%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO183+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 02:52:23 EDT 2022
% Result : Theorem 1.01s 1.37s
% Output : Refutation 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO183+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n027.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 12:55:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.01/1.37 *** allocated 10000 integers for termspace/termends
% 1.01/1.37 *** allocated 10000 integers for clauses
% 1.01/1.37 *** allocated 10000 integers for justifications
% 1.01/1.37 Bliksem 1.12
% 1.01/1.37
% 1.01/1.37
% 1.01/1.37 Automatic Strategy Selection
% 1.01/1.37
% 1.01/1.37
% 1.01/1.37 Clauses:
% 1.01/1.37
% 1.01/1.37 { ! distinct_points( X, X ) }.
% 1.01/1.37 { ! distinct_lines( X, X ) }.
% 1.01/1.37 { ! convergent_lines( X, X ) }.
% 1.01/1.37 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.01/1.37 ) }.
% 1.01/1.37 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.01/1.37 }.
% 1.01/1.37 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.01/1.37 , Z ) }.
% 1.01/1.37 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.01/1.37 , Y ) ) }.
% 1.01/1.37 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.01/1.37 , Y ) ) }.
% 1.01/1.37 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.01/1.37 , Y ), X ) }.
% 1.01/1.37 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.01/1.37 , Y ), Y ) }.
% 1.01/1.37 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.01/1.37 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.01/1.37 apart_point_and_line( Y, T ) }.
% 1.01/1.37 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.01/1.37 apart_point_and_line( Z, Y ) }.
% 1.01/1.37 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.01/1.37 apart_point_and_line( X, Z ) }.
% 1.01/1.37 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 1.01/1.37 Z ) }.
% 1.01/1.37 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 1.01/1.37 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.01/1.37 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.01/1.37 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.01/1.37 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.01/1.37 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.01/1.37 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.01/1.37 , convergent_lines( Y, Z ) }.
% 1.01/1.37 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.01/1.37 , unorthogonal_lines( Y, Z ) }.
% 1.01/1.37 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.01/1.37 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.01/1.37 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.01/1.37 }.
% 1.01/1.37 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.37 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.01/1.37 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.01/1.37 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 1.01/1.37 unorthogonal_lines( Y, T ) }.
% 1.01/1.37 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.01/1.37 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 1.01/1.37 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.01/1.37 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 1.01/1.37 }.
% 1.01/1.37 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 1.01/1.37 line_connecting( X, Y ) ) }.
% 1.01/1.37 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 1.01/1.37 intersection_point( X, Y ) ) }.
% 1.01/1.37 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 1.01/1.37 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 1.01/1.37 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 1.01/1.37 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 1.01/1.37 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 1.01/1.37 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 1.01/1.37 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 1.01/1.37 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 1.01/1.37 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 1.01/1.37 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.01/1.37 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 1.01/1.37 { distinct_points( skol1, skol2 ) }.
% 1.01/1.37 { convergent_lines( skol3, skol4 ) }.
% 1.01/1.37 { equal_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.01/1.37 { ! incident_point_and_line( skol1, skol3 ), ! incident_point_and_line(
% 1.01/1.37 skol2, skol3 ) }.
% 1.01/1.37
% 1.01/1.37 percentage equality = 0.000000, percentage horn = 0.620000
% 1.01/1.37 This a non-horn, non-equality problem
% 1.01/1.37
% 1.01/1.37
% 1.01/1.37 Options Used:
% 1.01/1.37
% 1.01/1.37 useres = 1
% 1.01/1.37 useparamod = 0
% 1.01/1.37 useeqrefl = 0
% 1.01/1.37 useeqfact = 0
% 1.01/1.37 usefactor = 1
% 1.01/1.37 usesimpsplitting = 0
% 1.01/1.37 usesimpdemod = 0
% 1.01/1.37 usesimpres = 3
% 1.01/1.37
% 1.01/1.37 resimpinuse = 1000
% 1.01/1.37 resimpclauses = 20000
% 1.01/1.37 substype = standard
% 1.01/1.37 backwardsubs = 1
% 1.01/1.37 selectoldest = 5
% 1.01/1.37
% 1.01/1.37 litorderings [0] = split
% 1.01/1.37 litorderings [1] = liftord
% 1.01/1.37
% 1.01/1.37 termordering = none
% 1.01/1.37
% 1.01/1.37 litapriori = 1
% 1.01/1.37 termapriori = 0
% 1.01/1.37 litaposteriori = 0
% 1.01/1.37 termaposteriori = 0
% 1.01/1.37 demodaposteriori = 0
% 1.01/1.37 ordereqreflfact = 0
% 1.01/1.37
% 1.01/1.37 litselect = none
% 1.01/1.37
% 1.01/1.37 maxweight = 15
% 1.01/1.37 maxdepth = 30000
% 1.01/1.37 maxlength = 115
% 1.01/1.37 maxnrvars = 195
% 1.01/1.37 excuselevel = 1
% 1.01/1.37 increasemaxweight = 1
% 1.01/1.37
% 1.01/1.37 maxselected = 10000000
% 1.01/1.37 maxnrclauses = 10000000
% 1.01/1.37
% 1.01/1.37 showgenerated = 0
% 1.01/1.37 showkept = 0
% 1.01/1.37 showselected = 0
% 1.01/1.37 showdeleted = 0
% 1.01/1.37 showresimp = 1
% 1.01/1.37 showstatus = 2000
% 1.01/1.37
% 1.01/1.37 prologoutput = 0
% 1.01/1.37 nrgoals = 5000000
% 1.01/1.37 totalproof = 1
% 1.01/1.37
% 1.01/1.37 Symbols occurring in the translation:
% 1.01/1.37
% 1.01/1.37 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.01/1.37 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 1.01/1.37 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 1.01/1.37 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.37 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.37 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 1.01/1.37 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 1.01/1.37 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 1.01/1.37 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 1.01/1.37 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 1.01/1.37 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.01/1.37 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 1.01/1.37 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 1.01/1.37 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 1.01/1.37 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 1.01/1.37 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 1.01/1.37 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 1.01/1.37 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 1.01/1.37 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 1.01/1.37 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.01/1.37 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 1.01/1.37 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 1.01/1.37 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 1.01/1.37 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.01/1.37 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.01/1.37 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.01/1.37 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 1.01/1.37
% 1.01/1.37
% 1.01/1.37 Starting Search:
% 1.01/1.37
% 1.01/1.37 *** allocated 15000 integers for clauses
% 1.01/1.37 *** allocated 22500 integers for clauses
% 1.01/1.37 *** allocated 33750 integers for clauses
% 1.01/1.37 *** allocated 15000 integers for termspace/termends
% 1.01/1.37 *** allocated 50625 integers for clauses
% 1.01/1.37 Resimplifying inuse:
% 1.01/1.37 Done
% 1.01/1.37
% 1.01/1.37 *** allocated 22500 integers for termspace/termends
% 1.01/1.37 *** allocated 75937 integers for clauses
% 1.01/1.37 *** allocated 33750 integers for termspace/termends
% 1.01/1.37 *** allocated 113905 integers for clauses
% 1.01/1.37
% 1.01/1.37 Intermediate Status:
% 1.01/1.37 Generated: 11106
% 1.01/1.37 Kept: 2064
% 1.01/1.37 Inuse: 333
% 1.01/1.37 Deleted: 1
% 1.01/1.37 Deletedinuse: 0
% 1.01/1.37
% 1.01/1.37 Resimplifying inuse:
% 1.01/1.37 Done
% 1.01/1.37
% 1.01/1.37 *** allocated 50625 integers for termspace/termends
% 1.01/1.37 *** allocated 170857 integers for clauses
% 1.01/1.37 Resimplifying inuse:
% 1.01/1.37 Done
% 1.01/1.37
% 1.01/1.37 *** allocated 75937 integers for termspace/termends
% 1.01/1.37
% 1.01/1.37 Intermediate Status:
% 1.01/1.37 Generated: 22398
% 1.01/1.37 Kept: 4079
% 1.01/1.37 Inuse: 504
% 1.01/1.37 Deleted: 16
% 1.01/1.37 Deletedinuse: 2
% 1.01/1.37
% 1.01/1.37 Resimplifying inuse:
% 1.01/1.37 Done
% 1.01/1.37
% 1.01/1.37 *** allocated 256285 integers for clauses
% 1.01/1.37
% 1.01/1.37 Bliksems!, er is een bewijs:
% 1.01/1.37 % SZS status Theorem
% 1.01/1.37 % SZS output start Refutation
% 1.01/1.37
% 1.01/1.37 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.01/1.37 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.01/1.37 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.01/1.37 , ! distinct_lines( X, Y ) }.
