100.80/101.24 distinct_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := T
% 100.80/101.24 T := X
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( Z, Y )
% 100.80/101.24 Y := orthogonal_through_point( Z, T )
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6122) {G6,W14,D3,L2,V4,M1} R(6026,13) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ),
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 parent0: (10227) {G1,W14,D3,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( Z, T ) ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( Z, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10228) {G2,W14,D3,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( Z, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 100.80/101.24 distinct_lines( X, Y ) }.
% 100.80/101.24 parent1[1]: (6122) {G6,W14,D3,L2,V4,M1} R(6026,13) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( Z, Y ), orthogonal_through_point( Z, T ) ),
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := orthogonal_through_point( Z, T )
% 100.80/101.24 Y := orthogonal_through_point( X, Y )
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6167) {G7,W14,D3,L2,V4,M1} R(6122,34) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Z ),
% 100.80/101.24 orthogonal_through_point( T, Y ) ) }.
% 100.80/101.24 parent0: (10228) {G2,W14,D3,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( Z, T ), orthogonal_through_point( X, Y ) ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( Z, Y ),
% 100.80/101.24 orthogonal_through_point( Z, T ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := T
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := X
% 100.80/101.24 T := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10229) {G5,W16,D5,L2,V3,M2} { ! convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( Y, Z ) ), ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( Y, Z ), orthogonal_through_point( Y,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ) }.
% 100.80/101.24 parent0[1]: (6029) {G4,W16,D5,L2,V3,M1} R(5820,174) { ! convergent_lines( Y
% 100.80/101.24 , orthogonal_through_point( X, Z ) ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, intersection_point( Y,
% 100.80/101.24 orthogonal_through_point( X, Z ) ) ), orthogonal_through_point( X, Z ) )
% 100.80/101.24 }.
% 100.80/101.24 parent1[1]: (6167) {G7,W14,D3,L2,V4,M1} R(6122,34) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ),
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Z ),
% 100.80/101.24 orthogonal_through_point( T, Y ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := intersection_point( X, orthogonal_through_point( Y, Z ) )
% 100.80/101.24 T := Y
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines
% 100.80/101.24 ( orthogonal_through_point( Y, Z ), orthogonal_through_point( Y,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), !
% 100.80/101.24 convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24 parent0: (10229) {G5,W16,D5,L2,V3,M2} { ! convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( Y, Z ) ), ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( Y, Z ), orthogonal_through_point( Y,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10230) {G3,W11,D5,L1,V2,M1} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24 parent0[1]: (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( Y, Z ), orthogonal_through_point( Y,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), !
% 100.80/101.24 convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24 parent1[0]: (46) {G2,W5,D3,L1,V2,M1} R(43,37) { convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( X, Y ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6725) {G9,W11,D5,L1,V2,M1} R(6706,46) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24 parent0: (10230) {G3,W11,D5,L1,V2,M1} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10232) {G2,W16,D5,L2,V3,M2} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24 parent0[1]: (6706) {G8,W16,D5,L2,V3,M2} R(6029,6167) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( Y, Z ), orthogonal_through_point( Y,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( Y, Z ) ) ) ), !
% 100.80/101.24 convergent_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 100.80/101.24 parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.24 convergent_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := orthogonal_through_point( X, Y )
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6726) {G9,W16,D5,L2,V3,M2} R(6706,43) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24 parent0: (10232) {G2,W16,D5,L2,V3,M2} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10233) {G4,W15,D6,L1,V0,M1} { convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 intersection_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24 ) ) ), skol2 ) }.
% 100.80/101.24 parent0[0]: (6725) {G9,W11,D5,L1,V2,M1} R(6706,46) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( X, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24 parent1[1]: (265) {G3,W10,D4,L2,V1,M2} R(44,26) { convergent_lines( X,
% 100.80/101.24 skol2 ), convergent_lines( orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( skol2, skol1 ), skol1 ), X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := orthogonal_through_point( skol2, skol1 )
% 100.80/101.24 Y := skol1
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 100.80/101.24 , intersection_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24 ) ) )
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (6852) {G10,W15,D6,L1,V0,M1} R(6725,265) { convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 intersection_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24 ) ) ), skol2 ) }.