% 1.01/1.37 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 1.01/1.37 Z ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 1.01/1.37 X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.01/1.37 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 1.01/1.37 X, Z ), distinct_lines( Y, Z ) }.
% 1.01/1.37 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 1.01/1.37 , Y ) }.
% 1.01/1.37 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 1.01/1.37 , X ), Y ) }.
% 1.01/1.37 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 1.01/1.37 parallel_through_point( Y, X ) ) }.
% 1.01/1.37 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 1.01/1.37 X, Y ) }.
% 1.01/1.37 (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 1.01/1.37 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.01/1.37 }.
% 1.01/1.37 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 1.01/1.37 (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! alpha1( X, Y )
% 1.01/1.37 }.
% 1.01/1.37 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 1.01/1.37 ( Y, X ), Y ) }.
% 1.01/1.37 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 1.01/1.37 orthogonal_through_point( Y, X ) ) }.
% 1.01/1.37 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 1.01/1.37 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 1.01/1.37 (38) {G0,W6,D2,L2,V2,M1} I { ! distinct_lines( X, Y ), ! equal_lines( X, Y
% 1.01/1.37 ) }.
% 1.01/1.37 (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 1.01/1.37 incident_point_and_line( X, Y ) }.
% 1.01/1.37 (48) {G0,W5,D3,L1,V0,M1} I { equal_lines( skol3, line_connecting( skol1,
% 1.01/1.37 skol2 ) ) }.
% 1.01/1.37 (49) {G0,W6,D2,L2,V0,M1} I { ! incident_point_and_line( skol1, skol3 ), !
% 1.01/1.37 incident_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 1.01/1.37 ( X, Y ) }.
% 1.01/1.37 (58) {G2,W9,D2,L3,V3,M3} R(56,4) { distinct_lines( Z, X ), ! distinct_lines
% 1.01/1.37 ( Z, Y ), distinct_lines( X, Y ) }.
% 1.01/1.37 (64) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 1.01/1.37 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 1.01/1.37 (65) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 1.01/1.37 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.37 (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 (68) {G2,W9,D2,L3,V3,M3} R(67,5) { convergent_lines( Z, X ), !
% 1.01/1.37 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 1.01/1.37 (75) {G1,W5,D3,L1,V0,M1} R(38,48) { ! distinct_lines( skol3,
% 1.01/1.37 line_connecting( skol1, skol2 ) ) }.
% 1.01/1.37 (108) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), X ) }.
% 1.01/1.37 (110) {G2,W8,D3,L2,V3,M2} R(108,5) { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.37 (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ), !
% 1.01/1.37 distinct_lines( Y, X ) }.
% 1.01/1.37 (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 1.01/1.37 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 1.01/1.37 apart_point_and_line( Z, X ) }.
% 1.01/1.37 (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 1.01/1.37 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.37 (143) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 1.01/1.37 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.37 (160) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y ),
% 1.01/1.37 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 (164) {G1,W6,D2,L2,V0,M1} R(49,43) { apart_point_and_line( skol2, skol3 ),
% 1.01/1.37 ! incident_point_and_line( skol1, skol3 ) }.
% 1.01/1.37 (165) {G2,W6,D2,L2,V0,M1} R(164,43) { apart_point_and_line( skol1, skol3 )
% 1.01/1.37 , apart_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 (166) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 1.01/1.37 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( Y, Z ) }.
% 1.01/1.37 (167) {G1,W12,D2,L4,V3,M3} R(19,21) { ! convergent_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 (180) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X ),
% 1.01/1.37 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.37 (197) {G4,W8,D3,L2,V3,M2} R(180,67) { convergent_lines( X,
% 1.01/1.37 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.37 (255) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 1.01/1.37 (306) {G2,W8,D3,L2,V3,M2} R(64,67) { convergent_lines( X, Z ), !
% 1.01/1.37 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 1.01/1.37 (348) {G3,W8,D3,L2,V3,M2} R(306,67) { ! convergent_lines( Y,
% 1.01/1.37 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.37 (572) {G3,W8,D3,L2,V1,M1} R(58,75) { ! distinct_lines( skol3, X ),
% 1.01/1.37 distinct_lines( line_connecting( skol1, skol2 ), X ) }.
% 1.01/1.37 (576) {G4,W8,D3,L2,V1,M1} R(572,122) { convergent_lines( X, line_connecting
% 1.01/1.37 ( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 1.01/1.37 (588) {G5,W11,D3,L3,V2,M2} R(576,13) { ! convergent_lines( Y, skol3 ),
% 1.01/1.37 convergent_lines( Y, X ), convergent_lines( X, line_connecting( skol1,
% 1.01/1.37 skol2 ) ) }.
% 1.01/1.37 (592) {G6,W5,D3,L1,V0,M1} F(588);r(2) { ! convergent_lines( line_connecting
% 1.01/1.37 ( skol1, skol2 ), skol3 ) }.
% 1.01/1.37 (594) {G7,W7,D4,L1,V1,M1} R(592,348) { ! convergent_lines( skol3,
% 1.01/1.37 parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 1.01/1.37 (635) {G8,W9,D5,L1,V2,M1} R(594,65) { ! convergent_lines( skol3,
% 1.01/1.37 parallel_through_point( parallel_through_point( line_connecting( skol1,
% 1.01/1.37 skol2 ), X ), Y ) ) }.
% 1.01/1.37 (2552) {G2,W14,D3,L4,V5,M1} R(132,143) { distinct_lines( X, Y ),
% 1.01/1.37 distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point( U, T
% 1.01/1.37 ) ), ! apart_point_and_line( T, X ) }.
% 1.01/1.37 (2553) {G2,W14,D3,L4,V5,M1} R(132,142) { distinct_lines( X, Y ),
% 1.01/1.37 distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U, T )
% 1.01/1.37 ), ! apart_point_and_line( T, X ) }.
% 1.01/1.37 (2561) {G3,W8,D3,L2,V3,M1} F(2553);r(56) { distinct_lines(
% 1.01/1.37 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.37 (2562) {G3,W8,D3,L2,V3,M1} F(2552);r(56) { distinct_lines(
% 1.01/1.37 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.37 (2578) {G4,W8,D3,L2,V1,M1} R(2562,165) { distinct_lines(
% 1.01/1.37 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 1.01/1.37 skol1, skol3 ) }.
% 1.01/1.37 (2607) {G5,W10,D3,L2,V2,M1} R(2578,2561) { distinct_lines(
% 1.01/1.37 orthogonal_through_point( X, skol2 ), skol3 ), distinct_lines(
% 1.01/1.37 parallel_through_point( Y, skol1 ), skol3 ) }.
% 1.01/1.37 (2965) {G6,W10,D3,L2,V2,M1} R(2607,122) { convergent_lines( skol3,
% 1.01/1.37 parallel_through_point( Y, skol1 ) ), distinct_lines(
% 1.01/1.37 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 1.01/1.37 (3017) {G7,W10,D3,L2,V2,M1} R(2965,122) { convergent_lines( skol3,
% 1.01/1.37 orthogonal_through_point( Y, skol2 ) ), convergent_lines( skol3,
% 1.01/1.37 parallel_through_point( X, skol1 ) ) }.
% 1.01/1.37 (3031) {G9,W5,D3,L1,V1,M1} R(3017,635) { convergent_lines( skol3,
% 1.01/1.37 orthogonal_through_point( X, skol2 ) ) }.