% 100.80/101.24 parent0: (10233) {G4,W15,D6,L1,V0,M1} { convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 intersection_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24 ) ) ), skol2 ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10235) {G1,W10,D4,L2,V3,M2} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ),
% 100.80/101.24 apart_point_and_line( X, Y ) }.
% 100.80/101.24 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 100.80/101.24 orthogonal_through_point( Y, X ) ) }.
% 100.80/101.24 parent1[2]: (4904) {G8,W17,D4,L3,V4,M2} R(294,3193) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.24 apart_point_and_line( T, X ), apart_point_and_line( T,
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := orthogonal_through_point( Y, Z )
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := X
% 100.80/101.24 T := X
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.24 apart_point_and_line( Z, X ) }.
% 100.80/101.24 parent0: (10235) {G1,W10,D4,L2,V3,M2} { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Y, Z ), X ), Y ),
% 100.80/101.24 apart_point_and_line( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10237) {G5,W12,D4,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24 parent0[1]: (2025) {G4,W8,D3,L2,V3,M1} F(2023);r(34) { distinct_lines(
% 100.80/101.24 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 100.80/101.24 parent1[1]: (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.24 apart_point_and_line( Z, X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := T
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (7325) {G10,W12,D4,L2,V4,M2} R(7277,2025) { distinct_lines(
% 100.80/101.24 orthogonal_through_point( T, Z ), X ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24 parent0: (10237) {G5,W12,D4,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := T
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := X
% 100.80/101.24 T := Y
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10238) {G3,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.24 distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Z
% 100.80/101.24 ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24 parent0[1]: (173) {G2,W8,D3,L2,V2,M1} F(166);r(0) { ! convergent_lines( X,
% 100.80/101.24 Y ), ! apart_point_and_line( intersection_point( X, Y ), X ) }.
% 100.80/101.24 parent1[1]: (7277) {G9,W10,D4,L2,V3,M1} R(4904,24) { ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ),
% 100.80/101.24 apart_point_and_line( Z, X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := intersection_point( X, Y )
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (7329) {G10,W12,D4,L2,V3,M1} R(7277,173) { ! convergent_lines
% 100.80/101.24 ( X, Z ), ! distinct_lines( orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24 parent0: (10238) {G3,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.24 distinct_lines( orthogonal_through_point( orthogonal_through_point( X, Z
% 100.80/101.24 ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 1 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10239) {G1,W12,D4,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24 parent0[1]: (7325) {G10,W12,D4,L2,V4,M2} R(7277,2025) { distinct_lines(
% 100.80/101.24 orthogonal_through_point( T, Z ), X ), ! distinct_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24 parent1[1]: (13) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 100.80/101.24 distinct_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Z
% 100.80/101.24 Y := T
% 100.80/101.24 Z := Y
% 100.80/101.24 T := X
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( orthogonal_through_point( Z, T ), Y )
% 100.80/101.24 Y := Z
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (9130) {G11,W12,D4,L2,V4,M1} R(7325,13) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ),
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24 parent0: (10239) {G1,W12,D4,L2,V4,M2} { distinct_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10240) {G11,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 100.80/101.24 T ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24 parent0[1]: (7329) {G10,W12,D4,L2,V3,M1} R(7277,173) { ! convergent_lines(
% 100.80/101.24 X, Z ), ! distinct_lines( orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24 parent1[1]: (9130) {G11,W12,D4,L2,V4,M1} R(7325,13) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Z, T ), Y ), Z ),
% 100.80/101.24 distinct_lines( orthogonal_through_point( X, Y ), Z ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( X, Z )
% 100.80/101.24 Y := intersection_point( X, Y )
% 100.80/101.24 Z := X
% 100.80/101.24 T := T
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (9294) {G12,W12,D4,L2,V3,M2} R(7329,9130) { ! convergent_lines
% 100.80/101.24 ( orthogonal_through_point( orthogonal_through_point( X, Z ),
% 100.80/101.24 intersection_point( X, Y ) ), X ), ! convergent_lines( X, Y ) }.