% 1.01/1.37 (3036) {G10,W8,D3,L2,V2,M2} R(3031,68) { convergent_lines( Y, skol3 ),
% 1.01/1.37 convergent_lines( orthogonal_through_point( X, skol2 ), Y ) }.
% 1.01/1.37 (3131) {G4,W8,D3,L2,V3,M1} R(160,23);r(180) { convergent_lines( Z, X ), !
% 1.01/1.37 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.37 (3155) {G5,W8,D3,L2,V3,M1} R(166,23);r(197) { convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 1.01/1.37 (3162) {G6,W10,D3,L2,V4,M2} R(3155,255) { ! convergent_lines(
% 1.01/1.37 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.37 (3214) {G2,W15,D2,L5,V4,M3} R(167,31) { ! convergent_lines( X, Y ), !
% 1.01/1.37 convergent_lines( Y, T ), unorthogonal_lines( Y, Z ), unorthogonal_lines
% 1.01/1.37 ( X, T ), unorthogonal_lines( X, Z ) }.
% 1.01/1.37 (3225) {G3,W9,D2,L3,V3,M2} F(3214);r(17) { ! convergent_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 1.01/1.37 (3279) {G4,W8,D3,L2,V3,M1} R(3225,23) { ! convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 1.01/1.37 (3280) {G4,W8,D3,L2,V3,M1} R(3225,23) { ! convergent_lines( X,
% 1.01/1.37 orthogonal_through_point( Y, Z ) ), unorthogonal_lines( X, Y ) }.
% 1.01/1.37 (3286) {G5,W7,D3,L1,V3,M1} R(3279,23) { ! convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 1.01/1.37 (3288) {G11,W5,D3,L1,V2,M1} R(3286,3036) { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), skol3 ) }.
% 1.01/1.37 (3497) {G5,W10,D3,L2,V4,M2} R(3280,3131) { convergent_lines( Z, X ), !
% 1.01/1.37 convergent_lines( orthogonal_through_point( X, Y ),
% 1.01/1.37 orthogonal_through_point( Z, T ) ) }.
% 1.01/1.37 (3724) {G7,W9,D4,L1,V2,M1} R(3497,592) { ! convergent_lines(
% 1.01/1.37 orthogonal_through_point( skol3, X ), orthogonal_through_point(
% 1.01/1.37 line_connecting( skol1, skol2 ), Y ) ) }.
% 1.01/1.37 (4175) {G12,W0,D0,L0,V0,M0} R(3162,3724);r(3288) { }.
% 1.01/1.37
% 1.01/1.37
% 1.01/1.37 % SZS output end Refutation
% 1.01/1.37 found a proof!
% 1.01/1.37
% 1.01/1.37
% 1.01/1.37 Unprocessed initial clauses:
% 1.01/1.37
% 1.01/1.37 (4177) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.01/1.37 (4178) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.01/1.37 (4179) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.01/1.37 (4180) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.01/1.37 , Z ), distinct_points( Y, Z ) }.
% 1.01/1.37 (4181) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 1.01/1.37 Z ), distinct_lines( Y, Z ) }.
% 1.01/1.37 (4182) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 1.01/1.37 ( X, Z ), convergent_lines( Y, Z ) }.
% 1.01/1.37 (4183) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.01/1.37 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.01/1.37 (4184) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.01/1.37 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.01/1.37 (4185) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.01/1.37 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.01/1.37 (4186) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.01/1.37 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.01/1.37 (4187) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 1.01/1.37 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.01/1.37 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.01/1.37 (4188) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.01/1.37 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.01/1.37 (4189) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.01/1.37 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.01/1.37 (4190) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.01/1.37 , Z ), convergent_lines( X, Z ) }.
% 1.01/1.37 (4191) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 1.01/1.37 , Y ) }.
% 1.01/1.37 (4192) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 1.01/1.37 , X ), Y ) }.
% 1.01/1.37 (4193) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.01/1.37 parallel_through_point( Y, X ) ) }.
% 1.01/1.37 (4194) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 1.01/1.37 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 (4195) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 1.01/1.37 ( X, Y ) }.
% 1.01/1.37 (4196) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.01/1.37 (4197) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.01/1.37 }.
% 1.01/1.37 (4198) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 1.01/1.37 }.
% 1.01/1.37 (4199) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 1.01/1.37 }.
% 1.01/1.37 (4200) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 1.01/1.37 (4201) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 1.01/1.37 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.37 (4202) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.01/1.37 orthogonal_through_point( Y, X ) ) }.
% 1.01/1.37 (4203) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 1.01/1.37 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.01/1.37 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 1.01/1.37 (4204) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 1.01/1.37 ( X, Y ) }.
% 1.01/1.37 (4205) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 1.01/1.37 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.01/1.37 (4206) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 1.01/1.37 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.01/1.37 (4207) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 1.01/1.37 }.
% 1.01/1.37 (4208) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 1.01/1.37 }.
% 1.01/1.37 (4209) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 1.01/1.37 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 1.01/1.37 (4210) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 1.01/1.37 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 (4211) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 1.01/1.37 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 1.01/1.37 (4212) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 1.01/1.37 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 1.01/1.37 (4213) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 1.01/1.37 parallel_through_point( X, Y ) ) }.
% 1.01/1.37 (4214) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 1.01/1.37 orthogonal_through_point( X, Y ) ) }.
% 1.01/1.37 (4215) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 1.01/1.37 , Y ) }.
% 1.01/1.37 (4216) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 1.01/1.37 }.
% 1.01/1.37 (4217) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 1.01/1.37 ) }.
% 1.01/1.37 (4218) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.01/1.37 }.
% 1.01/1.37 (4219) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 1.01/1.37 ( X, Y ) }.
% 1.01/1.37 (4220) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 1.01/1.37 Y ) }.
% 1.01/1.37 (4221) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 1.01/1.37 apart_point_and_line( X, Y ) }.
% 1.01/1.37 (4222) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 1.01/1.37 incident_point_and_line( X, Y ) }.
% 1.01/1.37 (4223) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 (4224) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 1.01/1.37 ( X, Y ) }.
% 1.01/1.37 (4225) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.01/1.37 (4226) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol4 ) }.
% 1.01/1.37 (4227) {G0,W5,D3,L1,V0,M1} { equal_lines( skol3, line_connecting( skol1,
% 1.01/1.37 skol2 ) ) }.
% 1.01/1.37 (4228) {G0,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1, skol3 ), !
% 1.01/1.37 incident_point_and_line( skol2, skol3 ) }.
% 1.01/1.37
% 1.01/1.37
% 1.01/1.37 Total Proof:
% 1.01/1.37
% 1.01/1.37 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.01/1.37 parent0: (4178) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.01/1.37 parent0: (4179) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.01/1.37 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.01/1.37 parent0: (4181) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 1.01/1.37 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 2
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 parent0: (4182) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.01/1.37 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 2
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.01/1.37 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.01/1.37 parent0: (4189) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.01/1.37 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 2
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 1.01/1.37 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.01/1.37 parent0: (4190) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.01/1.37 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 2
% 1.01/1.37 2 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 parent0: (4191) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 1.01/1.37 parallel_through_point( Y, X ), Y ) }.
% 1.01/1.37 parent0: (4192) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 1.01/1.37 parallel_through_point( Y, X ), Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 1.01/1.37 parallel_through_point( Y, X ) ) }.
% 1.01/1.37 parent0: (4193) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.01/1.37 parallel_through_point( Y, X ) ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 parent0: (4195) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 1.01/1.37 parent0: (4196) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 2 ==> 3
% 1.01/1.37 3 ==> 2
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.01/1.37 }.
% 1.01/1.37 parent0: (4197) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.01/1.37 }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 2 ==> 3
% 1.01/1.37 3 ==> 2
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 1.01/1.37 alpha1( X, Y ) }.
% 1.01/1.37 parent0: (4198) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 1.01/1.37 X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 1.01/1.37 alpha1( X, Y ) }.
% 1.01/1.37 parent0: (4199) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines
% 1.01/1.37 ( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.37 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.37 parent0: (4201) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 1.01/1.37 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 1.01/1.37 orthogonal_through_point( Y, X ) ) }.
% 1.01/1.37 parent0: (4202) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.01/1.37 orthogonal_through_point( Y, X ) ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 1.01/1.37 parent0: (4210) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 1.01/1.37 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 2
% 1.01/1.37 2 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (38) {G0,W6,D2,L2,V2,M1} I { ! distinct_lines( X, Y ), !
% 1.01/1.37 equal_lines( X, Y ) }.
% 1.01/1.37 parent0: (4217) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), !
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 1.01/1.37 incident_point_and_line( X, Y ) }.
% 1.01/1.37 parent0: (4222) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 1.01/1.37 incident_point_and_line( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (48) {G0,W5,D3,L1,V0,M1} I { equal_lines( skol3,
% 1.01/1.37 line_connecting( skol1, skol2 ) ) }.
% 1.01/1.37 parent0: (4227) {G0,W5,D3,L1,V0,M1} { equal_lines( skol3, line_connecting
% 1.01/1.37 ( skol1, skol2 ) ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (49) {G0,W6,D2,L2,V0,M1} I { ! incident_point_and_line( skol1
% 1.01/1.37 , skol3 ), ! incident_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 parent0: (4228) {G0,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1,
% 1.01/1.37 skol3 ), ! incident_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4422) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.01/1.37 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.01/1.37 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 parent0: (4422) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4425) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 1.01/1.37 distinct_lines( Z, Y ), ! distinct_lines( Z, X ) }.
% 1.01/1.37 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 parent1[1]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.01/1.37 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := Z
% 1.01/1.37 Y := X
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (58) {G2,W9,D2,L3,V3,M3} R(56,4) { distinct_lines( Z, X ), !
% 1.01/1.37 distinct_lines( Z, Y ), distinct_lines( X, Y ) }.
% 1.01/1.37 parent0: (4425) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 1.01/1.37 distinct_lines( Z, Y ), ! distinct_lines( Z, X ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 2
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4427) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 1.01/1.37 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 1.01/1.37 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 1.01/1.37 parallel_through_point( Y, X ), Y ) }.
% 1.01/1.37 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := parallel_through_point( X, Y )
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (64) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 1.01/1.37 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 1.01/1.37 parent0: (4427) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 1.01/1.37 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4430) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 1.01/1.37 convergent_lines( Z, parallel_through_point( X, Y ) ) }.
% 1.01/1.37 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 1.01/1.37 parallel_through_point( Y, X ), Y ) }.
% 1.01/1.37 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := Z
% 1.01/1.37 Y := parallel_through_point( X, Y )
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (65) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 1.01/1.37 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.37 parent0: (4430) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 1.01/1.37 convergent_lines( Z, parallel_through_point( X, Y ) ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4431) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.01/1.37 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 parent0: (4431) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4433) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 1.01/1.37 parent0[0]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (68) {G2,W9,D2,L3,V3,M3} R(67,5) { convergent_lines( Z, X ), !
% 1.01/1.37 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 1.01/1.37 parent0: (4433) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 2
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4436) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 1.01/1.37 line_connecting( skol1, skol2 ) ) }.
% 1.01/1.37 parent0[1]: (38) {G0,W6,D2,L2,V2,M1} I { ! distinct_lines( X, Y ), !
% 1.01/1.37 equal_lines( X, Y ) }.
% 1.01/1.37 parent1[0]: (48) {G0,W5,D3,L1,V0,M1} I { equal_lines( skol3,
% 1.01/1.37 line_connecting( skol1, skol2 ) ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := skol3
% 1.01/1.37 Y := line_connecting( skol1, skol2 )
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (75) {G1,W5,D3,L1,V0,M1} R(38,48) { ! distinct_lines( skol3,
% 1.01/1.37 line_connecting( skol1, skol2 ) ) }.
% 1.01/1.37 parent0: (4436) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 1.01/1.37 line_connecting( skol1, skol2 ) ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4437) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), X ) }.
% 1.01/1.37 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.37 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.37 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := orthogonal_through_point( X, Y )
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (108) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), X ) }.
% 1.01/1.37 parent0: (4437) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), X ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4438) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 1.01/1.37 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.01/1.37 parent1[0]: (108) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), X ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := orthogonal_through_point( X, Y )
% 1.01/1.37 Y := X
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (110) {G2,W8,D3,L2,V3,M2} R(108,5) { convergent_lines( X, Z )
% 1.01/1.37 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.37 parent0: (4438) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 1.01/1.37 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := Z
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4439) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 1.01/1.37 distinct_lines( Y, X ) }.
% 1.01/1.37 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 parent1[1]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.01/1.37 distinct_lines( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y )
% 1.01/1.37 , ! distinct_lines( Y, X ) }.
% 1.01/1.37 parent0: (4439) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 1.01/1.37 distinct_lines( Y, X ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4440) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 1.01/1.37 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 1.01/1.37 apart_point_and_line( Z, T ) }.
% 1.01/1.37 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.01/1.37 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.01/1.37 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.01/1.37 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Z
% 1.01/1.37 Y := X
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := Z
% 1.01/1.37 Y := T
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 1.01/1.37 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 1.01/1.37 apart_point_and_line( Z, X ) }.
% 1.01/1.37 parent0: (4440) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 1.01/1.37 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 1.01/1.37 apart_point_and_line( Z, T ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := T
% 1.01/1.37 Z := Z
% 1.01/1.37 T := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 2
% 1.01/1.37 2 ==> 0
% 1.01/1.37 3 ==> 3
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4442) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 1.01/1.37 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 1.01/1.37 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 1.01/1.37 parallel_through_point( Y, X ) ) }.
% 1.01/1.37 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.01/1.37 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := parallel_through_point( Y, X )
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 1.01/1.37 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.37 parent0: (4442) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 1.01/1.37 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Z
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4443) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 1.01/1.37 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 1.01/1.37 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 1.01/1.37 orthogonal_through_point( Y, X ) ) }.
% 1.01/1.37 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.01/1.37 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := orthogonal_through_point( Y, X )
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (143) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 1.01/1.37 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.37 parent0: (4443) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 1.01/1.37 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Z
% 1.01/1.37 Y := Y
% 1.01/1.37 Z := X
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4445) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 1.01/1.37 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 1.01/1.37 ( Z, Y ) }.
% 1.01/1.37 parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 1.01/1.37 alpha1( X, Y ) }.
% 1.01/1.37 parent1[3]: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (160) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 1.01/1.37 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 parent0: (4445) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 1.01/1.37 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 1.01/1.37 ( Z, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 2
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 3
% 1.01/1.37 3 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4447) {G1,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1
% 1.01/1.37 , skol3 ), apart_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 parent0[1]: (49) {G0,W6,D2,L2,V0,M1} I { ! incident_point_and_line( skol1,
% 1.01/1.37 skol3 ), ! incident_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 1.01/1.37 incident_point_and_line( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := skol2
% 1.01/1.37 Y := skol3
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (164) {G1,W6,D2,L2,V0,M1} R(49,43) { apart_point_and_line(
% 1.01/1.37 skol2, skol3 ), ! incident_point_and_line( skol1, skol3 ) }.
% 1.01/1.37 parent0: (4447) {G1,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1,
% 1.01/1.37 skol3 ), apart_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4448) {G1,W6,D2,L2,V0,M2} { apart_point_and_line( skol2,
% 1.01/1.37 skol3 ), apart_point_and_line( skol1, skol3 ) }.
% 1.01/1.37 parent0[1]: (164) {G1,W6,D2,L2,V0,M1} R(49,43) { apart_point_and_line(
% 1.01/1.37 skol2, skol3 ), ! incident_point_and_line( skol1, skol3 ) }.
% 1.01/1.37 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 1.01/1.37 incident_point_and_line( X, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := skol1
% 1.01/1.37 Y := skol3
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (165) {G2,W6,D2,L2,V0,M1} R(164,43) { apart_point_and_line(
% 1.01/1.37 skol1, skol3 ), apart_point_and_line( skol2, skol3 ) }.