% 100.80/101.24 parent0: (10240) {G11,W12,D4,L2,V3,M2} { ! convergent_lines( X, Y ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 100.80/101.24 T ), intersection_point( X, Y ) ), X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := T
% 100.80/101.24 T := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10242) {G2,W12,D4,L2,V3,M2} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ),
% 100.80/101.24 intersection_point( X, Z ) ), X ), ! convergent_lines( Z, X ) }.
% 100.80/101.24 parent0[1]: (9294) {G12,W12,D4,L2,V3,M2} R(7329,9130) { ! convergent_lines
% 100.80/101.24 ( orthogonal_through_point( orthogonal_through_point( X, Z ),
% 100.80/101.24 intersection_point( X, Y ) ), X ), ! convergent_lines( X, Y ) }.
% 100.80/101.24 parent1[1]: (43) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 100.80/101.24 convergent_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Z
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (9544) {G13,W12,D4,L2,V3,M2} R(9294,43) { ! convergent_lines(
% 100.80/101.24 Z, X ), ! convergent_lines( orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24 parent0: (10242) {G2,W12,D4,L2,V3,M2} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ),
% 100.80/101.24 intersection_point( X, Z ) ), X ), ! convergent_lines( Z, X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10246) {G3,W15,D4,L3,V4,M3} { ! convergent_lines( X, Y ),
% 100.80/101.24 convergent_lines( T, orthogonal_through_point( orthogonal_through_point(
% 100.80/101.24 Y, Z ), intersection_point( Y, X ) ) ), ! convergent_lines( T, Y ) }.
% 100.80/101.24 parent0[1]: (9544) {G13,W12,D4,L2,V3,M2} R(9294,43) { ! convergent_lines( Z
% 100.80/101.24 , X ), ! convergent_lines( orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( X, Y ), intersection_point( X, Z ) ), X ) }.
% 100.80/101.24 parent1[2]: (45) {G2,W9,D2,L3,V3,M3} R(43,5) { convergent_lines( Z, X ), !
% 100.80/101.24 convergent_lines( Z, Y ), convergent_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := Y
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := X
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( orthogonal_through_point( Y, Z ),
% 100.80/101.24 intersection_point( Y, X ) )
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := T
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (9775) {G14,W15,D4,L3,V4,M3} R(9544,45) { convergent_lines( Z
% 100.80/101.24 , orthogonal_through_point( orthogonal_through_point( Y, T ),
% 100.80/101.24 intersection_point( Y, X ) ) ), ! convergent_lines( Z, Y ), !
% 100.80/101.24 convergent_lines( X, Y ) }.
% 100.80/101.24 parent0: (10246) {G3,W15,D4,L3,V4,M3} { ! convergent_lines( X, Y ),
% 100.80/101.24 convergent_lines( T, orthogonal_through_point( orthogonal_through_point(
% 100.80/101.24 Y, Z ), intersection_point( Y, X ) ) ), ! convergent_lines( T, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := T
% 100.80/101.24 T := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 2
% 100.80/101.24 1 ==> 0
% 100.80/101.24 2 ==> 1
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 factor: (10249) {G14,W12,D4,L2,V3,M2} { convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Y, Z ),
% 100.80/101.24 intersection_point( Y, X ) ) ), ! convergent_lines( X, Y ) }.
% 100.80/101.24 parent0[1, 2]: (9775) {G14,W15,D4,L3,V4,M3} R(9544,45) { convergent_lines(
% 100.80/101.24 Z, orthogonal_through_point( orthogonal_through_point( Y, T ),
% 100.80/101.24 intersection_point( Y, X ) ) ), ! convergent_lines( Z, Y ), !
% 100.80/101.24 convergent_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := X
% 100.80/101.24 T := Z
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (9792) {G15,W12,D4,L2,V3,M2} F(9775) { ! convergent_lines( X,
% 100.80/101.24 Y ), convergent_lines( X, orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( Y, Z ), intersection_point( Y, X ) ) ) }.