% 1.01/1.37 parent0: (4448) {G1,W6,D2,L2,V0,M2} { apart_point_and_line( skol2, skol3 )
% 1.01/1.37 , apart_point_and_line( skol1, skol3 ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4450) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 1.01/1.37 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 1.01/1.37 unorthogonal_lines( Z, Y ) }.
% 1.01/1.37 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 1.01/1.37 ( X, Y ) }.
% 1.01/1.37 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.01/1.37 }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (166) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 1.01/1.37 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 1.01/1.37 unorthogonal_lines( Y, Z ) }.
% 1.01/1.37 parent0: (4450) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 1.01/1.37 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 1.01/1.37 unorthogonal_lines( Z, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 1
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 2
% 1.01/1.37 3 ==> 3
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4452) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 1.01/1.37 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 1.01/1.37 unorthogonal_lines( Z, Y ) }.
% 1.01/1.37 parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 1.01/1.37 alpha1( X, Y ) }.
% 1.01/1.37 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.01/1.37 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.01/1.37 }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Y
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (167) {G1,W12,D2,L4,V3,M3} R(19,21) { ! convergent_lines( X, Y
% 1.01/1.37 ), unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.37 unorthogonal_lines( X, Y ) }.
% 1.01/1.37 parent0: (4452) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 1.01/1.37 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 1.01/1.37 unorthogonal_lines( Z, Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 2
% 1.01/1.37 1 ==> 0
% 1.01/1.37 2 ==> 3
% 1.01/1.37 3 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4454) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 1.01/1.37 parent0[0]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 parent1[0]: (110) {G2,W8,D3,L2,V3,M2} R(108,5) { convergent_lines( X, Z ),
% 1.01/1.37 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := Y
% 1.01/1.37 Y := X
% 1.01/1.37 end
% 1.01/1.37 substitution1:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 subsumption: (180) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X )
% 1.01/1.37 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.37 parent0: (4454) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 1.01/1.37 substitution0:
% 1.01/1.37 X := X
% 1.01/1.37 Y := Z
% 1.01/1.37 Z := Y
% 1.01/1.37 end
% 1.01/1.37 permutation0:
% 1.01/1.37 0 ==> 0
% 1.01/1.37 1 ==> 1
% 1.01/1.37 end
% 1.01/1.37
% 1.01/1.37 resolution: (4457) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 1.01/1.37 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 1.01/1.37 parent0[0]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.01/1.37 convergent_lines( X, Y ) }.
% 1.01/1.37 parent1[1]: (180) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X )
% 1.01/1.37 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := orthogonal_through_point( X, Y )
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (197) {G4,W8,D3,L2,V3,M2} R(180,67) { convergent_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.38 parent0: (4457) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 1.01/1.38 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4459) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.38 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.38 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := X
% 1.01/1.38 Z := orthogonal_through_point( X, Y )
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (255) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 1.01/1.38 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 1.01/1.38 parent0: (4459) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4461) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 1.01/1.38 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 1.01/1.38 parent0[0]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.01/1.38 convergent_lines( X, Y ) }.
% 1.01/1.38 parent1[1]: (64) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 1.01/1.38 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (306) {G2,W8,D3,L2,V3,M2} R(64,67) { convergent_lines( X, Z )
% 1.01/1.38 , ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent0: (4461) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 1.01/1.38 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := X
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4462) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 1.01/1.38 parent0[1]: (306) {G2,W8,D3,L2,V3,M2} R(64,67) { convergent_lines( X, Z ),
% 1.01/1.38 ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent1[1]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.01/1.38 convergent_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := parallel_through_point( X, Z )
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (348) {G3,W8,D3,L2,V3,M2} R(306,67) { ! convergent_lines( Y,
% 1.01/1.38 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.38 parent0: (4462) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 1
% 1.01/1.38 1 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4463) {G2,W8,D3,L2,V1,M2} { ! distinct_lines( skol3, X ),
% 1.01/1.38 distinct_lines( line_connecting( skol1, skol2 ), X ) }.
% 1.01/1.38 parent0[0]: (75) {G1,W5,D3,L1,V0,M1} R(38,48) { ! distinct_lines( skol3,
% 1.01/1.38 line_connecting( skol1, skol2 ) ) }.
% 1.01/1.38 parent1[0]: (58) {G2,W9,D2,L3,V3,M3} R(56,4) { distinct_lines( Z, X ), !
% 1.01/1.38 distinct_lines( Z, Y ), distinct_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := line_connecting( skol1, skol2 )
% 1.01/1.38 Y := X
% 1.01/1.38 Z := skol3
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (572) {G3,W8,D3,L2,V1,M1} R(58,75) { ! distinct_lines( skol3,
% 1.01/1.38 X ), distinct_lines( line_connecting( skol1, skol2 ), X ) }.
% 1.01/1.38 parent0: (4463) {G2,W8,D3,L2,V1,M2} { ! distinct_lines( skol3, X ),
% 1.01/1.38 distinct_lines( line_connecting( skol1, skol2 ), X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4465) {G3,W8,D3,L2,V1,M2} { convergent_lines( X,
% 1.01/1.38 line_connecting( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 1.01/1.38 parent0[1]: (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 1.01/1.38 ! distinct_lines( Y, X ) }.
% 1.01/1.38 parent1[1]: (572) {G3,W8,D3,L2,V1,M1} R(58,75) { ! distinct_lines( skol3, X
% 1.01/1.38 ), distinct_lines( line_connecting( skol1, skol2 ), X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := line_connecting( skol1, skol2 )
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (576) {G4,W8,D3,L2,V1,M1} R(572,122) { convergent_lines( X,
% 1.01/1.38 line_connecting( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 1.01/1.38 parent0: (4465) {G3,W8,D3,L2,V1,M2} { convergent_lines( X, line_connecting
% 1.01/1.38 ( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4466) {G1,W11,D3,L3,V2,M3} { convergent_lines( X,
% 1.01/1.38 line_connecting( skol1, skol2 ) ), ! convergent_lines( Y, skol3 ),
% 1.01/1.38 convergent_lines( Y, X ) }.
% 1.01/1.38 parent0[1]: (576) {G4,W8,D3,L2,V1,M1} R(572,122) { convergent_lines( X,
% 1.01/1.38 line_connecting( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 1.01/1.38 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 1.01/1.38 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := skol3
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (588) {G5,W11,D3,L3,V2,M2} R(576,13) { ! convergent_lines( Y,
% 1.01/1.38 skol3 ), convergent_lines( Y, X ), convergent_lines( X, line_connecting(
% 1.01/1.38 skol1, skol2 ) ) }.
% 1.01/1.38 parent0: (4466) {G1,W11,D3,L3,V2,M3} { convergent_lines( X,
% 1.01/1.38 line_connecting( skol1, skol2 ) ), ! convergent_lines( Y, skol3 ),
% 1.01/1.38 convergent_lines( Y, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 2
% 1.01/1.38 1 ==> 0
% 1.01/1.38 2 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4468) {G5,W12,D3,L2,V0,M2} { ! convergent_lines( line_connecting
% 1.01/1.38 ( skol1, skol2 ), skol3 ), convergent_lines( line_connecting( skol1,
% 1.01/1.38 skol2 ), line_connecting( skol1, skol2 ) ) }.
% 1.01/1.38 parent0[1, 2]: (588) {G5,W11,D3,L3,V2,M2} R(576,13) { ! convergent_lines( Y
% 1.01/1.38 , skol3 ), convergent_lines( Y, X ), convergent_lines( X, line_connecting
% 1.01/1.38 ( skol1, skol2 ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := line_connecting( skol1, skol2 )
% 1.01/1.38 Y := line_connecting( skol1, skol2 )
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4469) {G1,W5,D3,L1,V0,M1} { ! convergent_lines(
% 1.01/1.38 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.01/1.38 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.01/1.38 parent1[1]: (4468) {G5,W12,D3,L2,V0,M2} { ! convergent_lines(
% 1.01/1.38 line_connecting( skol1, skol2 ), skol3 ), convergent_lines(
% 1.01/1.38 line_connecting( skol1, skol2 ), line_connecting( skol1, skol2 ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := line_connecting( skol1, skol2 )
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (592) {G6,W5,D3,L1,V0,M1} F(588);r(2) { ! convergent_lines(
% 1.01/1.38 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.01/1.38 parent0: (4469) {G1,W5,D3,L1,V0,M1} { ! convergent_lines( line_connecting
% 1.01/1.38 ( skol1, skol2 ), skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4470) {G4,W7,D4,L1,V1,M1} { ! convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 1.01/1.38 parent0[0]: (592) {G6,W5,D3,L1,V0,M1} F(588);r(2) { ! convergent_lines(
% 1.01/1.38 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.01/1.38 parent1[1]: (348) {G3,W8,D3,L2,V3,M2} R(306,67) { ! convergent_lines( Y,
% 1.01/1.38 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := line_connecting( skol1, skol2 )
% 1.01/1.38 Y := skol3
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (594) {G7,W7,D4,L1,V1,M1} R(592,348) { ! convergent_lines(
% 1.01/1.38 skol3, parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 1.01/1.38 parent0: (4470) {G4,W7,D4,L1,V1,M1} { ! convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4471) {G2,W9,D5,L1,V2,M1} { ! convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( parallel_through_point( line_connecting( skol1,
% 1.01/1.38 skol2 ), X ), Y ) ) }.
% 1.01/1.38 parent0[0]: (594) {G7,W7,D4,L1,V1,M1} R(592,348) { ! convergent_lines(
% 1.01/1.38 skol3, parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 1.01/1.38 parent1[1]: (65) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 1.01/1.38 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := skol3
% 1.01/1.38 Y := parallel_through_point( line_connecting( skol1, skol2 ), X )
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (635) {G8,W9,D5,L1,V2,M1} R(594,65) { ! convergent_lines(
% 1.01/1.38 skol3, parallel_through_point( parallel_through_point( line_connecting(
% 1.01/1.38 skol1, skol2 ), X ), Y ) ) }.
% 1.01/1.38 parent0: (4471) {G2,W9,D5,L1,V2,M1} { ! convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( parallel_through_point( line_connecting( skol1,
% 1.01/1.38 skol2 ), X ), Y ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4472) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 1.01/1.38 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 1.01/1.38 parent0[1]: (143) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent1[2]: (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 1.01/1.38 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 1.01/1.38 apart_point_and_line( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := T
% 1.01/1.38 Y := U
% 1.01/1.38 Z := Z
% 1.01/1.38 T := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (2552) {G2,W14,D3,L4,V5,M1} R(132,143) { distinct_lines( X, Y
% 1.01/1.38 ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point(
% 1.01/1.38 U, T ) ), ! apart_point_and_line( T, X ) }.
% 1.01/1.38 parent0: (4472) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 1.01/1.38 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := U
% 1.01/1.38 Z := T
% 1.01/1.38 T := X
% 1.01/1.38 U := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 2
% 1.01/1.38 1 ==> 0
% 1.01/1.38 2 ==> 1
% 1.01/1.38 3 ==> 3
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4477) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 1.01/1.38 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 1.01/1.38 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 1.01/1.38 parent0[1]: (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 1.01/1.38 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent1[2]: (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 1.01/1.38 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 1.01/1.38 apart_point_and_line( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := T
% 1.01/1.38 Y := U
% 1.01/1.38 Z := Z
% 1.01/1.38 T := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (2553) {G2,W14,D3,L4,V5,M1} R(132,142) { distinct_lines( X, Y
% 1.01/1.38 ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 1.01/1.38 , T ) ), ! apart_point_and_line( T, X ) }.
% 1.01/1.38 parent0: (4477) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 1.01/1.38 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 1.01/1.38 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := U
% 1.01/1.38 Z := T
% 1.01/1.38 T := X
% 1.01/1.38 U := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 2
% 1.01/1.38 1 ==> 0
% 1.01/1.38 2 ==> 1
% 1.01/1.38 3 ==> 3
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4483) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 1.01/1.38 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 1.01/1.38 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent0[0, 2]: (2553) {G2,W14,D3,L4,V5,M1} R(132,142) { distinct_lines( X,
% 1.01/1.38 Y ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 1.01/1.38 , T ) ), ! apart_point_and_line( T, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := parallel_through_point( Y, Z )
% 1.01/1.38 Z := X
% 1.01/1.38 T := Z
% 1.01/1.38 U := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4489) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 1.01/1.38 parallel_through_point( Y, Z ), X ), distinct_lines(
% 1.01/1.38 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.01/1.38 distinct_lines( X, Y ) }.
% 1.01/1.38 parent1[0]: (4483) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 1.01/1.38 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 1.01/1.38 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := parallel_through_point( Y, Z )
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4491) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 1.01/1.38 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 1.01/1.38 parent0[0, 1]: (4489) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 1.01/1.38 parallel_through_point( Y, Z ), X ), distinct_lines(
% 1.01/1.38 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := X
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (2561) {G3,W8,D3,L2,V3,M1} F(2553);r(56) { distinct_lines(
% 1.01/1.38 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent0: (4491) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 1.01/1.38 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4494) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent0[0, 2]: (2552) {G2,W14,D3,L4,V5,M1} R(132,143) { distinct_lines( X,
% 1.01/1.38 Y ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point
% 1.01/1.38 ( U, T ) ), ! apart_point_and_line( T, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := orthogonal_through_point( Y, Z )
% 1.01/1.38 Z := X
% 1.01/1.38 T := Z
% 1.01/1.38 U := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4500) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.01/1.38 distinct_lines( X, Y ) }.
% 1.01/1.38 parent1[0]: (4494) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := orthogonal_through_point( Y, Z )
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4502) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 1.01/1.38 parent0[0, 1]: (4500) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := X
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (2562) {G3,W8,D3,L2,V3,M1} F(2552);r(56) { distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent0: (4502) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4505) {G3,W8,D3,L2,V1,M2} { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 1.01/1.38 skol1, skol3 ) }.
% 1.01/1.38 parent0[1]: (2562) {G3,W8,D3,L2,V3,M1} F(2552);r(56) { distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent1[1]: (165) {G2,W6,D2,L2,V0,M1} R(164,43) { apart_point_and_line(
% 1.01/1.38 skol1, skol3 ), apart_point_and_line( skol2, skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := skol3
% 1.01/1.38 Y := X
% 1.01/1.38 Z := skol2
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (2578) {G4,W8,D3,L2,V1,M1} R(2562,165) { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 1.01/1.38 skol1, skol3 ) }.
% 1.01/1.38 parent0: (4505) {G3,W8,D3,L2,V1,M2} { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 1.01/1.38 skol1, skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4506) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 1.01/1.38 parallel_through_point( X, skol1 ), skol3 ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 1.01/1.38 parent0[1]: (2561) {G3,W8,D3,L2,V3,M1} F(2553);r(56) { distinct_lines(
% 1.01/1.38 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 1.01/1.38 parent1[1]: (2578) {G4,W8,D3,L2,V1,M1} R(2562,165) { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 1.01/1.38 skol1, skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := skol3
% 1.01/1.38 Y := X
% 1.01/1.38 Z := skol1
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (2607) {G5,W10,D3,L2,V2,M1} R(2578,2561) { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ), distinct_lines(
% 1.01/1.38 parallel_through_point( Y, skol1 ), skol3 ) }.
% 1.01/1.38 parent0: (4506) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 1.01/1.38 parallel_through_point( X, skol1 ), skol3 ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 1
% 1.01/1.38 1 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4508) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( X, skol1 ) ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 1.01/1.38 parent0[1]: (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 1.01/1.38 ! distinct_lines( Y, X ) }.
% 1.01/1.38 parent1[1]: (2607) {G5,W10,D3,L2,V2,M1} R(2578,2561) { distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ), distinct_lines(
% 1.01/1.38 parallel_through_point( Y, skol1 ), skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := skol3
% 1.01/1.38 Y := parallel_through_point( X, skol1 )
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (2965) {G6,W10,D3,L2,V2,M1} R(2607,122) { convergent_lines(
% 1.01/1.38 skol3, parallel_through_point( Y, skol1 ) ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 1.01/1.38 parent0: (4508) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( X, skol1 ) ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4509) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 1.01/1.38 orthogonal_through_point( X, skol2 ) ), convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( Y, skol1 ) ) }.