% 100.80/101.24 parent0: (10249) {G14,W12,D4,L2,V3,M2} { convergent_lines( X,
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( Y, Z ),
% 100.80/101.24 intersection_point( Y, X ) ) ), ! convergent_lines( X, Y ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 1
% 100.80/101.24 1 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10251) {G10,W14,D4,L2,V3,M2} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 100.80/101.24 Y ), Z ), X ) }.
% 100.80/101.24 parent0[1]: (6726) {G9,W16,D5,L2,V3,M2} R(6706,43) { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( X, Y ), orthogonal_through_point( X,
% 100.80/101.24 intersection_point( Z, orthogonal_through_point( X, Y ) ) ) ) }.
% 100.80/101.24 parent1[1]: (9792) {G15,W12,D4,L2,V3,M2} F(9775) { ! convergent_lines( X, Y
% 100.80/101.24 ), convergent_lines( X, orthogonal_through_point(
% 100.80/101.24 orthogonal_through_point( Y, Z ), intersection_point( Y, X ) ) ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := orthogonal_through_point( X, Y )
% 100.80/101.24 Y := Z
% 100.80/101.24 Z := X
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 X := orthogonal_through_point( orthogonal_through_point( X, Y ), Z )
% 100.80/101.24 Y := X
% 100.80/101.24 Z := Y
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 factor: (10252) {G10,W7,D4,L1,V3,M1} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24 parent0[0, 1]: (10251) {G10,W14,D4,L2,V3,M2} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ), !
% 100.80/101.24 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 100.80/101.24 Y ), Z ), X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (9799) {G16,W7,D4,L1,V3,M1} R(9792,6726);f { !
% 100.80/101.24 convergent_lines( orthogonal_through_point( orthogonal_through_point( X,
% 100.80/101.24 Y ), Z ), X ) }.
% 100.80/101.24 parent0: (10252) {G10,W7,D4,L1,V3,M1} { ! convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := X
% 100.80/101.24 Y := Y
% 100.80/101.24 Z := Z
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 0 ==> 0
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 resolution: (10253) {G11,W0,D0,L0,V0,M0} { }.
% 100.80/101.24 parent0[0]: (9799) {G16,W7,D4,L1,V3,M1} R(9792,6726);f { ! convergent_lines
% 100.80/101.24 ( orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X )
% 100.80/101.24 }.
% 100.80/101.24 parent1[0]: (6852) {G10,W15,D6,L1,V0,M1} R(6725,265) { convergent_lines(
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 intersection_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24 ) ) ), skol2 ) }.
% 100.80/101.24 substitution0:
% 100.80/101.24 X := skol2
% 100.80/101.24 Y := skol1
% 100.80/101.24 Z := intersection_point( orthogonal_through_point( skol2, skol1 ),
% 100.80/101.24 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 100.80/101.24 ) )
% 100.80/101.24 end
% 100.80/101.24 substitution1:
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 subsumption: (9996) {G17,W0,D0,L0,V0,M0} R(9799,6852) { }.
% 100.80/101.24 parent0: (10253) {G11,W0,D0,L0,V0,M0} { }.
% 100.80/101.24 substitution0:
% 100.80/101.24 end
% 100.80/101.24 permutation0:
% 100.80/101.24 end
% 100.80/101.24
% 100.80/101.24 Proof check complete!
% 100.80/101.24
% 100.80/101.24 Memory use:
% 100.80/101.24
% 100.80/101.24 space for terms: 166328
% 100.80/101.24 space for clauses: 450138
% 100.80/101.24
% 100.80/101.24
% 100.80/101.24 clauses generated: 14625628
% 100.80/101.24 clauses kept: 9997
% 100.80/101.24 clauses selected: 6356
% 100.80/101.24 clauses deleted: 198
% 100.80/101.24 clauses inuse deleted: 6
% 100.80/101.24
% 100.80/101.24 subsentry: 72246578
% 100.80/101.24 literals s-matched: 21522204
% 100.80/101.24 literals matched: 21520218
% 100.80/101.24 full subsumption: 14184190
% 100.80/101.24
% 100.80/101.24 checksum: -769214163
% 100.80/101.24
% 100.80/101.24
% 100.80/101.24 Bliksem ended
%------------------------------------------------------------------------------