% 1.01/1.38 parent0[1]: (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 1.01/1.38 ! distinct_lines( Y, X ) }.
% 1.01/1.38 parent1[1]: (2965) {G6,W10,D3,L2,V2,M1} R(2607,122) { convergent_lines(
% 1.01/1.38 skol3, parallel_through_point( Y, skol1 ) ), distinct_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := skol3
% 1.01/1.38 Y := orthogonal_through_point( X, skol2 )
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3017) {G7,W10,D3,L2,V2,M1} R(2965,122) { convergent_lines(
% 1.01/1.38 skol3, orthogonal_through_point( Y, skol2 ) ), convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( X, skol1 ) ) }.
% 1.01/1.38 parent0: (4509) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 1.01/1.38 orthogonal_through_point( X, skol2 ) ), convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( Y, skol1 ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4510) {G8,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 1.01/1.38 orthogonal_through_point( Y, skol2 ) ) }.
% 1.01/1.38 parent0[0]: (635) {G8,W9,D5,L1,V2,M1} R(594,65) { ! convergent_lines( skol3
% 1.01/1.38 , parallel_through_point( parallel_through_point( line_connecting( skol1
% 1.01/1.38 , skol2 ), X ), Y ) ) }.
% 1.01/1.38 parent1[1]: (3017) {G7,W10,D3,L2,V2,M1} R(2965,122) { convergent_lines(
% 1.01/1.38 skol3, orthogonal_through_point( Y, skol2 ) ), convergent_lines( skol3,
% 1.01/1.38 parallel_through_point( X, skol1 ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := skol1
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := parallel_through_point( line_connecting( skol1, skol2 ), X )
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3031) {G9,W5,D3,L1,V1,M1} R(3017,635) { convergent_lines(
% 1.01/1.38 skol3, orthogonal_through_point( X, skol2 ) ) }.
% 1.01/1.38 parent0: (4510) {G8,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 1.01/1.38 orthogonal_through_point( Y, skol2 ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4511) {G3,W8,D3,L2,V2,M2} { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), Y ), convergent_lines( Y, skol3 )
% 1.01/1.38 }.
% 1.01/1.38 parent0[1]: (68) {G2,W9,D2,L3,V3,M3} R(67,5) { convergent_lines( Z, X ), !
% 1.01/1.38 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 1.01/1.38 parent1[0]: (3031) {G9,W5,D3,L1,V1,M1} R(3017,635) { convergent_lines(
% 1.01/1.38 skol3, orthogonal_through_point( X, skol2 ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := skol3
% 1.01/1.38 Z := orthogonal_through_point( X, skol2 )
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3036) {G10,W8,D3,L2,V2,M2} R(3031,68) { convergent_lines( Y,
% 1.01/1.38 skol3 ), convergent_lines( orthogonal_through_point( X, skol2 ), Y ) }.
% 1.01/1.38 parent0: (4511) {G3,W8,D3,L2,V2,M2} { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, skol2 ), Y ), convergent_lines( Y, skol3 )
% 1.01/1.38 }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 1
% 1.01/1.38 1 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4512) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.38 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.38 parent1[2]: (160) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 1.01/1.38 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.38 unorthogonal_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := orthogonal_through_point( X, Y )
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4514) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 1.01/1.38 convergent_lines( Z, X ) }.
% 1.01/1.38 parent0[0]: (4512) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent1[1]: (180) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X )
% 1.01/1.38 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4515) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 1.01/1.38 parent0[0, 2]: (4514) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 1.01/1.38 convergent_lines( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3131) {G4,W8,D3,L2,V3,M1} R(160,23);r(180) { convergent_lines
% 1.01/1.38 ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent0: (4515) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := X
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4516) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 1.01/1.38 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 1.01/1.38 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 1.01/1.38 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.38 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.38 parent1[3]: (166) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 1.01/1.38 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Y, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := orthogonal_through_point( X, Y )
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4517) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 1.01/1.38 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 1.01/1.38 convergent_lines( X, Y ) }.
% 1.01/1.38 parent0[0]: (4516) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 1.01/1.38 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 1.01/1.38 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 1.01/1.38 parent1[0]: (197) {G4,W8,D3,L2,V3,M2} R(180,67) { convergent_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4518) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 1.01/1.38 parent0[0, 2]: (4517) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 1.01/1.38 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 1.01/1.38 convergent_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3155) {G5,W8,D3,L2,V3,M1} R(166,23);r(197) { convergent_lines
% 1.01/1.38 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 1.01/1.38 parent0: (4518) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4519) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( Z, T ), X ) }.
% 1.01/1.38 parent0[1]: (3155) {G5,W8,D3,L2,V3,M1} R(166,23);r(197) { convergent_lines
% 1.01/1.38 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 1.01/1.38 parent1[1]: (255) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 1.01/1.38 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := orthogonal_through_point( X, Y )
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := T
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := orthogonal_through_point( Z, T )
% 1.01/1.38 Y := X
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3162) {G6,W10,D3,L2,V4,M2} R(3155,255) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent0: (4519) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( Z, T ), X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 T := T
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 1
% 1.01/1.38 1 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4520) {G1,W15,D2,L5,V4,M5} { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.38 convergent_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 1.01/1.38 parent0[3]: (167) {G1,W12,D2,L4,V3,M3} R(19,21) { ! convergent_lines( X, Y
% 1.01/1.38 ), unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.38 unorthogonal_lines( X, Y ) }.
% 1.01/1.38 parent1[1]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := T
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3214) {G2,W15,D2,L5,V4,M3} R(167,31) { ! convergent_lines( X
% 1.01/1.38 , Y ), ! convergent_lines( Y, T ), unorthogonal_lines( Y, Z ),
% 1.01/1.38 unorthogonal_lines( X, T ), unorthogonal_lines( X, Z ) }.
% 1.01/1.38 parent0: (4520) {G1,W15,D2,L5,V4,M5} { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 1.01/1.38 convergent_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 T := T
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 2
% 1.01/1.38 2 ==> 4
% 1.01/1.38 3 ==> 1
% 1.01/1.38 4 ==> 3
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4535) {G2,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.01/1.38 convergent_lines( Y, Z ), unorthogonal_lines( Y, Z ), unorthogonal_lines
% 1.01/1.38 ( X, Z ) }.
% 1.01/1.38 parent0[3, 4]: (3214) {G2,W15,D2,L5,V4,M3} R(167,31) { ! convergent_lines(
% 1.01/1.38 X, Y ), ! convergent_lines( Y, T ), unorthogonal_lines( Y, Z ),
% 1.01/1.38 unorthogonal_lines( X, T ), unorthogonal_lines( X, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 T := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4559) {G1,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ),
% 1.01/1.38 unorthogonal_lines( Y, Z ) }.
% 1.01/1.38 parent0[1]: (4535) {G2,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.01/1.38 convergent_lines( Y, Z ), unorthogonal_lines( Y, Z ), unorthogonal_lines
% 1.01/1.38 ( X, Z ) }.
% 1.01/1.38 parent1[0]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 factor: (4563) {G1,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 1.01/1.38 parent0[1, 3]: (4559) {G1,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ),
% 1.01/1.38 unorthogonal_lines( Y, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3225) {G3,W9,D2,L3,V3,M2} F(3214);r(17) { ! convergent_lines
% 1.01/1.38 ( X, Y ), unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 1.01/1.38 parent0: (4563) {G1,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.01/1.38 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 2
% 1.01/1.38 2 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4565) {G1,W8,D3,L2,V3,M2} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 1.01/1.38 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.38 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.38 parent1[1]: (3225) {G3,W9,D2,L3,V3,M2} F(3214);r(17) { ! convergent_lines(
% 1.01/1.38 X, Y ), unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := orthogonal_through_point( X, Y )
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3279) {G4,W8,D3,L2,V3,M1} R(3225,23) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 1.01/1.38 parent0: (4565) {G1,W8,D3,L2,V3,M2} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 Z := Z
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4568) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z,
% 1.01/1.38 orthogonal_through_point( X, Y ) ), unorthogonal_lines( Z, X ) }.
% 1.01/1.38 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.38 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.38 parent1[2]: (3225) {G3,W9,D2,L3,V3,M2} F(3214);r(17) { ! convergent_lines(
% 1.01/1.38 X, Y ), unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := orthogonal_through_point( X, Y )
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3280) {G4,W8,D3,L2,V3,M1} R(3225,23) { ! convergent_lines( X
% 1.01/1.38 , orthogonal_through_point( Y, Z ) ), unorthogonal_lines( X, Y ) }.
% 1.01/1.38 parent0: (4568) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z,
% 1.01/1.38 orthogonal_through_point( X, Y ) ), unorthogonal_lines( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4569) {G1,W7,D3,L1,V3,M1} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Z ), orthogonal_through_point( X, Y ) ) }.
% 1.01/1.38 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 1.01/1.38 orthogonal_through_point( Y, X ), Y ) }.
% 1.01/1.38 parent1[1]: (3279) {G4,W8,D3,L2,V3,M1} R(3225,23) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := orthogonal_through_point( X, Y )
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3286) {G5,W7,D3,L1,V3,M1} R(3279,23) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 1.01/1.38 parent0: (4569) {G1,W7,D3,L1,V3,M1} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Z ), orthogonal_through_point( X, Y ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4570) {G6,W5,D3,L1,V2,M1} { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), skol3 ) }.
% 1.01/1.38 parent0[0]: (3286) {G5,W7,D3,L1,V3,M1} R(3279,23) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 1.01/1.38 parent1[1]: (3036) {G10,W8,D3,L2,V2,M2} R(3031,68) { convergent_lines( Y,
% 1.01/1.38 skol3 ), convergent_lines( orthogonal_through_point( X, skol2 ), Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := skol2
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := X
% 1.01/1.38 Y := orthogonal_through_point( X, Y )
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3288) {G11,W5,D3,L1,V2,M1} R(3286,3036) { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), skol3 ) }.
% 1.01/1.38 parent0: (4570) {G6,W5,D3,L1,V2,M1} { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4572) {G5,W10,D3,L2,V4,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 convergent_lines( orthogonal_through_point( Y, Z ),
% 1.01/1.38 orthogonal_through_point( X, T ) ) }.
% 1.01/1.38 parent0[1]: (3131) {G4,W8,D3,L2,V3,M1} R(160,23);r(180) { convergent_lines
% 1.01/1.38 ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 parent1[1]: (3280) {G4,W8,D3,L2,V3,M1} R(3225,23) { ! convergent_lines( X,
% 1.01/1.38 orthogonal_through_point( Y, Z ) ), unorthogonal_lines( X, Y ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Y
% 1.01/1.38 Y := Z
% 1.01/1.38 Z := X
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := orthogonal_through_point( Y, Z )
% 1.01/1.38 Y := X
% 1.01/1.38 Z := T
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3497) {G5,W10,D3,L2,V4,M2} R(3280,3131) { convergent_lines( Z
% 1.01/1.38 , X ), ! convergent_lines( orthogonal_through_point( X, Y ),
% 1.01/1.38 orthogonal_through_point( Z, T ) ) }.
% 1.01/1.38 parent0: (4572) {G5,W10,D3,L2,V4,M2} { convergent_lines( X, Y ), !
% 1.01/1.38 convergent_lines( orthogonal_through_point( Y, Z ),
% 1.01/1.38 orthogonal_through_point( X, T ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := X
% 1.01/1.38 Z := Y
% 1.01/1.38 T := T
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 1 ==> 1
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4573) {G6,W9,D4,L1,V2,M1} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( skol3, X ), orthogonal_through_point(
% 1.01/1.38 line_connecting( skol1, skol2 ), Y ) ) }.
% 1.01/1.38 parent0[0]: (592) {G6,W5,D3,L1,V0,M1} F(588);r(2) { ! convergent_lines(
% 1.01/1.38 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.01/1.38 parent1[0]: (3497) {G5,W10,D3,L2,V4,M2} R(3280,3131) { convergent_lines( Z
% 1.01/1.38 , X ), ! convergent_lines( orthogonal_through_point( X, Y ),
% 1.01/1.38 orthogonal_through_point( Z, T ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := skol3
% 1.01/1.38 Y := X
% 1.01/1.38 Z := line_connecting( skol1, skol2 )
% 1.01/1.38 T := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (3724) {G7,W9,D4,L1,V2,M1} R(3497,592) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( skol3, X ), orthogonal_through_point(
% 1.01/1.38 line_connecting( skol1, skol2 ), Y ) ) }.
% 1.01/1.38 parent0: (4573) {G6,W9,D4,L1,V2,M1} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( skol3, X ), orthogonal_through_point(
% 1.01/1.38 line_connecting( skol1, skol2 ), Y ) ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 0 ==> 0
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4574) {G7,W9,D5,L1,V2,M1} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( orthogonal_through_point( line_connecting(
% 1.01/1.38 skol1, skol2 ), Y ), Z ), skol3 ) }.
% 1.01/1.38 parent0[0]: (3724) {G7,W9,D4,L1,V2,M1} R(3497,592) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( skol3, X ), orthogonal_through_point(
% 1.01/1.38 line_connecting( skol1, skol2 ), Y ) ) }.
% 1.01/1.38 parent1[1]: (3162) {G6,W10,D3,L2,V4,M2} R(3155,255) { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), Z ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := X
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := skol3
% 1.01/1.38 Y := X
% 1.01/1.38 Z := orthogonal_through_point( line_connecting( skol1, skol2 ), Y )
% 1.01/1.38 T := Z
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 resolution: (4575) {G8,W0,D0,L0,V0,M0} { }.
% 1.01/1.38 parent0[0]: (4574) {G7,W9,D5,L1,V2,M1} { ! convergent_lines(
% 1.01/1.38 orthogonal_through_point( orthogonal_through_point( line_connecting(
% 1.01/1.38 skol1, skol2 ), Y ), Z ), skol3 ) }.
% 1.01/1.38 parent1[0]: (3288) {G11,W5,D3,L1,V2,M1} R(3286,3036) { convergent_lines(
% 1.01/1.38 orthogonal_through_point( X, Y ), skol3 ) }.
% 1.01/1.38 substitution0:
% 1.01/1.38 X := Z
% 1.01/1.38 Y := X
% 1.01/1.38 Z := Y
% 1.01/1.38 end
% 1.01/1.38 substitution1:
% 1.01/1.38 X := orthogonal_through_point( line_connecting( skol1, skol2 ), X )
% 1.01/1.38 Y := Y
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 subsumption: (4175) {G12,W0,D0,L0,V0,M0} R(3162,3724);r(3288) { }.
% 1.01/1.38 parent0: (4575) {G8,W0,D0,L0,V0,M0} { }.
% 1.01/1.38 substitution0:
% 1.01/1.38 end
% 1.01/1.38 permutation0:
% 1.01/1.38 end
% 1.01/1.38
% 1.01/1.38 Proof check complete!
% 1.01/1.38
% 1.01/1.38 Memory use:
% 1.01/1.38
% 1.01/1.38 space for terms: 55623
% 1.01/1.38 space for clauses: 171542
% 1.01/1.38
% 1.01/1.38
% 1.01/1.38 clauses generated: 23219
% 1.01/1.38 clauses kept: 4176
% 1.01/1.38 clauses selected: 509
% 1.01/1.38 clauses deleted: 45
% 1.01/1.38 clauses inuse deleted: 31
% 1.01/1.38
% 1.01/1.38 subsentry: 367679
% 1.01/1.38 literals s-matched: 135635
% 1.01/1.38 literals matched: 135285
% 1.01/1.38 full subsumption: 80480
% 1.01/1.38
% 1.01/1.38 checksum: 1234226589
% 1.01/1.38
% 1.01/1.38
% 1.01/1.38 Bliksem ended
%------------------------------------------------------------------------------